tag:blogger.com,1999:blog-65112258927937343622024-03-05T21:56:40.984+10:30Surf's D&D Blog...Surfarcher posts on D&D and RPGs in general... Right now his focus is on fifth edition D&D (aka D&D 5e)...Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.comBlogger31125tag:blogger.com,1999:blog-6511225892793734362.post-24915112285576455802015-07-02T07:34:00.000+09:302016-09-23T19:07:33.115+09:30D&D 5e Monsters: Part 11: Construction Consolidation<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<p><span style="color:lightyellow;"><i>Surf consolidates the data to date and extends it out... In preparation for the next round of analysis.</i></span></p>
<p> </p>
<a name="Top"></a><h3><u>Part 11: Construction Consolidation</u></h3>
<p>OK it's been quite a while since I posted on here and recently I realised that I hadn't posted the consolidated tables from our explorations into the math underpinning D&D 5e monsters.</p>
<p>Certainly life outside this blog has been very demanding and left very little time for analysis and blogging. But if I'm honest with myself I have to admit that I was feeling like this analysis had lost it's relevance with the release of the <i>Dungeon Master's Guide</i>. Asking around on the official D&D forums the responses I received seemed to confirm this... On top of this the effort that goes into these blog articles is mentally demanding - presenting an analysis requires far more effort that just tinkering in a spreadsheet for one's own pleasure!</p>
<p>Things might have sat like this for a whole lot longer, but <a href="https://plus.google.com/100070528873080081098/posts">+Connor Cavin</a> and several others started asking when I'd post my consolidated tables. Discussion turned to what I would be posting beyond that and I realised, there still was a group of folks interested in these articles continuing!</p>
<p>So I'm back to post the last couple of installments in this series. And from there we'll see where we go, tho I do have a few ideas I feel good about now.</p>
<p>So, if you enjoy these articles, let me know!</p>
<p>If there's something about the math behind D&D 5e you'd like to see explored, let me know!</p>
<p>And now on to the consolidated tables!</p>
<p style="clear:both;"> </p>
<a name="ConsolidatedTables"></a><h4>Consolidated Tables</h4>
<p>I'll omit the waffling here and get straight into the table, which I have extended out to CR30.</p>
<p>Most of the headers in the table below can be clicked to take you to the section of the article dealing with that stat.</p>
<div class="bluegrid"><table style="float:none;">
<tr><th rowspan="2">CR</th><th rowspan="2"><a href="http://surfarcher.blogspot.com/2014/12/d-5e-monsters-part-10-construction-cr.html">Challenge<br>Index</a></th><th colspan="2"><a href="http://surfarcher.blogspot.com.au/2014/08/d-5e-monsters-part-4-construction.html#Abilities">Ability Score</a></th><th rowspan="2"><a href="http://surfarcher.blogspot.com/2014/08/d-5e-monsters-interlude-bunch-of.html#AC">Armor<br>Class</a></th><th rowspan="2"><a href="http://surfarcher.blogspot.com.au/2014/08/d-5e-monsters-interlude-bunch-of.html#HP">Hit<br>Points</a></th><th rowspan="2"><a href="http://surfarcher.blogspot.com/2014/10/d-5e-monsters-part-9-construction.html#AttackBonus">Attack<br>Bonus</a></th><th rowspan="2"><a href="http://surfarcher.blogspot.com/2014/09/d-5e-monsters-part-7-construction-damage.html">Damage</a></th><th rowspan="2"><a href="http://surfarcher.blogspot.com.au/2014/09/d-5e-monsters-part-6-construction.html#TraitsOverview">Trait<br>Count</a></th><th rowspan="2"><a href="http://surfarcher.blogspot.com.au/2014/10/d-5e-monsters-part-8-construction.html#Action">Action<br>Count</a></th><th rowspan="2"><a href="http://surfarcher.blogspot.com.au/2014/08/d-5e-monsters-part-5-construction-ac.html#MiscStats">Misc<br>stats</a></th></tr>
<tr><th><a href="http://surfarcher.blogspot.com.au/2014/08/d-5e-monsters-part-4-construction.html#Abilities">Avg</a></th><th><a href="http://surfarcher.blogspot.com.au/2014/08/d-5e-monsters-part-4-construction.html#Abilities">Max</a></th></tr>
<tr><td>0</td><td>5</td><td>8</td><td>13</td><td>13</td><td>8</td><td>+3</td><td>1</td><td>1</td><td>1</td><td>1</td></tr>
<tr><td>⅛</td><td>8</td><td>9</td><td>14</td><td>13</td><td>11</td><td>+4</td><td>2</td><td>1</td><td>1</td><td>1</td></tr>
<tr><td>¼</td><td>11</td><td>10</td><td>15</td><td>13</td><td>13</td><td>+4</td><td>3</td><td>1</td><td>2</td><td>2</td></tr>
<tr><td>½</td><td>17</td><td>10</td><td>15</td><td>13</td><td>18</td><td>+4</td><td>4</td><td>1</td><td>2</td><td>2</td></tr>
<tr><td>1</td><td>23</td><td>11</td><td>16</td><td>13</td><td>28</td><td>+4</td><td>7</td><td>2</td><td>2</td><td>3</td></tr>
<tr><td>2</td><td>38</td><td>11</td><td>16</td><td>13</td><td>48</td><td>+5</td><td>13</td><td>2</td><td>2</td><td>3</td></tr>
<tr><td>3</td><td>54</td><td>12</td><td>17</td><td>13</td><td>68</td><td>+5</td><td>19</td><td>2</td><td>2</td><td>3</td></tr>
<tr><td>4</td><td>69</td><td>12</td><td>17</td><td>14</td><td>88</td><td>+6</td><td>25</td><td>2</td><td>2</td><td>4</td></tr>
<tr><td>5</td><td>84</td><td>13</td><td>18</td><td>14</td><td>108</td><td>+6</td><td>31</td><td>2</td><td>2</td><td>4</td></tr>
<tr><td>6</td><td>100</td><td>13</td><td>18</td><td>14</td><td>128</td><td>+7</td><td>37</td><td>2</td><td>2</td><td>4</td></tr>
<tr><td>7</td><td>115</td><td>14</td><td>19</td><td>15</td><td>148</td><td>+7</td><td>43</td><td>2</td><td>3</td><td>4</td></tr>
<tr><td>8</td><td>130</td><td>14</td><td>19</td><td>15</td><td>168</td><td>+8</td><td>49</td><td>2</td><td>3</td><td>4</td></tr>
<tr><td>9</td><td>145</td><td>15</td><td>20</td><td>15</td><td>188</td><td>+8</td><td>55</td><td>2</td><td>3</td><td>5</td></tr>
<tr><td>10</td><td>161</td><td>15</td><td>20</td><td>16</td><td>208</td><td>+9</td><td>61</td><td>2</td><td>3</td><td>5</td></tr>
<tr><td>11</td><td>176</td><td>16</td><td>21</td><td>16</td><td>228</td><td>+9</td><td>67</td><td>2</td><td>3</td><td>5</td></tr>
<tr><td>12</td><td>191</td><td>16</td><td>21</td><td>16</td><td>248</td><td>+10</td><td>73</td><td>2</td><td>4</td><td>5</td></tr>
<tr><td>13</td><td>207</td><td>17</td><td>22</td><td>17</td><td>268</td><td>+10</td><td>79</td><td>2</td><td>4</td><td>5</td></tr>
<tr><td>14</td><td>222</td><td>17</td><td>22</td><td>17</td><td>288</td><td>+11</td><td>85</td><td>2</td><td>4</td><td>6</td></tr>
<tr><td>15</td><td>237</td><td>18</td><td>23</td><td>17</td><td>308</td><td>+11</td><td>91</td><td>2</td><td>4</td><td>6</td></tr>
<tr><td>16</td><td>253</td><td>18</td><td>23</td><td>18</td><td>328</td><td>+12</td><td>97</td><td>3</td><td>4</td><td>6</td></tr>
<tr><td>17</td><td>268</td><td>19</td><td>24</td><td>18</td><td>348</td><td>+13</td><td>103</td><td>3</td><td>4</td><td>6</td></tr>
<tr><td>18</td><td>283</td><td>19</td><td>24</td><td>18</td><td>368</td><td>+13</td><td>109</td><td>3</td><td>5</td><td>6</td></tr>
<tr><td>19</td><td>298</td><td>20</td><td>25</td><td>19</td><td>388</td><td>+14</td><td>115</td><td>3</td><td>5</td><td>7</td></tr>
<tr><td>20</td><td>314</td><td>20</td><td>25</td><td>19</td><td>408</td><td>+14</td><td>121</td><td>3</td><td>5</td><td>7</td></tr>
<tr><td>21</td><td>329</td><td>21</td><td>26</td><td>19</td><td>428</td><td>+15</td><td>127</td><td>3</td><td>5</td><td>7</td></tr>
<tr><td>22</td><td>344</td><td>21</td><td>26</td><td>20</td><td>448</td><td>+15</td><td>133</td><td>3</td><td>5</td><td>7</td></tr>
<tr><td>23</td><td>360</td><td>22</td><td>27</td><td>20</td><td>468</td><td>+16</td><td>139</td><td>3</td><td>5</td><td>7</td></tr>
<tr><td>24</td><td>375</td><td>22</td><td>27</td><td>20</td><td>488</td><td>+16</td><td>145</td><td>3</td><td>6</td><td>8</td></tr>
<tr><td>25</td><td>390</td><td>23</td><td>28</td><td>21</td><td>508</td><td>+17</td><td>151</td><td>3</td><td>6</td><td>8</td></tr>
<tr><td>26</td><td>406</td><td>23</td><td>28</td><td>21</td><td>528</td><td>+17</td><td>157</td><td>3</td><td>6</td><td>8</td></tr>
<tr><td>27</td><td>421</td><td>24</td><td>29</td><td>21</td><td>548</td><td>+18</td><td>163</td><td>3</td><td>6</td><td>8</td></tr>
<tr><td>28</td><td>436</td><td>24</td><td>29</td><td>21</td><td>568</td><td>+18</td><td>169</td><td>3</td><td>6</td><td>8</td></tr>
<tr><td>29</td><td>451</td><td>25</td><td>30</td><td>22</td><td>588</td><td>+19</td><td>175</td><td>3</td><td>6</td><td>9</td></tr>
<tr><td>30</td><td>467</td><td>25</td><td>30</td><td>22</td><td>608</td><td>+19</td><td>181</td><td>4</td><td>7</td><td>9</td></tr>
</table></div>
<p style="clear:both;"> </p>
<p>We'll be back in the very near future to close this series off and set the scene for the new one!</p>
<p> </p>
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<td width="40%">
<a href="/2014/12/d-5e-monsters-part-10-construction-cr.html"><img src="http://i.imgur.com/d0lSZlO.png" alt="◄"> Part 10: CR Evaluation</a>
</td>
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<a href="/2014/07/d-5e-monsters-master-index.html"><img src="http://i.imgur.com/qRcTo6k.png" alt="▲"> Master Index</a>
</td>
<td style="text-align:right;">
Part 12: Conclusion <img src="http://i.imgur.com/bZ5DhBF.png" alt="►">
</td>
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</body></html>Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com1tag:blogger.com,1999:blog-6511225892793734362.post-48263965918012411622014-12-15T14:49:00.000+10:302016-09-23T19:04:37.471+09:30D&D 5e Monsters: Part 10: Construction: CR Evaluation<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<p><span style="color:lightyellow;"><i>As he waits for his Dungeon Master's Guide to arrive Surf shows how he assesses monster CR... </i></span></p>
<p> </p>
<a name="Top"></a><h3><u>Part 10: CR Evaluation</u></h3>
<p>I want to open this instalment of the series by apologising to everyone who has been waiting for it. I sit here waiting for my <i>Dungeon Master's Guide</i> to arrive and reflect on what a slippery beast <i>CR</i> has been to nail - I have have been chasing it relentlessly since my previous article. There are many ways it can be assessed and I have designed and evaluated no less than four separate <i>CR</i> assessment methods during this time. Each has their pros and cons, but none on its own quite manages to cover assessment of all monsters to date. The method presented here is the most reliable of the crop.</p>
<p>The development of a reliable <i>CR</i> assessment method has been a priority of mine since well before the release of <i>D&D 5e</i>. In fact you might say it was the catalyst for my original <a href="http://surfarcher.blogspot.com/2013/07/d-next-monsters-part-1-getting-started.html">D&D Next monster analysis series</a>, which ultimately that had enough impetus and interest to see the series reborn once <i>D&D 5e</i> was released.</p>
<p>On the journey from playtest to release there have been a few hints about <i>CR</i> calculation from <i>Wizards of the Coast</i>. To me key amongst these has been the following...</p>
<ul>
<li>Mike Mearls <a href="https://twitter.com/mikemearls/status/503967467459584000">tweeted</a> that <i>CR</i> "...calculation includes both offense (atks, dmg) and defense (AC, hp)".</li>
<li>In <a href="http://dnd.wizards.com/articles/features/building-adventures">Legends & Lore 07/07/2014</a> Mike tells us a bit about the relationship between <i>CR</i> and <i>XP</i>.</li>
<li>The <a href="http://dnd.wizards.com/articles/features/basicrules">Basic D&D DM PDF v1</a> gives some advice on encounter building, touching on CR.</li>
<li>In <a href="http://archive.wizards.com/DnD/Article.aspx?x=dnd/dndqa/20140425">D&D Next Q&A: 04/25/2014</a>, Rodney Thompson told us that we'll calculate <i>CR</i> "...by comparing the villain/monster that you've designed to a set of baseline values to determine its CR".</li>
</ul>
<p>We know the <i>Dungeon Master's Guide</i> will contain information on monster creation and evaluation, but we don't know just how much or what its nature will be. We don't know how mathematically focussed and "scientific" it will be or how much it will rely on the assessor's judgement. Our hopes may be high, but there are a lot of unknowns.</p>
<p>Based on our dissection of <i>D&D 5e</i> monster math we should now in a reasonable position to build a method for assessing <i>CR</i>, one that stands on it's own and can be of ongoing value. We do need to note that this method is only as good as the data on which it is based and that some of the specifics are necessarily subject to revision as more data and information come to light. The completion of our <i>Monster Manual</i> analysis and the release of the <i>Dungeon Master's Guide</i> are two key events which are likely to trigger such revision.</p>
<p>The method presented below uses a derived <i>Challenge Index</i> to assess <i>CR</i>. First we look at how an initial <a href="#ChallengeIndexBaseline">Challenge Index Baseline</a> can be determined. Then we will look at <a href="#ChallengeIndexAssessment">Challenge Index assessment</a> and its two major components, the <a href="#DefensiveIndex">Defensive Index</a> and the <a href="#OffensiveIndex">Offensive Index</a>; along with the <a href="#StandardAdjustments">standard adjustments</a> used during these calculations. Finally we review our baseline to produce a final <a href="#ChallengeIndexProgression">Challenge Index Progression</a> and reflect on <a href="#AssessmentAccuracy">the accuracy</a> of this method. To close off the article we will check how our <a href="#Example">Example monster</a> measures up.</p>
<p style="clear:both;"> </p>
<a name="ChallengeIndexBaseline"></a><h4>Challenge Index Baseline</h4>
<p>In order to assess monster <i>CR</i> we need something to measure monsters against. The more parameters we have to use directly in the comparison the more difficult the assessment becomes, using a single number is a more natural and elegant approach. In statistics an "index" is a composite number that aggregates multiple indicators in order to summarise and rank them. It's a way of bringing together multiple statistics for assessment. And that's a very good fit for what we want to do with <i>Challenge Rating</i>. In this case we can score defense and offense separately and combine them into a <i>Challenge Index</i>.</p>
<p>Before we get into how we determine a <i>Challenge Index</i> for an individual monster we need to determine the baseline <i>Challenge Index</i> progression. We can approach this in a number of ways, however a simple and elegant method is best when all else is equal. If our assessment method deals with many of the variables by their deviation from what is standard for that <i>CR</i> then we can assume that those are correct in our base progression. This means in our baseline they become a constant of "1", for multiplication and division operations, or "0", for addition and subtraction. That means we are able to simply ignore them and focus on <i>Hit Points</i> and <i>Damage</i> for our progression baseline, along with the weight each of those might have.</p>
<p>This would mean our baseline <i>Challenge Index</i> can be determined thus...<br>
CI_Progression=(CR_Hit_Points × Defensive_Weight) + (CR_Damage × Offensive_Weight)</p>
<p>This approach held up under preliminary analysis and testing, allowing effort to move on to evaluating all the creatures we have assessed to date. Of course this became an incremental and iterative process - make a pass over the monsters, assess the results, tweak our base progression, review the results, rinse and repeat. Numerous theories were tested, many discarded and some stayed for refinement, but such is life building an index up on data that isn't fully known. Slowly a method of evaluating actual <i>CR</i>, incorporating all defensive and offensive elements while demonstrating an <a href="#AssessmentAccuracy">acceptable level of accuracy</a>, came into focus.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtzQn_08FYfz861_l_JmcJdhyphenhyphendPoZksaou-2tuo8fTEy9Et5R8xlU11HjdxeM2x9K2VraeyQcDcuZSKYawT0mgRZDHeO2u0TyKvUSu32YXO7TMTY2Ek5xeYmGI87y4kBNYODqu8fzshzM/s1600/5e_pic_10a01_challenge_index_progression.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtzQn_08FYfz861_l_JmcJdhyphenhyphendPoZksaou-2tuo8fTEy9Et5R8xlU11HjdxeM2x9K2VraeyQcDcuZSKYawT0mgRZDHeO2u0TyKvUSu32YXO7TMTY2Ek5xeYmGI87y4kBNYODqu8fzshzM/s1600/5e_pic_10a01_challenge_index_progression.png" height="192" width="320" alt="CI, Damage & HP Progression"></a><div class="caption">CI, Damage & HP Progression</div></div>
<p><i>D&D 5e</i> monsters generally have <i>Hit Points</i> much higher than their <i>Damage</i> and this suggests that the Offensive Weighting would likely be at 1, or 100%, meaning we could omit it altogether. Although it did in fact work out this way the Offensive Weight remains in my spreadsheets to this day - it proved useful on occasion and I needed to prove that the Offensive Weighting could remain at 1. Defensive Weighting was clearly a value less than one - some fraction to bring its weight for evaluation purposes into line with offense. A number of passes over the data included reevaluating the value of this constant. Interestingly there were several candidates that kept resurfacing, but in the end 0.5, or 50%, was clearly the best match.</p>
<p>By graphing these derived numbers we can calculate a formula close to the resulting progression. And we see that the progression is similar to the following linear formula...<br>
CI_Progression=16 × CR + 5.2</p>
<p>This will not be our final progression table, as we'll revisit it once we have assessed all of our sample monsters. But it is a good starting point.</p>
<p><span class="prediction">Prediction:</span> TODO:</p>
<p style="clear:both;"> </p>
<a name="ChallengeIndexAssessment"></a><h4>Challenge Index Assessment</h4>
<p>Once we have a baseline challenge index chart to work from we need to understand how we should assess individual monsters. Indeed, to prove our progression chart we <b>need</b> to evaluate all of the monsters in our sample data and achieve a high level of accuracy with our results to feel confident using this table moving forward.</p>
<p>The high level process for determining challenge index is fairly simple, gaining complexity as we drill into its components. Because the components of challenge index are fairly self-contained (the braces mean they are essentially two separate numbers added togethor) we can express the calculation itself as...</p>
<table style="width:100%;margin-left:12px;">
<tr><td>Challenge_Index=Offensive_Index + Defensive_Index</td></tr>
</table>
<p>Since this process becomes moderately complex it seems wise to lay it out with a step-by-step plan that readers can follow. Those with an appetite for math and formulae need not fear, as these are also supplied at the start of each section...</p>
<ol>
<li>Take note of the monster's target <i>CR</i>, or intended <i>CR</i>. This is used at several points during the evaluation process to determine how a monster varies from "standard" for a given statistic. If it's a monster you are building yourself you'll know the target <i>CR</i> and if it's a published monster it will have a listed <i>CR</i>.<br>
<br>
If you don't know the monster's target <i>CR</i> you'll need to work it out roughly from the monster's <i>Proficiency Bonus</i>. The easiest way to do this is if the monster has a saving throw - simply subtract the appropriate ability modifier from that save. Alternatively you can work out the <i>Proficiency Bonus</i> from the creature's skills or <i>Actions</i>. Once you know the <i>Proficiency Bonus</i> check page 8 of the <i>Monster Manual</i> or page 4 of DMDnDBasicRules_v0.1.pdf. This will give you a range of <i>CRs</i> with that <i>Proficiency Bonus</i>. Pick one of these that seems appropriate, or simply one from the middle of the range.<br>
<br></li>
<li>Calculate the monster's <a href="#DefensiveIndex">Defensive Index</a>.<br>
<br></li>
<li>Calculate the monster's <a href="#OffensiveIndex">Offensive Index</a>.<br>
<br></li>
<li>Add the defensive and offensive indexes together to obtain the challenge index.<br>
<br></li>
<li>Check the challenge index against the chart in the <a href="#ChallengeIndexProgression">Challenge Index Progression</a> section. If it is outside the boundaries for the target <i>CR</i> we may have to redo our calculation against a higher or lower <i>CR</i>.<br>
<br></li></ol>
<p style="clear:both;"> </p>
<a name="DefensiveIndex"></a><h4>Defensive Index</h4>
<p>A monster's defensive index is a moderately complex appearing formula that incorporates a creature's various defensive capabilities and can be expressed as...</p>
<table style="width:100%;margin-left:12px;">
<tr><td colspan="2">Defensive_Index=(Monster_HP + Monster_HPAdj) ×</td></tr>
<tr><td style="width:110px"> </td><td>((Monster_AC + Monster_ACAdj + Monster_MS - CR_StdAC - CR_StdMS) × Unit_Val + 1) ×</td></tr>
<tr><td style="width:110px"> </td><td>Defense_Weight</td></tr>
</table>
<p>In reality this isn't too complicated to work out and lends itself well to a process. About half of this formula deals with calculating the Defense Multiplier and breaking this out into a separate precursor formula helps clarify things somewhat...</p>
<table style="width:100%;margin-left:12px;">
<tr><td>Defense_Multiplier=(Monster_AC + Monster_ACAdj + Monster_MS - CR_AC - CR_MS) × Unit_Val + 1</td></tr>
<tr><td>Defensive_Index=(Monster_HP + Monster_HPAdj) × Defense_Multiplier × Defense_Weight</td></tr>
</table>
<p>Let's have a look at the variables and constants that make up these formulae...</p>
<div class="textgrid"><table style="float:none;">
<tr><td width="135px"><b>Monster_AC</b></td><td>The listed Armor Class of the monster being evaluated.</td></tr>
<tr><td><b>Monster_ACAdj</b></td><td>A positive or negative notional adjustment to the monster's <i>AC</i> for <i>Traits</i>, <i>Reactions</i> and other elements not easily factored directly into that monster's base defences. For example a monster with the <i>Camoflage</i> <i>Trait</i> has a +1 here.<br>
<br>
Some common standard adjustment values can be found in the <a href="#StandardAdjustments">Standard Adjustments</a> section.</td></tr>
<tr><td><b>Monster_MS</b></td><td>The count of the monster's miscellaneous stats. Simply sum up the number of Saving Throws, Skills, Damage Resistances and Damage Immunities that the monster has.</td></tr>
<tr><td><b>CR_AC</b></td><td>The average <i>AC</i> for creatures of the target <i>CR</i> (from <a href="http://surfarcher.blogspot.com/2014/08/d-5e-monsters-interlude-bunch-of.html#AC">here</a>).</td></tr>
<tr><td><b>CR_MS</b></td><td>The average number of <i>Miscellaneous Stats</i> for the target <i>CR</i> (from <a href="http://surfarcher.blogspot.com.au/2014/08/d-5e-monsters-part-5-construction-ac.html#MiscStats">here</a>).</td></tr>
<tr><td><b>Unit_Val</b></td><td>This is a constant value denoting what a single increment or decrement to values like <i>AC</i> and <i>To-hit</i> are "worth". This should always be 0.05, or 5%.</td></tr>
<tr><td><b>Monster_HP</b></td><td>The listed <i>Hit Points</i> of the monster being evaluated.</td></tr>
<tr><td><b>Monster_HPAdj</b></td><td>A positive or negative notional adjustment to the monster's <i>Hit Points</i> to allow for various aspects of monsters not factored into that monster's base <i>HP</i> pool. For example a monster with the <i>Relentless</i> <i>Trait</i> has a +5 here.<br>
<br>
Some common standard adjustment values can be found in the <a href="#StandardAdjustments">Standard Adjustments</a> section.</td></tr>
<tr><td><b>Defense_Weight</b></td><td>A multiplier used to scale the Defensive Index up to an appropriate level for inclusion in the Challenge Index. This should be set to 0.5, or 50%.</td></tr>
</table></div>
<p>For those less mathematically inclined here is a step-by-step description of how to calculate a monster's Defensive Index...</p>
<ol>
<li>Determine the monster's Defense Multiplier...
<ol>
<li>Note the monster's <i>AC</i>.</li>
<li>Add any AC adjustments to the monster's <i>AC</i>. This can require some judgement on the part of the person assessing <i>CR</i>. Some known adjustments can be found <a href="#StandardAdjustments">here</a>.</li>
<li>Add the number of Saving Throws, Skills, Damage Resistances and Damage Immunities that the monster has.</li>
<li>Look up the standard <i>Armor Class</i> for the target <i>CR</i> <a href="http://surfarcher.blogspot.com/2014/08/d-5e-monsters-interlude-bunch-of.html#AC">here</a> and subtract that value.</li>
<li>Look up the average <i>Misc Stat</i> sco5e for the <i>CR</i> here and subtract that value.</li>
<li>Multiply the result by 0.05.</li>
<li>Add 1 to obtain the monsters Defense Multiplier.</li>
</ol></li>
<li>Note the monster's average <i>Hit Points</i>.</li>
<li>Add any adjustments to the <i>HP</i>. This can require some judgement on the part of the person assessing <i>CR</i>. Some known adjustments can be found <a href="#StandardAdjustments">here</a>.</li>
<li>Multiply the result by the Defense Multiplier calculated at 1 above.</li>
<li>Multiply the result by 0.5.</li>
</ol>
<p style="clear:both;"> </p>
<a name="OffensiveIndex"></a><h4>Offensive Index</h4>
<p>A monster's Offensive Index is calculated in a manner similar to its Defensive Index, it's just a little simpler and source values from different aspects of a monster. The formula for doing this may be represented as...</p>
<table style="width:100%;margin-left:12px;">
<tr><td colspan="2">Offensive_Index=(Monster_Damage + Monster_DmgAdj) ×</td></tr>
<tr><td style="width:110px"> </td><td>((Monster_Attack + Monster_AttAdj - CR_Attack) × Unit_Val + 1)</td></tr>
</table>
<p>Note the absence of an Offense_Weght or similar. Offense is factored at 100%, which is the same as using an Offense_Weight of 1.0. This results in no change and so that constant may be omitted altogethor.</p>
<p>As with Defensive Index we can make Offensive Index easier to digest by splitting it into two parts - calculation of the multiplier and the remainder of the computation...</p>
<table style="width:100%;margin-left:12px;">
<tr><td>Offense_Multiplier=(Monster_Attack + Monster_AttAdj - CR_Attack) × Unit_Val + 1</td></tr>
<tr><td>Offensive_Index=(Monster_Damage + Monster_DmgAdj) × Offense_Multiplier</td></tr>
</table>
<p>The variables and constants that make up these formulae are...</p>
<div class="textgrid"><table style="float:none;">
<tr><td width="135px"><b>Monster_Attack</b></td><td>The listed <i>To-hit</i> value for the primary attacks of the monster being evaluated. Note that for Spellcasters this is generally their "to hit with spell attacks" value.</td></tr>
<tr><td><b>Monster_AttAdj</b></td><td>A positive or negative notional adjustment to the monster's <i>To-hit</i> value for <i>Traits</i> and other elements not easily factored directly into that monster's attack bonus. For example a monster with the <i>Pack Tactics</i> <i>Trait</i> has a +1 here.<br>
<br>
Some common standard adjustment values can be found in the <a href="#StandardAdjustments">Standard Adjustments</a> section.</td></tr>
<tr><td><b>CR_Attack</b></td><td>The average <i>Attack Bonus</i> for creatures of the target <i>CR</i> (from <a href="http://surfarcher.blogspot.com/2014/10/d-5e-monsters-part-9-construction.html#AttackBonus">here</a>).</td></tr>
<tr><td><b>Unit_Val</b></td><td>This is a constant value denoting what a single increment or decrement to values like <i>AC</i> and <i>To-hit</i> are "worth". This should always be 0.05, or 5%.</td></tr>
<tr><td><b>Monster_Damage</b></td><td>The calculated average <i>Damage</i> of the monster being evaluated. Working this out can be an interesting and variable process. Much of the effort of monster construction and evaluation goes into this one aspect of <i>D&D 5e</i> monsters.<br>
<br>
Readers may find some help working this out in <a href="http://surfarcher.blogspot.com/2014/09/d-5e-monsters-part-7-construction-damage.html">Part 7</a>.
</td></tr>
<tr><td><b>Monster_DmgAdj</b></td><td>A positive or negative notional adjustment to the monster's average <i>Damage</i> to allow for various aspects of monsters not factored into that monster's assessed average <i>Damage</i>. For example a monster with that inflicts a 5hp disease (e.g., the Werewolf) has a +3.5 here.<br>
<br>
Some common standard adjustment values can be found in the <a href="#StandardAdjustments">Standard Adjustments</a> section.</td></tr>
</table></div>
<p>And the step-by-step process for calculating a monster's Offensive Index...</p>
<ol>
<li>Determine the monster's Offense Multiplier...
<ol>
<li>Note the monster's <i>To-hit</i> value for its primary attacks.</li>
<li>Add any adjustments to the monster's <i>To-hit</i> value. This can require some judgement on the part of the person assessing <i>CR</i>. Some known adjustments can be found <a href="#StandardAdjustments">here</a>.</li>
<li>Add the number of Saving Throws, Skills, Damage Resistances and Damage Immunities that the monster has.</li>
<li>Look up the average <i>Attack Bonus</i> for the <i>CR</i> <a href="http://surfarcher.blogspot.com/2014/10/d-5e-monsters-part-9-construction.html#AttackBonus">here</a> and subtract that value.</li>
<li>Multiply the result by 0.05.</li>
<li>Add 1 to obtain the monsters Offense Multiplier.</li>
</ol></li>
<li>Work out the monster's average <i>Damage</i>. This can be an interesting journey all on its own. You may gain some assistance from <a href="http://surfarcher.blogspot.com/2014/09/d-5e-monsters-part-7-construction-damage.html">Part 7</a>.</li>
<li>Add any adjustments to the <i>Damage</i>. This can require some judgement on the part of the person assessing <i>CR</i>. Some known adjustments can be found <a href="#StandardAdjustments">here</a>.</li>
<li>Multiply the result by the Offense Multiplier calculated at 1 above.</li>
</ol>
<p style="clear:both;"> </p>
<a name="StandardAdjustments"></a><h4>Standard Adjustments</h4>
<p>Some of the adjustment values used in assessing <i>CR</i> are unique to that particular monster, or are somewhat open to interpretation, and others do not appear to impact <i>CR</i> whatsoever. But many seem to be static and standardised. These <i>Traits</i>, <i>Reactions</i> and other aspects of monsters are relatively easily enumerated, or at least appear to be derived from elsewhere in a fairly predictable manner.</p>
<p>The following list is not complete and should be considered a work in progress. However it is what I am using at this point in time and is shared in the hope that others will find it useful in evaluating monster <i>CR</i>...</p>
<table style="margin-left:5px;">
<tr><td><b>Antimagic Susceptibility</b></td><td>-5 HP</td> <td> </td> <td><b>Keen Senses</b></td><td>+0.25 AC</td></tr>
<tr><td><b>Blood Frenzy</b></td><td>+2 To-hit</td> <td> </td> <td><b>Life Drain</b></td><td>+(Life Drain amount × 0.75) Damage</td></tr>
<tr><td><b>Camoflage</b></td><td>+1 AC</td> <td> </td> <td><b>Magic Resistance</b></td><td>+2.75 AC</td></tr>
<tr><td><b>Disease (5hp)</b></td><td>+3.5 Damage</td> <td> </td> <td><b>Pack Tactics</b></td><td>+1 To-hit</td></tr>
<tr><td><b>Echolocation</b></td><td>-6 AC</td> <td> </td> <td><b>Parry</b></td><td>+2.5 AC</td></tr>
<tr><td><b>False Appearance</b></td><td>+1 AC</td> <td> </td> <td><b>Rampage</b></td><td>+1 To-hit</td></tr>
<tr><td><b>Flyby</b></td><td>+1 AC</td> <td> </td> <td><b>Reckless</b></td><td>-4 AC, +4 To-hit</td></tr>
<tr><td><b>Frightful Presence</b></td><td>+2 To-hit</td> <td> </td> <td><b>Regeneration</b></td><td>+(Regeneration_Amount × 2) HP</td></tr>
<tr><td><b>Gaze Attack</b></td><td>+2.5 AC</td> <td> </td> <td><b>Relentless</b></td><td>+5 HP</td></tr>
<tr><td><b>Incorporeal Movement</b></td><td>+1 AC</td> <td> </td> <td><b>Sure Footed</b></td><td>+0.5 AC</td></tr>
<tr><td><b>Invisibility</b></td><td>+2.5 AC</td> <td> </td> <td><b>Vulnerability</b></td><td>-(Monster_HP × 0.2) HP</td></tr>
</table>
<p style="clear:both;"> </p>
<a name="ChallengeIndexProgression"></a><h4>Challenge Index Progression</h4>
<p>After evaluating all monsters and iteratively refining our approach we end up with a set of results fairly close to our initial <a href="#ChallengeIndexBaseline">Challenge Index Baseline</a>.</p>
<div class="bluegrid" style="clear:both;"><table style="width:200px;">
<tr><th rowspan="2">CR</th><th colspan="3">Challenge Index</th></tr>
<tr><th width="25%">Min</th><th width="25%">Target</th><th width="25%">Max</th></tr>
<tr><td>0</td><td>0</td><td>5</td><td>7</td></tr>
<tr><td>⅛</td><td>6</td><td>8</td><td>10</td></tr>
<tr><td>¼</td><td>9</td><td>11</td><td>15</td></tr>
<tr><td>½</td><td>13</td><td>17</td><td>21</td></tr>
<tr><td>1</td><td>19</td><td>23</td><td>32</td></tr>
<tr><td>2</td><td>29</td><td>38</td><td>48</td></tr>
<tr><td>3</td><td>44</td><td>54</td><td>63</td></tr>
<tr><td>4</td><td>60</td><td>69</td><td>78</td></tr>
<tr><td>5</td><td>75</td><td>84</td><td>94</td></tr>
<tr><td>6</td><td>90</td><td>100</td><td>109</td></tr>
<tr><td>7</td><td>106</td><td>115</td><td>124</td></tr>
<tr><td>8</td><td>121</td><td>130</td><td>139</td></tr>
<tr><td>9</td><td>136</td><td>145</td><td>155</td></tr>
<tr><td>10</td><td>151</td><td>161</td><td>170</td></tr>
</table></div>
<p>What we see in the results is a data that pretty closely matches the following linear equation...<br>
CI_Progression=15.3 × CR + 7.7</p>
<p>The results are a particularly good match for creatures of CR1 or higher, with over 90% of sample creatures evaluating to "within CR". Most monsters in this range that don't fall clearly within <i>CR</i> aren't too far from these <i>CR</i> boundaries.</p>
<p>Monsters lower than CR1 are less solid matches, with the apparent curve using this progression slicing in too high for most samples - the progression "as is" is just a bit too high for them. We can adjust easily for this by calculating the challenge index of monster below CR1 based on the CI of CR1. While this brings us much closer to target we find we are still a little out and we find that we need to apply a minor 0.22 adjustment to base CR to get the best match. This gives us...<br>
CI_below_CR1=CR1_CI × (CR + 0.22)</p>
<p>With our target values thus determined all that remains is to determine an acceptable level of overlap between adjacent Challenge Indexes and to produce an appropriate table.</p>
<p style="clear:both;"> </p>
<a name="AssessmentAccuracy"></a><h4>Assessment Accuracy</h4>
<p>Many readers will wonder up-front how accurate this method is. Let us consider for now the creatures available before the release of the <i>Monster Manual</i>, which is what my spreadsheet contains at the time of writing...<p>
<ul>
<li>129 monsters are of CR1 or higher and 117 of these fall within the boundaries of their intended <i>CR</i>.<br>
That is a 90.7% match rate.</li>
<li>95 monsters are below CR1 and 83 of these evaluate as appropriate for their <i>CR</i>.<br>
The match rate for these is 87.4%.</li>
<li>That's a total of 224 monsters, of which 200 clearly evaluate to "within intended <i>CR</i>".<br>
For an overall match rate of 89.3%.</li>
</ul>
<p>This raises a number of questions... Why do some monsters not fall within <i>CR</i>? Is this accurate enough? Do we have any other concerns about this level of accuracy? How useful is this approach?</p>
<p>It's not difficult to achieve a higher level of match by tweaking the overlap between challenge index values. This is an approach I am loath to apply as it removes a great deal of clarity from the <i>CR</i> evaluation process. I would be appaled to see a first-tier RPG company apply such crude measures.</p>
<p>Instead I believe that we will find the answers to most of these questions in closer examination of the data...</p>
<h5 style="clear:both;">1. Fuzzy Boundaries</h5>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKaUKJ91tUkMSrqJlO2iKcrlBSh0ZQ4CU-lX6hLJeAz7sE4BCf4hpBw6R9fW69eN1ScnXXhErtcLsCsiisLRVv1TW9S7RsA7SBAwUxE-9-m_sUkrEiBCMjHHVm4B3HkbHnWkym-n8-bVs/s1600/5e_pic_10a02_0-10_damage_scatter.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKaUKJ91tUkMSrqJlO2iKcrlBSh0ZQ4CU-lX6hLJeAz7sE4BCf4hpBw6R9fW69eN1ScnXXhErtcLsCsiisLRVv1TW9S7RsA7SBAwUxE-9-m_sUkrEiBCMjHHVm4B3HkbHnWkym-n8-bVs/s1600/5e_pic_10a02_0-10_damage_scatter.png" height="192" width="320" alt="Damage Scatter - CR0-CR10"></a><div class="caption">Damage Scatter - CR0-CR10</div></div>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJPB3BQg_S2CxrjlWiSvxwSkCu7QH7liBybdzercCCI8b6izPNkEatgjBO1YwjCR0UDuKQZzb9qhuc-yZMeO59IvkJZmusiI8FCpxz2dooH0yvTZPWr31yqyUw4LTFy4cgYlw5nm2Ou9Y/s1600/5e_pic_10a03_0-10_hp_scatter.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJPB3BQg_S2CxrjlWiSvxwSkCu7QH7liBybdzercCCI8b6izPNkEatgjBO1YwjCR0UDuKQZzb9qhuc-yZMeO59IvkJZmusiI8FCpxz2dooH0yvTZPWr31yqyUw4LTFy4cgYlw5nm2Ou9Y/s1600/5e_pic_10a03_0-10_hp_scatter.png" height="192" width="320" alt="HP Scatter - CR0-CR10"></a><div class="caption">HP Scatter - CR0-CR10</div></div>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZg66nYqF-Hsv6s6bgITNoPLkjANQjjHVhmyWJlyxcfzSOf9dY_PXIgouo7WNg9kReEyfKgDdXpnycug_tmccrURllvUEJ52MuxT3o2O8rw6OuhynHeWcvE-z5tMovYx9yvwNNnBNQj28/s1600/5e_pic_10a04_0-10_ci_scatter.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZg66nYqF-Hsv6s6bgITNoPLkjANQjjHVhmyWJlyxcfzSOf9dY_PXIgouo7WNg9kReEyfKgDdXpnycug_tmccrURllvUEJ52MuxT3o2O8rw6OuhynHeWcvE-z5tMovYx9yvwNNnBNQj28/s1600/5e_pic_10a04_0-10_ci_scatter.png" height="192" width="320" alt="CI Scatter - CR0-CR10"></a><div class="caption">CI Scatter - CR0-CR10</div></div>
<p>I believe that CR progression is a scale without hard boundaries between adjacent <i>CR</i>s, this means that some overlap between monsters of adjacent <i>CR</i> is likely to occur. We see evidence supporting this in our sample data.</p>
<p>The spread of values for both <i>Hit Points</i> and <i>Damage</i> vary significantly, overlapping with the data spread of adjacent <i>CR</i>s. Indeed the overlap in these "bands" is not only with those of immediately adjacent <i>CR</i>s, but with bands two or more steps removed. This is visually obvious if we drill in on creatures from CR0 through CR10 on scatter graphs. The same phenomenon can also be seen with both <i>AC</I> and <i>To-hit</i> values, the ceiling on those is simply lower and the overlaps spread further across the <i>CR</i> spectrum.</p>
<p>That said we expect a viable <i>CR</i> evaluation method to yield an index which tightens this data up significantly. If we use the method in this article to assess the <i>CR</i> of all CR0 through CR10 monsters in our sample data and then produce a scatter graph of the resulting challenge indexes by CR, we see that this is indeed the case. But we also see that there is still some overlap between the bands of adjacent <i>CR</i>s.</p>
<p>Why? Because the boundaries are "fuzzy" and do overlap.</p>
<p>Consider, regardless of the evaluation method, a scenario where the upper boundary for CR4 is Challenge Index 75 (or CI75) and where we have two similar monsters, one that evaluates to CI75 and another that evaluates to CI76. The CI76 creature simply has one <i>HP</i> more than its CI75 counterpart. Now, in terms of game experience, what is the difference between the two creatures? The answer is "almost nothing"! It's not noticeably harder to kill a monster with 101 <i>HP</i> than the same monster with 100 <i>HP</i>.</p>
<h5 style="clear:both;">2. Judgement Calls</h5>
<p>During the process of assessing any given monster there are frequently small judgement calls that need to be made. What is this effect "worth"? How much does that trait impact <i>AC</i>? While these can contribute small amounts of variation to a monster's final CI these are not the decisions I am talking about here. These judgement calls have a broader scope than that.</p>
<p>Consideration of the presence and nature of CR assessment's fuzzy boundries leads to some interesting conclusions...</p>
<ul>
<li>There are monsters that are "weak for their CR", "average for their CR" and "strong for their CR". Even when the difference is not pronounced it does still seem to be present.</li>
<li>The difference between a "High CR8" and a "Low CR9" monster can be very negligible. In fact it can be close to nothing.</li>
<li>Where a monster sits squarely in the border area between two adjacent <i>CR</i> bands, what do we do? We can go back and adjust it until it clearly falls into one <i>CR</i> or the other. But the data suggests that's not what <i>Wizards of the Coast</i> generally do. Instead it appears that someone has made a judgement call about whether the monster in question should be a "Strong" creature of the lower <i>CR</i> or a "Weak" monster of the higher <i>CR</i>.</li>
</ul>
<p>Do these suppositions have any merit? What signs can we see in our data that this has been done? Well quite a few, to be honest!</p>
<p>Take a look at the Young Green Dragon in the Basic D&D DM PDF. This monster is CR8, has 136<i>HP</i>, <i>AC</i>18, +7 <i>To-hit</i> and does an average 81.83 <i>Damage</i>.</p>
<p>Now compare it to the Bone Devil from the Monster Manual spoilers. This CR9 monster has 142<i>HP</i>, <i>AC</i>19, +8 <i>To-hit</i> and inflicts an average 46.00 <i>Damage</i>.</p>
<p>Sure the Bone Devil has 6 extra <i>Hit Points</i>, one extra <i>AC</i> and one extra <i>To-hit</i>. But it does barely more than half the damage of the Young Green Dragon. The general level of saves, resistances, immunities and other attributes are close enough between the two that we can treat them as roughly equivalent in those areas. And yet it's difficult to see the CR9 Bone Devil as a significantly tougher fight than the lower-CR Young Green Dragon!</p>
<p>Another significant comparison is the Chimera (CR6, 114hp, AC14, +6 to-hit, 67.42 damage) and the Stone Giant (CR7, 126hp, AC17, +9 to-hit, 38.00 damage). Both of these creatures are quite simple to play and to evaluate. But again it's a bit of a stretch to see the Stone Giant as a significantly tougher fight than the Chimera.</p>
<p>There are a number of other similar examples in our sample data.</p>
<p>Some monsters are clearly stronger than monsters in the next <i>CR</i> up and some are weaker than those in the next <i>CR</i> down.</p>
<p>That doesn't happen when there's a mathematically sound evaluation method, with firm boundaries between <i>CR</i>s, which requires minimal human intervention. Now I personally am pretty confident that the method we've used is mathematically sound so I can only conclude that there are times in <i>D&D 5e</i> monster <i>CR</i> assessment when a human judgement call is made and that this is most likely to occur with monsters that would otherwise be borderline.</p>
<h5 style="clear:both;">3. Granularity At Low CR</h5>
<p>A difference of one <i>Hit Point</i> for a CR30 creature is very little. But that same 1 <i>HP</i> difference is far more significant for a CR0 monster. The same holds true for damage and for many effects, <i>Traits</i> and other aspects of monsters. In the same way small differences in CI at the lowest <i>CR</i> bands is far more significant that at the highest <i>CR</i> bands.</p>
<p>As a result monsters of CR1 or lower can be amongst the most difficult to evaluate. For example the Thug (CR½, 32hp, AC11, +4 to-hit, 10 damage) and the Lion (CR1, 26hp, AC12, +5 to-hit, 10 damage) can be difficult to categorise with casual examination. One won't necessarily understand immediately that a lone Lion can quite easily take a level 1 PC down to 0 <i>HP</i> in a single round, due to it's high mobility, Pounce and the high proportion of it's attack with advantage (due to prone and Pack tactics). While a single Thug doesn't enjoy the same level of accuracy and will be hitting far less often.</p>
<p>Well informed judgement calls become more important at the lowest bands of <i>CR</i> due to this granularity issue.</p>
<p style="clear:both;"> </p>
<a name="Example"></a><h4>Example: Human Pyromancer</h4>
<p>OK so let's step through the process and see how our Human Pyromancer shapes up, based on this method!</p>
<div class="statblock"><table style="width:350px;">
<tr><td colspan="6"><h3>Human Pyromancer</h3></td></tr>
<tr><td colspan="6"><i>Medium humanoid (human), any alignment</i></td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><b>Armor Class</b> 12</td></tr>
<tr><td colspan="6"><b>Hit Points</b> 77 (14d8+14)</td></tr>
<tr><td colspan="6"><b>Speed</b> 30ft</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr class="attributes">
<td>STR<br>9 (-1)</td><td>DEX<br>14 (+2)</td><td>CON<br>12 (+1)</td><td>INT<br>19 (+4)</td><td>WIS<br>12 (+1)</td><td>CHA<br>12 (+1)</td>
</tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><b>Saving Throws</b> Dex +5, Int +7</td></tr>
<tr><td colspan="6"><b>Skills</b> Arcana +7, Perception +4</td></tr>
<tr><td colspan="6"><b>Damage Resistances</b> Fire</td></tr>
<tr><td colspan="6"><b>Languages</b> Common, Ignan</td></tr>
<tr><td colspan="6">Challenge 5 (1,700 XP)</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6">
<b>Spellcasting.</b> The pyromancer is a 5th-level spellcaster. Its<br>
spellcasting ability is Intelligence (spell save DC15, +7 to hit<br>
with spell attacks). The pyromancer has the following wizard<br>
spells prepared.<br>
<br>
Cantrips (at will): dancing lights, fire bolt<br>
1st level (3 slots): burning hands, disguise self<br>
2nd level (2 slots): invisibility, scorching ray<br>
3rd level (1 slot): fireball<br>
</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6">
<span style="font-size:16px">Actions</span><br>
<b>Dagger.</b> <i>Melee Weapon Attack:</i> +5 to hit, reach 5 ft., one target.<br>
<i>Hit:</i> 4 (1d4 + 2) piercing damage.
</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6">
<span style="font-size:16px">Reactions</span><br>
<b>Flame Shroud (Recharge 5-6).</b> When a ranged attack would hit<br>
the pyromancer, or it is targeted by a spell that has a range<br>
other than touch, the air around it bursts into shimmering,<br>
shifting flame for a few seconds. Until the start of the<br>
pyromancer's next turn ranged attacks against it, including the<br>
triggering attack, are made with Disadvantage and it has<br>
Advantage on saving throws against spells with a range other<br>
than touch. During this time it takes no damage from <i>magic<br>
missile</i>.
</td></tr>
</table></div>
<p>First up we calculate the Defensive Multipler. The only real trick here is estimating the impact of the Flame Shroud <i>Reaction</i>. Now this should kick in at least once per fight, effectively giving the Pyromancer a +5 to AC against ranged attacks for one round. Averaged out across an entire fight that's going to work out to somewhere between +1 and +2 to AC, let's be optimistic for now and call it a +2. The remaining values are readily apparent or accessible via the links provided in their section, which yields the following...<br>
Defense_Multiplier=(12+1+5-14-5)×0.05+1=1.0</p>
<p>The Defensive Index can now be calculated trivially...<br>
Defensive_Index=(77+0)×1.0×0.5=38.5</p>
<p>When computing the Offense Multiplier we need to ensure we use the <i>To hit</i> bonus from the Spellcasting <i>Trait</i>, but this task is otherwise straightforward...<br>
Offense_Multiplier=(7+0-6)×0.05+1=1.05</p>
<p>The remainder of the Offensive Index can now be calculated pretty easily once we have referred to the <a href="http://surfarcher.blogspot.com.au/2014/09/d-5e-monsters-part-7-construction-damage.html#Example">example monster section</a> of the damage analysis in this series...<br>
Offensive_Index=(49+0)×1.05=51.45</p>
<p>And now we simply add these two values togethor to gain the overall Challenge Index...<br>
Challenge Index=38.5+51.45=89.95≈90</p>
<p>Based on <a href="#ChallengeIndexProgression">the chart above</a> a CI of 90 is just a little above the target for CR5. This tells us that this particular monster should be a slightly stronger than average CR5 opponent.</p>
<p style="clear:both;"> </p>
<p>In then near future I'll combine all of the tables publish to date into a single consolidated post. So stay tuned!</p>
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<a href="/2014/10/d-5e-monsters-part-9-construction.html">><img src="http://i.imgur.com/d0lSZlO.png" alt="◄"> Part 9: Attack Bonus</a>
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<a href="/2015/07/d-5e-monsters-part-11-construction.html">Part 11: Construction Consolidation <img src="http://i.imgur.com/bZ5DhBF.png" alt="►"></a>
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Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-40614927904308567452014-10-07T09:37:00.000+10:302016-09-23T17:32:01.783+09:30D&D 5e Monsters: Part 9: Construction: Attack Bonus<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<p><span style="color:lightyellow;"><i>Surf has a short but thorough look at Attack Bonus... </i></span></p>
<p> </p>
<a name="Top"></a><h3><u>Part 9: Attack Bonus</u></h3>
<p>We are almost finished with our build-oriented approach, however we do need to sit back and consider how <a href="#AttackBonus">Attack Bonus</a> progresses and look at how that applies to our <a href="#Example">Example Monster</a> before we move on to the final part - assessing the actual <i>CR</i> we have achieved.</p>
<p style="clear:both;"> </p>
<a name="AttackBonus"></a><h4>Attack Bonus</h4>
<p>When constructing monsters with a build-oriented approach we assign <i>Ability Scores</i> well before determining dependent attributes, such as attack actions. And when evaluating a monster we often start by checking out its ability scores and how they align to the values we previously determined for that CR. Assuming we chose appropriate values at those points we shouldn't need to be too concerned about the "to hit" progression, right? Well yes, inside a build-oriented approach that's correct. But with a result-oriented methodology that's not the case, we certainly want to know those numbers for that approach. Additionally we need to know what these parameters should be for CR assessment, as it's a factor there.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAW3XtlNi9XdSoZkYNc8hE-sz7OYiJC_e1dFX-7SO4ts96BIBVfnwibugVyM1L6XVRtFROJG8Mfg0gEXXM2DrpJ2Uu5sfQ-y5L9sPsTZwOHNffBdpMBAExxmZMV_w0loOdi99BRqS5xWQ/s1600/5e_pic_09a01_monster_attack_scatter.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAW3XtlNi9XdSoZkYNc8hE-sz7OYiJC_e1dFX-7SO4ts96BIBVfnwibugVyM1L6XVRtFROJG8Mfg0gEXXM2DrpJ2Uu5sfQ-y5L9sPsTZwOHNffBdpMBAExxmZMV_w0loOdi99BRqS5xWQ/s1600/5e_pic_09a01_monster_attack_scatter.png" height="192" width="320" alt="Monster Attack Bonus Scatter"></a><div class="caption">Monster Attack Bonus Scatter</div></div>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7ZcnnypS6V7MwnyFXzaCbejpq8L2WQRTyuVRAu02awbQnnlNhQjpRqrtRSdoPBJD49nYLCRXyyDsrra8b48pP0WmXBIrWyaL0ZQTQNam78y-w2a7PCBHblA7y7GqO2nRxHhGMNIijhpA/s1600/5e_pic_09a02_monster_attack_average.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7ZcnnypS6V7MwnyFXzaCbejpq8L2WQRTyuVRAu02awbQnnlNhQjpRqrtRSdoPBJD49nYLCRXyyDsrra8b48pP0WmXBIrWyaL0ZQTQNam78y-w2a7PCBHblA7y7GqO2nRxHhGMNIijhpA/s1600/5e_pic_09a02_monster_attack_average.png" height="192" width="320" alt="Monster Attack Bonus Average"></a><div class="caption">Monster Attack Bonus Average</div></div>
<p>As part of my data entry I record the regular <i>Attack Bonus</i> of each creature, as it aligns with the standard method of generation we looked at in the last article. As one would expect this makes it rather simple to graph and analyze.</p>
<p>Plotting all the data in a scatter graph, with a linear trendline, the progression is quite easy to observe. The data points cluster relatively closely to the trendline for most <i>CRs</i>, although there are a few exceptions. In fact the average Standard Deviation for each <i>CR</i> is 1.2 and the average Var is 1.8. This tells us that we can be very comfortable with a +/-2 variability on the to-hit bonus we determine. And of course we can also adjust outside the +/-2 bounds if we make compensating adjustments elsewhere, but we need to be careful and it's probably best to have some experience building <i>D&D 5e</i> monsters before attempting it.</p>
<p>This narrow band progression is due to two main factors. Firstly, the attack bonus is almost always derived from an ability modifier that is very close to the standard maximums we looked at earlier in this series. Secondly, monsters almost always have the appropriate proficiency bonus for their <i>CR</i> applied to their attack bonus.</p>
<p>This leads us to expect a summarized version of this graph to be very close to the actual progression and that's exactly what we see. That said the relatively low volume of high-<i>CR</i> monsters in our sample does cause some variability at the end of the graph.</p>
<div class="bluegrid" style="clear:both;"><table style="width:110px;">
<tr><th>CR</th><th colspan="2">Attack<br>Bonus✝</th></tr>
<tr><td>0 </td><td>+3</td></tr>
<tr><td>⅛</td><td>+4</td></tr>
<tr><td>¼</td><td>+4</td></tr>
<tr><td>½</td><td>+4</td></tr>
<tr><td>1 </td><td>+4</td></tr>
<tr><td>2 </td><td>+5</td></tr>
<tr><td>3 </td><td>+5</td></tr>
<tr><td>4 </td><td>+6</td></tr>
<tr><td>5 </td><td>+6</td></tr>
<tr><td>6 </td><td>+7</td></tr>
<tr><td>7 </td><td>+7</td></tr>
<tr><td>8 </td><td>+8</td></tr>
<tr><td>9 </td><td>+8</td></tr>
<tr><td>10 </td><td>+9</td></tr>
<tr><td colspan="2" style="text-align:left">✝ Varies by +/-2</td></tr>
</table></div>
<p>There are already posts on various forums suggesting simplified linear progressions for values like this. I've yet to see one that is a close match to what we've observed here though. All those I have seen produce results too low or high at one end of the scale or another. So what is a good match?</p>
<p>To me a good match needs to be about +4 at CR1, run through +13 at CR17 and not quite hit +20 at CR30. We know the CR30 cap is +19, being +10 for max ability score of 30 (Player's basic rules version 0.2, page 7) and +9 for CR30 proficiency (DM's basic rules version 0.1, page 4). But it also needs to account for values below CR1. And while the average +2.2 at CR0 might be tricky to hit with a linear progression it certainly shouldn't be too far off the +3.7 at CR¼. Of course rounding will hide most of the details below CR1, but we should be close anyway as this lends confidence to our result.</p>
<p>Kudos here to <a href="https://apis.google.com/u/0/wm/1/101257859936075176888">+Ford Davis</a> for reminding me of the CR30 cap.</p>
<p>A small amount of time in Excel gives us a linear formula which meets most of the criteria above...<br>
Attack=0.53 × Target_CR + 3.49</p>
<p>As anticipated this progression doesn't quite produce a +2.2 value at CR0, giving a +3.49 which rounds to +3.0 instead, but it is a very close match for the remainder of our criteria. As previously discussed values for attributes below CR1 do tend to skew a bit because of the low granularity and this slight skew in accuracy isn't too big a deal as CR0 monsters pose almost no threat to PCs, even at level one. Note that a process-oriented build is normally going to result in a +2 if it uses ability scores close to those we previously discussed and our +/-2 margin does allow for the difference, while <i>Bounded Accuracy</i> further reduces possible issues to almost zero.</p>
<p>Personally I have no problems using this progression as-is rather than trying to compensate with hand editing. Naturally readers are welcome to tweak it to +2 for their own use.</p>
<p><span class="prediction">Prediction:</span> The majority of CR30 monsters will have a normal attack bonus in the range of +18 to +19.</p>
<p style="clear:both;"> </p>
<a name="Example"></a><h4>Example: Human Pyromancer</h4>
<p>We don't really have anything to add to our example monster in this instalment.</p>
<div class="statblock"><table style="width:350px;">
<tr><td colspan="6"><h3>Human Pyromancer</h3></td></tr>
<tr><td colspan="6"><i>Medium humanoid (human), any alignment</i></td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><b>Armor Class</b> 12</td></tr>
<tr><td colspan="6"><b>Hit Points</b> 77 (14d8+14)</td></tr>
<tr><td colspan="6"><b>Speed</b> 30ft</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr class="attributes">
<td>STR<br>9 (-1)</td><td>DEX<br>14 (+2)</td><td>CON<br>12 (+1)</td><td>INT<br>19 (+4)</td><td>WIS<br>12 (+1)</td><td>CHA<br>12 (+1)</td>
</tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><b>Saving Throws</b> Dex +5, Int +7</td></tr>
<tr><td colspan="6"><b>Skills</b> Arcana +7, Perception +4</td></tr>
<tr><td colspan="6"><b>Damage Resistances</b> Fire</td></tr>
<tr><td colspan="6"><b>Languages</b> Common, Ignan</td></tr>
<tr><td colspan="6">Challenge 5 (1,700 XP)</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6">
<b>Spellcasting.</b> The pyromancer is a 5th-level spellcaster. Its<br>
spellcasting ability is Intelligence (spell save DC15, +7 to hit<br>
with spell attacks). The pyromancer has the following wizard<br>
spells prepared.<br>
<br>
Cantrips (at will): dancing lights, fire bolt<br>
1st level (3 slots): burning hands, disguise self<br>
2nd level (2 slots): invisibility, scorching ray<br>
3rd level (1 slot): fireball<br>
</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6">
<span style="font-size:16px">Actions</span><br>
<b>Dagger.</b> <i>Melee Weapon Attack:</i> +5 to hit, reach 5 ft., one target.<br>
<i>Hit:</i> 4 (1d4 + 2) piercing damage.
</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6">
<span style="font-size:16px">Reactions</span><br>
<b>Flame Shroud (Recharge 5-6).</b> When a ranged attack would hit<br>
the pyromancer, or it is targeted by a spell that has a range<br>
other than touch, the air around it bursts into shimmering,<br>
shifting flame for a few seconds. Until the start of the<br>
pyromancer's next turn ranged attacks against it, including the<br>
triggering attack, are made with Disadvantage and it has<br>
Advantage on saving throws against spells with a range other<br>
than touch. During this time it takes no damage from <i>magic<br>
missile</i>.
</td></tr>
</table></div>
<p>All that we can really do here is consider the pyromancer's attack bonus.</p>
<p>The <i>Spellcasting</i> <i>Trait</i> includes a spell "to hit" value of +7. This is a one higher than the +6 we believe is standard for CR5, but well within the +/-2 standard variation we declared earlier. So this is a good fit.</p>
<p>Our <i>Dagger</i> action is really only present for opportunity actions and that means it's +5 "to hit" being one low of appropriate for its CR should be just fine too.</p>
<p>So overall I think the pyromancer sits well, from an attack bonus perspective.</p>
<p> </p>
<p>Next time we'll have a look at how we can evaluate a monster's <i>Actual CR</i> once we think we have finished working on it.</p>
<p> </p>
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<a href="/2014/10/d-5e-monsters-part-8-construction.html"><img src="http://i.imgur.com/d0lSZlO.png" alt="◄"> Part 8: Construction: Actions</a>
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<a href="/2014/07/d-5e-monsters-master-index.html"><img src="http://i.imgur.com/qRcTo6k.png" alt="▲"> Master Index</a>
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<a href="/2014/12/d-5e-monsters-part-10-construction-cr.html">Part 10: CR Evaluation <img src="http://i.imgur.com/bZ5DhBF.png" alt="►"></a>
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Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-64120425995293241572014-10-04T04:30:00.000+09:302016-09-23T16:20:59.628+09:30D&D 5e Monsters: Part 8: Construction: Actions<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<p><span style="color:lightyellow;"><i>Surf continues on into the final parts of the monster stat block... </i></span></p>
<p> </p>
<a name="Top"></a><h3><u>Part 8: Construction: Actions</u></h3>
<p>Some of these articles seem to take on a life of their own and grow longer in the writing. I originally intended to include the <i>Attack Bonus</i> analysis in this instalment, however I've decided to post this part on its own and continue working on <i>Attack Bonus</i> as its own separate article.</p>
<p>We will start with a general <a href="#ActionOverview">Overview</a> of the different actions - <a href="#Move">Move</a>, <a href="#Action">Action</a>, <a href="#Reaction">Reaction</a> and <a href="#BonusAction">Bonus Action</a>. From here we consider how we <a href="#BuildingAttackActions">Build Attack Actions</a> so that we can complete the stat block of our <a href="#Example">Example Monster</a>.</p>
<p style="clear:both;"> </p>
<a name="ActionOverview"></a><h4>Action Overview</h4>
<p>Monsters are subject to the same action economy as player characters, although some monsters are able to extend this action economy in ways that PCs cannot - most notably <i>Legendary Creatures</i>. Just like PCs each monster can move and take one <a href="#Actions">Action</a> on its turn. And just like PCs monsters also have a <a href="#Reactions">Reaction</a> and a <a href="#BonusActions">Bonus Action</a> that they may use, if they have a way of doing so.</p>
<p>Formally expressed actions use certain common elements to standardize documentation, though some actions may omit almost all of these components. The components themselves are pretty straightforward and tend to focus primarily on supporting attacks. These elements include the following...</p>
<ul>
<li><b>Name</b>: All formally presented actions start with a short descriptive name for that action, frequently this is a single word. For example "Bite".</li>
<li><b>Usage</b>: Some actions are of limited usage and this is normally noted in braces immediately after the attack name. For example "Recharge 5-6".</li>
<li><b>Attack Type</b>: Most attack actions employ a standardized short form to indicate the general attack range (for example melee or ranged) and type (for example weapon or spell), along with the keyword "attack". Common examples include "Melee Weapon Attack", "Ranged Weapon Attack" and "Ranged Spell Attack".<br>
Special attacks instead typically describe very briefly the attack type, range and shape. For example "The dragon exhales fire in a 60-foot cone".</li>
<li><b>Attack/Defense enumeration</b>: Attack actions normally specify either a "to hit" bonus or details of a saving throw that the target must make. For example "+14 to hit" or "DC21 Dexterity save".</li>
<li><b>Target/Range information</b>: Attack actions normally describe targeting information. For standardized short-form attacks this will be a range type (reach or range), a range outline in feet (including long range if applicable) and the number of targets. Examples include "reach 5', one target" and "range 120/360 ft., one target".<br>
Special attacks normally dovetail their action description into their target specification descriptively. For example "each creature in area" or "each creature that can see the..."</li>
<li><b>Hit/Miss section</b>: These sections of attack actions describe what happens when the attack hits or, in some cases, when it misses. This section describes damage amounts, damage types, conditions and ongoing damage/conditions. It may also include nested attack sections, which are effectively additional attacks.</li>
</ul>
<p style="clear:both;"> </p>
<a name="Move"></a><h4>Move</h4>
<p>Move actions are not formally expressed actions in <i>D&D 5e</i> and are almost expressly not to be used for purposes other than movement. Indeed a number of monster actions which could be considered movement are implemented using <i>Actions</i> and <i>Bonus Actions</i>, such as the Etherealness action of the Ghost.</p>
<p>In <i>D&D 5e</i> the use of move actions is normally described in the <i>Speed</i> section near the very top of the monster stat block.</p>
<p style="clear:both;"> </p>
<a name="Action"></a><h4>Action</h4>
<p>Combat-viable monsters almost universally have at least one <i>Action</i> and the majority of <i>Actions</i> are some form of attack, either as a direct attack or indirectly by enabling attacks, <i>Multiattack</i> being the most common of these.</p>
<p><i>Actions</i> appear to fall in five specific categories and these always seem to occur in the following order with in the <i>Actions</i> section, when present...</p>
<ol>
<li>Multiattack</li>
<li>Regular attacks</li>
<li>Special attacks/Non-attack actions</li>
<li>Limited use attacks</li>
</ol>
<h5 style="clear:both;">1. Multiattack</h5>
<div class="statblock"><table style="width:350px;"><tr><td>
<b>Multiattack.</b> The dragon can use its Frightful Presence. It then<br>
makes three attacks: one with its bite and two with its claws.
</td></tr></table></div>
<p><i>Multiattack</i> actions simply specify the name "Multiattack" and the other <i>Actions</i> which may be used when the creature's <i>Multiattack</i> action is used, including the number of times each may be used (if more than once).</p>
<p>The <i>Multiattack</i> action is one of the most common actions in <i>D&D 5e</i> and the mechanism by which many of this edition's monsters achieve the bulk of their <i>Damage</i>. The action's simple elegance makes it easy to tune in to the desired target damage range at design time and at game time allows the DM a good deal of flexibility dishing out damage with as much or as little focus as desired. We already see in the PC classes that increasing the number of attacks over levels is a common scaling method in <i>D&D 5e</i> and that may be one of the reasons <i>Multiattack</i> is so common in its monsters, but I believe it is also present specifically because of the control it yields to DMs and to monster designers.</p>
<p>The <i>Multiattack</i> action can be as simple as two uses of a single regular melee attack or as complex as five, or possibly more, different <i>Actions</i>.</p>
<h5 style="clear:both;">2. Regular Attacks</h5>
<div class="statblock"><table style="width:350px;"><tr><td>
<b>Tail.</b> <i>Melee Weapon Attack:</i> +7 to hit, reach 10 ft., one target.<br>
Hit: 18 (4d6 + 4) bludgeoning damage. If the target is a<br>
creature, it must succeed on a DC 14 Strength saving throw or<br>
be knocked prone.
</td></tr></table></div>
<p>Regular attacks are slim-line in design and implementation, generally steering clear of unnecessary complexity. These actions include a standardized short-form <b>Attack Type</b>, typically an <b>Attack Enumeration</b> of the "to hit" variety and short-form <b>Target/Range Information</b>. They generally also include a relatively simple <b>Hit section</b>, occasionally with a <b>Miss section</b>, and may include nested damage.</p>
<p>Almost all combat-viable creatures have at least one regular attack and many of the lowest CR creatures have nothing but regular attacks. In some cases regular attack actions are fallbacks used for things like opportunity attacks or as building blocks for <i>Multiattack</i> actions.</p>
<h5 style="clear:both;">3. Special Attacks/Non-Attack Actions</h5>
<div class="statblock"><table style="width:350px;"><tr><td>
<b>Rotting Gaze.</b> The nothic targets one creature it can see within<br>
30 feet of it. The target must succeed on a DC 12 Constitution<br>
saving throw against this magic or take 10 (3d6) necrotic<br>
damage.
</td></tr></table></div>
<p>Special attacks and non-attack actions generally eschew the use of short-form annotation. By definition the more free-form <b>Attack Type</b> description is used and in most cases the free-form <b>Attack/Defense enumeration</b> and <b>Target/Range information</b> are also observed. Both the <b>Hit section</b> and <b>Miss section</b> may be present, but they may also be omitted in favor of a more free-form description, particularly in the case of non-attack actions.</p>
<p>Special attacks may account for a significant portion of a monster's alpha damage (aka "burst damage" or "spike damage"), especially where special attacks are conditional. However, in most cases alpha damage is the domain of limited use attacks or of the <i>Spellcaster</i> <i>Trait</i>.</p>
<h5 style="clear:both;">4. Limited Use Attacks</h5>
<div class="statblock"><table style="width:350px;"><tr><td>
<b>Cold Breath (Recharge 5-6).</b> The wolf exhales a blast of<br>
freezing wind in a 15-foot cone. Each creature in that area<br>
must make a DC 12 Dexterity saving throw, taking 18 (4d8)<br>
cold damage on a failed save, or half as much damage on a<br>
successful one.
</td></tr></table></div>
<p>Limited use attacks are those that specify a <b>Usage</b> restricting how frequently they may be used. Attacks of this type generally inflict damage well above that which the creature would otherwise cause and its normal damage is normally comparatively lower to compensate. In other respects the limited use attack typically resembles either regular attacks or special attacks.</p>
<p>The limited use attack is one of two vectors in <i>D&D 5e</i> for implementing alpha damage (aka "burst damage" or "spike damage"), the other normal vector being the <i>Spellcasting</i> trait.</p>
<h5 style="clear:both;">Action Analysis</h5>
<p>Now that we have examined the different types of <i>Actions</i> we need to consider the number of actions that are appropriate for a creature of our target CR. Is it just random (and by inference static with an acceptable margin of variance)? Or is there some kind of progression?</p>
<p>Common sense and instinct suggest that higher level monsters are more complex and thus more likely to have more <i>Actions</i>, but let's check the facts analytically.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9aWC29YeQzPr5FInNRhR8AkyfOVrvGu35Gh6O77zk4CHnNgIvSMiY-hvxTlc-_9nVpWebWwE42VGYM1URfVAGS7lqRBvENiTkmdE9GXt05WvnU7kZ2ZEndvyDGNTGOfjCUmy1o5g1NDk/s1600/5e_pic_08a01_monster_action_scatter.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9aWC29YeQzPr5FInNRhR8AkyfOVrvGu35Gh6O77zk4CHnNgIvSMiY-hvxTlc-_9nVpWebWwE42VGYM1URfVAGS7lqRBvENiTkmdE9GXt05WvnU7kZ2ZEndvyDGNTGOfjCUmy1o5g1NDk/s1600/5e_pic_08a01_monster_action_scatter.png" height="192" width="320" alt="Monster Number of Actions Scatter"></a><div class="caption">Monster Number of Actions Scatter</div></div>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhv74y3dDZsRkyxALTrL2-GQnlIRepKcWdkAUG0xJYDAI4vaALYRtT-Z8XyWcqBT65HqljsYpzah4Tm7VTe61griIiCnVTPLujcYnocoQ0K-iurEFLRCcxc3nf202WRDa5Gb49RdRT7LZc/s1600/5e_pic_08a02_monster_action_average.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhv74y3dDZsRkyxALTrL2-GQnlIRepKcWdkAUG0xJYDAI4vaALYRtT-Z8XyWcqBT65HqljsYpzah4Tm7VTe61griIiCnVTPLujcYnocoQ0K-iurEFLRCcxc3nf202WRDa5Gb49RdRT7LZc/s1600/5e_pic_08a02_monster_action_average.png" height="192" width="320" alt="Monster Number of Actions Average"></a><div class="caption">Monster Number of Actions Average</div></div>
<p>Once we have recorded the number of <i>Actions</i> each monster has it's a relatively simple matter to create a scatter graph showing number of <i>Actions</i> by CR. Placing a trendline on this gives us an initial indication of whether there might be some kind of progression.</p>
<p>The graph suggests that there probably is a progression, although it is kind of difficult to tell exactly what. And the relative sparseness of our higher-level samples means the high CR end will be quite prone to skew. Still the shape of the samples tells us that a variation of +/-2 seems quite normal. In fact the Standard Deviation for this across all CRs is 0.89 and the average variability is 1.14. So we can be quite happy with +/-2 as our regular variation, understanding that there is scope to vary outside this if we feel that it's appropriate in a particular case.</p>
<p>Averaging the data out by CR and then producing a comparable graph reveals a likely progression. For the most part the data is quite well aligned and the progression itself is quite shallow. <i>D&D 5e</i>'s preference for simple elegance shows itself here - even the more complicated monsters in the new edition tend to be relatively simple to understand and run. I find this a refreshing difference to its immediately preceding editions.</p>
<div class="bluegrid" style="clear:both;"><table style="width:110px;">
<tr><th>CR</th><th colspan="2">Num<br>Actions✝</th></tr>
<tr><td>0 </td><td>1</td></tr>
<tr><td>⅛</td><td>1</td></tr>
<tr><td>¼</td><td>2</td></tr>
<tr><td>½</td><td>2</td></tr>
<tr><td>1 </td><td>2</td></tr>
<tr><td>2 </td><td>2</td></tr>
<tr><td>3 </td><td>2</td></tr>
<tr><td>4 </td><td>2</td></tr>
<tr><td>5 </td><td>2</td></tr>
<tr><td>6 </td><td>2</td></tr>
<tr><td>7 </td><td>3</td></tr>
<tr><td>8 </td><td>3</td></tr>
<tr><td>9 </td><td>3</td></tr>
<tr><td>10 </td><td>3</td></tr>
<tr><td colspan="2" style="text-align:left">✝ Varies by +/-2</td></tr>
</table></div>
<p>The summary graph tells us pretty clearly that a progression from 2 at CR1 to 7 at CR30 is probably appropriate and that we'd want to drop down to about 1 action somewhere around CR¼. How sure of this can we be? What margin is there for error? And how much does it matter if we are wrong?</p>
<p>Well we already mentioned the low Standard Deviation and Variability, which give us some surety. But as I said we are quite light on higher CR samples and this could skew that end of the trendline. Fortunately with such a short range of difference this is somewhat like <i>Bounded Accuracy</i>, we don't necessarily have to be exactly right - our margin for error isn't that big. Additionally these are only guidelines of what's generally appropriate at a nominated CR and we are designating a significant variation as standard so the impact of being out by a couple of <i>Actions</i> isn't big.</p>
<p>It only takes a couple of minutes to determine a linear progression that matches this pattern...<br>
Actions=0.17 × CR + 1.46</p>
<p>As a matter of practical advice I'd encourage monster designers to follow <i>D&D 5e</i>'s principle of elegant simplicity wherever possible with <i>Actions</i>. Look to expressing your monster concept clearly with a small number of concise <i>Actions</i> where possible.</p>
<p><span class="prediction">Prediction:</span> I think most of what we have covered so far is self-evident. The only predication I can make is about the accuracy of the progression we have detailed above. I believe we'll find it's not too far off.</p>
<p style="clear:both;"> </p>
<a name="Reaction"></a><h4>Reaction</h4>
<p>Just like PCs monsters have a <i>Reaction</i> they may use each turn and they can "spend" it in any of the standard ways - by readying an action, making an opportunity attack, dismounting as their mount falls or by using a spell with a casting time of "reaction". Some monsters can also use their <i>Reaction</i> in special ways, just as many PCs can, and if present this will be described in the monster's <i>Reactions</i> section.</p>
<div class="statblock"><table style="width:350px;"><tr><td>
<b>Parry.</b> The knight adds 2 to its AC against one melee attack<br>
that would hit it. To do so, the knight must see the attacker<br>
and be wielding a melee weapon.
</td></tr></table></div>
<p>The layout for a <i>Reaction</i> is normally its <b>Name</b>, an explanation of its trigger conditions and the details of the <i>Reaction's</i> results. While this might include any of the elements described in the <a href="#ActionOverview">Action Overview</a> most <i>Reactions</i> tend to be fairly freeform, with a layout similar to the <i>Special Attacks/Non-Attack Actions</i> discussed above.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh94bJ3G-KaZQsrC-ew033mbHMO4F_gQ2keV0PPAdoh83MAS2fMsWqPjAmc8VlVbAOGPoXjt0KhfFXHgieIdddm474z5gag3hfv_ky9ROWauOVzq8BqG6PMqnIEVsvQf3D9Wy76yWG73UA/s1600/5e_pic_08a03_monster_reaction_scatter.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh94bJ3G-KaZQsrC-ew033mbHMO4F_gQ2keV0PPAdoh83MAS2fMsWqPjAmc8VlVbAOGPoXjt0KhfFXHgieIdddm474z5gag3hfv_ky9ROWauOVzq8BqG6PMqnIEVsvQf3D9Wy76yWG73UA/s1600/5e_pic_08a03_monster_reaction_scatter.png" height="192" width="320" alt="Monster Reaction Scatter"></a><div class="caption">Monster Reaction Scatter</div></div>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIlPxyBUIcwScTtsePYnXRMv0TY_KQrOduWJ-3v41tnPX-x89qmw7BQ9JOtmksO-fzz9nnd-3kj-maMpuJi3J63X9URWFyNAzGIItWjlEiH02_mZBtv_Stal9kyiN8EF_g-N2cjoeHX6o/s1600/5e_pic_08a04_monster_reaction_average.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIlPxyBUIcwScTtsePYnXRMv0TY_KQrOduWJ-3v41tnPX-x89qmw7BQ9JOtmksO-fzz9nnd-3kj-maMpuJi3J63X9URWFyNAzGIItWjlEiH02_mZBtv_Stal9kyiN8EF_g-N2cjoeHX6o/s1600/5e_pic_08a04_monster_reaction_average.png" height="192" width="320" alt="Monster Reaction Average"></a><div class="caption">Monster Reaction Average</div></div>
<p>While most PCs manage to pick up a reaction by level 5 we find that <i>Reactions</i> are far less common amongst <i>D&D 5e</i>'s monsters.</p>
<p>If we note the number of reaction entries each creature has and then plot the results on a scatter graph it's immediately obvious that very few monsters have a special <i>Reaction</i>. In fact of our 225 sample monsters only 7 have a <i>Reaction</i> (that's 3.1%) and none of these has more than one.</p>
<p>By averaging this data out and graphing it again we get visual confirmation of just how unusual it is for <i>D&D 5e</i> monsters to use special <i>Reactions</i>. Besides one tiny "blip" we can see that the overall average for any given level is close to zero, as it is across all levels.</p>
<p>This means that the use of special <i>Reactions</i> isn't something that monsters in this edition rely upon. We can probably simply consider it a flourish and as such a way of adding a certain "flavor" to the odd monster.</p>
<p>Based on the principle of elegant simplicity I believe we should not normally give our monsters special <i>Reactions</i>. Instead we should save these for when there is a compelling reason - perhaps we want a creature to "feel" like a Fighter or a Rogue and give it a <i>Reaction</i> similar to one that class has. Or perhaps our mental picture of the monster compels us to give it a special <i>Reaction</i></p>
<p><span class="prediction">Prediction:</span> Special <i>Reactions</i> will remain quite rare as we see more monsters released by <i>Wizards of the Coast</i>.</p>
<p style="clear:both;"> </p>
<a name="BonusAction"></a><h4>Bonus Action</h4>
<p>As monsters may take a reaction each turn they may also take a <i>Bonus Action</i>, if they have a way of doing so.</p>
<div class="statblock"><table style="width:350px;"><tr><td>
<b>Rampage.</b> When the hyena reduces a creature to 0 hit points<br>
with a melee attack on its turn, the hyena can take a bonus<br>
action to move up to half its speed and make a bite attack.
</td></tr></table></div>
<p>A monster's <i>Bonus Action</i> use is not detailed in a separate dedicated section, instead it is incorporated within other sections already discussed, typically the <i>Traits</i> section. A monster's <i>Bonus Action</i> may sometimes also be spent as a conditional extension of an <i>Action</i>.</p>
<p>While some <i>Bonus Actions</i> do enable additional attacks or <i>Damage</i> (which must be factored into the creature's average damage) some do not, instead they enable additional movement or other activity.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnJrcZTid390oQglzbQ4iR15uukwFjcfS8frcISldNAYzl7AoWtVIbW0F2QO-xm5RWDYxDJcr5UV2hWDNeVuR9CZHHHrp_45KuJ0vgnPF4pPUxabzIxlwQUnIE_trudbfQMpesA8KmXlA/s1600/5e_pic_08a05_monster_bonus_action_scatter.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnJrcZTid390oQglzbQ4iR15uukwFjcfS8frcISldNAYzl7AoWtVIbW0F2QO-xm5RWDYxDJcr5UV2hWDNeVuR9CZHHHrp_45KuJ0vgnPF4pPUxabzIxlwQUnIE_trudbfQMpesA8KmXlA/s1600/5e_pic_08a05_monster_bonus_action_scatter.png" height="192" width="320" alt="Monster Bonus Action Scatter"></a><div class="caption">Monster Bonus Action Scatter</div></div>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzwTLEQg31J6Zl4b_BIGxNrX9t8rYHroKP3IVqY6XrOFCcJfHP3yvSLm8P0FEuIUTJRUcGY3Nww6TUPN8KJiKSnseo7bS6DjqtD3EvquMRk-8bR7ZIfC7d-Dtt4q-b7kaGtWu3RZmkMJA/s1600/5e_pic_08a06_monster_bonus_action_average.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzwTLEQg31J6Zl4b_BIGxNrX9t8rYHroKP3IVqY6XrOFCcJfHP3yvSLm8P0FEuIUTJRUcGY3Nww6TUPN8KJiKSnseo7bS6DjqtD3EvquMRk-8bR7ZIfC7d-Dtt4q-b7kaGtWu3RZmkMJA/s1600/5e_pic_08a06_monster_bonus_action_average.png" height="192" width="320" alt="Monster Bonus Action Average"></a><div class="caption">Monster Bonus Action Average</div></div>
<p>This brings us to consideration of <i>Bonus Action</i> progression and occurrence. Once again we tally up the number of <i>Bonus Actions</i> that each monster has and see what the data tells us. The first thing we see is that 24 of our 225 sample creatures (that's about 10.7%) have at least one <i>Bonus Actions</i>. And all but one of these have only a single <i>Bonus Action</i>.</p>
<p>The scatter graph of all samples makes this quite clear and we can see the CR2 Will-O'-Wisp clearly standing out above the rest. This tells us that most of the time our monsters won't need a <i>Bonus Action</i>, but if we choose to use one it should probably just be a single one. This is nicely in keeping with the principal of elegant simplicity.</p>
<p>The summary graph clearly reflects the approximate 10% occurrence of <i>Bonus Actions</i> and also reveals the low numbers of our high-CR samples, which results in some variability from about CR10 onwards.</p>
<p>Essentially monster mechanics which utilize <i>Bonus Actions</i> add complexity to monsters. If we consider the principals of elegant simplicity and easy operation together with the frequency of <i>Bonus Actions</i> it suggests we should think a little before using <i>Bonus Actions</i> on our monsters. If our monster feels a bit on the plain side and too simple maybe it's appropriate to spice it up a bit with a <i>Bonus Action</i>. If we want to give our monster the feel of a PC class maybe we could factor a <i>Bonus Action</i> into its composition.</p>
<p><i>Bonus Actions</i> don't add the complexity of <i>Reactions</i> so with these I believe it's more a matter of using our judgment.</p>
<p><span class="prediction">Prediction:</span> Once the <i>Monster Manual</i> analysis is complete I believe we will see that the distribution of <i>Bonus Actions</i> stays at around 10% across all CRs, that said it is possible that it will increase somewhat at higher CRs.</p>
<p style="clear:both;"> </p>
<a name="BuildingAttackActions"></a><h4>Building Attack Actions</h4>
<p>Building attack actions can be fairly freeform however there are some underlying construction guidelines we should observe, especially in the case of most regular attack actions.</p>
<p>Many monster designers feel more comfortable building monster attacks based on PC attacks and this works particularly well with weapon attacks. One selects a weapon, applies the appropriate modifier (Strength modifier for most melee weapons or Dexterity modifier for finesse and many ranged weapons) for to-hit and damage, then adds proficiency to the to-hit value. Monster size does appear to play a role here and that role seems to focus on damage dice.</p>
<div class="bluegrid"><table style="width:240px;">
<tr><th>Size</th><th>Modification</th></tr>
<tr><td>Tiny</td><td style="text-align:left">Light weapons only</td></tr>
<tr><td>Small</td><td style="text-align:left">Heavy weapons excluded</td></tr>
<tr><td>Medium</td><td style="text-align:left">N/A</td></tr>
<tr><td>Large</td><td style="text-align:left">2x weapon dice</td></tr>
<tr><td>Huge</td><td style="text-align:left">3x weapon dice</td></tr>
<tr><td>Gargantuan</td><td style="text-align:left">4x weapon dice</td></tr>
</table></div>
<p>Weapon attacks seem to be impacted by creature size. Creatures smaller than medium appear to have restrictions on the weapons they can use and creatures bigger than medium size gain multipliers to the number of weapon dice. These modifications are clearest when looking at creatures assigned attack actions corresponding to weapons in the players guide. But this can also be extrapolated from other attack actions.</p>
<p>I have included a table with my understanding of these modifications. Please do note that this table is based on my observations and reflections.
While these observations correspond with those made by other members of the <i>D&D 5e</i> analysis community (kudos to Coronoides from the RPG.net forums and to others) they may not be a perfect match to what <i>Wizards of the Coast</i> is using. But it should be useful until we receive official guidelines from <i>WotC</i>.</p>
<p>Many creatures have attack actions similar to spells and many monster designers find it easiest to build these using PC spells as a base. The most important thing here is to ensure that the <i>Spell Save DC</i> or <i>Spell Attack Modifier</i> are appropriately calculated, using the appropriate ability modifier as the spellcasting modifier, as we discussed in the <a href="http://surfarcher.blogspot.com.au/2014/09/d-5e-monsters-part-6-construction.html#Spellcasters">Spellcasting</a> section of <a href="http://surfarcher.blogspot.com.au/2014/09/d-5e-monsters-part-6-construction.html">Part 6</a>.</p>
<p>As monster designers gain more confidence building monsters in <i>D&D 5e</i> it's likely they'll tend to move away from reproducing PC attacks, except where appropriate, and instead move towards a more "pure form" of building monster attack actions. To those embarking down this path I would share the following notes and general pieces of advice...</p>
<ul>
<li>Decide on the base ability and work out its modifier. For direct physical attacks it should be Dexterity or Strength. For magic, mental and other similar attacks it should be Charisma, Intelligence or Wisdom. Usually it's the highest ability in that group, unless there's a compelling reason otherwise.</li>
<li>Assume the monster has proficiency with their attacks, unless it suits design for them <b>not</b> to have proficiency.</li>
<li>To_Hit=Base_Ability_Modifier + Proficiency_Bonus
<li>Save_DC=8 + Base_Ability_Modifier + Proficiency_Bonus
<li>Damage always seems to have a base damage which is then built upon, which should be in the form<br>
NdN + Base_Ability_Modifier. For example 2d8+4</li>
<li>There is no mixed damage in <i>D&D 5e</i>, different types of damage in the same attack are concatenated. The base damage comes first with other damage appended to it. For example we would not have "3d8+2 fire and force damage"; instead we might have "1d8+2 fire damage plus 2d8 force damage".</li>
<li>It's legitimate to nest additional damage within base damage, typically using a save. For example "1d8+2 bludgeoning damage, the target must make a DC12 wisdom save or take an additional 2d8 psychic damage".</li>
</ul>
<p style="clear:both;"> </p>
<a name="Example"></a><h4>Example: Human Pyromancer</h4>
<p>Applying this article's content to our example monster will produce a result that is essentially complete.</p>
<div class="statblock"><table style="width:350px;">
<tr><td colspan="6"><h3>Human Pyromancer</h3></td></tr>
<tr><td colspan="6"><i>Medium humanoid (human), any alignment</i></td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><b>Armor Class</b> 12</td></tr>
<tr><td colspan="6"><b>Hit Points</b> 77 (14d8+14)</td></tr>
<tr><td colspan="6"><b>Speed</b> 30ft</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr class="attributes">
<td>STR<br>9 (-1)</td><td>DEX<br>14 (+2)</td><td>CON<br>12 (+1)</td><td>INT<br>19 (+4)</td><td>WIS<br>12 (+1)</td><td>CHA<br>12 (+1)</td>
</tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><b>Saving Throws</b> Dex +5, Int +7</td></tr>
<tr><td colspan="6"><b>Skills</b> Arcana +7, Perception +4</td></tr>
<tr><td colspan="6"><b>Damage Resistances</b> Fire</td></tr>
<tr><td colspan="6"><b>Languages</b> Common, Ignan</td></tr>
<tr><td colspan="6">Challenge 5 (1,700 XP)</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><b>Spellcasting.</b> The pyromancer is a 5th-level spellcaster. Its<br>
spellcasting ability is Intelligence (spell save DC15, +7 to hit<br>
with spell attacks). The pyromancer has the following wizard<br>
spells prepared.<br>
<br>
Cantrips (at will): dancing lights, fire bolt<br>
1st level (3 slots): burning hands, disguise self<br>
2nd level (2 slots): invisibility, scorching ray<br>
3rd level (1 slot): fireball<br>
</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><span style="color:gold;">
<span style="font-size:16px">Actions</span><br>
<b>Dagger.</b> <i>Melee Weapon Attack:</i> +5 to hit, reach 5 ft., one target.<br>
<i>Hit:</i> 4 (1d4 + 2) piercing damage.
</span></td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><span style="color:gold;">
<span style="font-size:16px">Reactions</span><br>
<b>Flame Shroud (Recharge 5-6).</b> When a ranged attack would hit<br>
the pyromancer, or it is targeted by a spell that has a range<br>
other than touch, the air around it bursts into shimmering,<br>
shifting flame for a few seconds. Until the start of the<br>
pyromancer's next turn ranged attacks against it, including the<br>
triggering attack, are made with Disadvantage and it has<br>
Advantage on saving throws against spells with a range other<br>
than touch. During this time it takes no damage from <i>magic<br>
missile</i>.
</span></td></tr>
</table></div>
<p>Because we made a conscious choice to rely heavily on the <i>Spellcasting</i> trait for most of the pyromancer's damage we don't have a great deal to do in the <i>Actions</i> section. All we really need to do is to give it a melee attack action that it can use for opportunity attacks. To this end let's give it a <i>Dagger</i> attack.</p>
<p>A CR5 creature's <i>Proficiency</i> bonus is +3 and the dagger is a finesse weapon, so we'll use the dexterity modifier of +2 for this. There's no compelling reason to beef this up so we will just go with +5 to hit and 1d4+2 damage.</p>
<p>Now several times during these articles I have indicated that we would give our pyromancer some kind of "trick" against ranged spells and attacks. Something to help it get through that first round, until some of the PCs close on it. What I've had in mind is something like the <i>Shield</i> spell, however I see several issues with simply assigning the pyromancer <i>Shield</i>. First up our monster would be able to use this three times, not simply once. Secondly <i>Shield</i> works against weapon attacks, but doesn't provide any benefit against ranged spells. Finally <i>Shield</i> isn't fire-themed.</p>
<p>Because of the first two issues simply reskinning <i>Shield</i> isn't going to meet our needs. So we'll take what we can as inspiration from <i>Shield</i>, modify other parts and fill the gaps ourselves.</p>
<p>Shield is a reaction with a force flavor that gives a +5 defensive bonus until the start of the caster's next turn and nullifies magic missile. The +5 isn't much help against spells, but a +5 is about the same as advantage/disadvantage compared with a plain roll. So we can use advantage/disadvantage in its place and word a reaction that functions against ranged attacks, with a fire flavor.</p>
<p>If we imagine that the pyromancer is momentarily shrouded in shimmering fire that makes it difficult to target we can envision how this can all come together.</p>
<p>Finally we want to restrict use of this reaction somewhat so that it isn't used every round. We could make it a daily power, but I decided that it would be most interesting if there was a small chance the pyromancer could use it more than once per encounter, so I made it a recharge reaction.</p>
<p>Next time we'll look at how the pyromancer matches up to the to-hit curve and then we'll move on to assessing its actual CR.</p>
<p> </p>
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<a href="/2014/10/d-5e-monsters-part-9-construction.html">Part 9: Attack Bonus <img src="http://i.imgur.com/bZ5DhBF.png" alt="►"></a>
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Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-34873505756746161632014-09-18T05:00:00.000+09:302016-09-23T16:18:28.232+09:30D&D 5e Monsters: Part 7: Construction: Damage<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<p><span style="color:lightyellow;"><i>Surf branches from Spellcasting into Damage... </i></span></p>
<p> </p>
<a name="Top"></a><h3><u>Part 7: Construction: Damage</u></h3>
<p>I had really wanted to cover <i>Damage</i> in <a href="http://surfarcher.blogspot.com/2014/09/d-5e-monsters-part-6-construction.html">Part 6</a>, but simply ran out of both time and space. And the analysis of <i>Damage</i> represents a fair investment of both time and space. And there seems to be a lot of demand for the <i>Damage</i> post. So in this case I am going to give <i>Damage</i> an instalment all of its own.</p>
<p>To compound matters I had nearly completed this post when I discovered minor mistake in <i>Damage</i> calculations for about 5% of the data. That meant I had to review <b>all</b> <i>Damage</i> data to make sure it was solid... A further delay!</p>
<p>So let's get right into <a href="#Damage">Damage</a>, and then see how this fits in with our <a href="#Example">Example Monster</a>.</p>
<p style="clear:both;"> </p>
<a name="Damage"></a><h4>Damage</h4>
<p>First, an up-front reminder. As I have said before I believe that <i>D&D 5e</i> has somewhat decoupled the Damage/HP axis from the AC/Accuracy axis. As such I believe that it's not necessary to factor these into <i>Damage</i> calculations. The proof is in the pudding, or the numbers in this case, and you'll catch a glimpse of some of that here...</p>
<p>There are a several ways we can calculate <i>Damage</i> for the same creature and this consumes quite a bit of time at the data entry stage. What do we include as <i>Damage</i>? Just the stable "At will" standard actions each round? Do we factor in attack and defense modifiers? Critical hits? How do we factor in variable damage like spell lists? How about recharge actions and other "once off" type attacks? How do we best calculate the damage of area effects? Because of things like spell lists and recharge attacks what do we assume about the number of rounds in an "average combat"? How do we allow for saving throw clauses?</p>
<p>There is a lot to consider and we need to be as thorough as possible... But even with a strong desire to be thorough and a relatively small number of samples we still can't consider every possible variation. We need to lean on previous works, community feedback... sometimes we must resort to trail & error and sometimes even to gut instinct. When we follow these non-statistical leads we must pour time into validating them with good solid math.</p>
<p>The methods I use for calculating <i>Damage</i> are fairly close to the methods used by the wider <i>D&D</i> community for DPR and the community has had some exposure to it via my <a href="http://community.wizards.com/forum/product-and-general-dd-discussions/threads/4120806">PC Stats thread</a> on the <i>Wizards of the Coast</i> forums. As repeatedly highlighted the principal differences are that I have intentionally removed both attack bonus and critical hits from my <i>Damage</i> calculations.</p>
<p>These haven't been removed due to the difficulty of including them or through laziness, including these simply isn't very difficult. It's simply a matter of adding a couple more columns in my spreadsheets, which were in fact present until relatively recently. No these have been removed because <b>including them increases data spread and data skew</b>. The data becomes more spread out and single values significantly above or below the median carry disproportionate weight. In simpler terms, the data becomes less meaningful with these factored into the calculations. That's fairly solid evidence that their inclusion simply isn't a significant part of the foundational monster math. This may or may not have been a conscious design decision on the part of <i>Wizards of the Coast</i>, but it is statistically evident in the resulting <i>D&D 5e</i> monsters.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEdQ9DNrxHCwippHAaEPTcONGJcreEYAlJrwq8d2phpFFBOT66N5l1aGvKwQrBfGMYGeptPR097THm8HOxrS_KNVBjaJXmFBmu6MHILLI_1HcBIzUP_ydMj8JJLGUPiJsk24y8pplbu0M/s1600/5e_pic_07a01_monster_atwill_scatter.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEdQ9DNrxHCwippHAaEPTcONGJcreEYAlJrwq8d2phpFFBOT66N5l1aGvKwQrBfGMYGeptPR097THm8HOxrS_KNVBjaJXmFBmu6MHILLI_1HcBIzUP_ydMj8JJLGUPiJsk24y8pplbu0M/s1600/5e_pic_07a01_monster_atwill_scatter.png" height="192" width="320" alt="Monster Misc Stats Score Scatter"></a><div class="caption">Monster Regular Damage Scatter</div></div>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY2xfUOhKv0FJn0zXb99xF9Z_17hCQbg1TBPR6VWDtqXxnPE3Nlkd_jWHo7P6XY2tMT7a725TN14-FEmR45CtM7f2MV-Y7OHqEvOTFbVX_wxhxETWThpWraRyh0ltmsgKQNhOTcbcCXyo/s1600/5e_pic_07a02_monster_avgdmg_scatter.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY2xfUOhKv0FJn0zXb99xF9Z_17hCQbg1TBPR6VWDtqXxnPE3Nlkd_jWHo7P6XY2tMT7a725TN14-FEmR45CtM7f2MV-Y7OHqEvOTFbVX_wxhxETWThpWraRyh0ltmsgKQNhOTcbcCXyo/s1600/5e_pic_07a02_monster_avgdmg_scatter.png" height="192" width="320" alt="Monster Misc Stats Score Scatter"></a><div class="caption">Monster Average Damage Scatter</div></div>
<p>Explaining every aspect of every decision step-by-step would take a lot of space and chew through a lot of time. So I'll go through the process for one aspect of it here. Let's assume for a moment that the way that I am calculating <i>Damage</i> is basically correct. But should we focus on "Regular" (or "At Will") <i>Damage</i> or on overall Average <i>Damage</i>? Let's look at the two... </p>
<p>So what we can do is create two almost identical scatter graphs. These have the same boundaries, axis values, formatting, size, trendlines and source the same <b>rows</b> in our spreadsheet. One will source the "Regular" <i>Damage</i> column, which we'll show in blue, and the other will source the "Average" <i>Damage</i> column, which we'll show in red.</p>
<p>If we place these next to one another, what differences are there?</p>
<p>The first thing most folks will notice is that the trendline is significantly higher in the red scatter graph, a reflection of the higher numbers resulting from including the damage from recharge actions and other "alpha attacks".</p>
<p>The next thing the attentive eye will notice is that the data points in the red graph tend to cluster around the trendline more evenly, that many of the data points on the blue graph tend to be scattered below the trendline.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlZ7EEEeVbfwkd6cBUU5hpTHLG4aCY27tK1LKrOi4SF3DkURmdINmhBiZBrK4pSsJvpZw1_tpKQ0KpnXS3BTLNeNRpG4kq7111XM3Uy6NBj3Rq8e6zKe1JXot6Q3RBivsL02brEG0uRcQ/s1600/5e_pic_07a03_monster_atwill_averaged.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlZ7EEEeVbfwkd6cBUU5hpTHLG4aCY27tK1LKrOi4SF3DkURmdINmhBiZBrK4pSsJvpZw1_tpKQ0KpnXS3BTLNeNRpG4kq7111XM3Uy6NBj3Rq8e6zKe1JXot6Q3RBivsL02brEG0uRcQ/s1600/5e_pic_07a03_monster_atwill_averaged.png" height="192" width="320" alt="Monster Misc Stats Score Scatter"></a><div class="caption">Monster Regular Damage Scatter</div></div>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEin_VN-22cC_EirLL3xdiXmQmztU5MRAtx6ciJhtXNUNknsKp3Zlo1jLPJQjtNtjjUXQ6Hm6A9gaiIQJoZ0pkMrgskV2IRrvKgD6LWf8hYfrNDoEvNcBQlKQUz3gpk9TXyfKjffATOr1kQ/s1600/5e_pic_07a04_monster_avgdmg_averaged.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEin_VN-22cC_EirLL3xdiXmQmztU5MRAtx6ciJhtXNUNknsKp3Zlo1jLPJQjtNtjjUXQ6Hm6A9gaiIQJoZ0pkMrgskV2IRrvKgD6LWf8hYfrNDoEvNcBQlKQUz3gpk9TXyfKjffATOr1kQ/s1600/5e_pic_07a04_monster_avgdmg_averaged.png" height="192" width="320" alt="Monster Misc Stats Score Scatter"></a><div class="caption">Monster Average Damage Scatter</div></div>
<p>Let us now consider the consolidated data. We have some big pivot tables that encompass all of the data in our main worksheet. We can trivially average both perspectives on <i>Damage</i> by <i>CR</i> and then create the exact the same graphs from that summarized data. That makes it very natural to compare these summary graphs with the two detail graphs, and to one another.</p>
<p>The trendlines have clarified a little, but haven't changed a whole lot. This isn't a big surprise and is mainly due to the relatively sparse higher level data we have.</p>
<p>The data points in both graphs have evened up significantly compared to their unsummarized versions, of course.</p>
<p>The data points in the blue graph now tend to wander back and forth. First above the trendline for a while, then below for several levels, then crossing back a forth a few times. But the data on the red graph is now fairly close to a consistent line. There is, of course, some variation but the scattering is fairly close in most cases and pretty evenly on both sides of the trendline. The variability isn't anywhere near as pronounced as in the blue graph.</p>
<p>We also need to consider how both sets of data compare against PC <i>Hit Points</i>. My principle way of analyzing this was by manual comparison - I enjoy the flexibility this provides and the opportunities it affords to drill into and expand out various aspects of data. But I realize that isn't going to appeal to many readers, so I'll summarize what I saw and provide some graphs for visual purposes.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLDKINfI9oDhlwjO7Jngg8fYkvPD0FCIIHnfSbNEdFBqtpEgsKaXphtDa0650sqGGrejylelymXgW046LeqT3MHEw1GXVG5TJPU8O6k4Fdt_4czj10OGNQ1Dm6quLfVxQbbUcyaIsmcfI/s1600/5e_pic_07a05_monster_dmg_vs_pc_hp_scatter.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLDKINfI9oDhlwjO7Jngg8fYkvPD0FCIIHnfSbNEdFBqtpEgsKaXphtDa0650sqGGrejylelymXgW046LeqT3MHEw1GXVG5TJPU8O6k4Fdt_4czj10OGNQ1Dm6quLfVxQbbUcyaIsmcfI/s1600/5e_pic_07a05_monster_dmg_vs_pc_hp_scatter.png" height="192" width="320" alt="Monster Damage vs PC HP Scatter"></a><div class="caption">Monster Damage vs PC HP Scatter</div></div>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6xvWLCWiSBG6X8nJ_Ch3AA4zphlW4w5VJNQMUZ1JBlgUSHp57Gp-B_44AY4oQloodZ1JZmi_0ZAHk1Hw8g6GRspV-JWUf8xj-3rKcphB2biWMtHhC2mcJqj7gqhOBQiZCIpFHIeFWqUw/s1600/5e_pic_07a06_monster_dmg_vs_pc_hp_summary.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6xvWLCWiSBG6X8nJ_Ch3AA4zphlW4w5VJNQMUZ1JBlgUSHp57Gp-B_44AY4oQloodZ1JZmi_0ZAHk1Hw8g6GRspV-JWUf8xj-3rKcphB2biWMtHhC2mcJqj7gqhOBQiZCIpFHIeFWqUw/s1600/5e_pic_07a06_monster_dmg_vs_pc_hp_summary.png" height="192" width="320" alt="Monster Damage vs PC HP Summary"></a><div class="caption">Monster Damage vs PC HP Summary</div></div>
<p>For these purposes I've created two scatter graphs. The first graph plots the PC <i>Hit Point</i> progression along with the raw data for both regular monster <i>Damage</i> and average monster <i>Damage</i>. I added a trendline to each of these data sets, of the same color as its data points. The second graph is the same, but shows summarized data.</p>
<p>These graphs let us see the data we have just been discussing in one place and how that data relates to PC <i>Hit Point</i> progression.</p>
<p>It's pretty obvious from this that <i>Damage</i> is less than PC <i>Hit Points</i>, which will be no surprise to those with experience from earlier editions. But the question is what percent of PC <i>HP</i> should they be? What's not immediately obvious from a graph is what these numbers shake out to under closer scrutiny.</p>
<p>So a useful tool at this part of the analysis is determining the percent of the average PC <i>HP</i> progression that the summary monster <i>Damage</i> accounts for. This involves several avenues of further investigation.</p>
<p>This brings us to something interesting that's not immediately evident on any of the graphs - the relatively high damage of CR1 monsters. The average <i>Damage</i> for these is a whopping 120% of average PC <i>HP</i>! Regular <i>Damage</i> only lags behind this a very small amount at 117%. Since CR2 creatures are pretty much at normal I believe this is an artificial spike that produces a feeling of greater lethality at first level. Why is this the case? Well the data shows that the CR1 creatures have relatively low <i>HP</i> (less than 4 times that of an average PC's <i>Damage</i>, instead of the more normal 7-8 times that of average PC <i>Damage</i>). So the CR1 monsters' high <i>Damage</i> is balanced by their low <i>HP</i>. Since we have 26 CR1 monsters it seems a bit of a stretch to call this coincidence, so I'd have to say that the intent is for monsters at this level to play out this way.</p>
<p>If we consider the current CR1 creature statistics to simply be a result of a general monster design decision (like "We will make most CR1 creatures Glass Cannons") then this has very little impact on producing an appropriate progression formula. We simply need to ensure that they generally fall near the parameters we end up with and rely on our <i>CR</i> assessment to produce an appropriate ranking.</p>
<p>But for the purposes of determining baseline monster <i>Damage</i> as a percent of PC <i>Hit Points</i> we have to be careful to consider the implications of this spike. One way of doing this is checking two versions of certain stats, one version that includes CR1 and one that excludes it. For simplicity we will simply ignore CR1 in the remainder of this post, but be assured that I did consider it in my analysis.</p>
<p>One useful technique for determining which percentage to use is to select a sliding window of a set number of adjacent values (I used 4 for a total of 5 in the sample) and move through the entire range, allowing us to enumerate the most common groupings of percentages. As we'd expect this tends to wander to a bit for regular monster <i>Damage</i> and is comparatively stable for average monster <i>Damage</i>. That said there is a general trend to tapering down as we progress from CR2 through to CR30.</p>
<p>Another useful "tool" is to determine the average, median, standard deviation and variance percentages for both regular and average monster <i>Damage</i>. We can use these in conjunction with our sliding windows to make decisions which are better informed.</p>
<p>Regular monster <i>Damage</i> has an overall average of 59.4% and a median of 61.4%, with a StdDev of 15.5% and variability of 2.3. The average for the mapped percentage groups is 59.4% with a median of 66.2%. These percentage groups have a StdDev of 10.5% and variability of 1.1.</p>
<p>Average monster <i>Damage</i> overall average is 80.3% and median is 78.8%, with a StdDev of 11.7% and a variance of 1.3. The mapped percentage group average for these is 81.5% with a median of 82.0%. These groups have a StdDev of 4.6% and a variability of 2.1.</p>
<p>These numbers do more than just identify possible target percentages, they tell us what level of confidence we can have in those percentages. We can see that regular monster <i>Damage</i> has a good deal more variability and uncertainty than average monster <i>Damage</i>. We can be pretty confident that it's somewhere in the 45% to 75% range and probably in the 50% to 70% range. If we needed to we could take a punt on it being 60%, but we could be wrong. Average monster <i>Damage</i> looks a good deal more stable though, we can have high confident that it's in the 70% to 90% and almost certainly in the 75% to 85% range.</p>
<p>Can we gain any more confidence than this? Perhaps, but the thing is the sparse data at the higher CRs does lend a certain amount of skew to the data and gaining a higher level of confidence takes progressively more effort and analysis. There is one shortcut we can use though. The spreadsheet this analysis is in has a provisional <i>CR</i> evaluation built into it. This still isn't complete and requires more refining, but <i>Damage</i> is a big part of <i>CR</i>. We can try different values in this range and see how that impacts the <i>CR</i> assessment of the current crop of monsters.</p>
<div class="bluegrid" style="clear:both;"><table style="width:200px;">
<tr><th rowspan="2">CR</th><th colspan="3">Average Damage</th></tr>
<tr><th width="25%">Min</th><th width="25%">Target</th><th width="25%">Max</th></tr>
<tr><td>⅛</td><td>1</td><td>2</td><td>3</td></tr>
<tr><td>¼</td><td>2</td><td>3</td><td>4</td></tr>
<tr><td>½</td><td>3</td><td>4</td><td>6</td></tr>
<tr><td>1</td><td>5</td><td>7</td><td>11</td></tr>
<tr><td>2</td><td>9</td><td>13</td><td>17</td></tr>
<tr><td>3</td><td>15</td><td>19</td><td>23</td></tr>
<tr><td>4</td><td>21</td><td>25</td><td>29</td></tr>
<tr><td>5</td><td>27</td><td>31</td><td>35</td></tr>
<tr><td>6</td><td>33</td><td>37</td><td>41</td></tr>
<tr><td>7</td><td>39</td><td>43</td><td>47</td></tr>
<tr><td>8</td><td>45</td><td>49</td><td>53</td></tr>
<tr><td>9</td><td>51</td><td>55</td><td>59</td></tr>
<tr><td>10</td><td>57</td><td>61</td><td>65</td></tr>
<tr><td colspan="4" style="text-align:left">Note: <b><i>Typical</i></b> boundaries shown.</td></tr>
</table></div>
<p>The results of this suggest that 75% is the closest match to existing data and so we'll go with that until we have enough data to make a more accurate assessment.</p>
<p>Now, PC <i>Hit Point</i> progression can be expressed pretty simply as...<br>
HP=8 × Level + 1<br>
So it's easy to calculate monster average damage, we just have to ask ourselves "what is 75% of 8?"...<br>
Damage=6 × Level + 1</p>
<p>If we add this progression to our average monster <i>Damage</i> graphs we see it's very close to the trendlines we have on that data series. After a little experimentation an overlap of around 15% between adjacent <i>CR</i> values seemed like a good fit.</p>
<p>As always the boundaries shown are what most monsters at a given <i>CR</i> should generally fall within. It's possible to have monsters above or below the given damage parameters that are still within <i>CR</i> by compensating elsewhere.</p>
<p><span class="prediction">Prediction:</span> <i>Damage</i> will prove to be concerned with average <i>Damage</i> and this will be closer to 75% than to 80%.</p>
<p style="clear:both;"> </p>
<a name="Example"></a><h4>Example: Human Pyromancer</h4>
<p>Since our Pyromancer achieves all of its damage through spells what we need to do is assess the profile of its likely spell use. I always assume a creature that is played fairly intelligently by a DM who is somewhat familiar with it.</p>
<p>Let's assume that the Pyromancer generally lasts 3 turns in combat. This seems fitting because we've designed it to attack with surprise and from a distance, using some allies and/or the terrain to shield it from its enemies.</p>
<p>At this point some readers are probably thinking "but what if it only lasts two rounds". Well the answer is its average <i>Damage</i> will increase, because we calculate the most powerful attacks it is probably going to use and its spell slots prevent it from using its most powerful attack (Fireball) more than twice.</p>
<p>So we'll calculate two uses of Fireball and one use of Flaming Sphere.</p>
<p><b>Fireball:</b> A fireball does 8d6 damage and a d6 is worth 3.5 average damage. We'll assume it hits 2.5 targets on average (about the standard for AoE damage calculations). It's a spell with a "half damage on save" clause so we'll multiply that base by 1.5 (in the DPR world we'd multiply by 0.75, but that's because we normally multiply by 0.5 for misses and in this case we aren't factoring in misses just extra damage). That gives us...<br>
Damage=3.5 × 8 × 1.5 × 2.5=105</p>
<p style="clear:both;"><b>Flaming Sphere:</b> This is 2d6 so we use the 2.5 base average again. Again it's a "half damage on save" spell so we use the 1.5 multipler and assume the standard 2.5 targets. It is a concentration spell though and the most elegant way to factor in it hitting another creature is to simply increase its number of targets by 1. This gives us...<br>
Damage=3.5 × 2 × 1.5 × (2.5 + 1)=36.75</p>
<div class="statblock"><table style="width:300px;">
<tr><td colspan="6"><h3>Human Pyromancer</h3></td></tr>
<tr><td colspan="6"><i>Medium humanoid (human), any alignment</i></td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><b>Armor Class</b> 12</td></tr>
<tr><td colspan="6"><b>Hit Points</b> 77 (14d8+14)</td></tr>
<tr><td colspan="6"><b>Speed</b> 30ft</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr class="attributes">
<td>STR<br>9 (-1)</td><td>DEX<br>14 (+2)</td><td>CON<br>12 (+1)</td><td>INT<br>19 (+4)</td><td>WIS<br>12 (+1)</td><td>CHA<br>12 (+1)</td>
</tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><b>Saving Throws</b> Dex +5, Int +7</td></tr>
<tr><td colspan="6"><b>Skills</b> Arcana +7, Perception +4</td></tr>
<tr><td colspan="6"><b>Damage Resistances</b> Fire</td></tr>
<tr><td colspan="6"><b>Lanuguages</b> Common, Ignan</td></tr>
<tr><td colspan="6">Challenge 5 (1,700 XP)</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><b>Spellcasting.</b> The pyromancer is an <span style="color:gold;">5th-level</span><br>
spellcaster. Its spellcasting ability is Intelligence<br>
(spell save DC15, +7 to hit with spell attacks). The<br>
pyromancer has the following wizards spells<br>
prepared.<br>
<br>
Cantrips (at will): dancing lights, fire bolt<br>
1st level (<span style="color:gold;">3</span> slots): burning hands, disguise self<br>
2nd level (<span style="color:gold;">2</span> slots): invisibility, <span style="color:gold;">scorching ray</span><br>
3rd level (<span style="color:gold;">1</span> slot): fireball<br>
</td></tr>
</table></div>
<p>That gives us an average of 82.25... Which is very, very high for a CR5 monster. Even allowing for our very low <i>Hit Points</i> it is probably too high. What can we do to reduce this? Dropping down the number of times Fireball can be cast is obviously going to be important. What if we add Scorching Ray and reduce Fireball to a single casting?</p>
<p><b>Scorching Ray:</b> This level 2 spell creates three separate rays that each do 2d6 damage on a hit (the caster makes a ranged spell attack). That gives us...<br>
Damage=3.5 × 2 × 3=21</p>
<p>Introducing this opens up some different possibilities.<br>
For one Fireball, one Flaming Sphere and one use of Scorching Ray this gives us...<br>
Damage=(105 + 36.75 + 21) ÷ 3=54.25<br>
And one use of Fireball with two uses of Scorching Ray results in...<br>
Damage=(105 + 21 + 21) ÷ 3=49<br>
</p>
<p>We could go with either of these options and having both spells available to the Pyromancer would let the DM make that call. However I prefer simplicity so I will opt for the Fireball/Scorching Ray only option.</p>
<p style="clear:both;"> </p>
<p>Now there are a few things to note here.</p>
<p>First up, some DMs and certainly some players are going to cry out "but that's not a valid Wizard spell progression!". Correct, it's not. I invite those especially concerned with this to show me the rules that say monsters must follow exactly the same progression as PCs. I believe that monster Spellcasters based on the Wizard are just that, <b>based</b> on the Wizard.</p>
<p>Secondly, some folks are going to observe that a monster that does an average 50-ish <i>Damage</i> each round with an "alpha strike" of over 100 damage is very powerful and going to be quite a challenge for a same-level party. That is correct and I guesstimate that this monster will be in the upper end of its <i>CR</i>. But I believe it will fall within its <i>CR</i> boundaries. This is based on the provisional <i>CR</i> evaluation formula I am currently using, which will be refined and presented a couple of posts from now.</p>
<p> </p>
<p><b>As a final note</b><i> I start three weeks' vacation in a couple of days.</i> The next post (Attack Actions, Bonus Actions, Moves, Reactions) is looking fairly straightforward and I do plan on working on it during this time. But do be aware that posts may be less frequent during this time than some might hope.</p>
<p> </p>
<div class="bottombar"><table><tr>
<td>
<a href="/2014/09/d-5e-monsters-part-6-construction.html"><img src="http://i.imgur.com/d0lSZlO.png" alt="◄"> Part 6: Construction: Traits & Spellcasting</a>
</td>
<td width="110px" style="text-align:centre;">
<a href="/2014/07/d-5e-monsters-master-index.html"><img src="http://i.imgur.com/qRcTo6k.png" alt="▲"> Master Index</a>
</td>
<td style="text-align:right;">
<a href="/2014/10/d-5e-monsters-part-8-construction.html">Part 8: Construction: Actions <img src="http://i.imgur.com/bZ5DhBF.png" alt="►"></a>
</td>
</tr></table></div>
</body></html>Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-30832176064437150712014-09-08T05:00:00.000+09:302016-09-23T16:16:24.050+09:30D&D 5e Monsters: Part 6: Construction: Traits & Spellcasting<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<p><span style="color:lightyellow;"><i>Surf digs into Traits and takes a closer look at Spellcasting... </i></span></p>
<p> </p>
<a name="Top"></a><h3><u>Part 6: Construction: Traits & Spellcasting</u></h3>
<p><i>Traits</i> are a crucial part of many creatures, serving to provide both grit and flavour. Many creatures also rely on these exclusively for their combat relevance in the game. This can be the case with <i>Spellcasting</i>, which is an incredibly flexible <i>Trait</i>.</p>
<p>We'll start with a broader <a href="#TraitsOverview">Traits Overview</a> - the types of <i>Traits</i>, how those impact other areas and their distribution across levels. From there we'll consider how <a href="#Spellcasters">Spellcasters</a> are typically implemented in <i>D&D 5e</i>.</p>
<p>Looking at <i>Spellcasting</i> leads naturally into an analysis of <i>Damage</i> and my original plan was to include that on this instalment. Unfortunately I ran over on both time and content before I could cover this. So I will do a post on <i>Damage</i> all on its own, just as soon as it's ready.</p>
<p>Finally we'll apply what we have determined to our <a href="#Example">Example Monster</a>.</p>
<p> </p>
<a name="TraitsOverview"></a><h4>Traits Overview</h4>
<p><i>Traits</i> are facets that alter the way game rules apply to creatures with that <i>Trait</i>. The implementation of <i>Traits</i> is evidence that <i>D&D 5e</i>'s modularity is underpinned by an exception-based ruleset. It is also one of the main areas where templating is evident, since so many <i>Traits</i> are trivially transportable and we see them used by many unrelated creatures.</p>
<h5>Conditional vs Simple</h5>
<p>All <i>Traits</i> can be considered enablers and the majority are conditional.</p>
<p>Conditional <i>Traits</i> enable a benefit (or occasionally a penalty) based on a specific circumstance being met. Let's consider the following...</p>
<ul>
<li>While the gargoyle remains motionless, it is indistinguishable from an inanimate statue.</li>
<li>The badger has advantage on Wisdom (Perception) checks that rely on smell.</li>
<li>The crab can breathe air and water.</li>
</ul>
<p>In the first case the condition is that the Gargoyle is motionless. In the second the Badger only gains Advantage on a Perception check if that check relies on smell. The third case is more subtle yet it is still conditional - the Crab must be breathing either air or water in order to not drown. It would still drown in oil or a vacuum, for example.</p>
<p><i>Traits</i> that are not conditional can be considered simple enablers - they apply a flat modification to a creature without any prerequisite condition. Examples include the following...</p>
<ul>
<li>The elemental can enter a hostile creature’s space and stop there.</li>
<li>The banshee can magically sense the presence of living creatures up to 5 miles away. She knows the general direction they’re in but not their exact locations.</li>
<li>The crocodile can hold its breath for 15 minutes.</li>
</ul>
<p>These simple enabling <i>Traits</i> generally have minimal impact to the way the creature performs in combat and are relatively uncommon. That said some non-conditional <i>Traits</i> have direct combat impact. Some <i>Traits</i> can act as attacks (like the Medusa's <i>Petrifying Gaze</i>) or provide access to attacks and/or utility <i>Actions</i> and <i>Reactions</i>. The <i>Spellcasting</i> <i>Trait</i> being the most common of the latter.</p>
<h5>Categories</h5>
<p>A complementary way of viewing <i>Traits</i> is by their use or impact, as I see it these fall into three broad categories...</p>
<ul>
<li>Combat <i>Traits</i>: Have a direct bearing on combat. Examples include <i>Pack Tactics</i>, <i>Sneak Attack</i> and in many cases <i>Spellcasting</i>.</li>
<li>Stat Boost <i>Traits</i>: Serve to provide some kind of boost to a creature's basic stats, including providing advantage on skill checks and possibly saving throws. Examples include <i>Freeze</i>, <i>Keen Sight</i> and <i>Regeneration</i>.</li>
<li>Utility or Flavour <i>Traits</i>: Provide additional modifications to creatures for purposes that don't directly relate to combat or other mechanical considerations. Examples include <i>Shapechanger</i>, <i>Water Breathing</i> and in some cases <i>Spellcasting</i>.</li>
</ul>
<p>Because the two approaches are complementary they can be used togethor. What I see is that most combat and stat boost <i>Traits</i> are conditional, while most simple enabling <i>Traits</i> are of the utility/flavour type.</p>
<p>Note that the <i>Spellcasting</i> <i>Trait</i> is very flexible and variable, so we'll take a closer look at that shortly.</p>
<h5>Impact On Calculations</h5>
<p>It's important to note that <i>Traits</i> can impact basic stat calculations and that combat <i>Traits</i> and stat boost <i>Traits</i> sometimes need to be considered when assessing a monster's actual <i>CR</i>. For example the <i>Regeneration</i> <i>Trait</i> appears to factor into a monster's <i>HP</i> count and attack-type <i>Traits</i> (including <i>Spellcasting</i> in some cases) factor into a creature's <i>Damage</i> assessment.</p>
<h5>Distribution</h5>
<p>OK so that's all important and very good, but "How many Traits should I give my monster?" I hear you ask! Let's have a look at the numbers...</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHhXyWBylxT2PsxAKGNu5LN4eBRTL5NnSCZugIfqc_a7wAmvH-Bki_X6trPkubYVijMlet-JBQxqZf8vHAKNhuognmK5gcCoC6bvH46nEQNvps5viVnJfS0bM6kEvoq10WrAa4-6wjEb4/s1600/5e_pic_06a01_monster_traits_scatter.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHhXyWBylxT2PsxAKGNu5LN4eBRTL5NnSCZugIfqc_a7wAmvH-Bki_X6trPkubYVijMlet-JBQxqZf8vHAKNhuognmK5gcCoC6bvH46nEQNvps5viVnJfS0bM6kEvoq10WrAa4-6wjEb4/s1600/5e_pic_06a01_monster_traits_scatter.png" height="192" width="320" alt="Monster Traits Scatter"></a><div class="caption">Monster Traits Scatter</div></div>
<p>If we create a scatter graph showing the number of <i>Traits</i> each creature has we can see that the data is tight and at a pretty low level. If we then drop a couple of trendlines on this, one Linear and one either Power or Logarithmic, we can see that the variability of data is also fairly low. That is the data generally has a low Standard Deviation and Variability. While there are exceptions at a couple of CRs, Var and StdDev are mostly 1 or less, occasionally making it as far as 2.</p>
<p>That's a fancy way of enumerating what you can see plainly - on average monsters have 2 <i>Traits</i> and the normal variation is +/- 2.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQJZSkk3-mfvOaPgE5hKTp4kfRB2aimnT1FBLUUWKWZD7RuOBHY3FuikiqPs8NG9u9_JiNqr2A5W6Ej_G73FLeS1n0B7Q44s70zFDU_8QiKnWxHcNZkUW30H4l83dmh3_G712U40UXmXI/s1600/5e_pic_06a02_monster_traits_averaged.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQJZSkk3-mfvOaPgE5hKTp4kfRB2aimnT1FBLUUWKWZD7RuOBHY3FuikiqPs8NG9u9_JiNqr2A5W6Ej_G73FLeS1n0B7Q44s70zFDU_8QiKnWxHcNZkUW30H4l83dmh3_G712U40UXmXI/s1600/5e_pic_06a02_monster_traits_averaged.png" height="192" width="320" alt="Monster AC Averaged"></a><div class="caption">Monster Traits Averaged</div></div>
<p>If we summarise the data, take the result and use that to produce another scatter graph with the same two trendlines... Does this change much? Well no, it really doesn't. This only serves to condense the data points, but it has no significant impact on the trendlines... on the shape of the data.</p>
<p>This essentially leaves us with two options. The first is a Logarithmic (or Power) formula that starts at a couple of <i>Traits</i> at CR1, plateauing by CR5 and only very slowly progressing from there.</p>
<div class="bluegrid" style="clear:both;"><table style="width:110px;">
<tr><th>CR</th><th colspan="2">Num<br>Traits✝</th></tr>
<tr><td>0 </td><td>1</td></tr>
<tr><td>⅛</td><td>1</td></tr>
<tr><td>¼</td><td>1</td></tr>
<tr><td>½</td><td>1</td></tr>
<tr><td>1 </td><td>2</td></tr>
<tr><td>2 </td><td>2</td></tr>
<tr><td>3 </td><td>2</td></tr>
<tr><td>4 </td><td>2</td></tr>
<tr><td>5 </td><td>2</td></tr>
<tr><td>6 </td><td>2</td></tr>
<tr><td>7 </td><td>2</td></tr>
<tr><td>8 </td><td>2</td></tr>
<tr><td>9 </td><td>2</td></tr>
<tr><td>10 </td><td>2</td></tr>
<tr><td colspan="2" style="text-align:left">✝ Varies by +/-2</td></tr>
</table></div>
<p>The other option is a simple Linear formula. Based on the current crop of monsters I think we'll see that this is, in fact, a fairly flat Linear progression.</p>
<p>So exactly what kind of progression do I expect we'll see in the <i>Monster Manual</i>? Well after rounding we'd want CR1 to hit 2, but under CR1 we want 1. So we want to start CR1 at 1.5. At CR30 I believe we'll want to just hit 4, after rounding. So that at CR30 our target is 3.5.</p>
<p>A moment's work in Excel suggests something similar to this...<br>
Number Traits=0.07 x CR + 1.43</p>
<p>When using this formula it's important to keep in mind that that a variation of +/-2 is easily within the normal ranges. And realistically one can go to +/-4 by exercising a little care. What do I mean by that? Well adding six or eight combat-oriented <i>Traits</i> to a CR1 monster can produce creature much stronger than its CR indicates. Complementary and synergistic <i>Traits</i> can also be problematic here if not carefully considered.</p>
<p style="clear:both;"><span class="prediction">Prediction:</span> Analysis of the <i>Monster Manual</i> will reveal that number of <i>Traits</i> is a slow linear progression, as we have outlined above.</p>
<p> </p>
<a name="Spellcasters"></a><h4>Spellcasters</h4>
<p>The <i>Spellcasting</i> <i>Trait</i> effectively grafts the core PC system for spellcasters onto a monster. <i>Spellcasting</i> and its close relative <i>Innate Spellcasting</i> are arguably the most versatile and powerful <i>Traits</i> commonly found in the current crop of <i>D&D 5e</i> monsters. There are several caster archetypes obvious in the current crop of monsters and we'll have a look at these once we've considered the structure of <i>Spellcasting</i>.</p>
<h5>Spellcasting Overview</h5>
<p><i>Spellcasting</i> and <i>Innate Spellcasting</i> are discussed on pages 5 & 6 of the <i>DM Basic Rules v0.1</i> available in <a href="http://dnd.wizards.com/articles/features/basicrules?x=dnd/basicrules">Basic D&D</a>. This section sheds a little light on how to use monsters with this <i>Trait</i> and, if we read between the lines, even gives us a few clues to how they are built. Combined with the elements of <i>Spellcasting</i> that we see on monsters with that <i>Trait</i> we gain a pretty clear understanding of how that <i>Trait</i> is implemented. The components are...</p>
<ul>
<li><b>Spellcaster Level</b> is used to index several elements of the <i>Trait</i> from the appropriate class. It is usually several levels over the CR of the creature (typically 3 levels higher), but I don't believe there's a simple formula applied to this. Instead I think it serves as a type of "dial" to tune in damage, support or utility reuqirements for the monster. <i>Spellcaster Level</i> is normally followed by several dependant attributes...
<ul>
<li><b>Spellcaster Ability</b> is usually the highest of Int, Wis or Cha.</li>
<li><b>Spell Save DC</b> in most cases is calculated as...<br>
DC=8 + Proficiency_Bonus + Spellcaster_Ability_Modifier<br>
The occasional creature seems to have a bonus or penalty on top of this. I suspect this is either a racial bonus or a manua "tweak" to adjust particularly powerful or weak casters.</li>
<li><b>Spell Attack Bonus</b> is simply calculated as...<br>
Bonus=Proficiency_Bonus + Spellcaster_Ability_Modifier</li>
<li><b>Spellcaster Class</b> dictates the cantrips, spell slots, available spells, etc as detailed below</li>
</ul>
</li>
<li><b>Cantrips</b> are gained as normal for a <i>PC</i> caster of the appropriate <i>Class</i> and <i>Level</i>.</li>
<li><b>Spell Slots</b> are applied as normal for a <i>PC</i> caster of the appropriate <i>Class</i> and <i>Level</i>.</li>
<li><b>Spell List</b> details the spells the monster knowns or has prepared (as per its <i>Spellcaster Class</i>). Note that these are usually fewer than for a <i>PC</i> of the same caster class and level, typically one fewer at each spell level, however it may be up to the same number as the equivalent <i>PC</i> caster class and level. My suggestion is that only spells that fit the monster's underlying design concepts are added. Simply adding spells to match the number that <i>PC</i>s of that <i>Class</i> and <i>Level</i> have might seem intuitive, but ultimately it makes the monster more difficult to operate and therefore less effective.</li>
<li><b>Domain Features</b> available to the class may also be added to the monster.</li>
<li>Note that Monsters may cast spells using a higher slot if one is available and if that spell allows casting at a higher spell level.</li>
<li>Note the section on modifying a monster's spell list and the warning that this may impact that monster's strength relative to its <i>CR</i>, making it stronger or weaker than its <i>CR</i> indicates. An obvious reason for this is that many monsters with the <i>Spellcasting</i> <i>Trait</i> achieve most of their damage via their spells.</li>
</ul>
<h5>Archetype: Attack Caster</h5>
<p>Some monsters with <i>Spellcasting</i> achieve most or all of their combat relevance through this <i>Trait</i>, with the primary focus being on spells that inflict damage and/or conditions. For example, the <i>Evil Mage</i> from page 57 of the <i>Starter Set</i> only does 3 damage each round without its spells. But look at its <i>Spell List</i>...</p>
<ul>
<li>Cantrips (at will): light, mage hand, shocking grasp</li>
<li>1st Level (4 slots): charm person, magic missile</li>
<li>2nd Level (3 slots): hold person, misty step</li>
</ul>
<p>So this monster can cast <i>Magic Missile</i> using a level 2 slot three times, allowing it to do 14 <i>Damage</i> each round.</p>
<h5>Archetype: Defense Caster</h5>
<p>Some monsters don't use <i>Spellcasting</i> for direct aggression, instead their spells focus on assisting their allies. These creatures often play support roles in combat, healing and buffing, or rely on buffing their own attacks (ala "Gish" creatures). The <i>Acolyte</i> on p53 of the <i>DM Basic Rules v0.1</i> is a good example of this archetype...</p>
<ul>
<li>Cantrips (at will): light, sacred flame, thaumaturgy</li>
<li>1st level (3 slots): bless, cure wounds, sanctuary</li>
</ul>
<p>While the <i>Acolyte</i> does achieve its best damage using <i>Sacred Flame</i> that isn't its main role in combat. Instead this creature's best use is casting its 1st level spells.</p>
<h5>Archetype: Utility Caster</h5>
<p>Some creatures with a casting <i>Trait</i> don't use their magic skills for purposes that directly impact combat calculations, which isn't to say that that their spells have no direct impact on combat. All current examples of this are creatures with <i>Innate Spellcasting</i>, but there's no reason this can't be equally well implemented using <i>Spellcasting</i>. Let's consider the <i>Rakshasa</i>'s spell list...</p>
<ul>
<li>At will: detect thoughts, disguise self, mage hand, minor illusion</li>
<li>3/day each: charm person, detect magic, invisibility, major image, suggestion</li>
<li>1/day each: dominate person, fly, plane shift, true seeing</li>
</ul>
<p>The <i>Rakshasa</i>'s spell list clearly is not intended for head-on combat. Instead it is well suited to the creature's preference for working behind the scenes and for infiltration. This isn't to say its spells have no combat application, but in that context they are focussed on safely escaping confrontation rather than defeating enemies.</p>
<h5>Archetype: Flavour Caster</h5>
<p>We can expect to see the odd creatures with <i>Spellcasting</i> or <i>Innate Spellcasting</i> where the spells have no combat application whatsoever. The example that currently jumps to mind is the <i>Yuan-ti Malison</i> from the <i>Horde Of The Dragon Queen</i>...</p>
<ul>
<li>At will: animal friendship (snakes only)</li>
<li>3/day: suggestion</li>
</ul>
<p>Very thematic, but with little or no combat application.</p>
<h5>Archetypes vs Real Monsters</h5>
<p>The thing is actual monsters closely matching the Archetypes listed above are pretty rare. There are some, as our examples show, but few of these are "pure" examples of their type. What's most common is for monsters to mix types. So a creature that is primarily an Attack Caster will frequently dabble in defensive casting and may also have a dash of utility casting.</p>
<p>This kind of selective, well-thought-out mixing is fine and can result in a more robust opponent. But I would again caution against going overboard and giving a <i>Spellcaster</i> too many spells. I feel a clear, succinct monster is easier to operate than an overly complex one. Of course, this is my own perspective and preference, not something based on any particular analysis or metrics.</p>
<p><span class="prediction">Prediction:</span> When we see casters of the Flavour archetype their Caster Level will be relatively lower (for their CR) than that of casters that focus on Attack or Defense casting.</p>
<p style="clear:both;"> </p>
<a name="Example"></a><h4>Example: Human Pyromancer</h4>
<p>OK let's apply this all to our pyromancer. Now what <i>Traits</i> do we want to give this monster? <i>Spellcasting</i> is obvious, as we've alluded to in both this and previous installments. But what about other <i>Traits</i>? I did toy with the idea of giving the <i>Pyromancer</i> something to mitigate damage to its allies, but I don't think that's really in keeping with the ideas behind this monster. Likewise some kind of spell penetration <i>Trait</i> could be appropriate, but I think that's simply going to complicate things without yielding any real benefit. So I've opted simply to go with <i>Spellcasting</i>.</p>
<div class="statblock"><table style="width:300px;">
<tr><td colspan="6"><h3>Human Pyromancer</h3></td></tr>
<tr><td colspan="6"><i>Medium humanoid (human), any alignment</i></td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><b>Armor Class</b> 12</td></tr>
<tr><td colspan="6"><b>Hit Points</b> 77 (14d8+14)</td></tr>
<tr><td colspan="6"><b>Speed</b> 30ft</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr class="attributes">
<td>STR<br>9 (-1)</td><td>DEX<br>14 (+2)</td><td>CON<br>12 (+1)</td><td>INT<br>19 (+4)</td><td>WIS<br>12 (+1)</td><td>CHA<br>12 (+1)</td>
</tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><b>Saving Throws</b> Dex +5, Int +7</td></tr>
<tr><td colspan="6"><b>Skills</b> Arcana +7, Perception +4</td></tr>
<tr><td colspan="6"><b>Damage Resistances</b> Fire</td></tr>
<tr><td colspan="6"><b>Lanuguages</b> Common, Ignan</td></tr>
<tr><td colspan="6">Challenge 5 (1,700 XP)</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr style="color:gold;"><td colspan="6"><b>Spellcasting.</b> The pyromancer is an 8th-level<br>
spellcaster. Its spellcasting ability is Intelligence<br>
(spell save DC15, +7 to hit with spell attacks). The<br>
pyromancer has the following wizards spells<br>
prepared.<br>
<br>
Cantrips (at will): dancing lights, fire bolt<br>
1st level (4 slots): burning hands, disguise self<br>
2nd level (3 slots): flaming sphere, invisibility<br>
3rd level (2 slots): fireball<br>
</td></tr>
</table></div>
<p>The pyromancer is an intelligence-based caster loosely modelled on the wizard. We'll peg its <i>Caster Level</i> at 8 for now, 3 higher than its CR. The remaining stats are trivial to determine, <a href="#Spellcasters">as described above</a>.</p>
<p>This brings us to its <i>Spell List</i>. We already know we are doing a fire-themed caster and as a glass cannon it makes sense for it to focus on the attack caster archetype. All this makes the core of spells we would choose pretty obvious: fire bolt, burning hands, flaming sphere and fireball. This works pretty nicely for the pyromancer being a ranged caster without a lot of close-quarter options - fireball will account for most of the pyromancer's damage and burning hands gives it some melee relevance.</p>
<p>Next we'll splash in some flavour and utility with dancing lights, disguise self and invisibility. I did think about adding mage armor or shield, but that makes our monster a lot more resiliant in melee combat than our original design. Instead I will be adding an interesting litle reaction in a later installment.</p>
<p>In the forthcoming Damage installment we'll reflect on how our example creature shapes up damage-wise and see if we need to make any adjustments.</p>
<p> </p>
<div class="bottombar"><table><tr>
<td width="40%">
<a href="/2014/08/d-5e-monsters-interlude-bunch-of.html"><img src="http://i.imgur.com/d0lSZlO.png" alt="◄"> Interlude: A Bunch Of Monsters!</a>
</td>
<td width="110px" style="text-align:centre;">
<a href="/2014/07/d-5e-monsters-master-index.html"><img src="http://i.imgur.com/qRcTo6k.png" alt="▲"> Master Index</a>
</td>
<td style="text-align:right;">
<a href="/2014/09/d-5e-monsters-part-7-construction-damage.html">Part 7: Construction: Damage <img src="http://i.imgur.com/bZ5DhBF.png" alt="►"></a>
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Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-24686270439371196862014-08-25T13:05:00.000+09:302016-09-23T16:14:26.546+09:30D&D 5e Monsters: Interlude: A Bunch Of Monsters!<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<p><span style="color:lightyellow;"><i>Wow! Lots of new critters! Time for a stocktake and review... </i></span></p>
<p> </p>
<a name="Top"></a><h3><u>Interlude: A Bunch Of Monsters!</u></h3>
<p>Well in the last week or so a whole bunch of monsters have made their way to us! There was an update to <i>Horde Of The Dragon Queen</i>, the <i>Player's Handbook</i> was released, a new version of <i>Basic D&D</i> was released with over 150 monsters and there have been a number of <i>Monster Manual</i> creature spoilers released.</p>
<p>As a result my sample size jumped from 33 monsters to 209!</p>
<p>On top of that there have been several tweaks to PC data via the <a href="http://community.wizards.com/forum/product-and-general-dd-discussions/threads/4120806">PC Stats thread</a> on the <i>Wizards of the Coast</i> forums.</p>
<p>All this means one thing... It's time to stop and review what we have done so far. This will delay the next scheduled post a few days, but it's important to do.</p>
<p>I think it's best to cover this all in one big post, so forgive me if this one gets a bit long. To make it up to you here's a handy-dandy index...</p>
<ul>
<li><a href="#CR">Challenge Rating</a></li>
<li><a href="#Size">Size</a></li>
<li><a href="#AbilityScores">Ability Scores</a></li>
<li><a href="#HP">Hit Points</a></li>
<li><a href="#AC">Armor Class</a></li>
<li><a href="#MiscStats">Miscellaneous Stats</a></li>
<li><a href="#Example">Example Monster</a></li>
</ul>
<p> </p>
<a name="CR"></a><h4>Challenge Rating</h4>
<p>Most of the mechanical items we talked about in the <a href="http://surfarcher.blogspot.com/2014/07/d-5e-monsters-part-3-construction-cr.html#CR">CR section of Part 3</a> have either been ratified or remain unchanged. The <i>DM Basic Rules v0.1</i> released at <a href="http://dnd.wizards.com/articles/features/basicrules?x=dnd/basicrules">Basic D&D</a> does provide some insight and a couple of useful tables that replace some of what we discussed.</p>
<p>The <i>Proficiency Bonus By Challenge Rating</i> table on page 4 shows that we were correct about using CR to select a monster's proficiency. It also handily extends monster Proficieny below CR1 and above CR20 for us.</p>
<p>The <i>Experience Points By Challenge Rating</i> table on page 5 shows that we were very close with our <i>XP</i> values, at least in the CR0 through CR10 range. If we take our formula and extend out past CR10 to CR30 we find some inaccuracies creep in, though. As I previously said, our small set of sample data made it unwise to project out past CR10.</p>
<p>Rather than smply work off a formula for the curve <i>Wizards of the Coast</i> have, in effect, spliced three curves togethor. What I can see by CR is this...</p>
<ul>
<li>CR <1: These creatures look like they are hand-fashioned off of CR1 creatures. One could probably model the first and second curves togethor by going to a fairly complex polynomial.</li>
<li>CR 1 - 20: Matches a polynomial 3 equation similar to this:<br>
XP = 1.1553x^3 + 31.119x^2 + 166.47x - 43.52</li>
<li>CR 21+: Another curve greatly increases XP gain for defeating monsters, which is appropriate since PCs will supposedly be fighting creatures far more powerful than themselves. This appears to be a polynomial equation similar to the following:<br>
XP = 564.39x^2 - 15148x + 101214</li>
</ul>
<p>This is pretty much of academic interest, but it does serve to illustrate the dangers of computing data values based on too small a sample size.</p>
<p><span class="prediction">Reflection:</span> I predicted that we would see creatures of CR30 or even beyond. The Tarrasque spoiler from the <i>Monster Manual</i> is CR30, confirming my prediction.</p>
<p> </p>
<a name="Size"></a><h4>Size</h4>
<p>As with <i>Challenge Rating</i>, most of the elements we discussed in the <a href="http://surfarcher.blogspot.com/2014/07/d-5e-monsters-part-3-construction-cr.html#Size">Size section of Part 3</a> are ratified or remain unchanged by the <i>DM Basic Rules v0.1</i> in the recent <a href="http://dnd.wizards.com/articles/features/basicrules?x=dnd/basicrules">Basic D&D</a> release.</p>
<p>The <i>Hit Dice By Size</i> on page 3 of the <i>DM Basic Rules v0.1</i> shows that our belief regarding the link between <i>Size</i> and <i>Hit Dice</i> was correct and that we estimated the <i>Hit Dice</i> size for <i>Huge</i> and <i>Gargantuan</i> creatures correctly.</p>
<p>Naturally there were no references to the linkage between <i>Size</i> and <i>Speed</i>.</p>
<p><span class="prediction">Reflection:</span> It's a bit hard to draw any conclusions about my prediction about monster sizes at higher levels, since we still have very few higher-CR monsters to look at. But at this stage I see no reason to doubt my prediction.</p>
<p> </p>
<a name="AbilityScores"></a><h4>Ability Scores</h4>
<p>On reviewing <i>Ability Score</i> values and referring back to the <a href="http://surfarcher.blogspot.com.au/2014/08/d-5e-monsters-part-4-construction.html#Abilities">Ability Score section of Part 4</a> I find that the greater sample data has upheld the findings of that post. In fact the trendlines we use have firmed up very considerably and now naturally align quite closely to the formulae and table we constructed in there! I can only see this as statistical ratification.</p>
<p>I'd be quite comfortable extending this out to CR15 based on the data we now have.</p>
<p><span class="prediction">Reflection:</span> While there is no definative proof of the prediction I made that peak attributes would reach 30 past CR20 I feel very comfortable clarifying that this will become the common peak <i>Ability Score</i> closer to CR30 than CR25.</p>
<p> </p>
<a name="HP"></a><h4>Hit Points</h4>
<p>Before considering the impact the new mass of monsters has on the <a href="http://surfarcher.blogspot.com.au/2014/08/d-5e-monsters-part-4-construction.html#HP">Hit Points section of Part 4</a>, let's stop a moment and consider the community input on my assessment of PC statistics. It's important to consider this first because, as we said in part 4, these aspects of monster math are built on PC math.</p>
<p>Over the last couple of weeks the <i>Wizards of the Coast</i> community has discussed this on my <a href="http://community.wizards.com/forum/product-and-general-dd-discussions/threads/4120806">PC Stats thread</a> over on the <i>WotC</i> forums. A number of changes have been suggested to the way I have calculated this data and most of it has been incorporated into my math. But the funny things is, at the end of the day it hasn't significantly changed the curves I described in part 4. Yes, some of the variations in the progression changed. But in the end the curve formula remained unchanged. Which makes things a bit easier in this review.</p>
<p>So PC <i>Damage</i> remains as previously defined...<br>
PC Damage=4.55 x Level ^ 0.72</p>
<div class="bluegrid" style="clear:both;"><table style="width:200px;">
<tr><th rowspan="2">CR</th><th colspan="3">Hit Points</th></tr>
<tr><th width="25%">Min</th><th width="25%">Target</th><th width="25%">Max</th></tr>
<tr><td>0</td><td>1</td><td>8</td><td>10</td></tr>
<tr><td>⅛</td><td>9</td><td>11</td><td>13</td></tr>
<tr><td>¼</td><td>12</td><td>13</td><td>17</td></tr>
<tr><td>½</td><td>14</td><td>18</td><td>26</td></tr>
<tr><td>1</td><td>21</td><td>28</td><td>43</td></tr>
<tr><td>2</td><td>33</td><td>48</td><td>63</td></tr>
<tr><td>3</td><td>53</td><td>68</td><td>83</td></tr>
<tr><td>4</td><td>73</td><td>88</td><td>103</td></tr>
<tr><td>5</td><td>93</td><td>108</td><td>123</td></tr>
<tr><td>6</td><td>113</td><td>128</td><td>143</td></tr>
<tr><td>7</td><td>133</td><td>148</td><td>163</td></tr>
<tr><td>8</td><td>153</td><td>168</td><td>183</td></tr>
<tr><td>9</td><td>173</td><td>188</td><td>203</td></tr>
<tr><td>10</td><td>193</td><td>208</td><td>223</td></tr>
<tr><td colspan="4" style="text-align:left">Note: <b><i>Typical</i></b> boundaries shown.</td></tr>
</table></div>
<p>Now the new monsters... Gaining such a significant injection new data showed up something interesting things about the relationship between PC <i>Damage</i> and monster <i>Hit Points</i>! I found the new data pretty interesting and spent a fair bit of time re-analyzing <i>HP</i> as a result.</p>
<p>It turns out the PC <i>Damage</i>:Monster <i>HP</i> ratio isn't a static 5, as previously posted. It's very clear that the multiplier actually starts somewhere down near 3.5 or 4 and trends up very quickly to an average of 7 then scales out to around 12 at CR30.</p>
<p>I did some pretty extensive analysis of this, attacking the problem from several different angles. By the end I had several potential formulae that could potentially be used to build monster <i>HP</i>. But profiling these I found most of my methods of correlation pointed towards the use of a Logarithmic expression to determine the multipiler. I believe it's close to the following...<br>
Multiplier=0.31 x LN(CR) + 3.7<br>
Which yields a monster <i>HP</i> formula something like this...<br>
HP=(4.55 x CR ^ 0.72) * (0.31 x LN(CR) + 3.7)</p>
<p style="clear:both;">It's a little convoluted, but testing showed some positive flags...</p>
<ul>
<li>A close relationship to observable <i>HP</i> data on both scatter and summary graphs.</li>
<li>A match <i>HP</i> summary data.</li>
<li>General tightening up of data clusters, aligning with sampled data.</li>
<li>Very close matches when use in my provisional <i>CR</i> assessment formula.</li>
<li>Data not matching my provisional <i>CR</i> assessment formula is fairly evenly split above and below targets.</li>
</ul>
<div class="bluegrid" style="clear:both;"><table style="width:300px;">
<tr><th rowspan="2">CR</th><th rowspan="2">Con<br>Mod</th><th colspan="6">Hit Dice</th></tr>
<tr>
<th width="12%">Tiny<br>(d4)</th>
<th width="12%">Small<br>(d6)</th>
<th width="12%">Medium<br>(d8)</th>
<th width="12%">Large<br>(d10)</th>
<th width="12%">Huge<br>(d12)</th>
<th width="12%">Garg'n<br>(d20)</th>
</tr>
<tr><td>0</td><td>-1</td><td>5</td><td>3</td><td>2</td><td>2</td><td>1</td><td>1</td></tr>
<tr><td>⅛</td><td>-1</td><td>7</td><td>4</td><td>3</td><td>2</td><td>2</td><td>1</td></tr>
<tr><td>¼</td><td>0</td><td>5</td><td>4</td><td>3</td><td>2</td><td>2</td><td>1</td></tr>
<tr><td>½</td><td>0</td><td>7</td><td>5</td><td>4</td><td>3</td><td>3</td><td>2</td></tr>
<tr><td>1</td><td>0</td><td>11</td><td>8</td><td>6</td><td>5</td><td>4</td><td>3</td></tr>
<tr><td>2</td><td>0</td><td>19</td><td>14</td><td>11</td><td>9</td><td>7</td><td>5</td></tr>
<tr><td>3</td><td>1</td><td>19</td><td>15</td><td>12</td><td>10</td><td>9</td><td>6</td></tr>
<tr><td>4</td><td>1</td><td>25</td><td>20</td><td>16</td><td>14</td><td>12</td><td>8</td></tr>
<tr><td>5</td><td>1</td><td>31</td><td>24</td><td>20</td><td>17</td><td>14</td><td>9</td></tr>
<tr><td>6</td><td>1</td><td>37</td><td>28</td><td>23</td><td>20</td><td>17</td><td>11</td></tr>
<tr><td>7</td><td>2</td><td>33</td><td>27</td><td>23</td><td>20</td><td>17</td><td>12</td></tr>
<tr><td>8</td><td>2</td><td>37</td><td>31</td><td>26</td><td>22</td><td>20</td><td>13</td></tr>
<tr><td>9</td><td>2</td><td>42</td><td>34</td><td>29</td><td>25</td><td>22</td><td>15</td></tr>
<tr><td>10</td><td>2</td><td>46</td><td>38</td><td>32</td><td>28</td><td>24</td><td>17</td></tr>
</table></div>
<p>It's unlikely any single formula can adequately match all sampled data - which is a significant factor behind my belief that CR assessment is a measure of composite data. However this formula achieves a high proportion of match, with its trendline being mainly centred within sample data.</p>
<p>And the result of this relates very well to a simple linear equation which can be used in its place seamlessly...<br>
HP=20 x CR + 8</p>
<p>Now that I had reset the monster <i>HP</i> progression values I had to re-baseline the monster <i>HD</i> table. This is a job that takes a couple of hours or so by hand and I had already done it three times. So I invested a couple of hours writing up a VBA macro to compute it all. Now with the press of a button it's all recalculated in less than a second.</p>
<p>Being an ex-programmer pays off from time to time!</p>
<p style="clear:both;"><span class="prediction">Reflection:</span> I indicated that I believed monster <i>Hit Points</i> would be more variable than monster <i>Damage</i>, once we were able to analyse the <i>Monster Manual</i>. I've seen nothing to suggest that I should recant this.</p>
<p> </p>
<a name="AC"></a><h4>Armor Class</h4>
<p>The significant increase in sample size has served to clarify <i>AC</i> significantly. In fact sample size is now big enough for us to realistically estimate <i>AC</i> independently of PC <i>Attack Bonus</i>, if we choose to do so. This opens up several avenues of correlation that we did not have in the <a href="http://surfarcher.blogspot.com.au/2014/08/d-5e-monsters-part-5-construction-ac.html#AC">Armor Class section of Part 5</a>.</p>
<p>Examining trendlines on scatter and summary graphs reveals a very linear progression of monster <i>AC</i>, with values still fairly tightly grouped at +/-5 of trendlines. Note that when looking past CR20 we do need to be careful of skew as both the CR24 Ancient Red Dragon and the CR30 Tarrasque likely have an <i>AC</i> near the top of their range.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdi2QSEo_2vQDQJZarKY0lkGC-SVyecOfUUCyFaQEqRNYtC3w_e3PlYX8JCZeluwk1BFsPTum5SrViPtdkeTlmb2_ST_WLVn1_Q7TewlOiyIk89BIA4D_Nq4NwwrIlYWm6veHtEbQzHR4/s1600/5e_pic_05aa01_AC_curve_vs_line.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdi2QSEo_2vQDQJZarKY0lkGC-SVyecOfUUCyFaQEqRNYtC3w_e3PlYX8JCZeluwk1BFsPTum5SrViPtdkeTlmb2_ST_WLVn1_Q7TewlOiyIk89BIA4D_Nq4NwwrIlYWm6veHtEbQzHR4/s1600/5e_pic_05aa01_AC_curve_vs_line.png" height="192" width="320" alt="AC curve vs linear"></a><div class="caption">AC curve vs linear</div></div>
<p>Reassessing our data from a PC <i>Attack Bonus</i> perspective also shows that the relationship between it and <i>AC</i> has clarified. Between CR1 and CR20 we can see that same-level PCs consistently need to roll an 8 or better to hit the monster. Considering that PC <i>Attack Bonus</i> is a curve how do we resolve this to a linear monster <i>AC</i> progression?</p>
<p>Well, it's not as difficult as some readers might expect.</p>
<p>Simply plotting the two on the same graph provides some understanding of this. The red line on the graph shows PC <i>Attack Bonus</i> plus 8 (in other words, it's a pure derivation). The blue line represents a linear equation closely matching the summary data I have crunched in my spreadsheet. You'll se that the results of the two will be quite close, particularly after rounding.</p>
<div class="bluegrid" style="clear:both;"><table style="width:110px;">
<tr><th rowspan="2">CR</th><th colspan="2">Armor Class</th></tr>
<tr><th>Average</th></tr>
<tr><td>0 </td><td>13</td></tr>
<tr><td>⅛</td><td>13</td></tr>
<tr><td>¼</td><td>13</td></tr>
<tr><td>½</td><td>13</td></tr>
<tr><td>1 </td><td>13</td></tr>
<tr><td>2 </td><td>13</td></tr>
<tr><td>3 </td><td>13</td></tr>
<tr><td>4 </td><td>14</td></tr>
<tr><td>5 </td><td>14</td></tr>
<tr><td>6 </td><td>14</td></tr>
<tr><td>7 </td><td>15</td></tr>
<tr><td>8 </td><td>15</td></tr>
<tr><td>9 </td><td>15</td></tr>
<tr><td>10 </td><td>16</td></tr>
</table></div>
<p>Now some readers might feel concerned about the small disparities between the two. But as we previously noted <i>Bounded Accuracy</i> means that <i>AC</i> varies more within a given <i>CR</i> than it does across all <i>CRs</i>. And it's very normal to see <i>AC</i> variance up to +/-5 of normal within a given <i>CR</i>'s monsters. We even see variation beyond this occasionally. So it really is something we simply do not need to be concerned with.</p>
<p>The linear equation itself is quite simple, of course...<br>
AC=0.32 x CR + 12.5</p>
<p>Readers will note that several resulting <i>AC</i> values are different on the new table, mainly at the lowest levels. But the differences are pretty minimal and this again highlights the reasons behind our decision to restrict ourselves to CR10 and below until the <i>Monster Manual</i> is released.</p>
<p><span class="prediction">Reflection:</span> It looks like average monster <i>AC</i> may peak at 22 at CR29 or CR30, rather than at CR25.</p>
<p style="clear:both;"> </p>
<a name="MiscStats"></a><h4>Miscellaneous Stats</h4>
<p>The <i>Misc Stats</i> area is another place where the increase in sample data has served only to suggest that our findings in the <a href="http://surfarcher.blogspot.com.au/2014/08/d-5e-monsters-part-5-construction-ac.html#MiscStats">Miscellaneous Statistics section of Part 5</a>
are correct.</p>
<p>While the scatter graph contained many more data points its trendline remained completely unchanged. The summary graph also gained more data points (because we have sample monsters at levels where we previously did not) and this changed the high-value end of the trendline... Only a small amount.</p>
<p><span class="prediction">Reflection:</span> I've not seen anything to suggest that I should change the predictions I made in this area.</p>
<p style="clear:both;"> </p>
<a name="Example"></a><h4>Example: Human Pyromancer</h4>
<p>Let's see how our findings impact our sample monster. We'll also make a couple of other minor tweaks/corrections to the Pyromancer...</p>
<div class="statblock"><table style="width:300px;">
<tr><td colspan="6"><h3>Human Pyromancer</h3></td></tr>
<tr><td colspan="6"><i>Medium humanoid (human), any alignment</i></td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><b>Armor Class</b> 12</td></tr>
<tr><td colspan="6"><b>Hit Points</b> <span style="color:gold;">88 (16d8+16)</span></td></tr>
<tr><td colspan="6"><b>Speed</b> 30ft</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr class="attributes">
<td>STR<br>9 (-1)</td><td>DEX<br>14 (+2)</td><td>CON<br>12 (+1)</td><td>INT<br>19 (+4)</td><td>WIS<br>12 (+1)</td><td>CHA<br>12 (+1)</td>
</tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6"><b>Saving Throws</b> Dex +5, Int +7</td></tr>
<tr><td colspan="6"><b>Skills</b> Arcana <span style="color:gold;">+7, Perception +4</span></td></tr>
<tr><td colspan="6"><b>Damage Resistances</b> Fire</td></tr>
<tr><td colspan="6"><b>Lanuguages</b> Common, Ignan</td></tr>
<tr><td colspan="6">Challenge 5 (<span style="color:gold;">1,800 XP</span>)</td></tr>
</table></div>
<p>While our chosen <i>Challenge Rating</i> of 5 remains unchanged we do need to update the Pyromancer's <i>XP</i> reward from 1,700 to 1,800.<p>
<p><i>Size</i> and <i>Ability Score</i> values remain unchanged.</p>
<p>Based on the updated data the creature's <i>Hit Points</i> are probably a bit <b>too</b> low, even for a glass cannon. We could either increase number of <i>HD</i> or we could increase the Pyromancer's <i>Constitution Score</i>. Since changes in <i>HD</i> generally result in smaller incremental changes I tweaked this up by two to 16, resulting in an average <i>HP</i> of 88.</p>
<p>Although we have made some updates to <i>Armor Class</i> in this post it's important we remember that <i>AC</i> tends to vary more within a given <i>CR</i> than it does when across all <i>CR</i>s, thanks to <i>Bounded Accuracy</i>. As such I believe that <i>AC</i> does not need to be updated for the Pyromancer.</p>
<p>While we don't need to make any changes to <i>Miscellaneous Stats</i> base don this post, I did notice an error in the Pyromancer as listed last installment. I had intended to give it proficiency in <i>Perception</i>, which is much more useful for monsters than <i>Arcana</i>. And I accidentally left off the actual <i>Arcana</i> bonus. I've corrected these in this version and will go back and edit my previous post shortly.</p>
<p> </p>
<div class="bottombar"><table><tr>
<td width="45%">
<a href="/2014/08/d-5e-monsters-part-5-construction-ac.html"><img src="http://i.imgur.com/d0lSZlO.png" alt="◄"> Part 5: Construction: AC & Other Attributes</a>
</td>
<td width="60px" style="text-align:centre;">
<a href="/2014/07/d-5e-monsters-master-index.html"><img src="http://i.imgur.com/qRcTo6k.png" alt="▲"> Master Index</a>
</td>
<td style="text-align:right;">
<a href="/2014/09/d-5e-monsters-part-6-construction.html">Part 6: Construction: Traits & Spellcasting <img src="http://i.imgur.com/bZ5DhBF.png" alt="►"></a>
</td>
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Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-48127208428671839652014-08-13T11:22:00.000+09:302016-09-23T16:09:30.514+09:30D&D 5e Monsters: Part 5: Construction: AC & Other Attributes<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<p><span style="color:lightyellow;"><i>Where Surf deals with the Armor Class curve and does some other attribute analysis... </i></span></p>
<p> </p>
<a name="Top"></a><h3><u>Part 5: Construction: AC & Other Attributes</u></h3>
<p>Apologies to those patient readers who were expecting a blog post last week. Real life is unimaginative and unforgiving. It left me without time to peice this post togethor until now.</p>
<p>To complete the top four sections of the <i>D&D 5e</i> monster stat block we need to understand <a href="#AC">Armor Class</a>, the <a href="#MiscStats">Miscellaneous Stats</a> that a creature has and set appropriate values on our <a href="#Example">Example Monster</a>.</p>
<p> </p>
<a name="AC"></a><h4>Armor Class</h4>
<p>Monster <i>Armor Class</i> has a close relationship with PC <i>Attack Bonus</i>. While our small sample size does present some difficulties here we can do some analysis on PC <i>Attack Bonus</i> to help us leverage value from the samples we have. Yes, there will be some element of uncertainty, but it will be smaller than many people expect.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0TRgKbYTRVPNbrqcoApQvd78QizJNL0gK_behnGehpyULiWO5g4SVZDS_Rz38haYMmoBIOJNsXt7GwNk_qeDGwWnKx6e3zrzf8bla2At7o5hn2AKJvYReFs0jq3KBL2aD-YZ1d9bewB8/s1600/5e_pic_05a01_monster_ac_scatter.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0TRgKbYTRVPNbrqcoApQvd78QizJNL0gK_behnGehpyULiWO5g4SVZDS_Rz38haYMmoBIOJNsXt7GwNk_qeDGwWnKx6e3zrzf8bla2At7o5hn2AKJvYReFs0jq3KBL2aD-YZ1d9bewB8/s1600/5e_pic_05a01_monster_ac_scatter.png" height="192" width="320" alt="Monster AC Scatter"></a><div class="caption">Monster AC Scatter</div></div>
<p>If we plot all of the monster <i>AC</i> values by level we get an interesting little scatter graph, with most of the data on the left hand side because of the predominantly low level nature of our sample data. A trendline will be less impacted by this low-level skew, however the sparseness of higher level data does tend to make the trendline somewhat unreliable. But remember, that's why we are constraining ourselves to CR10 and below.</p>
<p>What's important here is that we get a sense of roughly where the average is for the data we have, what we think the trendline should look like and what kind of variability we should expect to see at a given level.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTYtpZssMI6hk6VrJ8mAkMt8mVdY4GJxAwtqpfiL19BYIBPT7X6oE8k0TRgxOmVcZfOkhUpdMy6iiBBqnQGP9dJTBeEKC1_hc2TmaKv2zmHSGtygG9tjqw5spjGJmqk4khAsdPhyFDSdk/s1600/5e_pic_05a02_monster_ac_average.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTYtpZssMI6hk6VrJ8mAkMt8mVdY4GJxAwtqpfiL19BYIBPT7X6oE8k0TRgxOmVcZfOkhUpdMy6iiBBqnQGP9dJTBeEKC1_hc2TmaKv2zmHSGtygG9tjqw5spjGJmqk4khAsdPhyFDSdk/s1600/5e_pic_05a02_monster_ac_average.png" height="192" width="320" alt="Monster AC Average"></a><div class="caption">Monster AC Average</div></div>
<p>We can also average monster <i>AC</i> data and plotting the results on another graph, adding a trendline to this graph too. We can then consider the similarities and differences between the two, along with what these might signify. As you can see this tightens up the clusters and brings the lower level data into sharper focus. Unfortunately this doesn't directly help with our higher level samples.</p>
<p>That said this is probably enough to crack this particular nut for CR0 through CR10... That is, if we do some analysis of related PC data and then leverage off it.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdyY15TvBqtTzVUcE591JveEtjZkqiYl4Vm5rzmWygk2nyxRPFvBIDYx5mjx-huPLn-qLHogp1fFRzpZJ8J7Dc5IGZSkt4kqeIdnyhygL047JpJbGqG38A8wTDv9O5DUSCSeIqxKa-T4M/s1600/5e_pic_05a03_pc_avg_attack.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdyY15TvBqtTzVUcE591JveEtjZkqiYl4Vm5rzmWygk2nyxRPFvBIDYx5mjx-huPLn-qLHogp1fFRzpZJ8J7Dc5IGZSkt4kqeIdnyhygL047JpJbGqG38A8wTDv9O5DUSCSeIqxKa-T4M/s1600/5e_pic_05a03_pc_avg_attack.png" height="192" width="320" alt="Average PC Attack"></a><div class="caption">Average PC Attack</div></div>
<p>To achieve this I had to go and analyze <i>Attack Bonus</i> data for PC <i>Classes</i>, as I had previously done for PC <i>Damage</i> in order to properly analyze monster <i>Hit Points</i>. Since I was doing this anyway I also did the initial analysis on PC <i>AC</i>, updated my previous PC data spreadsheet and floated a new <a href="http://community.wizards.com/forum/product-and-general-dd-discussions/threads/4120806">PC Stat Curves</a> thread on the <i>Wizards of the Coast</i> forums. Hopefully this proves useful to others and you are welcome to look at it yourself and comment back on that thread, if you are so inclined.</p>
<p>The casual reader might be forgiven for assuming that we can express the PC <i>Attack Bonus</i> using a simple linear expression, or possibly a power expression. While we can get fairly close to the trendline we see in that graph using a linear or power equation, but to achieve something close to an exact match we need to use a simple polynomial similar to this one:<br>
Attack = -0.0062 x Level ^ 2 + 0.495 x Level + 4.012</p>
<p>This curve is particularly useful for several reasons. It almost perfectly matches the projected progression, having a 0.2 variance that only tells at four points due to rounding - levels 5, 9, 10 and 13. AT these points the rounded value slips one above or below the actual PC class values. I think that falls with the margin for error in the observed PC data itself. The progression below level 1, where we might match with CR, looks appropriate. Past level 20 the progression becomes quite shallow, which should be appropriate for building CR21+ creatures. Additionally the equation is one of the least complicated polynomials. It seems fairly elegant to me.</p>
<div class="bluegrid" style="clear:both;"><table style="width:110px;">
<tr><th rowspan="2">CR</th><th colspan="2">Armor Class</th></tr>
<tr><th>Average</th></tr>
<tr><td>0 </td><td>13</td></tr>
<tr><td>⅛</td><td>13</td></tr>
<tr><td>¼</td><td>13</td></tr>
<tr><td>½</td><td>13</td></tr>
<tr><td>1 </td><td>14</td></tr>
<tr><td>2 </td><td>14</td></tr>
<tr><td>3 </td><td>14</td></tr>
<tr><td>4 </td><td>15</td></tr>
<tr><td>5 </td><td>15</td></tr>
<tr><td>6 </td><td>16</td></tr>
<tr><td>7 </td><td>16</td></tr>
<tr><td>8 </td><td>17</td></tr>
<tr><td>9 </td><td>17</td></tr>
<tr><td>10 </td><td>17</td></tr>
</table></div>
<p>Now, what should an average <i>D&D 5e</i> character roll to hit an average CR-equivalent creature? Subtracting our average PC <i>Attack</i> bonus from the <i>AC</i> of an average CR-equivalent monster we see that it's very close to an average of 9 for our level 1 through 4 sample range. I guess it's possible that it could be an 8 or a 10, but we'll need the kind of data the <i>Monster Manual</i> will supply to work that out for sure. So for now we'll go with a 9.</p>
<p>Thus all we need to do is add 9 to the simple polynomial equation I posted above. This can be easily expressed as...<br>
AC = (-0.0062 x Target_CR ^ 2 + 0.495 x Target_CR + 4.012) + 9</p>
<p>The table on the left displays these values, rounded to the nearest integer, for CR0 through CR10.</p>
<p>That said it's really important to understand that the there appears to be a margin of at least +/-5 on this average. So it's perfectly legitimate for a CR1 monster to have an <i>AC</i> anywhere from 9 to 19 or for a CR10 monster to have an AC between 12 and 22, without compensating significantly in any of it's other stats.</p>
<p>Furthermore this is a guideline only and experienced 5e monster designers shouldn't have any qualms about going even further outside the boundaries, though they should probably ensure they do apply some kind of mitigation elsewhere in their creature. More inexperienced monster designers should probably aim to stay in or near these boundaries until they gain some confident building creatures with this system.</p>
<p>You see, the <i>D&D 5e</i> monster system "feels" very strongly like a "rule of sense" type system. The emphasis is more on the art of monster design than in <i>D&D 4e</i>, for example. And this is an area where <i>Bounded Accuracy</i> really makes itself felt.</p>
<p><span class="prediction">Prediction:</span> Based on my analysis so far I think it's pretty obvious that there is a progression, flattened though it may be, for <i>AC</i> and, by inference, <i>Attack Bonus</i>. On top of that I reckon some folks are going to cry foul when they realise that there is the case. Those people will be missing the point. <i>Bounded Accuracy</i> isn't about there being no progression on this axis. It's about the progression being quite muted so that monsters can stay relevant across more levels.</p>
<p><span class="prediction">Prediction:</span> I think average monster <i>AC</i> will peak at about 22 around level 25.</p>
<p style="clear:both;"> </p>
<a name="MiscStats"></a><h4>Miscellaneous Stats</h4>
<p>In general the miscellaneous statistics (those in the same section as <i>Challenge</i>) seem to follow the rule of common sense. A creature native to the Elemental Plane Of Fire is probably immune to fire damage and an especially sneaky creature in all probability has proficiency in Stealth. So the main driver for miscellaneous stats does appear to be logic.</p>
<p>Additionally it's pretty obvious that <i>D&D 5e</i> monsters strongly leverage off a templating system and this starts to become evident in miscellaneous statistics. Undead are immune to poison damage and both the charmed and poisoned conditions, for example. Since the use of templating layers up attributes on a creature systems that use it usually cautioned not to apply too many templates as the creature may become overpowered for it's level (or CR in the case of <i>D&D 5e</i>). The impact on analysis is to increase the observed variability of creatures, which is consistent with my observations.</p>
<p>With this all said there does appear to be a general progression of these stats as CR increases. Whether this is by design or incidental, simply being a result of increasing complexity and toughness, is a moot point. The pattern is present and, given sufficient data, it can be enumerated.</p>
<p>But do we have enough data? Well yes and no. The release of the <i>Player's Handbook</i>, the update of <i>Horde Of The Dragon Queen</i> and certain spoilers from the <i>Monster Manual</i> have helped and those stats have been included in this part of this post. We can be fairly confident of this pattern out to CR10 and I'll illustrate why shortly.</p>
<p>By experimenting with different ways of combining the miscellaneous stats I came up with a method that keeps the variance minimal and makes sense - simply add up the number of <i>Saving Throws</i>, <i>Skills</i>, <i>Damage Resistances</i> and <i>Damage Immunities</i> the creature has, arriving at a "misc stats score". This method should be considered provisional and how it actually fits with the build process <i>Wizards of the Coast</i> will present remains to be seen. That said it does appear to work with the current crop of monsters.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcMeD2fe68TbvS5CoB1EhnSRnGKIVrg8v4aq3ABgl7KYJb2Ncfz9_UwBaOVDlZgLkyynR2XyvjDdaGaMyveuuS4AwHP2Ldlalb98JECoTc1YAr26kSQHHOWylvxt03JTZecggoSiaQq3Q/s1600/5e_pic_05a04_monster_misc_stats_scatter.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcMeD2fe68TbvS5CoB1EhnSRnGKIVrg8v4aq3ABgl7KYJb2Ncfz9_UwBaOVDlZgLkyynR2XyvjDdaGaMyveuuS4AwHP2Ldlalb98JECoTc1YAr26kSQHHOWylvxt03JTZecggoSiaQq3Q/s1600/5e_pic_05a04_monster_misc_stats_scatter.png" height="192" width="320" alt="Monster Misc Stats Score Scatter"></a><div class="caption">Monster Misc Stats Score Scatter</div></div>
<p>Creating a scatter graph of these scores and placing a linear trendline on the graph suggests an interesting pattern. Based on this graph CR1 creatures typically score just over 2 and CR30 creatures score around 11. And we can see at the lower CRs that the variability seems to be about +/-5.</p>
<p>Of course, the dearth of higher level data will generally cause that end of the trendline to be unreliable and to wander. That's why we aren't looking past CR10 until we have more data.</p>
<p>So how can we gain some confidence in the lower level data? Let me illustrate the approach I have used in this particular case.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTn20mo_NHozmAsBpkV3PtB9SMnrNetYImL3_sCpob0eyLf07z1-o9QsjrQEAdM2i_wFsemT7YyX5QfCuruon_-e9ah7FschM6nbCq7sQJi1qYemVzNCJoeVrkihtbhls0TcDmLmUB_uM/s1600/5e_pic_05a05_monster_misc_stats_avg.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTn20mo_NHozmAsBpkV3PtB9SMnrNetYImL3_sCpob0eyLf07z1-o9QsjrQEAdM2i_wFsemT7YyX5QfCuruon_-e9ah7FschM6nbCq7sQJi1qYemVzNCJoeVrkihtbhls0TcDmLmUB_uM/s1600/5e_pic_05a05_monster_misc_stats_avg.png" height="192" width="320" alt="Monster Misc Stats Score Average"></a><div class="caption">Monster Misc Stats Score Average</div></div>
<p>What I did was generate a pivot table of average by CR, scatter graph that and place a linear trendline on the graph. See the Blue data points and blue trendline on the <i>Monster Misc Stats Score Average</i> figure.</p>
<p>As you can see this produces a fairly different trendline to the preceeding graph, primarily on the righthand side, where data is most sparse. This trendline would suggest CR1 creatures score just under 4 and that CR30 creatures scoure about 7.5.</p>
<p>Overlaying the trendline from the first figure in red highlights the disparity</p>
<p>So how do we reconcile these? Splitting the difference is a pretty common-sense approach. Past CR10 things start to become increasingly uncertain. Restricting ourselves to CR10 and below (check out the green box) we can see that the margin for error is very low and that we can have high confidence in this approach at those levels.</p>
<p>Now let's have a look at what I've observed about each of the miscellaneous stats...</p>
<div class="textgrid"><table style="float:none;"><tr><td width="135px"><b>Saving Throws</b></td><td>Monsters may add proficiency to their saving throws in the same way as PCs.<br>
Counts towards <i>Misc Stat Score</i>.</td></tr>
<tr><td><b>Skills</b></td><td>Skills are calculated for monsters in the same way as for PCs. Monsters may add their proficiency modifier to skills they are trained in.<br>
Counts towards <i>Misc Stat Score</i>.</td></tr>
<tr><td><b>Damage Vulnerabilities</b></td><td>These are pretty rare in <i>D&D 5e</i>, with only 1.8% of current samples having a vulnerability. These don't seem to be used to compensate for other strengthening attributes, though one could use them to provide an Achilles Heal for a creature that is particualrly strong for it's CR.<br>
Best advice here is to only apply a vulnerability where there is an especially compelling reason for your monster to have one.<br>
<b>Does not</b> count towards <i>Misc Stat Score</i>.</td></tr>
<tr><td><b>Damage Resistance</b></td><td>Damage resistance is pretty common in 5e.<br>
Note that resistance to <i>bludgeoning, peircing and slashing from nonmagical/non-adamantine/unsilvered weapons</i> seems to be the replacement for the "immune to damage from nonmagical weapons" in older editions and counts as one Damage Resistance.<br>
Counts towards <i>Misc Stat Score</i>.</td></tr>
<tr><td><b>Damage Immunities</b></td><td>In <i>D&D 5e</i> these are rarer than <i>Damage Resistances</i>, but 19.4% of the current sample have them.<br>
Given they are somewhat stronger than an equivalent resistance I had hoped weight them as "worth" more than resistances. However, this simply introduced greater skew and variability. I'd suggest that best advice is to go light on <i>Damage Immunities</i>, but to use them where there is a compelling reason in your creature's background.<br>
Counts towards <i>Misc Stat Score</i>.</td></tr>
<tr><td><b>Condition Immunities</b></td><td>Creatures with resistance or immunity to a particular damage type normally also have immunity to it's corresponding condition, if there is one.<br>
Otherwise these should be applied where there is a compelling background/story reason.<br>
<b>Does not</b> count towards <i>Misc Stat Score</i>.</td></tr>
<tr><td><b>Senses</b></td><td>Most creatures have one additional sense. Some have none, some have two or even more. There doesn't seem to be any consideration here beyond story/background.<br>
<b>Does not</b> count towards <i>Misc Stat Score</i>.</td></tr>
<tr><td><b>Languages</b></td><td>The number of languages a monster knows seems to be purely defined by story/background considerations, or "the rule of sense".<br>
<b>Does not</b> count towards <i>Misc Stat Score</i>.</td></tr>
</table></div>
<p style="clear:both;">As we can see "the rule of sense" and the concept of "the art of monster building" are alive and well in <i>D&D 5e</i>. And along with those all the baggage and concerns from earlier editions that had the same focus.</p>
<div class="bluegrid" style="clear:both;"><table style="width:110px;">
<tr><th>CR</th><th>Average Misc Stat Score✝</th></tr>
<tr><td>0 </td><td>1</td></tr>
<tr><td>⅛</td><td>1</td></tr>
<tr><td>¼</td><td>2</td></tr>
<tr><td>½</td><td>2</td></tr>
<tr><td>1 </td><td>3</td></tr>
<tr><td>2 </td><td>3</td></tr>
<tr><td>3 </td><td>3</td></tr>
<tr><td>4 </td><td>4</td></tr>
<tr><td>5 </td><td>4</td></tr>
<tr><td>6 </td><td>4</td></tr>
<tr><td>7 </td><td>4</td></tr>
<tr><td>8 </td><td>4</td></tr>
<tr><td>9 </td><td>5</td></tr>
<tr><td>10 </td><td>5</td></tr>
<tr><td colspan="2" style="text-align:left">✝ Varies by +/-5</td></tr>
</table></div>
<p>So what "score" should we use for each CR? Well using the medium value between the two in our last graph it's pretty easy to come up with a formula that produces appropriate results...<br>
Score = 0.2 x CR + 2.8</p>
<p>Note that I have hand-editted the vlaues for CRs of less than 1 to save complexity. We could produce a solid match using a Power or Poly2 formula, but I don't think this rates the extra time that would be involved.</p>
<p><span class="prediction">Prediction:</span> I think <i>Monster Manual</i> analysis will confirm we are on the right track here and that we'll find that CR30 creature do have an average score around 9 using this approach.</p>
<p><span class="prediction">Prediction:</span> I expect the <i>Dungeon Master's Guide's</i> section on monster construction will suggest using "the rule of sense".</p>
<p style="clear:both;"> </p>
<a name="Example"></a><h4>Example: Human Pyromancer</h4>
<p>If we recall our Glass Canon with an Arcane Fire theme we'll remember it isn't going to be especially hard to hit, but focusses on dealing damage.</p>
<div class="statblock"><table style="width:300px;">
<tr><td colspan="6"><h3>Human Pyromancer</h3></td></tr>
<tr><td colspan="6"><i>Medium humanoid (human), any alignment</i></td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr style="color:gold;"><td colspan="6"><b>Armor Class</b> 12</td></tr>
<tr><td colspan="6"><b>Hit Points</b> 77 (14d8+14)</td></tr>
<tr><td colspan="6"><b>Speed</b> 30ft</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr class="attributes">
<td>STR<br>9 (-1)</td><td>DEX<br>14 (+2)</td><td>CON<br>12 (+1)</td><td>INT<br>19 (+4)</td><td>WIS<br>12 (+1)</td><td>CHA<br>12 (+1)</td>
</tr>
<tr><td colspan="6"><hr></td></tr>
<tr style="color:gold;"><td colspan="6"><b>Saving Throws</b> Dex +5, Int +7</td></tr>
<tr style="color:gold;"><td colspan="6"><b>Skills</b> Arcana +7, Perception +4</td></tr>
<tr style="color:gold;"><td colspan="6"><b>Damage Resistances</b> Fire</td></tr>
<tr style="color:gold;"><td colspan="6"><b>Lanuguages</b> Common, Ignan</td></tr>
<tr><td colspan="6">Challenge 5 (1,700 XP)</td></tr>
</table></div>
<p>That doesn't mean the Pyromancer won't have a couple of little tricks to make it a little more viable. Our plan is for melee characters to get close and then for it to go down quickly.</p>
<p>The Pyronmancer is unarmored so adds it's <i>Dexterity Modifier</i> to it's <i>AC</i>. This puts it on the low side of appropriate for it's CR, which is fine.</p>
<p>As a CR5 creature it'll typically have 4 significant miscellanoues stats, though it may have anywhere from 0 to 9. Now, what is thematic?</p>
<p>As a caster with a casting attribute of <i>Intelligence</i> it makes sense go give it proficiency on that, though proficiency on <i>Dexterity</i> is also appropriate and helps encourage melee characters to deal with it, so I have added both... After it's not that common for monsters to make intelligence saves.</p>
<p>Arcana is an obvious choice for <i>Skills</i>, though of rather limited application for a monster. We'll also give the Pyromancer something useful in combat - proficiency in <i>Perception</i>.</p>
<p>The choice of fire resistance is an obvious one, given the creature's theme.</p>
<p>Given the Pyromancer is human I'll give it Common and an additional language. Ignan, the language of Fire Elementals and their kin, seems like a good fit.</p>
<p> </p>
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<a href="/2014/08/d-5e-monsters-part-4-construction.html"><img src="http://i.imgur.com/d0lSZlO.png" alt="◄"> Part 4: Construction: Ability Scores & HP</a>
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<a href="/2014/08/d-5e-monsters-interlude-bunch-of.html">Interlude: A Bunch Of Monsters! <img src="http://i.imgur.com/bZ5DhBF.png" alt="►"></a>
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Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-62158446073471778332014-08-02T04:30:00.000+09:302016-09-23T16:01:58.209+09:30D&D 5e Monsters: Part 4: Construction: Ability Scores & HP<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<p><span style="color:lightyellow;"><i>Where Surf maps out some of the parameters and progression around monster Ability Scores and Hit Points... </i></span></p>
<p> </p>
<a name="Top"></a><h3><u>Part 4: Construction: Ability Scores & HP</u></h3>
<p>Before getting into things I'd like to thank the guy who forwarded <b>Appendix B</b> of the <a href="http://dnd.wizards.com/products/tabletop-games/rpg-products/hoard-dragon-queen">Horde Of The Dragon Queen</a> PDF to me - you know who you are and you have my thanks. The 5 monsters in it have been entered into my spreadsheets and these all fit analysis to date. The highest CR of these was a CR4 Dragonborn NPC.</p>
<p>Onwards!</p>
<p><i>D&D 5e</i> monsters rely heavily on their <a href="#Abilities">Ability Scores</a> to implement much of their mechanics. Once we have determined these we are in a position to compute dependant stats, like <a href="#HP">Hit Points</a>. After considering these two aspects of <i>D&D 5e</i> monsters we'll apply the results to our <a href="#Example">Example Monster</a>.</p>
<p> </p>
<a name="Abilities"></a><h4>Ability Scores</h4>
<p>I spent some time analysing monster ability scores. I looked at standard arrays. I looked at some point-buy approaches. And I looked at combinations of the two. I also tried to factor in possible racial bonuses. Now it's quite possible a combination of these approaches is being used, but if they are it's something not evident to me.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimUGEf553HTCsl-6Nj7UoYMtA1NZWdePXqul-6SfmyBl-dZm6jDBqfhaDXgpWyPkUBLWaufcIBJ3KAObMss6dBt7vK0PRVi85AgmCpCdw1emY946BxiBlk1F_tDfVU4c_zPfO5Ll4WF30/s1600/5e_pic_04a01_attr_raw.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimUGEf553HTCsl-6Nj7UoYMtA1NZWdePXqul-6SfmyBl-dZm6jDBqfhaDXgpWyPkUBLWaufcIBJ3KAObMss6dBt7vK0PRVi85AgmCpCdw1emY946BxiBlk1F_tDfVU4c_zPfO5Ll4WF30/s1600/5e_pic_04a01_attr_raw.png" height="192" width="320" alt="Raw Max & Average Ability"></a><div class="caption">Raw Max & Average Ability</div></div>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWbXzwC0feVj8wOB2i0-ZVaNAQl2Kq1FkzegXPxgH0ShzaWojBQPyE5Bgh3LjY65Cwth9MYNiP4AY8WI1sAcIuTS2Ey0bs6GtEpoXtkFZ2hCsx0gywCmoFtYMFNqKzZGgftDFpMOelsuw/s1600/5e_pic_04a02_attr_analyzed.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWbXzwC0feVj8wOB2i0-ZVaNAQl2Kq1FkzegXPxgH0ShzaWojBQPyE5Bgh3LjY65Cwth9MYNiP4AY8WI1sAcIuTS2Ey0bs6GtEpoXtkFZ2hCsx0gywCmoFtYMFNqKzZGgftDFpMOelsuw/s1600/5e_pic_04a02_attr_analyzed.png" height="192" width="320" alt="Analyzed Max & Average Ability"></a><div class="caption">Analyzed Max & Average Ability</div></div>
<p>What <b>is</b> apparent is that monster ability scores adhere to an average based approach, at least for the data available at the time of writing.</p>
<p>Dropping a trendline on a scatter graph of each creature's maximum and average ability score produces some interesting results. We can see that the two are generally an equal distance apart. That said, the predominance of the very low level monsters does skew the trendline.</p>
<p>If we do some aggregation on the data we can work out both the average maximum attribute score and the average attribute score for creatures at each CR. We can then create a scatter graph of this data and plot trendlines on the two sets of data. This shows us that average ability score remains pretty consistent and that the relationship between it and average maximum ability score is also normally fairly consistent. There is a little skew due to the <i>Young Green Dragon</i>, but that creature has sacrifices it's high score a little in order to improve some of it's secondary scores.</p>
<div class="bluegrid" style="clear:both;"><table style="width:170px;">
<tr><th rowspan="2">CR</th><th colspan="2">Ability Scores</th></tr>
<tr><th width="35%">Average</th><th width="35%">Maximum✝</th></tr>
<tr><td>0 </td><td>8</td><td>13</td></tr>
<tr><td>⅛</td><td>9</td><td>14</td></tr>
<tr><td>¼</td><td>10</td><td>15</td></tr>
<tr><td>½</td><td>10</td><td>15</td></tr>
<tr><td>1 </td><td>11</td><td>16</td></tr>
<tr><td>2 </td><td>11</td><td>16</td></tr>
<tr><td>3 </td><td>12</td><td>17</td></tr>
<tr><td>4 </td><td>12</td><td>17</td></tr>
<tr><td>5 </td><td>13</td><td>18</td></tr>
<tr><td>6 </td><td>13</td><td>18</td></tr>
<tr><td>7 </td><td>14</td><td>19</td></tr>
<tr><td>8 </td><td>14</td><td>19</td></tr>
<tr><td>9 </td><td>15</td><td>20</td></tr>
<tr><td>10 </td><td>15</td><td>20</td></tr>
<tr><td colspan="3" style="text-align:left"> ✝ <b><i>Typical</i></b> maximum.</td></tr>
</table></div>
<p>This data makes it pretty simple to construct a linear progression out to level 10 that we can be quite confident of. We focus on the CR1 through CR10 creatures for matching the curve and identifying the appropriate formula. For creatures lower than CR1 I simply entered data matching the analysis. I could have built a poly2 or poly3 formula to produce the same results. But I figure people following this series would rather me not waste several hours, possibly delaying the next post by an extra day as a result.</p>
<p>With a few minutes work we can obtain a simple linear formula that fits our requirements very well...<br>
Average Ability=0.5 x CR + 10.5</p>
<p>Our analysis of the data tell us that the maximum attribute value is typically five higher than the average attribute value for the CR, but sometimes they are seven or even more. That's fine as long as the creature's abilities average out to a value close to the average for the <i>Target CR</i>.</p>
<p>Since monster designers will be building these creatures in the context of <i>D&D 5e</i> discarding the remainders is the most appropriate approach here and I have used that method to construct the table for this section.</p>
<p>You can use the top-right table from page 9 of the <a href="http://www.wizards.com/dnd/Article.aspx?x=dnd/basicrules">Basic D&D v0.1</a> PDF to determine each ability's modifier based on the ability score. If you use spreadsheets the following formula should work perfectly (assuming your data is in cell A1):<br>
=FLOOR((A1-10)/2,1)</p>
<p><span class="prediction">Prediction:</span> We know that maximum monster ability scores will be 30. My prediction is that we won't commonly see this in monsters until past CR20. I think it'll plateua shortly after that CR out to the CR25 or CR30 maximum I predicted in my last post.</p>
<p style="clear:both;"> </p>
<a name="HP"></a><h4>Hit Points</h4>
<p>Monster <i>Hit Points</i> are one of the most important aspects of <i>D&D 5e</i> monsters, along with the creature's damage output. I believe that these two stats are the principle elements used to determine a creature's <i>Actual CR</i>, but we'll look at that in a later post.</p>
<p>During my <a href="http://surfarcher.blogspot.com/2013/07/d-next-monsters-part-1-getting-started.html">D&D Next Monster Analysis</a> we saw that there is an important relationship between PC <i>Damage</i> and monster <i>HP</i>. In fact PC <i>Damage Output</i> is the main consideration for determining appropriate monster <i>HP</i> and that is clearly still the case in <i>D&D 5e</i>.</p>
<p>In order to analyse monster <i>Damage</i> and <i>Hit Points</i> I had to enter that same data for PC <i>Classes</i> into a spreadsheet and use that data in the analysis of monster stats. This data was presented to the community for review, comment and reuse in <a href="http://community.wizards.com/forum/player-help/threads/4115906">this thread</a> on the <i>Wizards of the Coast</i> forums.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUI6NOTYb0qSLNjNT6MZB6G9EZ2kEGGRzP_KYBid_oWRNhvMfZYRFdpOdKN_mj7FvHDJVfMTRbfPrXfZNcO66cywXuRKDZEws4maqSY4Tcgkl_cWHsWa0mg0Lac1b4uW0-KYJo4p27Gw0/s1600/5e_pic_04a03_pc_dmg.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUI6NOTYb0qSLNjNT6MZB6G9EZ2kEGGRzP_KYBid_oWRNhvMfZYRFdpOdKN_mj7FvHDJVfMTRbfPrXfZNcO66cywXuRKDZEws4maqSY4Tcgkl_cWHsWa0mg0Lac1b4uW0-KYJo4p27Gw0/s1600/5e_pic_04a03_pc_dmg.png" height="192" width="320" alt="Average/Total PC Damage"></a><div class="caption">Average/Total PC Damage</div></div>
<p>Graphing the sum and average of PC <i>Damage</i> reveals some interesting patterns. At levels 5, 11 and 17 PCs see a significant gain in damage output - a jump of about 5 damage on top of their normal progression. In other words they double the damage gain they normally make over an <b>entire tier</b> of play. This kind of "stepping" is often used in game design to help build a feeling that characters make significant gains in power by advancing into new tiers of play. <i>Wizards of the Coast</i> has used this before and even told us this would be the case at these levels in recent <i>Legends & Lore</i> posts and on Twitter.</p>
<p><i>Wizards of the Coast</i> <b>didn't</b> tell us about the flatter damage gain in the final tier and it's final damage step at level 20. But this is hardly surprising since PCs typically take on Deities and Greater Demon Lords at this point in the game. Interestingly this also lends some support to the idea that creatures higher than CR20 will be part of the game.</p>
<p>I've read a number of comments on the net about folks finding 5e monsters difficult to figure out. They often point to power curves like those in <i>D&D 4e</i> and talk about how predictable and incremental these are. Folks seem to find the stepping in 5e problematic because they can't look to the underlying curve. The thing is, even if <i>Wizards of the Coast</i> are simply cobbling all of 5e together in a huge spreadsheet without using coherent formulae and curves... Why curves will still tend to be there! And this is no exception.</p>
<div style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKLqi16U6OxYj_xPL_CzZy2N1WlOZIPVA0RdAPsq92irvZMkr2J1y-T8uOAlnG5atzKGjk2aZ2bpPTaN8X276K_8APMFcAE-3nv2gAgcddIWQ77zvwuy7b1ZtWPvRXQAPLIgdZDevJxyo/s1600/5e_pic_04a04_monster_hp.png"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKLqi16U6OxYj_xPL_CzZy2N1WlOZIPVA0RdAPsq92irvZMkr2J1y-T8uOAlnG5atzKGjk2aZ2bpPTaN8X276K_8APMFcAE-3nv2gAgcddIWQ77zvwuy7b1ZtWPvRXQAPLIgdZDevJxyo/s1600/5e_pic_04a04_monster_hp.png" height="192" width="320" alt="PC Damage/Monster HP Curve"></a><div class="caption">PC Damage/Monster HP Curve</div></div>
<p>If we take the average PC damage output from our first graph we can plot a simple Power trendline over it. We can angle this trendline so that much of the regular damage progression in each tier aligns with the trendline. The dip before the step at the end of each tier falls away below this and the steps at levels 5, 11 and 17 (and the one at level 20) pop up to just above the trendline.</p>
<p>And thus the magic of curve-matching reveals to us the <i>actual</i> power curve for PC <i>Damage</i> in <i>D&D 5e</i>...<br>
Damage=4.55 x Level ^ 0.72</p>
<p>So how do the <i>Hit Points</i> of monsters from the <i>Starter Set</i> (and <i>Horde of the Dragon Queen</i>) relate to PC <i>Damage</i>? Well what I did was compare those with the actual PC stats at the same level as the <i>CR</i> in question. For monsters with a <i>CR</i> under CR1 there needed to be a slight manual workaround in the comparison - to gain the base equivalent PC <i>Damage</i> I had to determine it from the level 1 PC data.</p>
<div class="bluegrid" style="clear:both;"><table style="width:200px;">
<tr><th rowspan="2">CR</th><th colspan="3">Hit Points</th></tr>
<tr><th width="25%">Min</th><th width="25%">Target</th><th width="25%">Max</th></tr>
<tr><td>0 </td><td>1 </td><td>1 </td><td>3 </td></tr>
<tr><td>⅛ </td><td>3 </td><td>5 </td><td>7 </td></tr>
<tr><td>¼</td><td>6 </td><td>8 </td><td>11 </td></tr>
<tr><td>½</td><td>11 </td><td>14 </td><td>19 </td></tr>
<tr><td>1 </td><td>18 </td><td>23 </td><td>31 </td></tr>
<tr><td>2 </td><td>29 </td><td>37 </td><td>44 </td></tr>
<tr><td>3 </td><td>43 </td><td>50 </td><td>57 </td></tr>
<tr><td>4 </td><td>55 </td><td>62 </td><td>68 </td></tr>
<tr><td>5 </td><td>67 </td><td>72 </td><td>96 </td></tr>
<tr><td>6 </td><td>77 </td><td>83 </td><td>78 </td></tr>
<tr><td>7 </td><td>87 </td><td>92 </td><td>88 </td></tr>
<tr><td>8 </td><td>97 </td><td>102</td><td>98 </td></tr>
<tr><td>9 </td><td>106</td><td>111</td><td>107</td></tr>
<tr><td>10 </td><td>115</td><td>119</td><td>115</td></tr>
<tr><td colspan="4" style="text-align:left">Note: <b><i>Typical</i></b> boundaries shown.</td></tr>
</table></div>
<p>To be honest things break down a little bit below CR1 anyway. For example, what's the difference between a CR⅛ and a CR0 creature's hitpoints? We are talking about the difference between say 2hp and 4hp. Most PCs can kill either with a single hit. They differentiate more when we introduce <i>Damage</i> into the equation, but we'll leave that for it's own post.</p>
<p>If we divide the average monster <i>HP</i> by the average PC <i>Damage</i> for the same level/CR we see that it is consistently a 5. What does this mean? Well a party of 4 PCs shaping up against a monster of the same <i>CR</i> as their level can expect that opponent to survive for about two rounds, on average.</p>
<p>From here it's pretty simple to build an appropriate formula for Monster <i>Hit Points</i>. In this case we'll round any remainders to the nearest whole number and assume a minimum value of one. Here's what I came up with...<br>
HP=(4.55 x CR ^ 0.72) x 5</p>
<p>We could assume that the halfway point between each of these values is the cut-off point for each <i>CR</i>, but that isn't the case. There appears to be some overlap between adjacent <i>CR</i>s. This is mainly constrained within a 5% overlap, however the <i>Hit Points</i> of some monsters is significantly above or below these limits. In most of these cases there is a corresponding opposite variation in <i>Damage</i> and the remainder of the cases compensate in some other manner. This supports the supposition that <i>Damage</i> is a significant factor when it comes to assessing <i>Actual CR</i>.</p>
<div class="bluegrid" style="clear:both;"><table style="width:300px;">
<tr><th rowspan="2">CR</th><th rowspan="2">Con<br>Mod</th><th colspan="6">Hit Dice</th></tr>
<tr>
<th width="12%">Tiny<br>(d4)</th>
<th width="12%">Small<br>(d6)</th>
<th width="12%">Medium<br>(d8)</th>
<th width="12%">Large<br>(d10)</th>
<th width="12%">Huge<br>(d12)</th>
<th width="12%">Garg'n<br>(d20)</th>
</tr>
<tr><td>0 </td><td>-1</td><td>1 </td><td>- </td><td>- </td><td>- </td><td>- </td><td>- </td></tr>
<tr><td>⅛ </td><td>-1</td><td>3 </td><td>1 </td><td>1 </td><td>- </td><td>- </td><td>- </td></tr>
<tr><td>¼</td><td>+0</td><td>3 </td><td>2 </td><td>2 </td><td>1 </td><td>1 </td><td>- </td></tr>
<tr><td>½</td><td>+0</td><td>2 </td><td>3 </td><td>3 </td><td>2 </td><td>2 </td><td>1 </td></tr>
<tr><td>1 </td><td>+0</td><td>9 </td><td>7 </td><td>5 </td><td>3 </td><td>3 </td><td>2 </td></tr>
<tr><td>2 </td><td>+0</td><td>16</td><td>12</td><td>9 </td><td>6 </td><td>5 </td><td>4 </td></tr>
<tr><td>3 </td><td>+1</td><td>16</td><td>12</td><td>10</td><td>7 </td><td>6 </td><td>5 </td></tr>
<tr><td>4 </td><td>+1</td><td>21</td><td>16</td><td>13</td><td>10</td><td>9 </td><td>6 </td></tr>
<tr><td>5 </td><td>+1</td><td>25</td><td>20</td><td>16</td><td>12</td><td>11</td><td>8 </td></tr>
<tr><td>6 </td><td>+1</td><td>29</td><td>23</td><td>19</td><td>15</td><td>14</td><td>9 </td></tr>
<tr><td>7 </td><td>+2</td><td>26</td><td>21</td><td>18</td><td>15</td><td>14</td><td>9 </td></tr>
<tr><td>8 </td><td>+2</td><td>29</td><td>24</td><td>20</td><td>17</td><td>16</td><td>11</td></tr>
<tr><td>9 </td><td>+2</td><td>32</td><td>27</td><td>22</td><td>18</td><td>17</td><td>12</td></tr>
<tr><td>10 </td><td>+2</td><td>35</td><td>29</td><td>24</td><td>20</td><td>19</td><td>13</td></tr>
</table></div>
<p>Once we have decided on a target <i>Hit Point</i> value for the creature we need to decide how many <i>Hit Dice</i> it should have to be at or near that target. This isn't necessarily as staightforward as one might think and it's best that we understand how <i>Average HP</i> is calculated...<br>
Average HP=(Num_HD x Dice_Avg) + (Num_HD x Con_Mod)</p>
<p>As we can see this pretty much the traditional pre-<i>D&D 4e</i> method for determining monster <i>HP</i>.</p>
<p>The fiddly part here is determining the appropriate <i>HD</i> for a monster based on it's <i>Target HD</i>, incorporating the creature's Constitution modifier into the equation. To help facilitate this I spent a couple of hours precalculating a table of the number of a given HD needed to achieve close to a given <i>Target CR</i>'s target <i>Hit Points</i>, assuming the creature has a constitution of average for that <i>Target CR</i>.</p>
<p>Hopefully this helps put folks in the right ballpark when building monsters for a given <i>Target CR</i>. But in many cases readers will find that they still need to tinker a bit with number of <i>HD</i> and the creature's Constitution score. In these cases modifying number of <i>HD</i> generally results in the smallest incremental changes, while changes to Constitution normally result in bigger differences.</p>
<p>So how do the monsters in the <i>Starter Set</i> and in Appendix B of <i>Horde Of The Dragon Queen</i> fit these tables?</p>
<ul>
<li>Between the <i>Starter Set</i> and Appendix B of <i>Horde Of The Dragon Queen</i> there are 33 creatures.</li>
<li>15 of these 33 have <i>HP</i> outside the boundaries I described.</li>
<li>8 of these 15 could be have inappropriate hitpoints after factoring in their <i>Damage</i>, using my provisional method.</li>
<li>4 of these 8 are more than 3 hitpoints outside the ranges we have discussed. I consider 3 or less to be an acceptable margin of error in this area.</li>
</ul>
<p>So these 4 creatures could be considered "outside CR", but is this the case?</p>
<table>
<tr><td valign="top">Flameskull</td><td>This creature falls well short of minimum target <i>HP</i>. Looking at the Flameskull we can see that it has considerable resistances and immunities, possibly more than other creatures of this <i>CR</i> will have. But the real trick here seems like the <i>Rejuvenation</i> trait. PCs will probably have to fight this creature twice to beat it! So we can consider it valid. Additionally I did not include <i>Damage</i> from it's <i>Spellcasting</i> trait and this should probably compensate it's <i>HP</i> a modest amount.</td></tr>
<tr><td valign="top">Langdedrosa Cyanwrath</td><td>This creature from <i>Horde of the Dragon Queen</i> seems to fall a bit short on both <i>HP</i> and <i>Damage</i>. But if we look closely at it we can see that it has quite high <i>Alpha Damage</i>. I suspect that this has been factored in as approximately 7 or more in their base <i>Damage</i>, which would see them within an appropriate <i>Actual CR</i>.</td></tr>
<tr><td valign="top">Spectator</td><td>While the Spectator's <i>HP</i> are below the minimum for it's <i>CR</i> that's not why it falls below CR. Instead this comes back to difficulties accurately determining the creature's <i>Damage</i> output. Only one of the Spectator's four eye attacks cause damage and so only that eye's damage has been calculated. If we assume that the it's <i>Spell Reflection</i> and the effect of another eye combined would be "worth" at least 12 damage we find that it falls neatly within it's <i>CR</i>.</td></tr>
<tr><td valign="top">Zombie</td><td>The Zombie's <i>HP</i> are much more than we'd expect for a CR¼ creature, in fact they are more in line with a CR1 monster. On the flip-side it's <i>Damage</i> is more appropriate to a CR⅛ or even a CR0 monster. Combined with it's slow movement I think the Zombie is probably OK. As I've inferred before, the tighter margins below CR1 allow for less leeway with creatures that push the boundaries of our definitions. </td>
</tr>
</table>
<p><span class="prediction">Prediction:</span> Once the <i>Monster Manual</i> has been released I believe we'll see that creature <i>Hit Points</i> will vary outside their suggested boundaries more frequently than their <i>Damage</i> does.</p>
<p style="clear:both;"> </p>
<a name="Example"></a><h4>Example: Human Pyromancer</h4>
<p>As I said in my last post the Pyromance will be a ranged glass cannon with a focus on Arcane fire.</p>
<div class="statblock"><table style="width:300px;">
<tr><td colspan="6"><h3>Human Pyromancer</h3></td></tr>
<tr><td colspan="6"><i>Medium humanoid (human), any alignment</i></td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr style="color:gold;"><td colspan="6">Hit Points: 77 (14d8+14)</td></tr>
<tr><td colspan="6">Speed: 30ft</td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr class="attributes" style="color:gold;">
<td>STR<br>9 (-1)</td><td>DEX<br>14 (+2)</td><td>CON<br>12 (+1)</td><td>INT<br>19 (+4)</td><td>WIS<br>12 (+1)</td><td>CHA<br>12 (+1)</td>
</tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6">Challenge 5 (1,700 XP)</td></tr>
</table></div>
<p>I'm loosely modelling it on the <i>Wizard</i> class, so I will focus on Intelligence as it's main stat. To compensate I will give it below average Strength, because of all those years studying dusty tomes. The Pyromancer's Dexterity will be slightly above average - he looks after his fingers and practices a lot of arcane gestures and exercises. The remaining stats I will leave at average for a CR5 creature.</p>
<p>This monster is going to rely on cover and it's allies to protect it, rather than high defences and an ocean of health. So I am going to set it's <i>Hit Points</i> below the minimum suggested for a CR5 creature. This will allow me to push it's <i>Damage</i> up quite high for it's <i>Actual CR</i>. Tweaking number of <i>HD</i> and not adjusting the creature's Constitution score is the easiest way to do this fine tuning.</p>
<p> </p>
<div class="bottombar"><table><tr>
<td width="40%">
<a href="/2014/07/d-5e-monsters-part-3-construction-cr.html"><img src="http://i.imgur.com/d0lSZlO.png" alt="◄"> Part 3: Construction: CR & Size</a>
</td>
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<a href="/2014/07/d-5e-monsters-master-index.html"><img src="http://i.imgur.com/qRcTo6k.png" alt="▲"> Master Index</a>
</td>
<td style="text-align:right;">
<a href="/2014/08/d-5e-monsters-part-5-construction-ac.html">Part 5: Construction: AC & Traits <img src="http://i.imgur.com/bZ5DhBF.png" alt="►"></a>
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Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com1tag:blogger.com,1999:blog-6511225892793734362.post-7425137850090182542014-07-29T13:16:00.001+09:302016-09-23T15:59:04.439+09:30D&D 5e Monsters: Part 3: Construction: CR & Size<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<p><span style="color:lightyellow;"><i>Surf gets side-tracked for a while... But that's a good thing!</i></span></p>
<p> </p>
<a name="Top"></a><h3><u>Part 3: Construction: CR & Size</u></h3>
<p>OK I want to open this article with a couple of apologies.</p>
<p>First up, some folks felt that "two introductions" for this series was excessive. I can understand this and I'd normally agree - be assured that I agonised over this when I was writing <a href="http://surfarcher.blogspot.com.au/2014/07/d-5e-monsters-part-2-construction.html">Before Building</a>. But in the end I decided that a process-oriented build really does demand that the conceptual pre-work be done. It is far, far more important for this kind of build than for a result-oriented build. To those who felt put-out I do apologise and can assure you that it is <i>not</i> how I prefer to write a series of articles, so you shouldn't expect a repeat any time soon.</p>
<p>Secondly, I apologise for the lateness of this article. I originally indicated I'd post it almost a week ago, but as I started writing <a href="#Top">Part 3</a> I realised how fundamental CR is to the process. I was faced with a choice - do some quick and dirty analysis to work around it or do some solid analysis. So I chose the latter and disappeared down a rabbit hole for a while.</p>
<p>I think most readers will be happy that I did... I certainly hope so!</p>
<p>Let's have a look at the two foundational components of a <i>D&D 5e</i> monster - <a href="#CR">CR</a> and <a href="#Size">Size</a>. Then we'll use these to fill out some peices of an <a href="#Example">example monster</a>.</p>
<p> </p>
<a name="CR"></a><h4>Challenge Rating</h4>
<p>So I had committed to leaving <i>Challenge Rating</i> (aka "CR") analysis until the <i>Monster Manual</i> hit the shelves, but as I dug into 5e monsters I developed a deeper appreciation of something I had previously suspected. While CR clearly <b>is</b> a measure of how appropriate a given creature is for a same-level party to fight, it is <u>also</u> a foundational element in building 5e monsters. When we decide to build an opponent for the PCs, regardless of the approach we use, we have an idea of how challenging it should be. We may or may not have formalised it, but we do have an idea. I starting thinking of this as <b><i>Target CR</i></b> in order to differentiate it from the actual final <i>CR</i>.</p>
<p>I came to this realisation as I was doing some analysis to work around using CR when building monsters. Ultimately this lead me to analyze PC data earlier than anticipated. Interested readers might check out <a href="http://community.wizards.com/forum/player-help/threads/4115906">this thread</a> on the wizards.com forums where I posted the data I crunched about <i>Classes</i>.</p>
<p>Several key components of monsters are based directly on <i>Target CR</i>...</p>
<p>A monster's <i>Hitpoints</i> are the result of it's number of <i>Hit Dice</i>, it's size and it's <i>Ability Score</i> modifiers. But how many hitpoints should my monster have? <i>Target CR</i> yields a <i>Target HP</i> range towards which we can build.</p>
<div class="bluegrid"><table style="width:150px;">
<tr><th>CR</th><th>XP</th></tr>
<tr><td>0</td><td>10</td></tr>
<tr><td>1/8</td><td>25</td></tr>
<tr><td>1/4</td><td>50</td></tr>
<tr><td>1/2</td><td>100</td></tr>
<tr><td>1</td><td>200</td></tr>
<tr><td>2</td><td>450</td></tr>
<tr><td>3</td><td>700</td></tr>
<tr><td>4</td><td>1100</td></tr>
<tr><td>✝5</td><td>1700</td></tr>
<tr><td>✝6</td><td>2300</td></tr>
<tr><td>✝7</td><td>3000</td></tr>
<tr><td>8</td><td>3900</td></tr>
<tr><td>✝9</td><td>4800</td></tr>
<tr><td>✝10</td><td>5900</td></tr>
<tr><td colspan="3" style="text-align:left"> ✝ Not in the Starter Set</td></tr>
</table></div>
<p>Monster <i>Damage</i> output results from a creature's traits and actions. A combat-focussed creature's damage is influenced by it's <i>Ability Score</i> modifiers, it's size, the weapon it uses, the number of attacks it makes and several other factors. A creature that focusses on casting spells mainly produces damage according to it's caster level. Creatures with other approaches produce their damage output via other methods. But what should this damage output be? <i>Target CR</i> gives us an appropriate range for this.</p>
<p><i>Proficiency</i> for monsters is indexed directly off the creature's CR. We can simply use the <i>Character Advancement</i> table on page 10 of the <a href="http://www.wizards.com/dnd/Article.aspx?x=dnd/basicrules">Basic D&D v0.1</a> and use CR instead of level.</p>
<p><i>Ability Scores</i> also appear to scale based on CR. We'll look at this more closely in <a href="http://surfarcher.blogspot.com/2014/08/d-5e-monsters-part-4-construction.html">Part 4: Construction: Abilities & HP</a>.</p>
<p><i>Experience Points</i> seem to be tightly bound to <i>CR</i>. While there are a number of gaps the <i>XP</i> rewards for the monsters presented in the <i>Starter Set</i> make it quite easy to fill in these gaps up to level 10 with a reasonable level of confidence. We can estimate values for the missing CRs using the following moderate polynomial:<br>
XP = -0.3553xCR^3 + 60.485xCR^2 + 5.5534xCR + 155.52</p>
<p>It's important to note that our limited sample size makes it difficult to be confident of certain numbers past a reasonable level or CR. In this case we can have a high level of confidence that we are in the right <i>ballpark</i> with these XP numbers. Some of them might be a hundred XP or so out but they'll be pretty close and more than good enough for most uses. We'll revisit these as soon as there's more data, but it's what we have to use for now.</p>
<p>Note that I won't provide tables out past CR10 until we have at least some examples of creatures at these higher levels to analyze.</p>
<p><span class="prediction">Prediction:</span> I believe we'll see creatures up to at <u>least</u> CR25 in the <i>Monster Manual</i>, probably out to CR30 and maybe even beyond.</p>
<p> </p>
<a name="Size"></a><h4>Size</h4>
<p>Monster <i>Size</i> partners with <i>Target CR</i> to provide targets for most of the building blocks of a 5e monster, either directly or indirectly.</p>
<p><i>Size</i> has a direct bearing on <i>Hit Points</i> (via <i>Hit Dice</i>), weapon damage dice and on speed. It may also influence other aspects of monsters.</p>
<div class="bluegrid"><table style="width:150px;">
<tr><th>Size</th><th>HD</th><th>Speed</th></tr>
<tr><td>Tiny</td><td>d4</td><td>10'</td></tr>
<tr><td>Small</td><td>d6</td><td>20'</td></tr>
<tr><td>Medium</td><td>d8</td><td>30'</td></tr>
<tr><td>Large</td><td>d10</td><td>40'</td></tr>
<tr><td>✝Huge</td><td>d12</td><td>50'</td></tr>
<tr><td>✝Gargantuan</td><td>d20</td><td>60'</td></tr>
<tr><td colspan="3" style="text-align:left"> ✝ Not in the Starter Set</td></tr>
</table></div>
<p>Page 71 of the <a href="http://www.wizards.com/dnd/Article.aspx?x=dnd/basicrules">Basic D&D v0.1</a> PDF outlines the appropriate size categories in <i>D&D 5e</i> and Appendix B of the <i>Starter Set</i> shows us the <i>HD</i> size for most of these. Appendix B doesn't tell us the <i>HD</i> size for Huge or Gargantuan creatures, but it's pretty reasonable to assume that these are simply the next dice sizes up from Large.</p>
<p><i>Speed</i> is normally thought of as an aspect of race - it's listed in the <i>Racial Traits</i> section of the <a href="http://www.wizards.com/dnd/Article.aspx?x=dnd/basicrules">Basic D&D v0.1</a> PDF, for example. I believe that this is primarily because <i>Size</i> is a component of <i>Race</i>. Note that <i>Speed</i> is not a "hard" aspect of size, rather it is a starting point that can be modified and tuned to suit the specific creature you are building. Variance up to one size category above or below seems to be quite normal.</p>
<p><span class="prediction">Prediction:</span> Because of the relationship between <i>Size</i> and <i>Hit Points</i> I believe monsters of the smaller sizes will become less frequent as <i>CR</i> increases and that creatures past say CR10 will be predominantly Medium or bigger. We'll need the volume of data expected in the <i>Monster Manual</i> to confirm this.</p>
<p> </p>
<a name="Example"></a><h4>Example: Human Pyromancer</h4>
<p>Since this part of my blog focuses on the build-oriented approach to <i>D&D 5e</i> monster creation I thought it would be appropriate to provide some example monsters for illustration purposes. In these examples we'll normally omit parts of the stat block which we have not yet dealt with.</p>
<div class="statblock"><table style="width:300px;">
<tr><td colspan="6"><h3>Human Pyromancer</h3></td></tr>
<tr><td colspan="6"><i>Medium humanoid (human), any alignment</i></td></tr>
<tr><td colspan="6"><hr></td></tr>
<tr><td colspan="6">Speed: 30ft</td></tr>
<tr><td colspan="6"><hr style="border-color:inherit"></td></tr>
<tr><td colspan="6">Challenge 5 (1,700 XP)</td></tr>
</table></div>
<p>The idea behind the <i>Human Pyromancer</i> is a "Glass Cannon" ranged attacker with an aracane fire theme. The intent is for this monster to blast the PCs from a distance, while receiving protection from melee type monsters and cover. Once the PCs get up close it should be all over for this guy. With some lower level meat-shield support it could be the central piece of a toughish level 5 or 6 encounter. It should have some longevity out to level 10 or so as lower-end ranged support for higher-CR melee creatures.</p>
<p>From a monster design perspective it will allow us to explore how spellcasting monsters are built in <i>D&D 5e</i> and thus also explore the math associated with casters. It will also allow us to illustrate the flexibility the <i>CR</i> guidelines for <i>HP</i> and <i>Damage</i> support.</p>
<p> </p>
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<td width="40%">
<a href="/2014/07/d-5e-monsters-part-2-construction.html"><img src="http://i.imgur.com/d0lSZlO.png" alt="◄"> Part 2: Construction: Before Building</a>
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<a href="/2014/07/d-5e-monsters-master-index.html"><img src="http://i.imgur.com/qRcTo6k.png" alt="▲"> Master Index</a>
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<td style="text-align:right;">
<a href="/2014/08/d-5e-monsters-part-4-construction.html">Part 4: Construction: Abilities & HP <img src="http://i.imgur.com/bZ5DhBF.png" alt="►"></a>
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Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-75847165789314644652014-07-17T08:00:00.000+09:302016-09-23T15:55:50.032+09:30D&D 5e Monsters: Part 2: Construction: Before Building<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<p><span style="color:lightyellow;"><i>Surf talks about the preparations we need to make before building out a D&D 5e monster...</i></span></p>
<p> </p>
<h3><u>Part 2: Construction: Before Building</u></h3>
<p>So what do we need before we start building a <i>D&D 5e</i> monster?</p>
<p>Well some way of recording the result, of course. And some way of doing some rudimentary calculations. The average laptop, tablet or smartphone should suffice. Or good old pen and paper.</p>
<p>But that's not really the point of this post. What we <b>really</b> need is the idea for the monster. That might seem obvious to most folk reading this, but with a process-oriented build methodology this is a pretty important thing!</p>
<p>You need a clear idea of the critter you are going to build!</p>
<p>Some might consider this some sort of "generic before-you-build-monsters advice", but this clear image does have a direct impact on monster creation. True, a certain amount of this mental image might be considered "fluff". But a good deal of it <b>is</b> directly relevant to the build process itself.</p>
<p>If you have a good idea for a monster this shouldn't take much time or effort to work out.</p>
<p>Following are the areas I generally try to have a handle on and the kinds of questions I try to consider.</p>
<p> </p>
<h4>Physical Aspects</h4>
<p>This is all about the creature's physical appearance and physical presence (or lack thereof!).</p>
<p>Key questions to consider...</p>
<ul>
<li>How big is the creature in relation to an average adult human?</li>
<li>What does the creature look like?</li>
<li>How capable is it, physically?</li>
<li>What else about it's physical form is unusual? Whether above or below average. Or simply unusual.</li>
</ul>
<p> </p>
<h4>Modus Operandi</h4>
<p>This area is all about how the creature gets along in the world.</p>
<p>Key questions to consider...</p>
<ul>
<li>Is it a melee type? Ranged? A caster? Something else?</li>
<li>How does it attack?</li>
<li>How does it defend itself?</li>
<li>What are it's mental/spiritual/supernatural capabilities?</li>
<li>What kind of persona does it have?</li>
<li>How does it relate to other creatures?</li>
</ul>
<p> </p>
<h4>Nature And Nurture</h4>
<p>These aspects of a creature influence all kinds of things, from how creatures behave to skills to their attacks and more.</p>
<p>Key questions to consider...</p>
<ul>
<li>What is the creature's natural environment?</li>
<li>What's the racial heritage?</li>
<li>How do the creature's instincts tell it to behave?</li>
<li>What was the creature's upbringing?</li>
</ul>
<p> </p>
<p>These questions aren't relevant all of the time. But considering these areas and thinking along these lines help us get a solid mental picture of the creature. And that becomes useful as soon as we start building the mechanics.</p>
<p> </p>
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<a href="/2014/07/d-5e-monsters-part-1-starter-set_16.html"><img src="http://i.imgur.com/d0lSZlO.png" alt="◄"> Part 1: Starter Set Monsters</a>
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<a href="/2014/07/d-5e-monsters-master-index.html"><img src="http://i.imgur.com/qRcTo6k.png" alt="▲"> Master Index</a>
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<td style="text-align:right;">
<a href="/2014/07/d-5e-monsters-part-3-construction-cr.html">Part 3: Construction: The Core Choices <img src="http://i.imgur.com/bZ5DhBF.png" alt="►"></a>
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Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-85214296390552471442014-07-16T10:34:00.001+09:302016-09-23T17:25:47.694+09:30D&D 5e Monsters: Part 1: Starter Set Monsters<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<p><span style="color:lightyellow;"><i>In which Surf shares some observations on monsters in the D&D 5e Starter Set and tells us what we can expect in upcoming articles...</i></span></p>
<p> </p>
<h3><u>Starter Set Monsters</u></h3>
<p>First up no, this is not another <i>Starter Set</i> unboxing. This is not another <i>"I just got the Starter Set"</i> post. I was lucky enough to gain access to the <i>Starter Set</i> <i><b>monsters</b></i> about a week early and commenced my analysis then. I have yet to open my own personal copy of the <i>Starter Set</i>... It's waiting for me to finish writing this post!</p>
<p> </p>
<h4>First Impressions</h4>
<p>The <i>D&D</i> 5e <i>Starter Set</i> contains the adventure <i>Lost Mine Of Phandelver</i>, which in turn includes the ten page <i>Appendix B: Monsters</i>. The first two pages of <i>Appendix B</i> discuss monster statistics and the remaining eight pages contain 27 monsters.</p>
<p>Now my goal with monster analysis has always been to peel back the covers on the underlying math, allowing us to construct reliable and appropriate Monsters. As you might imagine I wasn't expecting to be able to unlock much about 5e monsters with a sample size of a mere 27 low-level creatures! I was resigned to waiting for the <i>Monster Manual</i> release on the 3rd of October before I could do any useful analysis.</p>
<p>But I was to receive a very pleasant surprise!</p>
<p> </p>
<h4>The Good</h4>
<p>It's apparent that after the last playtest packet <i>Wizards Of The Coast</i> wiped the slate clean and started fresh with both monster math and monster construction. It's readily evident that the monsters in the <i>Starter Set</i> support a straightforward method of monster construction. A few hours of preliminary analysis confirmed that the creatures all follow a consistent set of rules that facilitate a straightforward, process-oriented build method. On the few occasions where a creatures falls outside these rules the exception is for obvious reasons. Reasons that apply uniformly across other similar examples. This build process has some similarities to the way PCs are built, but is somewhat simpler and and looser.</p>
<p>Another benefit of following a process-oriented build is that it encourages the DM to think about the monster they are constructing as something more than raw numbers. It also promotes variety in the pool of creatures that emerge over time.</p>
<p>My instincts tell me that there is likely more than one way that <i>D&D 5e</i> monsters can be built. In fact, I get the feeling that if a result-oriented method isn't directly supported one can be built without too much difficulty... Given a sufficient volume of monster samples to draw on.</p>
<p> </p>
<h4>The Bad</h4>
<p>The biggest issue facing analysis is the tiny sample size. Although a lot is obvious about 5e monsters from the <i>Starter Set</i> there are a number of areas we simply cannot break down until we have a larger sample size. Challenge Rating (aka CR) and Damage are the two key areas that present this difficulty.</p>
<p>Another problem resulting from the small sample of low level monsters is, of course, scaling to higher levels. The <i>Starter Set</i> does include creatures from CR0 through to CR8, but there is only one CR8 creature (the <i>Young Green Dragon</i>) and one CR4 creature (the <i>Flameskull</i>). The rest of the monsters range fairly evenly from CR0 through CR3. Until we can analyse a volume of higher level monsters we won't be certain of how our results scale or of any stepping or bumps needed along the way.</p>
<p>Finally, there is a downside to using a process-oriented build methodology. While these approaches generally have some resiliancy built into them the final result may still be significantly weaker or stronger than anticipated. There are ways to compensate for this or check against it, but these are difficult to discover with small sample sizes.</p>
<p> </p>
<h4>The Ugly</h4>
<p>An analysis hoping to prove useful in the short term will need to deal with the issues described above. And this is where it gets a bit dirty. The only real option is to plainly flag where there's a shortfall, use a placeholder that seems appropriate and revisit the area once more data is available.</p>
<p> </p>
<h4>Where To From Here?</h4>
<p>Based on the above observations and assumptions I decided to make a rough long-term plan for my <i>D&D 5e</i> monster analysis. This plan has five distinct phases...</p>
<ol>
<li><b>Monster Construction.</b> In this first phase we'll flesh out what I've explored of monster design, flagging items as described above. This phase will be driven primarily out of <i>Basic D&D</i> and the <i>Starter Set</i>. I expect it to last only a few short weeks and plan to make 2-3 blog posts a week during this period.</li>
<li><b>Preparation.</b> Once the first phase is completed I will prepare for the deeper analysis the <i>Monster Manual</i> release will trigger. This will mainly consist of analysis of PC data, similar to the <a href="http://surfarcher.blogspot.com/2013/08/d-next-monsters-part-2-class.html">Class Analysis</a> I did for my <i>D&D Next</i> series. During this time new official <i>D&D 5e</i> monsters may also be release and, if appropriate, I will post updates for the Monster Construction phase. <i>Basic D&D</i> and the <i>Player's Handbook</i> will be the main sources of this work. New blog posts will be few and far between during this period.</li>
<li><b>Monster Manual Data Entry.</b> The day I get my hands on the new <i>Monster Manual</i> I'll be consumed with entering all of the monsters into a spreadsheet and doing the preliminary number crunching. Don't expect any blog posts during this period, but it will only last a couple of weeks.</li>
<li><b>Review.</b> The first thing we'll do with our <i>Monster Manual</i> data is check our Monster Construction guidelines. We'll make any necessary corrections and fill in any gaps we can. Then we'll look to extend it to higher level creatures. This will probably take a couple of weeks.</li>
<li><b>Deep Analysis.</b> Finally I'll embark on a much deeper analysis of monsters. The results of this will look similar to much of my <a href="http://surfarcher.blogspot.com.au/2013/07/d-next-monsters-part-1-getting-started.html">D&D Next Monster Analysis</a>. It's difficult to estimate how long this will take or how frequent blog posts will be. But the aim is to produce tables that support a result-oriented monster construction methodology.</li>
</ol>
<p> </p>
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<a href="http://surfarcher.blogspot.com/2014/07/d-5e-monsters-master-index.html"> <img src="http://i.imgur.com/d0lSZlO.png" alt="◄">
Master Index</a>
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<a href="http://surfarcher.blogspot.com/2014/07/d-5e-monsters-master-index.html"> <img src="http://i.imgur.com/qRcTo6k.png" alt="▲">
Master Index</a>
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<td style="text-align:right;">
<a href="http://surfarcher.blogspot.com/2014/07/d-5e-monsters-part-2-construction.html">Part 2: Before Building <img src="http://i.imgur.com/bZ5DhBF.png" alt="►"></a>
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Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-49464219810050764822014-07-15T08:01:00.005+09:302016-09-23T15:40:35.583+09:30D&D 5e Monsters: Master Index<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<p><span style="color:lightyellow;"><i>The momentum of Surf's <a href="/2013/07/d-next-monsters-part-1-getting-started.html">D&D Next Monster Analysis</a> overflows into the 5e release and Surf pokes an analysis stick at D&D 5e Monsters...</i></span></p>
<p> </p>
<p>I was fortunate enough to get access to part of the <i>D&D 5e Starter Set</i> several days in advance. The <i>Appendix B: Monsters</i> section from the <i>Lost Mine Of Phandelver</i> booklet is the key item of interest from a monster analysis perspective and with this in hand I was able to complete my initial analysis in very short order.</p>
<p>With the <i>Starter Set</i> released today it seemed like a good time to launch the 5e monster math articles!</p>
<h3><u>Index</u></h3>
<p>Here's a quick map of what the series covers...</p>
<ul>
<li><a href="/2014/07/d-5e-monsters-part-1-starter-set_16.html">Part 1: Starter Set Monsters</a></li>
<li><a href="/2014/07/d-5e-monsters-part-2-construction.html">Part 2: Construction: Before Building</a></li>
<li><a href="/2014/07/d-5e-monsters-part-3-construction-cr.html">Part 3: Construction: CR & Size</a></li>
<li><a href="/2014/08/d-5e-monsters-part-4-construction.html">Part 4: Construction: Ability Scores & HP</a></li>
<li><a href="/2014/08/d-5e-monsters-part-5-construction-ac.html">Part 5: Construction: AC & Other Attributes</a></li>
<li><a href="/2014/08/d-5e-monsters-interlude-bunch-of.html">Interlude: A Bunch Of Monsters!</a></li>
<li><a href="/2014/09/d-5e-monsters-part-6-construction.html">Part 6: Construction: Traits & Spellcasting</a></li>
<li><a href="/2014/09/d-5e-monsters-part-7-construction-damage.html">Part 7: Construction: Damage</a></li>
<li><a href="/2014/10/d-5e-monsters-part-8-construction.html">Part 8: Construction: Actions</a></li>
<li><a href="/2014/10/d-5e-monsters-part-9-construction.html">Part 9: Construction: Attack Bonus</a></li>
<li><a href="/2014/12/d-5e-monsters-part-10-construction-cr.html">Part 10: Construction: CR Evaluation</a></li>
<li><a href="/2015/07/d-5e-monsters-part-11-construction.html">Part 11: Construction Consolidation</a></li>
</ul>
<p>Keep in mind that this is an intended map. As things progress our course may alter, but don't worry I'll keep this index up to date!</p>
<p> </p>
<div class="bottombar"><table><tr>
<td> </td>
<td style="text-align:right;vertical-align:middle;">
<a href="/2014/07/d-5e-monsters-part-1-starter-set_16.html">Part 1: Starter Set Monsters <img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5hy7Jp03uMh20OS0sZ_MkD1SBbrx28yaqyu8le_n-lFYw3uEDcdwFElwzRVjiJon1nvyPH1YFYRL3sLoDHBr8mKL4I4FK2NSZC4iniO0Vz6jNsVceEEHsDEGdPJEVr7qUGKmup7qD15U/s1600/arrow-right.png" alt=">>"></a>
</td>
</tr></table></div>
</body></html>
Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-51692690974213567682014-06-17T04:30:00.000+09:302014-06-17T04:30:00.925+09:30D&D Next Monsters: Part 16: Rebooting The Math: Consolidation<!DOCTYPE html><html b:version='2' class='v2' dir='ltr'><head>
<title>D&D Next Monsters: Part 16: Rebooting The Math: Consolidation</title>
<link type='text/css' rel='stylesheet' href='blog.css' />
</head>
<body>
<span style="color:red;"><p><i>While this blog does <u>not</u> contain material published by Wizards of the Coast it does contain materials summarized and extrapolated from the D&D Next playtest packets. By continuing to read this blog you are consenting to the terms of the Wizards online playtest agreement, which you can view at <a href="http://www.dndnext.com/">dndnext.com</a>.</i></p></span>
<span style="color:lightyellow;"><p><i>Wherein Surf has a shot at correcting the math in the final playtest's monsters....</i></p></span>
<p>OK this took a <b>lot</b> longer than expected, for various reasons. I got caught up proving my changes against character progression data. My work life went insane (think 60 and 70 hour weeks). I really enjoyed working through this and hope readers feel it was worth the wait.</p>
<h3><u>Consolidation</u></h3>
<p>All I have really done in this instalment is consolidate the tables from the previous five articles.</p>
<p>Readers interested in what comes next in my line of <i>D&D</i> monster math analysis should check the end of this article.</p>
<p>Without further ado I give you the...</p>
<p style="clear:both;"> </p>
<h4>Updated Monster Build Table</h4>
<p>Note that I have used the formulas recommended in the last 5 articles. If you want to use an alternative formula for an attribute you'll need to do some work... Or maybe contact me and hope I have some time to spare!</p>
<div class="bluegrid"><table style="float:none;">
<tr><th rowspan="2">Level</th><th colspan="4">AC</th><th colspan="4">HP</th><th rowspan="2">Attack</th><th colspan="4">Damage</th></tr>
<tr><th>Easy</th><th>Average</th><th>Tough</th><th>Solo</th><th>Easy</th><th>Average</th><th>Tough</th><th>Solo</th><th>Easy</th><th>Average</th><th>Tough</th><th>Solo</th></tr>
<tr><td>1</td><td>11</td><td>13</td><td>14</td><td>15</td><td>4</td><td>10</td><td>18</td><td>25</td><td>+2</td><td>2</td><td>3</td><td>4</td><td>6</td></tr>
<tr><td>2</td><td>12</td><td>14</td><td>15</td><td>16</td><td>7</td><td>18</td><td>31</td><td>44</td><td>+3</td><td>4</td><td>7</td><td>11</td><td>14</td></tr>
<tr><td>3</td><td>12</td><td>14</td><td>15</td><td>16</td><td>10</td><td>24</td><td>43</td><td>61</td><td>+4</td><td>7</td><td>11</td><td>17</td><td>22</td></tr>
<tr><td>4</td><td>13</td><td>15</td><td>16</td><td>17</td><td>12</td><td>31</td><td>54</td><td>77</td><td>+4</td><td>9</td><td>15</td><td>22</td><td>30</td></tr>
<tr><td>5</td><td>14</td><td>16</td><td>17</td><td>18</td><td>15</td><td>37</td><td>64</td><td>92</td><td>+5</td><td>11</td><td>18</td><td>27</td><td>37</td></tr>
<tr><td>6</td><td>14</td><td>16</td><td>17</td><td>18</td><td>17</td><td>43</td><td>75</td><td>107</td><td>+5</td><td>13</td><td>22</td><td>32</td><td>43</td></tr>
<tr><td>7</td><td>15</td><td>17</td><td>18</td><td>19</td><td>19</td><td>48</td><td>85</td><td>121</td><td>+6</td><td>15</td><td>25</td><td>37</td><td>49</td></tr>
<tr><td>8</td><td>15</td><td>17</td><td>18</td><td>19</td><td>22</td><td>54</td><td>94</td><td>135</td><td>+6</td><td>17</td><td>28</td><td>42</td><td>55</td></tr>
<tr><td>9</td><td>16</td><td>18</td><td>19</td><td>20</td><td>24</td><td>59</td><td>104</td><td>148</td><td>+7</td><td>18</td><td>31</td><td>46</td><td>61</td></tr>
<tr><td>10</td><td>16</td><td>18</td><td>19</td><td>20</td><td>26</td><td>65</td><td>113</td><td>161</td><td>+7</td><td>20</td><td>34</td><td>50</td><td>67</td></tr>
<tr><td>11</td><td>17</td><td>19</td><td>20</td><td>21</td><td>28</td><td>70</td><td>122</td><td>174</td><td>+7</td><td>22</td><td>36</td><td>55</td><td>73</td></tr>
<tr><td>12</td><td>17</td><td>19</td><td>20</td><td>21</td><td>30</td><td>75</td><td>131</td><td>187</td><td>+8</td><td>24</td><td>39</td><td>59</td><td>79</td></tr>
<tr><td>13</td><td>18</td><td>20</td><td>21</td><td>22</td><td>32</td><td>80</td><td>140</td><td>200</td><td>+8</td><td>25</td><td>42</td><td>64</td><td>85</td></tr>
<tr><td>14</td><td>18</td><td>20</td><td>21</td><td>22</td><td>34</td><td>85</td><td>148</td><td>212</td><td>+8</td><td>27</td><td>46</td><td>68</td><td>91</td></tr>
<tr><td>15</td><td>19</td><td>21</td><td>22</td><td>23</td><td>36</td><td>90</td><td>157</td><td>224</td><td>+9</td><td>29</td><td>49</td><td>73</td><td>97</td></tr>
<tr><td>16</td><td>19</td><td>21</td><td>22</td><td>23</td><td>38</td><td>94</td><td>165</td><td>236</td><td>+9</td><td>31</td><td>52</td><td>78</td><td>104</td></tr>
<tr><td>17</td><td>19</td><td>21</td><td>22</td><td>23</td><td>40</td><td>99</td><td>174</td><td>248</td><td>+9</td><td>33</td><td>56</td><td>84</td><td>112</td></tr>
<tr><td>18</td><td>20</td><td>22</td><td>23</td><td>24</td><td>42</td><td>104</td><td>182</td><td>260</td><td>+10</td><td>36</td><td>60</td><td>90</td><td>119</td></tr>
<tr><td>19</td><td>20</td><td>22</td><td>23</td><td>24</td><td>43</td><td>109</td><td>190</td><td>271</td><td>+10</td><td>38</td><td>64</td><td>96</td><td>128</td></tr>
<tr><td>20</td><td>21</td><td>23</td><td>24</td><td>25</td><td>45</td><td>113</td><td>198</td><td>283</td><td>+10</td><td>41</td><td>68</td><td>103</td><td>137</td></tr>
<tr><td>21</td><td>21</td><td>23</td><td>24</td><td>25</td><td>47</td><td>118</td><td>206</td><td>294</td><td>+11</td><td>44</td><td>73</td><td>110</td><td>147</td></tr>
<tr><td>22</td><td>21</td><td>23</td><td>24</td><td>25</td><td>49</td><td>122</td><td>214</td><td>306</td><td>+11</td><td>47</td><td>79</td><td>118</td><td>157</td></tr>
<tr><td>23</td><td>22</td><td>24</td><td>25</td><td>26</td><td>51</td><td>127</td><td>222</td><td>317</td><td>+12</td><td>51</td><td>84</td><td>127</td><td>169</td></tr>
<tr><td>24</td><td>22</td><td>24</td><td>25</td><td>26</td><td>52</td><td>131</td><td>230</td><td>328</td><td>+12</td><td>54</td><td>91</td><td>136</td><td>181</td></tr>
<tr><td>25</td><td>23</td><td>25</td><td>26</td><td>27</td><td>54</td><td>136</td><td>237</td><td>339</td><td>+13</td><td>58</td><td>97</td><td>146</td><td>195</td></tr>
</table></div>
<p style="clear:both;"> </p>
<h4>Towards the future</h4>
<p>With final fifth edition material due to be released in a few short weeks it is unlikely that I will devote any more time to analysis of <i>D&D Next</i> monsters.</p>
<p>The good news is that the launch of <i>D&D 5e</i> will incorporate <a href="http://www.wizards.com/dnd/Article.aspx?x=dnd/4ll/20140527">Basic D&D</a> as a spearhead. <i>Basic D&D</i> will be a free download that includes essential monsters. I will download and commence analysis of these creatures within hours (possibly minutes) of the PDF's release.</p>
<p>Hopefully the backbone of my <i>D&D Next</i> monster analysis is a close fit with the final product. That should enable a rapid release of monster analysis.</p>
<p style="clear:both;"> </p>
<span style="color:lightyellow;"><p>See you in July!</p></span>
</body></html>Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-3433293990697214352014-06-12T07:27:00.000+09:302014-06-17T07:37:02.894+09:30D&D Next Monsters: Part 15: Rebooting The Math: Damage Review<!DOCTYPE html><html b:version='2' class='v2' dir='ltr'><head>
<title>D&D Next Monsters: Part 15: Rebooting The Math: Damage Review</title>
<link type='text/css' rel='stylesheet' href='blog.css' />
</head>
<body>
<span style="color:red;"><p><i>While this blog does <u>not</u> contain material published by Wizards of the Coast it does contain materials summarized and extrapolated from the D&D Next playtest packets. By continuing to read this blog you are consenting to the terms of the Wizards online playtest agreement, which you can view at <a href="http://www.dndnext.com/">dndnext.com</a>.</i></p></span>
<span style="color:lightyellow;"><p><i>Wherein Surf has a shot at correcting the math in the final playtest's monsters....</i></p></span>
<p>OK this took a <b>lot</b> longer than expected, for various reasons. I got caught up proving my changes against character progression data. My work life went insane (60 and 70 hour weeks plus call-outs). I really enjoyed working through this though, when time allowed, and hope readers feel it was worth the wait.</p>
<p> </p>
<h3><u>Damage</u></h3>
<h4>Scaling Up</h4>
<p><i>D&D Next's</i> mathematical foundation places most of it's emphasis on damage, rather than accuracy. Thus shifts in damage are most significant for PCs and monsters alike, as opposed to 4th edition where shifts in accuracy were most significant. The more I examined <i>Damage</i> (and it's counterpart <i>Hitpoints</i>) the more this drove home to me. Monster damage is strongly based on PC hitpoints, as we expected. Moreover it's a fairly consistent percentage of PC hitpoints, though there is an apparent error in the final packet's crop of monsters.</p>
<div style="clear:both;">
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-05-01-dmg_vs_pc_hp.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-05-01-dmg_vs_pc_hp.png" height="192" width="320" alt="Damage vs PC HP - Actual & Expected" /></a><div class="caption">Damage vs PC HP - Actual & Expected</div></div>
<p>If we divide the average damage of <i>Average</i> monsters by PC <i>Hit Points</i> for the same level we see this sequence: 0.30, 0.27, 0.26, 0.26, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.24, 0.24, 0.24, 0.24, 0.24, 0.24, 0.24, 0.24. This means that <b><i>monster damage gets lower as level increases</i></b>. There are no compensating spikes in damage at any point. Given the aims of the new version of the game I would have expected a progression something like: 0.20, 0.22, 0.24, 0.25, ..., 0.25, 0.27, 0.30. There are a number of variations, but I would have expected to see a sequence somewhat similar to that.</p>
</div>
<p>That's not to say we can't gain useful information from the existing data. For one thing, it gives us an idea of the relationship between <i>Easy</i>, <i>Average</i>, <i>Tough</i> and <i>Solo</i> Damage, telling us how Damage scales out. It also gives us a pretty good idea what Damage should look like for an <i>Average</i> creature at a given level, which tells us something about how Damage scales up.</p>
<p>As you might expect, the existing sequence averages at 0.25 and it's median is 0.25, varying by 0.015. So an <i>Average</i> creature should inflict damage equivalent to 25% of a same-level PC's maximum <i>Hit Points</i>, varying by only 1.5% over all levels - a range of 23.5% - 26.5%. In reality level 1 creatures could be as low as 20%, quickly climbing to around 25% by level 4 or 5. And at the highest level damage up to 30% could be appropriate.</p>
<p>Of course, there are a number of ways we can construct Damage curves that are low at the earliest few levels and high in the last few levels.</p>
<p>Again, I spent far too much time on this and won't bore the reader with all of the grisly details. Basically I created a graph of a linear 0.26 curve and then layered various experimental curves over this. I built curves that somewhat visually balance the area above and below this 0.26 baseline. By using more variable curves than that in the original data the low and high ends of the resulting data fell a little outside the 0.235 - 0.265 range, but in a way that contributes to the easy-low, harder-high ideal.</p>
<p>Naturally I found a lot of interesting and potentially useful curves. But few will be interested in hearing about all of those and most I have simply discarded.<p>
<div style="clear:both;">
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-05-02-dmg_linear.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-05-02-dmg_linear.png" height="192" width="320" alt="Damage Progression: Linear" /></a><div class="caption">Damage Progression: Linear</div></div>
<p>Linear formulae could work here. Obviously a curve that is static at 25% of PC hitpoints <i>might</i> be used, but there's nothing in that that contributes to "easy at lowest levels, hardest at highest levels". If we use a formula that progressively increases from 16% of same-level PC hitpoints and ends at around 27% we find something a bit more useful. Level 1 monsters are going to be a bit easier to defeat and level 20 monsters will take somewhat more damage than average. In a pinch this is a serviceable progression.</p>
</div>
<div style="clear:both;">
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-05-03-dmg_power.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-05-03-dmg_power.png" height="192" width="320" alt="Damage Progression: Power" /></a><div class="caption">Damage Progression: Power</div></div>
<p>A Power based formula is another good place to start. This time again we start our curve at almost 20%, sweeping up to 25% at level 5. From here we gently trend upwards to around 27% at level 25. With this formula damage doesn't scale up significantly past level 5 and thus it's contribution to "harder higher" is fairly minimal.</p>
</div>
<div style="clear:both;">
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-05-04-dmg_poly3.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-05-04-dmg_poly3.png" height="192" width="320" alt="Damage Progression: Poly3" /></a><div class="caption">Damage Progression: Poly3</div></div>
<p>A progression that actively contributes to "easy low, hard high" will require us to use a moderate polynomial formula. I found an elegant little poly3 equation that I like, it's similar in shape to our derived calculation but customizable. It starts at around 17% and quickly trends up to almost 26% at level 3. From levels 4 through 20 it averages just over 25%, varying by +/- 1%. I believe this is the best all-round formula for most groups and it's the one I've used in the summary table.</p>
</div>
<p style="clear:both;"> </p>
<h4>Scaling Out</h4>
<p>Monsters in <i>D&D Next</i> appear to scale out with multipliers of about 0.5 for <i>Easy</i>, 1.25 for <i>Tough</i> and 1.50 for <i>Solo</i> creatures. To me this seems a bit on the weak side.</p>
<div class="bluegrid"><table style="width:210px;">
<tr><th colspan="5">Damage</th></tr>
<tr><th>Level</th><th>Easy</th><th>Normal</th><th>Tough</th><th>Solo</th></tr>
<tr><td>1</td><td>2</td><td>3</td><td>4</td><td>6</td></tr>
<tr><td>2</td><td>4</td><td>7</td><td>11</td><td>14</td></tr>
<tr><td>3</td><td>7</td><td>11</td><td>17</td><td>22</td></tr>
<tr><td>4</td><td>9</td><td>15</td><td>22</td><td>30</td></tr>
<tr><td>5</td><td>11</td><td>18</td><td>27</td><td>37</td></tr>
<tr><td>6</td><td>13</td><td>22</td><td>32</td><td>43</td></tr>
<tr><td>7</td><td>15</td><td>25</td><td>37</td><td>49</td></tr>
<tr><td>8</td><td>17</td><td>28</td><td>42</td><td>55</td></tr>
<tr><td>9</td><td>18</td><td>31</td><td>46</td><td>61</td></tr>
<tr><td>10</td><td>20</td><td>34</td><td>50</td><td>67</td></tr>
<tr><td>11</td><td>22</td><td>36</td><td>55</td><td>73</td></tr>
<tr><td>12</td><td>24</td><td>39</td><td>59</td><td>79</td></tr>
<tr><td>13</td><td>25</td><td>42</td><td>64</td><td>85</td></tr>
<tr><td>14</td><td>27</td><td>46</td><td>68</td><td>91</td></tr>
<tr><td>15</td><td>29</td><td>49</td><td>73</td><td>97</td></tr>
<tr><td>16</td><td>31</td><td>52</td><td>78</td><td>104</td></tr>
<tr><td>17</td><td>33</td><td>56</td><td>84</td><td>112</td></tr>
<tr><td>18</td><td>36</td><td>60</td><td>90</td><td>119</td></tr>
<tr><td>19</td><td>38</td><td>64</td><td>96</td><td>128</td></tr>
<tr><td>20</td><td>41</td><td>68</td><td>103</td><td>137</td></tr>
<tr><td>21</td><td>44</td><td>73</td><td>110</td><td>147</td></tr>
<tr><td>22</td><td>47</td><td>79</td><td>118</td><td>157</td></tr>
<tr><td>23</td><td>51</td><td>84</td><td>127</td><td>169</td></tr>
<tr><td>24</td><td>54</td><td>91</td><td>136</td><td>181</td></tr>
<tr><td>25</td><td>58</td><td>97</td><td>146</td><td>195</td></tr>
</table></div>
<p>Let us consider an average-ish level 20 melee type character with 264 hitpoints compared against some theoretical monsters. We'll use our polynomial formula from above, assume all attacks hit and leave aside critical hits. We'll also consider a 30% "swing" in damage on any given hit.</p>
<p>A 20th level <i>Solo</i> creature will deal damage equivalent between 27% and 50% of full PC health, averaging 39%. Now, a <i>Solo</i> is "worth" about four regular creatures of the same level. Yet a level 20 average creature deals 26% of full PC HP damage. Four of them would on average deal 103% of full PC HP damage! There's a big difference between those two percentages!</p>
<p>What about a 25th level <i>Solo</i>? It will deal between 39% and 72% of a <u>level 20</u> PCs full health as damage, averaging 55%. That's a far cry from the 148% damage that four average level 25 monsters would deal!</p>
<p>So to me it's obvious that these multipliers need some updating.</p>
<p>We do need to be careful though, as we could make creatures too overpowering. If we edge the <i>Solo</i> multiplier up to 2.0 the level 25 <i>Solo</i> creature would then do between 51% and 96% of full PC HP as damage, averaging around 73%. To me that "feels" about right for a fight that is supposed to be extremely challenging for a party of level 20 PCs. It may even be necessary to stretch the multiplier to 2.5 (64% to 119% of full PC HP, averaging 92%), but that should be carefully tested first.</p>
<p>What I have gone with for the purposes of this article is 0.6 for <i>Easy</i>, 1.5 for <i>Tough</i> and 2.0 for <i>Solo</i> creatures.</p>
<p>For the reader's convenience I have included a full hitpoints table to the left that corresponds to the derived/power formulas.</p>
<p style="clear:both;"> </p>
<p><b>Formulae:</b><ul>
<li> Damage (derived) ~= (Level x 13 + 4) * (0.0031 x Level + 0.1969)</li>
<li> Damage (static linear) = 3.6292 x Level - 0.9125</li>
<li> Damage (power) = 3.385 x Level ^ 1.0172</li>
<li> Damage (poly3) = 0.0062 x Level ^ 3 - 0.1886 x Level ^ 2 + 4.8052 x Level - 1.8186</li>
<li> Easy Damage = Damage x 0.60</li>
<li> Hard Damage = Damage x 1.50</li>
<li> Solo Damage = Damage x 2.00</li>
</ul></p>
<p> </p>
<p style="clear:both;"> </p>
<span style="color:lightyellow;"><p>Check back Monday for <a href="http://surfarcher.blogspot.com/2014/06/d-next-monsters-part-16-rebooting-math.html">revised monster building tables...</a></p></span>
</body></html>Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-11083895975751022232014-04-17T16:54:00.000+09:302014-06-12T09:26:49.710+09:30D&D Next Monsters: Part 14: Rebooting The Math: Attack Review<!DOCTYPE html><html b:version='2' class='v2' dir='ltr'><head>
<title>D&D Next Monsters: Part 14: Rebooting The Math: Attack Review</title>
<link type='text/css' rel='stylesheet' href='blog.css' />
</head>
<body>
<span style="color:red;"><p><i>While this blog does <u>not</u> contain material published by Wizards of the Coast it does contain materials summarized and extrapolated from the D&D Next playtest packets. By continuing to read this blog you are consenting to the terms of the Wizards online playtest agreement, which you can view at <a href="http://www.dndnext.com/">dndnext.com</a>.</i></p></span>
<span style="color:lightyellow;"><p><i>Surf reboots monster Attack Bonus....</i></p></span>
<p>I really sank too much time into this one.</p>
<h3><u>Attack Bonus</u></h3>
<p>I spent quite a lot of time tinkering with <i>Attack Bonus</i>. Way too much time probably, since it really didn't need a "hard reboot". So I might use this as an example to explain why the simplest formula producing an appropriate result is usually the best choice. And why we might sometimes go with a more complicated option.</p>
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-04-01-ac_hit_derived.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-04-01-ac_hit_derived.png" height="192" width="320" alt="Attack Bonus - Derived" /></a><div class="caption">Attack Bonus - Derived</div></div>
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-04-02-ac_hit_power_matched.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-04-02-ac_hit_power_matched.png" height="192" width="320" alt="Attack Bonus - Power (Matched)" /></a><div class="caption">Attack Bonus - Power (Matched)</div></div>
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-04-03-ac_hit_power.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-04-03-ac_hit_power.png" height="192" width="320" alt="Attack Bonus - Power (Scaled)" /></a><div class="caption">Attack Bonus - Power (Scaled)</div></div>
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-04-04-ac_hit_poly.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-04-04-ac_hit_poly.png" height="192" width="320" alt="Attack Bonus - Poly" /></a><div class="caption">Attack Bonus - Poly</div></div>
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-04-05-ac_hit_comparison.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-04-05-ac_hit_comparison.png" height="192" width="320" alt="Attack Bonus Comparison" /></a><div class="caption">Attack Bonus Comparison</div></div>
<h4>Scaling Up</h4>
<p>So first up, were there any issues with <i>Attack</i> scaling up? If so what? Well for the most part <i>Attack</i> scales appropriately. At lowest levels (1 through 4) monsters need a higher roll to hit PCs (11.6, 10.5, 9.9 and 9.6). This stabilises to around 9.5 from levels 5 through 15, but then starts to climb a little again. Yes the highest level monsters find it slightly harder to hit same-level PCs than the mid-level ones. That's kind of the opposite of what I'd expect with "easy low/harder high". We can correct it pretty easily tho.</p>
<p>We are already verifying our existing formula against PC <i>Armor Class</i> and calculating an <i>Attack</i> formula from PC <i>AC</i> is easy enough, indeed the only trick is properly reflecting the "easy low, hard high" part. Based on our analysis we are looking for a formula where monsters hit same level PCs with a 1d20 roll of 12 or 13 at level 1, dropping down to 10 by level 5 and staying around there through to endgame levels. It would be nice to toughen things up slightly at level 25 by hitting same-level PCs on a naked roll of 9.</p>
<p>Incorporating a simple exponential into our basic equation gives a very good match here. As long as we ignore the "toughen up a bit by level 25" part it's pretty easy to produce a stand-alone Power formula that fairly closely matches this progression.</p>
<p>If we want to dial the difficulty up a bit at level 25 we'll want our base <i>Attack</i> bonus to tick over to 13 at that level. It's pretty easy to produce a Power formula that achieves that, but as we'd expect this does vary away from our derived formula somewhat. If we check out the portions above and below the 9.55 baseline though we can see that it should be an acceptable formula to use. While some might argue that this could be a little on the tough side at higher levels they would be forgetting the role that <i>Bounded Accuracy</i> plays here. Small variations in accuracy (thus AC and Attack Bonus) are less important in <i>D&D Next</i> than in it's immediate predecessors.</p>
<p>That said we can pretty easily produce a poly3 formula that is closer to the "easy low, harder high" ideal. The curve for this formula stays near our 9.55 baseline for most of it's course, as you'd guess it dips down well below it at lower levels and sweeps up to a solid 13 from level 20 through to level 25.</p>
<p>So how do we choose between these candidates?</p>
<p>There are a few "tools" that are useful here. First, I placed a simple reference line showing a "to hit roll" of 9.55 and took careful notice of how the candidate curves related to this. Secondly, I added a linear trendline to each graph allowing us to evaluate the overall balance of the portions of curve above and below our 9.55 reference line. Finally, I added a column to the data table with a simple formula showing whether any given candidate value was less than, equal to or greater than the corresponding derived value.</p>
<p>We can also look at the similarities between the results of a candidate formula and the derived formula. As a table how much variation is there between the two? As a graph with a trendline how similar are they? What are the repercussions of the differences?</p>
<p>Finally, I also graphed the candidate forumlae against the derived one. This allows us to visually consider the repercussions of the variations between the formulae.</p>
<div class="bluegrid"><table style="width:220px;">
<tr><th colspan="5">Attack Bonus</th></tr>
<tr><th>Level</th><th>Derived</th><th>Matched</th><th>Scaled</th><th>Poly</th></tr>
<tr><td>1</td><td>2</td><td>2</td><td>2</td><td>2</td></tr>
<tr><td>2</td><td>4</td><td style="background-color:lightpink;">3</td><td style="background-color:lightpink;">3</td><td style="background-color:lightpink;">3</td></tr>
<tr><td>3</td><td>5</td><td style="background-color:lightpink;">4</td><td style="background-color:lightpink;">4</td><td style="background-color:lightpink;">4</td></tr>
<tr><td>4</td><td>5</td><td>5</td><td style="background-color:lightpink;">4</td><td style="background-color:lightpink;">4</td></tr>
<tr><td>5</td><td>5</td><td>5</td><td>5</td><td>5</td></tr>
<tr><td>6</td><td>6</td><td>6</td><td>6</td><td style="background-color:lightpink;">5</td></tr>
<tr><td>7</td><td>6</td><td>6</td><td>6</td><td>6</td></tr>
<tr><td>8</td><td>6</td><td>6</td><td style="background-color:lightpink;">7</td><td>6</td></tr>
<tr><td>9</td><td>7</td><td>7</td><td>7</td><td>7</td></tr>
<tr><td>10</td><td>7</td><td>7</td><td>7</td><td>7</td></tr>
<tr><td>11</td><td>7</td><td>7</td><td style="background-color:lightpink;">8</td><td>7</td></tr>
<tr><td>12</td><td>8</td><td>8</td><td>8</td><td>8</td></tr>
<tr><td>13</td><td>8</td><td>8</td><td style="background-color:lightpink;">9</td><td>8</td></tr>
<tr><td>14</td><td>8</td><td>8</td><td style="background-color:lightpink;">9</td><td>8</td></tr>
<tr><td>15</td><td>8</td><td style="background-color:lightpink;">9</td><td style="background-color:lightpink;">9</td><td style="background-color:lightpink;">9</td></tr>
<tr><td>16</td><td>9</td><td>9</td><td style="background-color:lightpink;">10</td><td>9</td></tr>
<tr><td>17</td><td>9</td><td>9</td><td style="background-color:lightpink;">10</td><td>9</td></tr>
<tr><td>18</td><td>9</td><td>9</td><td style="background-color:lightpink;">10</td><td style="background-color:lightpink;">10</td></tr>
<tr><td>19</td><td>9</td><td style="background-color:lightpink;">10</td><td style="background-color:lightpink;">11</td><td style="background-color:lightpink;">10</td></tr>
<tr><td>20</td><td>10</td><td>10</td><td style="background-color:lightpink;">11</td><td>10</td></tr>
<tr><td>21</td><td>10</td><td>10</td><td style="background-color:lightpink;">11</td><td style="background-color:lightpink;">11</td></tr>
<tr><td>22</td><td>10</td><td>10</td><td style="background-color:lightpink;">12</td><td style="background-color:lightpink;">11</td></tr>
<tr><td>23</td><td>11</td><td>11</td><td style="background-color:lightpink;">12</td><td style="background-color:lightpink;">12</td></tr>
<tr><td>24</td><td>11</td><td>11</td><td style="background-color:lightpink;">12</td><td style="background-color:lightpink;">12</td></tr>
<tr><td>25</td><td>11</td><td>11</td><td style="background-color:lightpink;">13</td><td style="background-color:lightpink;">13</td></tr>
</table></div>
<p>If we consider the Power formula's trendline and it's relationship to the 9.55 baseline we can clearly see that this formula produces a noticeable deviation above the baseline from about level 10. Examining the actual data points shows that from level 9 monster accuracy steadily increases above our baseline. That said the deviation is always within a +/-2 range that <i>Bounded Accuracy</i> should be able to accommodate. This formula could be useful in the context of "easy low/hard high" and it's simplicity commends it.</p>
<p>The polynomial formula's trendline balances quite evenly on the baseline. It has an interesting curve in both it's head and tail. The low level curve is a little less shouldered than that of the derived equation and the high level curve has a similar shape to the low level one, popping it's level 25 value above that of the Power curve. Ultimately this formula should result in a "closer to baseline" experience from levels 5 through 20 than the Power curve. It should contribute to "easy low/hard high" at least as well as the Power formula. While it is more complex than the Power equation it has a certain elegance I find compelling.</p>
<p>So how much difference is there really between the three formula we are considering? Not much, particularly after rounding - check out the table. Thanks to <i>Bounded Accuracy</i> the difference is actually pretty minimal - in fact there is generally more variation within samples of the same level than there is across levels.</p>
<p>All else being equal, we generally use the simplest formula producing a valid result. But sometimes "all else being equal" is subjective. Elegant solutions, for example, are important in many circles. In our case I think our objectives at lowest and highest levels have some subtlety about them that our moderate polynomial helps us meet. On it's own it might be negligible, but if we consistently make the same kind of decisions across all the attributes the net effect can be precisely the one feel I believe <i>WotC</i> are aiming for with monsters.</p>
<p>At the end of the day it's up to you to decide which you prefer to use in your own campaign. That said I prefer to use the poly3 formula in my own games.</p>
<h4>Scaling Up</h4>
<p><i>Attack</i> bonus doesn't scale out across different monster types. That said a variation of up to +/-2 within a level is pretty common, with some compensation usually made elsewhere in the creature's makeup.</p>
<p style="clear:both;">
<h4>Formulae</h4>
<ul>
<li> Attack (derived) ~= (Level x 0.28 + 13.72) - 9.55 - 7 x exp(-0.9 x Level)</li>
<li> Attack (matched power) = 2.3403 x Level ^ 0.4796</li>
<li> Attack (power) = 2 x Level ^ 0.57</li>
<li> Attack (poly) = 0.0012 x Level ^ 3 - 0.0507 x Level ^ 2 + 1.0028 x Level + 0.9833</li>
</ul></p>
<p> </p>
<p style="clear:both;"> </p>
<span style="color:lightyellow;"><p>Check back after Easter for the <a href="http://surfarcher.blogspot.com/2014/06/d-next-monsters-part-15-rebooting-math.html">Damage reboot</a>...</p></span>
</body></html>Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-54720482468124142042014-04-11T06:49:00.000+09:302014-06-17T07:38:44.850+09:30D&D Next Monsters: Part 13: Rebooting The Math: Hitpoint Review<!DOCTYPE html><html b:version='2' class='v2' dir='ltr'><head>
<title>D&D Next Monsters: Part 13: Rebooting The Math: Hitpoint Review</title>
<link type='text/css' rel='stylesheet' href='blog.css' />
</head>
<body>
<span style="color:red;"><p><i>While this blog does <u>not</u> contain material published by Wizards of the Coast it does contain materials summarized and extrapolated from the D&D Next playtest packets. By continuing to read this blog you are consenting to the terms of the Wizards online playtest agreement, which you can view at <a href="http://www.dndnext.com/">dndnext.com</a>.</i></p></span>
<span style="color:lightyellow;"><p><i>Wherein Surf reboots monster hitpoints....</i></p></span>
<p>Reworking monster hitpoints was also relatively easy.</p>
<h3><u>Hit Points</u></h3>
<h4>Scaling Up</h4>
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-03-01-hp_vs_dmg_current.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-03-01-hp_vs_dmg_current.png" height="192" width="320" alt="HP vs PC Damage - Current" /></a><div class="caption">HP vs PC Damage - Current</div></div>
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-03-02-hp_vs_dmg_derived.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-03-02-hp_vs_dmg_derived.png" height="192" width="320" alt="HP vs PC Damage - Derived" /></a><div class="caption">HP vs PC Damage - Derived</div></div>
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-03-03-hp_vs_dmg_power.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-03-03-hp_vs_dmg_power.png" height="192" width="320" alt="HP vs PC Damage - Power" /></a><div class="caption">HP vs PC Damage - Power</div></div>
<p>Under further analysis the HP progression of <i>Normal</i> creatures still seemed appropriate. Initially a <i>Normal</i> monster will take 1.04x of standard PC damage (aka StdDmg) to go down. This makes them pretty easy for any modestly damage-focused PC to take out. By level 5 they are up to 1.53x StdDam, reaching 2.0 at level 15 and 2.14 at level 20. If we extend this trend out to level 25 we get 2.26. While this progression is appropriate I have made a minor correction to my previous <i>Normal</i> formula based on further analysis. This is simply a byproduct of marrying up formula with derived results.</p>
<p>The key to revising this data is a Power based curve for the Monster_HP:PC_Damage ratio. Building this out appropriately was not a difficult task. And from this it was fairly easy to match an appropriate Power formula to the final curve.</p>
<h4>Scaling Out</h4>
<p>Where I feel <i>Hitpoints</i> need some tuning is in the modifiers for <i>Tough</i> and <i>Solo</i> creatures. Based on their XP a <i>Tough</i> is "worth" just under two <i>Normal</i> creatures, with a <i>Solo</i> being "worth" four <i>Normal</i> critters. Yet the HP multiplier for a <i>Tough</i> appears to be 1.5 and for a <i>Solo</i> seems to be 2.0. Now I <b>get</b> that making these multipliers 2.0 and 4.0, respectively, can cause problems. Who really wants to simply whack away at a sack of hitpoints forever, right? And as monsters scale up they accumulate an increasing suite of resistances, immunities and other mitigations. But even so the multipliers for scaling out are obviously quite low. This is one of the reasons that higher level monsters feel comparatively weaker. So I've conservatively increased these multipliers.</p>
<p style="clear:both;"> </p>
<div class="bluegrid"><table style="width:210px;">
<tr><th colspan="5">Hitpoints</th></tr>
<tr><th>Level</th><th>Easy</th><th>Normal</th><th>Tough</th><th>Solo</th></tr>
<tr><td>1 </td><td>4</td><td>10</td><td>18</td><td>25 </td></tr>
<tr><td>2 </td><td>7</td><td>18</td><td>31</td><td>44 </td></tr>
<tr><td>3 </td><td>10</td><td>24</td><td>43</td><td>61 </td></tr>
<tr><td>4 </td><td>12</td><td>31</td><td>54</td><td>77 </td></tr>
<tr><td>5 </td><td>15</td><td>37</td><td>64</td><td>92 </td></tr>
<tr><td>6 </td><td>17</td><td>43</td><td>75</td><td>107</td></tr>
<tr><td>7 </td><td>19</td><td>48</td><td>85</td><td>121</td></tr>
<tr><td>8 </td><td>22</td><td>54</td><td>94</td><td>135</td></tr>
<tr><td>9 </td><td>24</td><td>59</td><td>104</td><td>148</td></tr>
<tr><td>10</td><td>26</td><td>65</td><td>113</td><td>161</td></tr>
<tr><td>11</td><td>28</td><td>70</td><td>122</td><td>174</td></tr>
<tr><td>12</td><td>30</td><td>75</td><td>131</td><td>187</td></tr>
<tr><td>13</td><td>32</td><td>80</td><td>140</td><td>200</td></tr>
<tr><td>14</td><td>34</td><td>85</td><td>148</td><td>212</td></tr>
<tr><td>15</td><td>36</td><td>90</td><td>157</td><td>224</td></tr>
<tr><td>16</td><td>38</td><td>94</td><td>165</td><td>236</td></tr>
<tr><td>17</td><td>40</td><td>99</td><td>174</td><td>248</td></tr>
<tr><td>18</td><td>42</td><td>104</td><td>182</td><td>260</td></tr>
<tr><td>19</td><td>43</td><td>109</td><td>190</td><td>271</td></tr>
<tr><td>20</td><td>45</td><td>113</td><td>198</td><td>283</td></tr>
<tr><td>21</td><td>47</td><td>118</td><td>206</td><td>294</td></tr>
<tr><td>22</td><td>49</td><td>122</td><td>214</td><td>306</td></tr>
<tr><td>23</td><td>51</td><td>127</td><td>222</td><td>317</td></tr>
<tr><td>24</td><td>52</td><td>131</td><td>230</td><td>328</td></tr>
<tr><td>25</td><td>54</td><td>136</td><td>237</td><td>339</td></tr>
</table></div>
<p>For the reader's convenience I have included a full hitpoints table to the left that corresponds to the derived/power formulas.</p>
<p><b>Formulae:</b><ul style="margin-left: 200px;">
<li> HP (derived) = (1.04 x Level ^ 0.24) * (9.581 x Level ^ 0.57065)</li>
<li> HP (Power) = 10 x Level ^ 0.81</li>
<li> Easy HP = HP x 0.40</li>
<li> Tough HP = HP x 1.75</li>
<li> Solo HP = HP x 2.50</li>
</ul></p>
<p> </p>
<p style="clear:both;"> </p>
<span style="color:lightyellow;"><p>Check back in a few days for the <a href="http://surfarcher.blogspot.com.au/2014/04/d-next-monsters-part-14-rebooting-math.html">Attack Bonus reboot</a>...</p></span>
</body></html>Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-67029110528174723882014-04-09T06:00:00.000+09:302014-04-11T07:01:03.250+09:30D&D Next Monsters: Part 12: Rebooting The Math: AC Review<!DOCTYPE html><html b:version='2' class='v2' dir='ltr'><head>
<title>D&D Next Monsters: Part 12: Rebooting The Math: AC Review</title>
<link type='text/css' rel='stylesheet' href='blog.css' />
</head>
<body>
<span style="color:red;"><p><i>While this blog does <u>not</u> contain material published by Wizards of the Coast it does contain materials summarized and extrapolated from the D&D Next playtest packets. By continuing to read this blog you are consenting to the terms of the Wizards online playtest agreement, which you can view at <a href="http://www.dndnext.com/">dndnext.com</a>.</i></p></span>
<span style="color:lightyellow;"><p><i>Surf remixes monster Armor Class....</i></p></span>
<p>Monster AC was probably the least difficult part of rebooting monster math...</p>
<p style="clear:both;"> </p>
<h3><u>Armor Class</u></h3>
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-02-01-ac_hit_current.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-02-01-ac_hit_current.png" height="192" width="320" alt="Current PC Hit Roll Required" /></a><div class="caption">Current PC Hit Roll Required</div></div>
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-02-02-ac_hit_derived.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-02-02-ac_hit_derived.png" height="192" width="320" alt="Derived PC Hit Roll Required" /></a><div class="caption">Derived PC Hit Roll Required</div></div>
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-02-03-ac_hit_poly2.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-02-03-ac_hit_poly2.png" height="192" width="320" alt="Poly2 PC Hit Roll Required" /></a><div class="caption">Poly2 PC Hit Roll Required</div></div>
<div imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-02-04-ac_hit_poly3.png"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/mmr-02-04-ac_hit_poly3.png" height="192" width="320" alt="Poly3 PC Hit Roll Required" /></a><div class="caption">Poly2 PC Hit Roll Required</div></div>
<h4>Scaling Up</h4>
<p>A modest amount of analysis reveals an obvious issue with the way monster AC in the final packet scales up. At level 1 same-level monsters can be hit on a 9, but this value <i>declines</i> as level increases. A level 20 PC can hit Asmodeus on an roll of 6 and a first level PC only needs to roll 13 to hit him. And this is in keeping with the AC progression evident in the current monsters. Ideally level 1&2 PCs would hit same-levels monsters on a 9, then from levels 5 through 20 they hit on 10 or 11, finally they'd hit level 25 <i>Normal</i> creatures with a roll of about 11 or 12.</p>
<p>Is it appropriate for level 1 PCs to only hit level 20 monsters on a 19 or 20? I think so.</p>
<p>These actual required dice roll numbers are a very good fit for a simple power equation (roll=9 x Level ^ 0.08). For a derived formula we simply add the PC attack bonus (attack_bonus=Level x 0.368 + 3.798) to this required roll. The result of this isn't something we can easily match with a simple Power or Logarithmic formula, much less a Linear formula. It is, however, trivially matched using a simple Polynomial formula.</p>
<p>A little curve matching gives us a poly2 formula which produces results functionally equivalent to our derived formula, after rounding. Note the graphs on this page plot data before rounding. Once rounding is applied the derived and poly2 curves have only three minor points of difference. There is significantly more variation within monster samples of the same type an level than this variation represents. We can make a choice between a simpler variation and a perfect match at this point. I personally was happy to this poly2 formula for some time and it's perfectly appropriate for most DMs' use.</p>
<p>That said I know there will be those who strongly desire a closer match. For these readers I have provided a poly3 equation which exactly reproduces the derived curve, once rounded.</p>
<p style="clear:both;"> </p>
<div class="bluegrid"><table style="width:175px;">
<tr><th>Level</th><th>Derived</th><th>Poly2</th><th>Poly3</th></tr>
<tr><td>1</td><td>13</td><td>13</td><td>13</td></tr>
<tr><td>2</td><td>14</td><td>14</td><td>14</td></tr>
<tr><td>3</td><td>15</td><td style="background-color:lightpink;">14</td><td>15</td></tr>
<tr><td>4</td><td>15</td><td>15</td><td>15</td></tr>
<tr><td>5</td><td>16</td><td>16</td><td>16</td></tr>
<tr><td>6</td><td>16</td><td>16</td><td>16</td></tr>
<tr><td>7</td><td>17</td><td>17</td><td>17</td></tr>
<tr><td>8</td><td>17</td><td>17</td><td>17</td></tr>
<tr><td>9</td><td>18</td><td>18</td><td>18</td></tr>
<tr><td>10</td><td>18</td><td>18</td><td>18</td></tr>
<tr><td>11</td><td>19</td><td>19</td><td>19</td></tr>
<tr><td>12</td><td>19</td><td>19</td><td>19</td></tr>
<tr><td>13</td><td>20</td><td>20</td><td>20</td></tr>
<tr><td>14</td><td>20</td><td>20</td><td>20</td></tr>
<tr><td>15</td><td>20</td><td style="background-color:lightpink;">21</td><td>20</td></tr>
<tr><td>16</td><td>21</td><td>21</td><td>21</td></tr>
<tr><td>17</td><td>21</td><td>21</td><td>21</td></tr>
<tr><td>18</td><td>22</td><td>22</td><td>22</td></tr>
<tr><td>19</td><td>22</td><td>22</td><td>22</td></tr>
<tr><td>20</td><td>22</td><td style="background-color:lightpink;">23</td><td>22</td></tr>
<tr><td>21</td><td>23</td><td>23</td><td>23</td></tr>
<tr><td>22</td><td>23</td><td>23</td><td>23</td></tr>
<tr><td>23</td><td>24</td><td>24</td><td>24</td></tr>
<tr><td>24</td><td>24</td><td>24</td><td>24</td></tr>
<tr><td>25</td><td>25</td><td>25</td><td>25</td></tr>
</table></div>
<h4>Scaling Out</h4>
<p>My review didn't suggest that any corrections to the previously discussed method for scaling out AC were required. The Easy (-2), Hard (+1) and Tough (+2) multipliers appear to still be quite appropriate.</p>
<p> </p>
<h4>Formulae</h4>
To summarise the formulae discussed for the AC reboot...
<p><ul>
<li> AC (derived) = (9 x Level ^ 0.08) + (Level x 0.368 + 3.798)</li>
<li> AC (poly2) = -0.0049 x Level ^ 2 + 0.5959 x Level + 12.681</li>
<li> AC (poly3) = 0.0004 x Level ^ 3 - 0.0205 x Level ^ 2 + 0.7453 x Level + 12.445</li>
<li> Easy AC = AC - 2</li>
<li> Tough AC = AC + 1</li>
<li> Solo AC = AC + 2</li>
</ul></p>
<p>And to the left you will find a table containing the "scaling up" values for the two key formulae, after appropriate rounding.</p>
<p style="clear:both;"> </p>
<span style="color:lightyellow;"><p>Check back in a couple of days for the <a href="http://surfarcher.blogspot.com/2014/04/d-next-monsters-part-13-rebooting-math.html">Hit Points review</a>...</p></span>
</body></html>Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-15003094297487259552014-04-08T07:21:00.000+09:302014-04-11T07:05:00.285+09:30D&D Next Monsters: Part 11: Rebooting The Math: Introduction<!DOCTYPE html><html b:version='2' class='v2' dir='ltr'><head>
<title>D&D Next Monsters: Part 11: Rebooting The Math: Introduction</title>
<link type='text/css' rel='stylesheet' href='blog.css' />
</head>
<body>
<span style="color:red;"><p><i>While this blog does <u>not</u> contain material published by Wizards of the Coast it does contain materials summarized and extrapolated from the D&D Next playtest packets. By continuing to read this blog you are consenting to the terms of the Wizards online playtest agreement, which you can view at <a href="http://www.dndnext.com/">dndnext.com</a>.</i></p></span>
<span style="color:lightyellow;"><p><i>Wherein Surf has a shot at updating the math of the final playtest's monsters....</i></p></span>
<p>OK this took a <b>lot</b> longer than expected, for various reasons. I initially thought this would be a relatively short article. OK, it could get on the long side, but <u>surely</u> it would be a single article. Well as I worked through the details several times over the whole thing unfolded into a much bigger body of work than I expected. I also got pretty caught up proving my changes against character progression data. To cap it all off my work life went insane - think 60 to 70 hour weeks as standard for months. I really enjoyed working through this though and it provided some much needed diversion from real life on several occasions. I hope readers feel it was worth the wait.</p>
<p style="clear:both;"> </p>
<h3><u>Why Make Changes?</u></h3>
<p>This is a question you might find yourself asking if you haven't played <i>D&D Next</i> much, or have only played at very low levels.</p>
<p>While lower level <i>D&D Next</i> monsters certainly feel appropriate in play there are issues with monster progression. Somewhere past level 5 we notice that same-level monsters seem to be getting easier to defeat, a trend that becomes quite pronounced by about level 10. Some of the causes are quite obvious when comparing the table from <a href="http://surfarcher.blogspot.com/2013/12/d-next-monsters-part-10-final-packet.html">Part 10</a> with PC progression data. But other factors are more subtle.</p>
<p>My hope was to revise the math such that monsters would be viable for a 1-20 campaign and provide sufficient flexibility for all Dungeon Masters.</p>
<p style="clear:both;"> </p>
<h3><u>Goals</u></h3>
<p>I initially mapped out some goals for this revision. While I reviewed and refined these a few times these changes were more to the wording of the goals than to the intent. I chose not to give the goals a priority or number as I feel they are all equally important.</p>
<h4>Scale Up</h4>
<p>Monsters need to "scale up" appropriately. That is, the challenge of <i>Normal</i> type monsters shouldn't taper off as monster level increases. Yes, there is a design objective that the lowest level monsters should be relatively easier to defeat than mid-level monsters and we need to ensure this remains the case and this does introduce some interesting challenges. But as Normal monsters scale up from about level 5 they should provide the same level of challenge to a same level party, if anything becoming slightly more difficult in endgame levels. In fact I believe endgame monster should be correspondingly more difficult - I call this the "easy low/hard high" goal.</p>
<h4>Scale Out</h4>
<p>Monsters also need to "scale out" appropriately. <i>Easy</i>, <i>Tough</i> and <i>Solo</i> creatures all have statistics derived from the <i>Normal</i> type of monster of their level - typically by applying a multiplier. Issues scaling up <i>Normal</i> monsters are magnified when this multiplier is too low. This is less apparent at lower levels but becomes progressively more apparent at higher levels. Given that the current crop of high-level monsters is composed of all <i>Solo</i> creatures, with the odd <i>Tough</i> creature, this is likely a significant contributor to the current issues with high level monsters.</p>
<h4>Complement PC Progression</h4>
<p>The general "shape" of monster progression needs to either be in line with the "shape" of PC progression <b>or</b> it must complement that progression. Again - the lowest level monsters should be significantly easier for same-level PCs to defeat than higher level monsters and the very highest level monsters should pose a significant challenge to a same-level party. Monsters of level 19 and 20 should be harder for a same-level party to overcome than level 15 monsters. This can be a little tricky if one wants to end up with a self-contained progression that isn't directly dependent on PC progression. It can be quite a balancing act.</p>
<h4>Extend Beyond Level 20</h4>
<p>DMs have always thrown monsters at the party that are of higher level than the PCs. Some editions obfuscated this, but there has always been a mechanism to determine how suitable a creature is to fight the PCs and this amounts to "monster level", at least in a logical sense. A natural extension of this is D&D's long history of monsters of a level higher than the PCs can ever reach - generally named entities of greater-deity power. Entities like Bahamut, Demogorgon, Lolth, Orcus, Tiamat and Vecna should not be faced with impunity! Since PC level progression finishes at level 20 I felt it would be useful to extend monster math to level 25.</p>
<p style="clear:both;"> </p>
<h3><u>Bringing The Goals Together</u></h3>
<p>Many of these goals carry interdependencies - some subtle and some obvious. So there are some interesting challenges bringing them together. For example, scaling up monster progression too aggressively can create some serious problems with level 25 creatures - there's a good chance few level 20 PCs will ever be able to win against them. By the same token there are some good opportunities for our goals to work together - for example scaling out to level 25 properly provides a very useful way for DMs to ensure tough "capstone" fights at the end of their campaign, but still be able to tune content to their group.</p>
<p>Careful consideration of components and their impact on the whole are a must!</p>
<p style="clear:both;"> </p>
<h3><u>Development And Formulae...</u></h3>
<p>You might have noticed that the further this series progresses, the more complicated the formulae become. So it's worth stopping briefly here and considering how monster math is likely developed and what this means to formula selection.</p>
<p><i>Wizards of the Coast</i> have indicated in several different sources that monster math is dependent upon PC math. Thus it's important for them to fine-tune PC progression before they approach finalizing monster math. That pretty strongly suggests that the actual monster attribute forumlae <i>WotC</i> are using aren't simply stand-alone formulae. Rather, each is likely a formula that includes a reference to PC progression formula (or formulae!). This is one of the things that spreadsheets excel at and I imagine they have some rather interesting spreadsheets. Which you and I will likely never see, unfortunate as that may be.</p>
<p>There are upsides and downsides to this. On the positive side it's very easy to observe the impact of changing a basic value far-removed from the final numbers of interest and then see the widespread impact. This "what if" analysis is another thing spreadhsheets are very good at - things like "if PC Armor Class progresses faster what to-hit bonus would monsters need to still hit on a roll of 10?" are relatively easy to check. The negative side includes issues like the magnification of minor oversights and of errors in dependent math.</p>
<p>While I necessarily consider and include dependent formulae I generally prefer to use stand-alone formulae. The obvious reason for this is portability. But the deeper reason is the ability to produces progression curves that in some way complement our goals. This proved particularly useful with the "easy low/hard high" goal.</p>
<p>In this series I have opted to present the simplest formula that I feel produce a sufficiently accurate result. In some cases there is variation away from the actual related PC progression data, however this is either complementary or not significant.</p>
<p> </p>
<p style="clear:both;"> </p>
<span style="color:lightyellow;"><p>Check back tomorrow for the <a href="http://surfarcher.blogspot.com/2014/04/d-next-monsters-part-12-rebooting-math.html">AC Review</a>...</p></span>
</body></html>Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-20699378519913779872013-12-29T11:03:00.000+10:302014-04-08T07:34:54.764+09:30D&D Next Monsters: Part 10: Final Packet Analysis<body>
<span style="color:red;"><p><i>While this blog does <u>not</u> contain material published by Wizards of the Coast it does contain materials summarized and extrapolated from the D&D Next playtest packets. By continuing to read this blog you are consenting to the terms of the Wizards online playtest agreement, which you can view at <a href="http://www.dndnext.com/">dndnext.com</a>.</i></p></span>
<span style="color:lightyellow;"><p><i>Surf does a full review for the final playtest packet....</i></p></span>
<p>First up, my apologies to anyone waiting on these installments. Unimaginative real life has a great deal to answer for and this is a part-time gig.</p>
<p>With the final playtest packet release we saw some changes to monsters. Most monsters were relegated to the <b>Older Playtest Adventures and Bestiaries</b> folder and <i>Wizards of the Coast</i> seem to have done a pass of reviews over the main <i>Bestiary</i> itself and included creatures for <i>Murder In Baldur's Gate</i>. So I started from scratch, redoing my entire analysis - after all, this was the final packet so I might as well be thorough, right? Of course, I didn't ignore all of my previous work. It is interesting, after all, to see what's been altered, what's been added and what's been removed.</p>
<p style="clear:both;"> </p>
<h3><u>So What Changed?</u></h3>
<p>Well no creatures have been removed, although a number of creatures have had a trait or action removed. A number of creatures were altered, mainly creatures in the level one through three range. This makes sense since WotC have mentioned several times that they intend these low level creatures to provide easier same-level fights than at higher level and the changes made to them are consistent with this.</p>
<p>With a little analysis it becomes evident that many aspects of monsters now exhibit non-linear progression curves. There are no obvious exponential or polynomial curves, but we see both logarithmic and power curves. These help give us the easier level 1-3 creatures.</p>
<p>One of the other things that is obvious is the tweaking of these "easy" creatures' Armor Class. This seems to be about 2 bouts below that of a "normal" creatures of the same level. This is mainly obvious at level 1, where we have 21 "easy" creatures and 15 "average creatures". At level 2 it's more difficult to tell since we only have 12 "easy" creatures and 13 "average" creatures.</p>
<p style="clear:both;"> </p>
<h3><u>Sample Size</u></h3>
<p>One of the issues with the changes in the final playtest is the greatly reduced sample size. With so few creatures at each level it's now more difficult to accurately determine underlying numbers. That means we don't quite have the confidence in those numbers that we had with previous packets. We can extrapolate from our previous work and from other numbers and works. We can also go back through sample monsters at each level and compare them to our numbers. Both of which help improve confidence in our results.</p>
<p>The <a href="http://community.wizards.com/forums/98651">D&D Next forums</a> have been particularly useful for locating related analysis. For example, the <a href="http://community.wizards.com/forum/dd-next-general-discussion/threads/3944236">DPR Calculations</a> thread contains carefully calculated attack and damage numbers for many classes, thoroughly reviewed by the Wizards Community.</p>
<p style="clear:both;"> </p>
<h3><u>Findings</u></h3>
<p>All the areas we've been looking at have seen some kind of change....</p>
<b><u>Armor Class</u></b>
<p><b>Observations:</b> Overall we've seen some significant "tightening up" of AC, which we knew was coming. The effective range for an Average monster contracted from 12 through 18 to 13 through 17. What's glaringly obvious, and less expected, is that there is now a clear disparity between the Easy monsters and the other monsters. An Easy monster seems to have an AC 1-2 points lower than other monsters of it's level. The formula for AC seems to have remained a linear curve.</p>
<p><b>Formulae:</b><ul>
<li> AC ~= Level x 0.20 + 13</li>
<li> Easy AC = AC - 2</li>
</ul></p>
<b><u>Hit Points</u></b>
<p><b>Observations:</b> Considering the Average monster as the base of HP, this area has seen little change. Much of the actual change to hitpoints has been to Easy creatures. Previously these had about 70% of the hitpoints of Average creatures, but this now seems to have been reduced to 40%. In addition it seems that a Power curve is now a better fit for progression, which helps ensure lower level creatures tend to be more easily defeated by same-level PCs. Hit Points appear to have been changed to a fairly flat power curve.</p>
<p><b>Formulae:</b><ul>
<li> HP ~= 10 x Level ^ 0.81</li>
<li> Easy HP = HP x 0.4</li>
<li> Tough HP = HP x 1.5</li>
<li> Solo HP = HP x 2.0</li>
</ul></p>
<b><u>Attack Bonus</u></b>
<p><b>Observations:</b> This is another area that saw significant change, standardising level 1 creatures to a +2 attack bonus and scaling standard creature attack bonus through to +9 at level 20. There seems to be no stable variation between Easy and Solo creatures of the same level. The formula for Attack Bonus now seems to be a logarithmic curve.</p>
<p><b>Formulae:</b><ul>
<li> Attack ~= 2.06 x log(Level) + 2.38</li>
<li> No apparent variations</li>
</ul></p>
<b><u>Damage</u></b>
<p><b>Observations:</b> Damage seems to be the least impacted stat, in fact all changes in this area simply seem to have brought most creatures more into line with previous analysis. That said the Easy/Normal/Hard/Solo variations did shift a little and have been updated. Damage still appears to be a linear formula, but it's a little different to what we previously used.</p>
<p><b>Formulae:</b><ul>
<li> Damage ~= 3.10 x Level + 2.00</li>
<li> Easy Damage = Damage x 0.50</li>
<li> Hard Damage = Damage x 1.25</li>
<li> Solo Damage = Damage x 1.50</li>
</ul></p>
<p style="clear:both;"> </p>
<h3><u>Monster Building Table</u></h3>
<p>All of which yields the following table...</p>
<div class="bluegrid"><table style="float:none;">
<tr><th rowspan="2" style="width:10%;">Level</th><th rowspan="2" style="width:9%;">AC *</th><th colspan="4">Hitpoints</th><th rowspan="2" style="width:9%;">Attack</th><th colspan="4">Damage</th></tr>
<tr><th style="width:9%;">Easy</th><th style="width:9%;">Average</th><th style="width:9%;">Tough</th><th style="width:9%;">Solo</th><th style="width:9%;">Easy</th><th style="width:9%;">Average</th><th style="width:9%;">Tough</th><th style="width:9%;">Solo</th></tr>
<tr><td>1</td><td>13</td><td>4</td><td>10</td><td>15</td><td>20</td><td>+2</td><td>3</td><td>5</td><td>6</td><td>8</td></tr>
<tr><td>2</td><td>13</td><td>7</td><td>18</td><td>26</td><td>35</td><td>+4</td><td>4</td><td>8</td><td>10</td><td>12</td></tr>
<tr><td>3</td><td>14</td><td>10</td><td>24</td><td>37</td><td>49</td><td>+5</td><td>6</td><td>11</td><td>14</td><td>17</td></tr>
<tr><td>4</td><td>14</td><td>12</td><td>31</td><td>46</td><td>61</td><td>+5</td><td>7</td><td>14</td><td>18</td><td>22</td></tr>
<tr><td>5</td><td>14</td><td>15</td><td>37</td><td>55</td><td>74</td><td>+6</td><td>9</td><td>18</td><td>22</td><td>26</td></tr>
<tr><td>6</td><td>14</td><td>17</td><td>43</td><td>64</td><td>85</td><td>+6</td><td>10</td><td>21</td><td>26</td><td>31</td></tr>
<tr><td>7</td><td>14</td><td>19</td><td>48</td><td>73</td><td>97</td><td>+6</td><td>12</td><td>24</td><td>30</td><td>36</td></tr>
<tr><td>8</td><td>15</td><td>22</td><td>54</td><td>81</td><td>108</td><td>+7</td><td>13</td><td>27</td><td>34</td><td>40</td></tr>
<tr><td>9</td><td>15</td><td>24</td><td>59</td><td>89</td><td>119</td><td>+7</td><td>15</td><td>30</td><td>37</td><td>45</td></tr>
<tr><td>10</td><td>15</td><td>26</td><td>65</td><td>97</td><td>129</td><td>+7</td><td>17</td><td>33</td><td>41</td><td>50</td></tr>
<tr><td>11</td><td>15</td><td>28</td><td>70</td><td>105</td><td>139</td><td>+7</td><td>18</td><td>36</td><td>45</td><td>54</td></tr>
<tr><td>12</td><td>15</td><td>30</td><td>75</td><td>112</td><td>150</td><td>+7</td><td>20</td><td>39</td><td>49</td><td>59</td></tr>
<tr><td>13</td><td>16</td><td>32</td><td>80</td><td>120</td><td>160</td><td>+8</td><td>21</td><td>42</td><td>53</td><td>63</td></tr>
<tr><td>14</td><td>16</td><td>34</td><td>85</td><td>127</td><td>170</td><td>+8</td><td>23</td><td>45</td><td>57</td><td>68</td></tr>
<tr><td>15</td><td>16</td><td>36</td><td>90</td><td>135</td><td>179</td><td>+8</td><td>24</td><td>49</td><td>61</td><td>73</td></tr>
<tr><td>16</td><td>16</td><td>38</td><td>94</td><td>142</td><td>189</td><td>+8</td><td>26</td><td>52</td><td>65</td><td>77</td></tr>
<tr><td>17</td><td>16</td><td>40</td><td>99</td><td>149</td><td>198</td><td>+8</td><td>27</td><td>55</td><td>68</td><td>82</td></tr>
<tr><td>18</td><td>17</td><td>42</td><td>104</td><td>156</td><td>208</td><td>+8</td><td>29</td><td>58</td><td>72</td><td>87</td></tr>
<tr><td>19</td><td>17</td><td>43</td><td>109</td><td>163</td><td>217</td><td>+8</td><td>30</td><td>61</td><td>76</td><td>91</td></tr>
<tr><td>20</td><td>17</td><td>45</td><td>113</td><td>170</td><td>226</td><td>+9</td><td>32</td><td>64</td><td>80</td><td>96</td></tr>
</table>* -2 AC for Easy creatures.</div>
<p style="clear:both;"> </p>
<h3><u>Thoughts....</u></h3>
<p>WotC have previously indicated that a design goal for <i>D&D Next</i> is for lower level monsters to be easier for same-level PCs to overcome than higher level monsters. The math changes in the final packet certainly nudge creature stats in that direction. However nothing has been done to address the feeling that higher level monsters are still much too easy.</p>
<p>There are a few factors at work here and we'll see what we can do to address these early in the new year.
<p> </p>
<p style="clear:both;"> </p>
<span style="color:lightyellow;"><p>Check back next week for the <a href="http://surfarcher.blogspot.com/2014/04/d-next-monsters-part-11-rebooting-math.html">Part 10: Final Packet Analysis</a>...</p></span>
</body>Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-5622449396599482792013-08-29T08:15:00.001+09:302013-12-29T11:06:03.828+10:30D&D Next Monsters: Part 9: XP Curves & KpL...<span style="color:red;"><p><i>While this blog does <u>not</u> contain material published by Wizards of the Coast it does contain materials summarized and extrapolated from the D&D Next playtest packets. By continuing to read this blog you are consenting to the terms of the Wizards online playtest agreement, which you can view at <a href="http://www.dndnext.com/">dndnext.com</a>.</i></p></span>
<span style="color:lightyellow;"><p><i>Surf looks at monster XP progression....</i></p></span>
<p>So <a href="https://plus.google.com/109659591453191902524">+Jonathan Black</a> asked <a href="https://plus.google.com/101512522568834873171">+Mike Mearls</a> about the discrepancies between low, mid and high level character progression. Specifically <i>"Why does it take more xp to go from 10 to 11 than 11 to 12?"</i>. Mike didn't answer, but this raised some questions about monster XP progression in my mind, so I decided to take a look...</p>
<p style="clear:both;"> </p>
<h3><u>PC Progression</u></h3>
<div class="bluegrid"><table style="width:200px;">
<tr><th>Level</th><th>XP</th><th>Difference</th></tr>
<tr><td>1</td><td>0</td><td>0</td></tr>
<tr><td>2</td><td>250</td><td>250</td></tr>
<tr><td>3</td><td>950</td><td>700</td></tr>
<tr><td>4</td><td>2,250</td><td>1,300</td></tr>
<tr><td>5</td><td>4,750</td><td>2,500</td></tr>
<tr><td>6</td><td>9,500</td><td>4,750</td></tr>
<tr><td>7</td><td>16,000</td><td>6,500</td></tr>
<tr><td>8</td><td>25,000</td><td>9,000</td></tr>
<tr><td>9</td><td>38,000</td><td>13,000</td></tr>
<tr><td>10</td><td>56,000</td><td>18,000</td></tr>
<tr><td>11</td><td>77,000</td><td style="background-color:lightpink;">21,000</td></tr>
<tr><td>12</td><td>96,000</td><td style="background-color:lightpink;">19,000</td></tr>
<tr><td>13</td><td>120,000</td><td>24,000</td></tr>
<tr><td>14</td><td>150,000</td><td>30,000</td></tr>
<tr><td>15</td><td>190,000</td><td>40,000</td></tr>
<tr><td>16</td><td>230,000</td><td>40,000</td></tr>
<tr><td>17</td><td>280,000</td><td>50,000</td></tr>
<tr><td>18</td><td>330,000</td><td>50,000</td></tr>
<tr><td>19</td><td>390,000</td><td>60,000</td></tr>
<tr><td>20</td><td>460,000</td><td>70,000</td></tr>
</table></div>
<p>First up let's take a look at what Jonathan is talking about. Let's take the PC progression table and subtract the previous level's value from each level. This gives us the XP a character needs to gain to go up to the next level.</p>
<p>Now to gain a level we expect that we should need to gain more XP than we needed to gain last level. Or at least the same. But not less. Now take a look at the differences at levels 11 & 12.</p>
<p>The only explanation for this is human error. I believe this is a simple transposition mistake. If we swap the two values around then everything is perfect. This is the kind of think I'd expect <i>Wizards of the Coast</i> to fix quietly.</p>
<p>Swapping these two values works perfectly. In mathematical terms there isn't much real impact and it's probably not worth the headache of getting your whole group to understand the issue and agree that XP to reach level 11 should be 75,000 rather than 77,000. But if you are keen that's the only change required.</p>
<p>Of course, working through this got the old mental cogs turning...</p>
<p style="clear:both;"> </p>
<h3><u>PC Progression vs Monster XP</u></h3>
<p>Looking at PC progression got me thinking about the relationship between it and monster-at-level XP values. There's a relationship between the two, regardless of how loosely <i>Wizards of the Coast</i> have defined it. Obviously the PC progression chart helps us here, as does the Average column of the encounter design table (which is essentially the XP for one Average monster for that level). One of the design concepts of <i>D&D Next</i> also tells us what to expect. That is <i>"...fast advancement at lower levels with more gradual advancement at mid- and high levels"</i>.</p>
<p style="clear:both;"> </p>
<h3><u>Monster XP Curve</u></h3>
<a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/xp_avg_monster_xp.png" imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/xp_avg_monster_xp.png" height="192" width="320" alt="Average Monster XP by Level" /></a>
<p>Simply graphing the Average monster XP by level shows us that it's all over the place. I'd say "quite out of whack at higher levels". The trendline on the graph shows the kind of progression I'd expect.<p>
<p>What we see is that after level 11 there's a lot of XP that's just way higher than we'd expect. One could argue that this doesn't matter because the encounter math is built on the assumption that monster XP values use the same table. And running some quick pivots show that's the case.</p>
<div class="bluegrid"><table style="width:200px;">
<tr><th>Level</th><th>Easy</th><th>Average</th><th>Tough</th></tr>
<tr><td>1</td><td>10</td><td>20</td><td>40</td></tr>
<tr><td>2</td><td>40</td><td>60</td><td>110</td></tr>
<tr><td>3</td><td>70</td><td>100</td><td>200</td></tr>
<tr><td>4</td><td>110</td><td>160</td><td>320</td></tr>
<tr><td>5</td><td>150</td><td>230</td><td>460</td></tr>
<tr><td>6</td><td>220</td><td>330</td><td>650</td></tr>
<tr><td>7</td><td>290</td><td>440</td><td>880</td></tr>
<tr><td>8</td><td>400</td><td>600</td><td>1,200</td></tr>
<tr><td>9</td><td>510</td><td>770</td><td>1,500</td></tr>
<tr><td>10</td><td>670</td><td>1,000</td><td>2,000</td></tr>
<tr><td>11</td><td>850</td><td>1,300</td><td>2,600</td></tr>
<tr><td>12</td><td>1,080</td><td>1,600</td><td>3,300</td></tr>
<tr><td>13</td><td>1,400</td><td>2,100</td><td>4,100</td></tr>
<tr><td>14</td><td>1,700</td><td>2,600</td><td>5,200</td></tr>
<tr><td>15</td><td>2,200</td><td>3,400</td><td>6,700</td></tr>
<tr><td>16</td><td>2,900</td><td>4,300</td><td>8,600</td></tr>
<tr><td>17</td><td>3,600</td><td>5,500</td><td>10,900</td></tr>
<tr><td>18</td><td>4,700</td><td>7,000</td><td>14,000</td></tr>
<tr><td>19</td><td>5,900</td><td>8,900</td><td>17,700</td></tr>
<tr><td>20</td><td>7,500</td><td>11,300</td><td>22,500</td></tr>
</table></div>
<p>And yet this argument misses something important - the impact to PC progression. These higher XP rewards, and higher associated encounter XP budgets, mean that PCs level up with fewer fights than if the correct values were being used.</p>
<p>When we are levelling up too quickly we feel that the game is too easy. So these over-curve XP values likely play a part in the feeling that <i>D&D Next</i> combats are too easy at mid and high level. Not that they are the only factor.</p>
<p>Regardless of whether it's necessary, it is pretty easy to determine the "right" values. We just add an extra column to our graph, copy the current values into it and then adjust them until each point sits on our trendline. We can even sprinkle in some of the usual RPG industry "rounding magic" to make the final table a bit more palatable to the human mind (people like to see zeros on the ends of longer numbers).</p>
<p>Which gives us a handy new encounter budget/monster XP chart.</p>
<p>Now, let's see if it proves useful...</p>
<p style="clear:both;"> </p>
<h3><u>Kills Per Level</u></h3>
<a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/xp_kpl_current.png" imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/xp_kpl_current.png" height="192" width="320" alt="Kills per Level (Current)" /></a>
<a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/xp_kpl_revised.png" imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/xp_kpl_revised.png" height="192" width="320" alt="Kills per Level (Revised)" /></a>
<p>If we subtract the XP needed to reach the <b>next</b> level from the XP needed to reach <b>this</b> level and divide the result by the XP value of an Average monster of this level we learn the <i>Kills per Level</i> (aka Kills/Level aka KpL) for this level. We can trivially do this for every level and then graph the result.</p>
<p>And the result is <u><i><b>really</b></i></u> interesting!</p>
<p>Yes, the values are scattered. And yes, we can correct this pretty easily simply by using our new Encounter/Monster XP table (see the "Revised" graph). But what's interesting is the curve! <i>Wizards of the Coast</i> seem to have decided that from level 10 we need to have far fewer fights each level. I'm guessing that's because they didn't plan to release many mid- or high-level creatures during the playtest and only planned to get a feel for what the epic tier of play was like.</p>
<p>And I reckon this is a factor in the feeling that the higher levels of play are too easy.</p>
<p style="clear:both;"> </p>
<h3><u>Correcting It...</u></h3>
<div class="bluegrid"><table style="width:200px;">
<tr><th>Level</th><th>Curved Tail</th><th>Plateau</th></tr>
<tr><td>1</td><td>0</td><td>0</td></tr>
<tr><td>2</td><td>250</td><td>250</td></tr>
<tr><td>3</td><td>1,100</td><td>1,100</td></tr>
<tr><td>4</td><td>3,100</td><td>3,100</td></tr>
<tr><td>5</td><td>6,500</td><td>6,500</td></tr>
<tr><td>6</td><td>11,800</td><td>11,700</td></tr>
<tr><td>7</td><td>19,700</td><td>19,300</td></tr>
<tr><td>8</td><td>30,600</td><td>29,800</td></tr>
<tr><td>9</td><td>45,600</td><td>44,200</td></tr>
<tr><td>10</td><td>64,800</td><td>62,600</td></tr>
<tr><td>11</td><td>89,600</td><td>86,400</td></tr>
<tr><td>12</td><td>121,000</td><td>117,000</td></tr>
<tr><td>13</td><td>159,000</td><td>155,000</td></tr>
<tr><td>14</td><td>207,000</td><td>204,000</td></tr>
<tr><td>15</td><td>266,000</td><td>265,000</td></tr>
<tr><td>16</td><td>341,000</td><td>344,000</td></tr>
<tr><td>17</td><td>433,000</td><td>443,000</td></tr>
<tr><td>18</td><td>550,000</td><td>570,000</td></tr>
<tr><td>19</td><td>697,000</td><td>732,000</td></tr>
<tr><td>20</td><td>883,000</td><td>936,000</td></tr>
</table></div>
<p>There are pretty much two options for correcting this. The first is simple, we halve the XP budget and XP value for encounters and creatures over level 10.</p>
<p>The second option is not something I'd ordinarily recommend, but the more I look at it the more convinced I am that it's the right way to go. It's an option you'd have to sell to your group - updating the PC progression table. Generally I prefer options the DM can silently use behind the scenes, but if PC progression is at fault then that is what is most appropriate to correct as other corrections will have side effects. Some of which won't be immediately obvious.</p>
<p>If we do this we need to decide how we want our progression to look. For my money I like a "curved tail" curve that starts like the current curve, it curves up to 25KpL at level 8, from there gently curves down to 21 KpL at level 20. The other option I'll present is a "plateau" curve which also starts similarly, curving up to 24 KpL at level 8, from there ever so gently dropping down to 23KpL at level 20. Again, I applied a little rounding to make the final numbers more natural for humans.</p>
<p>Then again, none of this matters if you don't use the PC progression table... Like my own group. When the DM simply decides how often everyone levels up this whole article become a moot point.</p>
<p>But it was an interesting moot point...<p>
<p> </p>
<p style="clear:both;"> </p>
<span style="color:lightyellow;"><p>Check back next week for the <a href="http://surfarcher.blogspot.com/2013/12/d-next-monsters-part-10-final-packet.html">Part 10: Final Packet Analysis</a>...</p></span>
Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-88199309156534312632013-08-20T14:54:00.001+09:302013-08-29T08:23:37.852+09:30D&D Next Monsters: Part 8: Putting It All Together<span style="color:red;"><p><i>While this blog does <u>not</u> contain material published by Wizards of the Coast it does contain materials summarized and extrapolated from the D&D Next playtest packets. By continuing to read this blog you are consenting to the terms of the Wizards online playtest agreement, which you can view at <a href="http://www.dndnext.com/">dndnext.com</a>.</i></p></span>
<span style="color:lightyellow;"><p><i>Surf brings togethor the AC, Attack, Damage and Hitpoint analysis....</i></p></span>
<p>Well with all that number-crunching done let's put all of our results togethor into a consolidated table!</p>
<p style="clear:both;"> </p>
<h3><u>Monster Building Table</u></h3>
<div class="bluegrid"><table style="float:none;">
<tr><th rowspan="2" style="width:10%;">Level</th><th rowspan="2" style="width:9%;">AC</th><th colspan="4">Hitpoints</th><th rowspan="2" style="width:9%;">Attack</th><th colspan="4">Damage</th></tr>
<tr><th style="width:9%;">Easy</th><th style="width:9%;">Average</th><th style="width:9%;">Tough</th><th style="width:9%;">Solo</th><th style="width:9%;">Easy</th><th style="width:9%;">Average</th><th style="width:9%;">Tough</th><th style="width:9%;">Solo</th></tr>
<tr><td>1</td><td>12</td><td>7</td><td>10</td><td>13</td><td>20</td><td>+4</td><td>4</td><td>5</td><td>6</td><td>10</td></tr>
<tr><td>2</td><td>12</td><td>11</td><td>16</td><td>20</td><td>31</td><td>+4</td><td>6</td><td>8</td><td>9</td><td>15</td></tr>
<tr><td>3</td><td>13</td><td>15</td><td>21</td><td>27</td><td>42</td><td>+5</td><td>8</td><td>10</td><td>12</td><td>20</td></tr>
<tr><td>4</td><td>13</td><td>19</td><td>27</td><td>34</td><td>53</td><td>+5</td><td>10</td><td>13</td><td>15</td><td>25</td></tr>
<tr><td>5</td><td>13</td><td>22</td><td>32</td><td>42</td><td>64</td><td>+5</td><td>12</td><td>15</td><td>18</td><td>30</td></tr>
<tr><td>6</td><td>13</td><td>26</td><td>38</td><td>49</td><td>75</td><td>+6</td><td>14</td><td>18</td><td>21</td><td>35</td></tr>
<tr><td>7</td><td>14</td><td>30</td><td>43</td><td>56</td><td>86</td><td>+6</td><td>16</td><td>20</td><td>24</td><td>40</td></tr>
<tr><td>8</td><td>14</td><td>34</td><td>49</td><td>63</td><td>97</td><td>+6</td><td>18</td><td>23</td><td>27</td><td>45</td></tr>
<tr><td>9</td><td>14</td><td>38</td><td>54</td><td>70</td><td>108</td><td>+6</td><td>20</td><td>25</td><td>30</td><td>50</td></tr>
<tr><td>10</td><td>15</td><td>42</td><td>60</td><td>77</td><td>119</td><td>+7</td><td>22</td><td>28</td><td>33</td><td>55</td></tr>
<tr><td>11</td><td>15</td><td>46</td><td>65</td><td>85</td><td>130</td><td>+7</td><td>24</td><td>30</td><td>36</td><td>60</td></tr>
<tr><td>12</td><td>15</td><td>49</td><td>71</td><td>92</td><td>141</td><td>+7</td><td>26</td><td>33</td><td>39</td><td>65</td></tr>
<tr><td>13</td><td>16</td><td>53</td><td>76</td><td>99</td><td>152</td><td>+8</td><td>28</td><td>35</td><td>42</td><td>70</td></tr>
<tr><td>14</td><td>16</td><td>57</td><td>82</td><td>106</td><td>163</td><td>+8</td><td>30</td><td>38</td><td>45</td><td>75</td></tr>
<tr><td>15</td><td>16</td><td>61</td><td>87</td><td>113</td><td>174</td><td>+8</td><td>32</td><td>40</td><td>48</td><td>80</td></tr>
<tr><td>16</td><td>16</td><td>65</td><td>93</td><td>120</td><td>185</td><td>+9</td><td>34</td><td>43</td><td>51</td><td>85</td></tr>
<tr><td>17</td><td>17</td><td>69</td><td>98</td><td>127</td><td>196</td><td>+9</td><td>36</td><td>45</td><td>54</td><td>90</td></tr>
<tr><td>18</td><td>17</td><td>72</td><td>104</td><td>135</td><td>207</td><td>+9</td><td>38</td><td>48</td><td>57</td><td>95</td></tr>
<tr><td>19</td><td>17</td><td>76</td><td>109</td><td>142</td><td>218</td><td>+9</td><td>40</td><td>50</td><td>60</td><td>100</td></tr>
<tr><td>20</td><td>18</td><td>80</td><td>115</td><td>149</td><td>229</td><td>+10</td><td>42</td><td>53</td><td>63</td><td>105</td></tr>
</table></div>
<p style="clear:both;"> </p>
<h3><u>Where's The Art?</u></h3>
<p>The DM Guidelines PDF says that "Encounter building is a mixture of art and science as you combine these threats together" and traditionally this has been even more the case with monster design. But with tables like the one above some feel that monster design is shallow and inflexible.</p>
<p>Not so, I say! Tables like this simply provide a baseline for monster design that let us produce flexible monsters that provide a reliable threat at their target level. The art comes in the various traits, actions, reactions and adjustments that can and should be made,</p>
<p>Below follow my thoughts on modifying the aspects of monsters converred during this analysis. Some of it is based on analysis and math, some of it is based on my opinion. I've tried to indicate where this is the case, but your mileage may vary. Of course, I take no responsibility for how you choose to use the information in this article and if your creation eats your mother and destroys your house don't come looking for me!</P>
<p style="clear:both;"> </p>
<h3><u>Armor Class</u></h3>
<p><b>Trivial</b> changes to AC should generally be limited to +/-1 for most creatures, without compensating in some other way.</p>
<p><b>Adjustments</b> to AC are commonly compensated for by counter-adjustmenting hitpoints, tho adjusting other aspects of a creature can work too. In a sense giving a creature an additional +1 to AC is like giving it 5% more hitpoints. So a sensible rule of thumb is to compensate for a +1 AC with -5% of original hitpoints or vice versa.</p>
<p><b>Maximum</b> adjustment will depend on the creature being created or modified, to some extent. Changes should probably be capped at about +/-5 AC and even these should be thought out and compensated for very carefully.</p>
<p><b>Traits</b> which alter AC are fairly rare in the game. There are a few, such as "Soft Belly" (e.g., Ankheg) that are used to compensate for creatures with a somewhat high AC.</p>
<p style="clear:both;"> </p>
<h3><u>Hitpoints</u></h3>
<p><b>Trivial</b> hitpoint modifications should be limited to around 2% (rounded up).</p>
<p><b>Adjustments</b> to balance hitpoint changes are often made to AC or damage. As noted above a shift of 5% hitpoints can be compensated for by adjusting AC one point. A 2 point change to hitpoints can also be compensated for with a 1 point shift in damage (+2 hp, -1 damage). Another way of compensating for hitpoint changes is with traits that temporarily drop hitpoints or AC.</p>
<p><b>Maximum</b> alterations to hitpoints should probably be no more than +/-50%.</p>
<p><b>Traits</b> and actions directly effecting hit points are quite rare, including Relentless (Orcs), Regeneration and any healing effects. These active effects are usually compensated for in some way, such as a vulnerability or adjusting the creature's base hitpoints.<tr />Passive traits are a whole different kettle of fish. It seems that <i>D&D Next</i> assumes a certain level of damage mitigation for creatures by their level. The higher a creature's level is the more resistances, immunities and similar traits it has.<br />This isn't an area I have analysed properly yet, but hope look at in the future. In the meantime I strongly recommend looking at creatures of a similar level when building or levelling/delevelling monsters.</p>
<p style="clear:both;"> </p>
<h3><u>Attack</u></h3>
<p><b>Trivial</b> tweaking of attack bonus should generally be limited to +/-1 if one doesn't plan to compensate for the change elsewhere.</p>
<p><b>Adjustments</b> to attack bonus are often made to damage or hitpoints. A 1 point shift in Attack Bonus can be balanced with a 5% shift in damage or a 10% shift in hitpoints.</p>
<p><b>Maximum</b> attack bonus tweaking should probably be limited to +/-2.</p>
<p><b>Traits</b> that adjust attack bonus are scarce. The most common of these is undoubtedly <i>Pack Tactics</i>, however this is capped at +5 <b>and</b> most creatures with this trait have a much lower attack bonus than is normal for their level. When used this way the trait is sort of self-balancing. Other traits like <i>Bushwhacker</i> (Goblins) and Captivating (Harpies) grant advanatge on attacks conditionally and overall probably amount to no more than a +1 to attack over the course of a combat. So generally </p>
<p style="clear:both;"> </p>
<h3><u>Damage</u></h3>
<p><b>Trivial</b> damage tweaks can be made in the order of +/-2% without compensating elsewhere.</p>
<p><b>Adjustments</b> to compensate for damage changes are typically made to attack bonus, to hitpoints, or to both. A 5% change to damage can be adjusted for with a 1 point change in Attack Bonus or a 10% change in hitpoints.</p>
<p><b>Maximum</b> changes to Damage, where compensating measures are taken, should probably be around +/-50%.</p>
<p><b>Traits</b> that adjust damage are relatively common. However, most of these traits should be factored into the creature's base damage - this includes damaging auras, damage on death, bonus damage (e.g., on surprise), berserk and other similar traits.</p>
<p> </p>
<p style="clear:both;"> </p>
<span style="color:lightyellow;"><p>Check back in a few days for the next installment <a href="http://surfarcher.blogspot.com/2013/08/d-next-monsters-part-9-xp-curves-kpl.html">Part 9: XP Curves & KpL</a>...</p></span>
Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com1tag:blogger.com,1999:blog-6511225892793734362.post-53562804971087294442013-08-19T07:00:00.000+09:302013-08-20T14:59:09.252+09:30D&D Next Monsters: Part 7: Damage Analysis...<span style="color:red;"><p><i>While this blog does <u>not</u> contain material published by Wizards of the Coast it does contain materials summarized and extrapolated from the D&D Next playtest packets. By continuing to read this blog you are consenting to the terms of the Wizards online playtest agreement, which you can view at <a href="http://www.dndnext.com/">dndnext.com</a>.</i></p></span>
<span style="color:lightyellow;"><p><i>In the last article Surf unearthed the math behind hitpoints. Today we look at the last of these major monster stats - Damage....</i></p></span>
<p>Meh to crud with the intro... let's dive right in this time!</p>
<p style="clear:both;"> </p>
<h3><u>High-Level Data</u></h3>
<p>During this particular analysis we consider a creature's “At-Will” damage and it's “Damage Per Round” (aka DPR). </p>
<div class="textgrid"><table style="width:125px;float:none;">
<tr><th> </th><th><u>At-Will</u></th><th><u>DPR</u></th></tr>
<tr><td>Average:</td><td>15.47</td><td>17.00</td></tr>
<tr><td>Stdev:</td><td>15.83</td><td>16.80</td></tr>
<tr><td>Var:</td><td>251.08</td><td>282.32</td></tr>
</table></div>
<p>As we saw with character classes, back in <a href="http://surfarcher.blogspot.com.au/2013/08/d-next-monsters-part-2-class.html">Part 2</a>, damage is lower than hitpoints and thus it's variability is lower than hitpoints. Because of <i>Bounded Accuracy</i> it's still considerably higher than AC or Attack bonus though. We expect that monster damage should scale relative to PC hitpoints so this is a good sign.</p>
<div class="datagrid"><table style="width:300px;">
<tr><th colspan="6">StdDevp of At-Will Damage by XP</th></tr>
<tr><th>Level</th><th>Easy</th><th>Average</th><th>Tough</th><th>Solo</th><th>Total</th></tr>
<tr><td>1</td><td style="background-color:lightgreen;">1.56</td><td style="background-color:lightgreen;">1.31</td><td style="background-color:lightpink;">0.00</td><td> </td><td style="background-color:lightgreen;">1.62</td></tr>
<tr><td>2</td><td style="background-color:lightgreen;">2.12</td><td style="background-color:lightgreen;">1.85</td><td style="background-color:lightgreen;">2.56</td><td> </td><td style="background-color:lightgreen;">2.41</td></tr>
<tr><td>3</td><td> </td><td style="background-color:lightgreen;">2.68</td><td style="background-color:lightgreen;">3.01</td><td style="background-color:lightpink;">0.00</td><td style="background-color:lightgreen;">2.94</td></tr>
<tr><td>4</td><td style="background-color:lightpink;">0.00</td><td style="background-color:lightgreen;">3.59</td><td style="background-color:lightgreen;">3.77</td><td> </td><td style="background-color:lightgreen;">3.70</td></tr>
<tr><td>5</td><td style="background-color:lightpink;">0.00</td><td style="background-color:lightgreen;">5.46</td><td style="background-color:lightgreen;">4.88</td><td> </td><td style="background-color:lightgreen;">5.22</td></tr>
<tr><td>6</td><td> </td><td> </td><td style="background-color:lightgreen;">6.89</td><td style="background-color:lightpink;">4.00</td><td style="background-color:lightgreen;">6.87</td></tr>
<tr><td>7</td><td> </td><td> </td><td style="background-color:lightblue;">9.29</td><td style="background-color:lightgreen;">7.55</td><td style="background-color:lightgreen;">8.36</td></tr>
<tr><td>8</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">9.80</td><td style="background-color:lightpink;">9.80</td></tr>
<tr><td>9</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">2.24</td><td style="background-color:lightpink;">2.24</td></tr>
<tr><td>10</td><td> </td><td> </td><td> </td><td style="background-color:lightblue;">14.33</td><td style="background-color:lightblue;">14.33</td></tr>
<tr><td>11</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">7.59</td><td style="background-color:lightpink;">7.59</td></tr>
<tr><td>12</td><td> </td><td> </td><td style="background-color:lightpink;">9.17</td><td style="background-color:lightpink;">9.40</td><td style="background-color:lightblue;">11.85</td></tr>
<tr><td>13</td><td> </td><td> </td><td style="background-color:lightpink;">9.09</td><td style="background-color:lightpink;">11.11</td><td style="background-color:lightblue;">10.61</td></tr>
<tr><td>14</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">31.60</td><td style="background-color:lightpink;">31.60</td></tr>
<tr><td>15</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">0.00</td><td style="background-color:lightpink;">0.00</td></tr>
<tr><td>16</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>17</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>18</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">2.00</td><td style="background-color:lightpink;">2.00</td></tr>
<tr><td>19</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>20</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">6.00</td><td style="background-color:lightpink;">6.00</td></tr>
<tr><th>Total</th><th>2.27</th><th>4.88</th><th>10.20</th><th>21.84</th><th>15.83</th></tr>
</table></div>
<p>When looking at the stdev table we need to remember to ignore the pink data points. The low amount of data makes these cells very "swingy". That's why we have some cells with a value of 0.00 (there's only one sample, or the small number of samples have the same value). In other cases it results in quite large values (like 31.60).</p>
<p>Again, there is the linear increase in variation each level.</p>
<p>We'll face similar issues to our hitpoint analysis here. That's mostly associated with sparseness of data at higher levels. But, as before, the blue datapoints at levels 10, 12 and 13 can be used to guide us and the pink data points may be handy as very rough indicators that we are in the neighbourhood of what we need.</p>
<p style="clear:both;"> </p>
<div class="datagrid"><table style="width:300px;">
<tr><th colspan="6">At-Will Damage Average by XP</th></tr>
<tr><th>Level</th><th>Easy</th><th>Average</th><th>Tough</th><th>Solo</th><th>Total</th></tr>
<tr><td>1</td><td style="background-color:lightgreen;">3.61</td><td style="background-color:lightgreen;">4.77</td><td style="background-color:lightpink;">8.00</td><td> </td><td style="background-color:lightgreen;">4.08</td></tr>
<tr><td>2</td><td style="background-color:lightgreen;">6.25</td><td style="background-color:lightgreen;">6.50</td><td style="background-color:lightgreen;">8.70</td><td> </td><td style="background-color:lightgreen;">7.10</td></tr>
<tr><td>3</td><td> </td><td style="background-color:lightgreen;">8.04</td><td style="background-color:lightgreen;">9.32</td><td style="background-color:lightpink;">12.00</td><td style="background-color:lightgreen;">8.77</td></tr>
<tr><td>4</td><td style="background-color:lightpink;">9.00</td><td style="background-color:lightgreen;">10.96</td><td style="background-color:lightgreen;">12.09</td><td> </td><td style="background-color:lightgreen;">11.43</td></tr>
<tr><td>5</td><td style="background-color:lightpink;">11.00</td><td style="background-color:lightgreen;">14.44</td><td style="background-color:lightgreen;">14.17</td><td> </td><td style="background-color:lightgreen;">14.28</td></tr>
<tr><td>6</td><td> </td><td> </td><td style="background-color:lightgreen;">18.48</td><td style="background-color:lightpink;">13.00</td><td style="background-color:lightgreen;">18.17</td></tr>
<tr><td>7</td><td> </td><td> </td><td style="background-color:lightblue;">23.00</td><td style="background-color:lightgreen;">27.96</td><td style="background-color:lightgreen;">26.61</td></tr>
<tr><td>8</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">27.70</td><td style="background-color:lightpink;">27.70</td></tr>
<tr><td>9</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">36.40</td><td style="background-color:lightpink;">36.40</td></tr>
<tr><td>10</td><td> </td><td> </td><td> </td><td style="background-color:lightblue;">36.61</td><td style="background-color:lightblue;">36.61</td></tr>
<tr><td>11</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">58.33</td><td style="background-color:lightpink;">58.33</td></tr>
<tr><td>12</td><td> </td><td> </td><td style="background-color:lightpink;">40.07</td><td style="background-color:lightpink;">56.25</td><td style="background-color:lightblue;">44.93</td></tr>
<tr><td>13</td><td> </td><td> </td><td style="background-color:lightpink;">54.00</td><td style="background-color:lightpink;">56.57</td><td style="background-color:lightblue;">55.80</td></tr>
<tr><td>14</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">66.50</td><td style="background-color:lightpink;">66.50</td></tr>
<tr><td>15</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">86.00</td><td style="background-color:lightpink;">86.00</td></tr>
<tr><td>16</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>17</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>18</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">94.00</td><td style="background-color:lightpink;">94.00</td></tr>
<tr><td>19</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>20</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">82.00</td><td style="background-color:lightpink;">82.00</td></tr>
<tr><th>Total</th><th>4.50</th><th>9.28</th><th>15.29</th><th>40.90</th><th>15.47</th></tr>
</table></div>
<h3><u>Average Tables</u></h3>
<p>What we find when we start digging through the averages is a lot of similarity with hitpoints. The values may be lower, but the patterns are very similar. Some of this is due to our categorisation methods, but many of these similarities persist between the "by HP" and "by XP" views. This not unexpected and another good sign that our theories on the relationships between the different PC and monster stats are on the right track.</p>
<p>Again, it's very obvious that there's a relationship between each type of monster at a given level. If you are having trouble seeing this try looking at the bottom total. That's an obviously skewed summary, one that inflates Solo creatures somewhat. But it does give you a feel of the relationships.</p>
<p>The same apparent miscategorisation we noticed in the hitpoints analysis is also present. Closer examination shows us there really don't seem to be any Tough creatures at levels 12 and 13. For those we'll again just use the Total in the Solo column's place.</p>
<p style="clear:both;"> </p>
<div class="datagrid"><table style="width:300px;">
<tr><th colspan="6">DPR Average by XP</th></tr>
<tr><th>Level</th><th>Easy</th><th>Average</th><th>Tough</th><th>Solo</th><th>Total</th></tr>
<tr><td>1</td><td style="background-color:lightgreen;">3.75</td><td style="background-color:lightgreen;">4.98</td><td style="background-color:lightpink;">8.00</td><td> </td><td style="background-color:lightgreen;">4.25</td></tr>
<tr><td>2</td><td style="background-color:lightgreen;">6.52</td><td style="background-color:lightgreen;">6.81</td><td style="background-color:lightgreen;">8.98</td><td> </td><td style="background-color:lightgreen;">7.39</td></tr>
<tr><td>3</td><td> </td><td style="background-color:lightgreen;">8.27</td><td style="background-color:lightgreen;">9.97</td><td style="background-color:lightpink;">12.00</td><td style="background-color:lightgreen;">9.21</td></tr>
<tr><td>4</td><td style="background-color:lightpink;">9.00</td><td style="background-color:lightgreen;">11.67</td><td style="background-color:lightgreen;">12.67</td><td> </td><td style="background-color:lightgreen;">12.07</td></tr>
<tr><td>5</td><td style="background-color:lightpink;">11.00</td><td style="background-color:lightgreen;">15.17</td><td style="background-color:lightgreen;">15.18</td><td> </td><td style="background-color:lightgreen;">15.11</td></tr>
<tr><td>6</td><td> </td><td> </td><td style="background-color:lightgreen;">20.05</td><td style="background-color:lightpink;">13.00</td><td style="background-color:lightgreen;">19.64</td></tr>
<tr><td>7</td><td> </td><td> </td><td style="background-color:lightblue;">27.71</td><td style="background-color:lightgreen;">30.17</td><td style="background-color:lightgreen;">29.52</td></tr>
<tr><td>8</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">35.93</td><td style="background-color:lightpink;">35.93</td></tr>
<tr><td>9</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">38.57</td><td style="background-color:lightpink;">38.57</td></tr>
<tr><td>10</td><td> </td><td> </td><td> </td><td style="background-color:lightblue;">39.57</td><td style="background-color:lightblue;">39.57</td></tr>
<tr><td>11</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">59.42</td><td style="background-color:lightpink;">59.42</td></tr>
<tr><td>12</td><td> </td><td> </td><td style="background-color:lightpink;">41.32</td><td style="background-color:lightpink;">59.69</td><td style="background-color:lightblue;">46.83</td></tr>
<tr><td>13</td><td> </td><td> </td><td style="background-color:lightpink;">57.00</td><td style="background-color:lightpink;">56.92</td><td style="background-color:lightblue;">56.94</td></tr>
<tr><td>14</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">69.88</td><td style="background-color:lightpink;">69.88</td></tr>
<tr><td>15</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">86.00</td><td style="background-color:lightpink;">86.00</td></tr>
<tr><td>16</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>17</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>18</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">94.00</td><td style="background-color:lightpink;">94.00</td></tr>
<tr><td>19</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>20</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">106.00</td><td style="background-color:lightpink;">106.00</td></tr>
<tr><th>Total</th><th>4.67</th><th>9.75</th><th>16.40</th><th>43.78</th><th>16.54</th></tr>
</table></div>
<p>As with the hitpoints analysis all four tables look like promising ways of reconstructing monster damage data.</p>
<p>And, again, I'll opt to build all four and then compare them. I won't bore my dear readers with an explanation of why.</p>
<p>Time to check out the graphs.</p>
<p style="clear:both;"> </p>
<h3><u>Graphs</u></h3>
<a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_dmg_atwill_by_hp.png" imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_dmg_atwill_by_hp.png" height="192" width="320" alt="At-Will Damage by HP" /></a>
<a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_dmg_atwill_by_xp.png" imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_dmg_atwill_by_xp.png" height="192" width="320" alt="At-Will Damage by XP" /></a>
<a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_dmg_dpr_by_hp.png" imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_dmg_dpr_by_hp.png" height="192" width="320" alt="DPR by HP" /></a>
<a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_dmg_dpr_by_xp.png" imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_dmg_dpr_by_xp.png" height="192" width="320" alt="DPR by XP" /></a>
<p>Right now many of you are probably sitting there saying to yourselves "Er. If the Damage data is so similar to the Hitpoints data, <b>why</b> do the graphs look so different?!?" And that's a fair question.</p>
<p>There are several reasons for the apparent differences. The scale is, of course, different and this accounts for some of the variation. The way the actual averages fall out within the scale is a little different to, which is to be expected but nonetheless contributes to the apparent differences.</p>
<p>The most obvious difference is in the trendlines, but we do expect some of our trendlines to wander because of the scant data above level 7. But if we remove the trendlines we see that the general placement of all the datapoints is very similar. And, as mentioned in the <b>Average Tables</b> section, the distances between the different types at each level are relatively close.</p>
<p>The patterns are close. And although the trendlines are really only a useful guide or indicator, they look more useful for damage analysis than for hitpoint analysis.</p>
<p>These graphs also give us another important clue. If you go back and look at the graphs for hitpoints and think about how the datapoints are clustered around the trendlines you'll see that it's about the same for the two "by HP" graphs and the same again for the two "by XP" graphs - the clustering is only very slightly "tighter" for the "HP Calc" graph in each pair... But these graphs are a different story. In these graphs the data for the DPR version of each pair is a good deal more tightly clustered around it's trendline, which is predictably most noticable with the Solo datapoints and trendline.</p>
<p>This is a pretty solid indicator that the math behind monster damage is built around projected DPR, rather than "At-Will" DPR. I'll still create all four tables, but that's my tip for this one.</p>
<p style="clear:both;"> </p>
<h3><u>Choosing Between Damage Tables</u></h3>
<p>After building the four tables I like to go back and examine each. How close is the table to the original? Is there a section of the table that doesn't match the table we are trying to duplicate? Or are there small variations scattered throughout? What about the base numbers? Are they unusual numbers like 4.23791? Or are they close to more "natural" numbers for humans to use? And the derived numbers?</p>
<p>What's quickly obvious is that the "by HP" tables aren't a great match. We can set up forumals so that most of the table matches fairly well - but ther's always a section of the resultant table that "drifts" away from the source table. That's a pretty good indication that we are on the wrong track.</p>
<p>The "by XP" tables, on the other hand, tend to line up easily and naturally. We do have small variations scattered throughout the table, but that's something we'd expect - it's highly unlikely our sample data is will just spell the table out for us, we expect variation. The "DPR by XP" table, in particular, is a very close match that uses natural values and increments. It's the best match, so my tip panned out on this occasion. Sometimes we get lucky, other times we have to keep slogging through until we find what we need.</p>
<p style="clear:both;"> </p>
<h3><u>Damage Table</u></h3>
<div class="bluegrid"><table style="width:250px;">
<tr><th>Level</th><th>Easy</th><th>Average</th><th>Hard</th><th>Solo</th></tr>
<tr><td>1</td><td>4.00</td><td>5.00</td><td>6.00</td><td>10.00</td></tr>
<tr><td>2</td><td>6.00</td><td>7.50</td><td>9.00</td><td>15.00</td></tr>
<tr><td>3</td><td>8.00</td><td>10.00</td><td>12.00</td><td>20.00</td></tr>
<tr><td>4</td><td>10.00</td><td>12.50</td><td>15.00</td><td>25.00</td></tr>
<tr><td>5</td><td>12.00</td><td>15.00</td><td>18.00</td><td>30.00</td></tr>
<tr><td>6</td><td>14.00</td><td>17.50</td><td>21.00</td><td>35.00</td></tr>
<tr><td>7</td><td>16.00</td><td>20.00</td><td>24.00</td><td>40.00</td></tr>
<tr><td>8</td><td>18.00</td><td>22.50</td><td>27.00</td><td>45.00</td></tr>
<tr><td>9</td><td>20.00</td><td>25.00</td><td>30.00</td><td>50.00</td></tr>
<tr><td>10</td><td>22.00</td><td>27.50</td><td>33.00</td><td>55.00</td></tr>
<tr><td>11</td><td>24.00</td><td>30.00</td><td>36.00</td><td>60.00</td></tr>
<tr><td>12</td><td>26.00</td><td>32.50</td><td>39.00</td><td>65.00</td></tr>
<tr><td>13</td><td>28.00</td><td>35.00</td><td>42.00</td><td>70.00</td></tr>
<tr><td>14</td><td>30.00</td><td>37.50</td><td>45.00</td><td>75.00</td></tr>
<tr><td>15</td><td>32.00</td><td>40.00</td><td>48.00</td><td>80.00</td></tr>
<tr><td>16</td><td>34.00</td><td>42.50</td><td>51.00</td><td>85.00</td></tr>
<tr><td>17</td><td>36.00</td><td>45.00</td><td>54.00</td><td>90.00</td></tr>
<tr><td>18</td><td>38.00</td><td>47.50</td><td>57.00</td><td>95.00</td></tr>
<tr><td>19</td><td>40.00</td><td>50.00</td><td>60.00</td><td>100.00</td></tr>
<tr><td>20</td><td>42.00</td><td>52.50</td><td>63.00</td><td>105.00</td></tr>
</table></div>
<p>The damage table is even simpler than the hitpoints table! Average damage for a level is obtained by taking level, adding one and multiplying the result by 2.5. An easy creature only inflicts 80% of an Average creature's damage, while a Hard creature inflicts %120 of that damage and a Solo inflicts 200% of that damage.</p>
<p>This can be expressed as...
<ul> <li> Average_Dmg = (level + 1) x 2.5</li>
<li> Easy_Dmg = Average_HP x 0.8</li>
<li> Tough_Dmg = Average_HP x 1.2</li>
<li> Solo_Dmg = Average_HP x 2.0</li>
</ul></p>
<p>This particular table aligns quite nicely with our source table, with most of the green/blue values being very close. A few do, of course, deviate from our source data. But this is easily accounted for by variations in the source data and certainly within expectations.</p>
<p>So how much can we adjustment a creature's damage without causing problems? We do see variation of 25%-30% of DPR within any given level and type, but that will normally be accompanied by adjustment of other attributes - as it should be. I'll stick with what I said about hitpoints - I wouldn't recommend adjusting by more than +/-2% of damage without compensating elsewhere.</p>
<p>My biggest concern with damage is, again, Solo creatures. As with hitpoints, there's a disparity between their XP award and their damage output. I do understand that having a creature that does an average of almost an entire PC's hitpoints in damage is a problem. But I'm not sure that the answer to that is docking their damage output. We'll look at how we can improve Solo creatures in a later installment of this series.</p>
<p style="clear:both;"> </p>
<h3><u>Validation</u></h3>
<p>Our primary validation of monster damage is against PC hitpoints. If we divide the Damage for an Average creature at a given level by the hitpoints of an average PC of the same level we get a fraction. That fraction is the percent of PC hitpoints that Average monster does. If there is a direct relatonship between the two then this number should stay fairly constant through the levels. And what we see is that this number averages 0.23 (23%) with a variance of 0.000 and a stdev of 0.008. Which is pretty compelling!</p>
<p>Our secondary validation was against PC damage. Monster damage starts out at about 41% of PC damage and slowly progress to 131% of PC damage. This sounds weird, but if we look more closely we see that most of this disparity is in the first couple of levels. At level three it's 75% of PC damage and progresses evenly.</p>
<p>So, while Solo creatures ahve some shortcomings that need to be addressed this table should closely reflect the current damage progression and be suitable for most DMs to use.</p>
<p> </p>
<p style="clear:both;"> </p>
<span style="color:lightyellow;"><p>Check back tomorrow for the next installment <a href="http://surfarcher.blogspot.com/2013/08/d-next-monsters-part-8-putting-it-all.html">Part 8: Putting It All Together</a>...</p></span>
Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-60032389212099588412013-08-12T07:00:00.000+09:302013-08-19T07:59:45.767+09:30D&D Next Monsters: Part 6: Hitpoint Analysis...<span style="color:red;"><p><i>While this blog does <u>not</u> contain material published by Wizards of the Coast it does contain materials summarized and extrapolated from the D&D Next playtest packets. By continuing to read this blog you are consenting to the terms of the Wizards online playtest agreement, which you can view at <a href="http://www.dndnext.com/">dndnext.com</a>.</i></p></span>
<span style="color:lightyellow;"><p><i>In the last couple of articles Surf examined both Armor Class and Attack bonus. He now turns his attention to Hit Points....</i></p></span>
<p>One thing that becomes quickly obvious to someone browsing <i>D&D Next</i> monsters is that Bounded Accuracy doesn’t apply to hitpoints. The system uses hitpoints, and by association damage, to scale up levels. What we expect here is a steady linear increase over levels, but one higher (or “faster”) than the increase of AC and Attack bonus.</p>
<p style="clear:both;"> </p>
<h3><u>High-Level Data</u></h3>
<p>During this particular analysis we consider both the “natural” creature hitpoints and the “modified” hitpoints. </p>
<div class="textgrid"><table style="width:125px;float:none;">
<tr><th> </th><th><u>HP Std</u></th><th><u>HP Mod</u></th></tr>
<tr><td>Average:</td><td>43.57</td><td>48.00</td></tr>
<tr><td>Stdev:</td><td>43.23</td><td>48.04</td></tr>
<tr><td>Var:</td><td>1,869.15</td><td>2,307.94</td></tr>
</table></div>
<p>What we see here is that hitpoints are much more variable within the data than AC or Attack Bonus. This provides some support for our initial thoughts on hitpoints.</p>
<div class="datagrid"><table style="width:300px;">
<tr><th colspan="6">StdDevp of HP Std by XP</th></tr>
<tr><th>Level</th><th>Easy</th><th>Average</th><th>Tough</th><th>Solo</th><th>Total</th></tr>
<tr><td>1</td><td style="background-color:lightgreen;">3.04</td><td style="background-color:lightgreen;">2.89</td><td style="background-color:lightpink;">0.00</td><td> </td><td style="background-color:lightgreen;">3.74</td></tr>
<tr><td>2</td><td style="background-color:lightgreen;">3.06</td><td style="background-color:lightgreen;">4.52</td><td style="background-color:lightgreen;">9.97</td><td> </td><td style="background-color:lightgreen;">7.03</td></tr>
<tr><td>3</td><td> </td><td style="background-color:lightgreen;">11.59</td><td style="background-color:lightgreen;">16.79</td><td style="background-color:lightpink;">0.00</td><td style="background-color:lightgreen;">14.49</td></tr>
<tr><td>4</td><td style="background-color:lightpink;">0.00</td><td style="background-color:lightgreen;">7.32</td><td style="background-color:lightgreen;">11.10</td><td> </td><td style="background-color:lightgreen;">9.51</td></tr>
<tr><td>5</td><td style="background-color:lightpink;">0.00</td><td style="background-color:lightgreen;">9.94</td><td style="background-color:lightgreen;">14.19</td><td> </td><td style="background-color:lightgreen;">12.48</td></tr>
<tr><td>6</td><td> </td><td> </td><td style="background-color:lightgreen;">16.99</td><td style="background-color:lightpink;">8.00</td><td style="background-color:lightgreen;">16.61</td></tr>
<tr><td>7</td><td> </td><td> </td><td style="background-color:lightblue;">17.32</td><td style="background-color:lightgreen;">24.59</td><td style="background-color:lightgreen;">25.24</td></tr>
<tr><td>8</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">12.35</td><td style="background-color:lightpink;">12.35</td></tr>
<tr><td>9</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">30.10</td><td style="background-color:lightpink;">30.10</td></tr>
<tr><td>10</td><td> </td><td> </td><td> </td><td style="background-color:lightblue;">45.86</td><td style="background-color:lightblue;">45.86</td></tr>
<tr><td>11</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">28.71</td><td style="background-color:lightpink;">28.71</td></tr>
<tr><td>12</td><td> </td><td> </td><td style="background-color:lightpink;">37.60</td><td style="background-color:lightpink;">23.70</td><td style="background-color:lightblue;">34.95</td></tr>
<tr><td>13</td><td> </td><td> </td><td style="background-color:lightpink;">30.24</td><td style="background-color:lightpink;">41.26</td><td style="background-color:lightblue;">41.26</td></tr>
<tr><td>14</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">29.30</td><td style="background-color:lightpink;">29.30</td></tr>
<tr><td>15</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">0.00</td><td style="background-color:lightpink;">0.00</td></tr>
<tr><td>16</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>17</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>18</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">28.50</td><td style="background-color:lightpink;">28.50</td></tr>
<tr><td>19</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>20</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">25.50</td><td style="background-color:lightpink;">25.50</td></tr>
<tr><th>Total</th><th>6.36</th><th>13.47</th><th>35.54</th><th>47.00</th><th>43.19</th></tr>
</table></div>
<p>If we are correct we should also see a relatively linear increase in deviation each level. Considering only our green and blue cells that does seem to be the case.</p>
<p>The problem here is that it’s more difficult to be sure we have picked the right target number at the upper levels, where there’s less data. We’ll do what we have done previously - try to ensure levels 1-7 are quite close and that levels 10, 12 and 13 aren’t too far off. And we’ll hopefully end up in roughly the right neighbourhood for level 20.</p>
<p>Something else we need to be mindful of here is using the “by HP” division. We are examining the hitpoints of our data and using the category based on our arbitrary ideas of hitpoint division will likely introduce an artificial skew to our results. So we can look at those divisions, but where there’s a discrepancy between it and the “by XP” category we should go with the XP category.</p>
<p style="clear:both;"> </p>
<div class="datagrid"><table style="width:300px;">
<tr><th colspan="6">HP Std Average by XP</th></tr>
<tr><th>Level</th><th>Easy</th><th>Average</th><th>Tough</th><th>Solo</th><th>Total</th></tr>
<tr><td>1</td><td style="background-color:lightgreen;">5.50</td><td style="background-color:lightgreen;">10.17</td><td style="background-color:lightpink;">11.00</td><td> </td><td style="background-color:lightgreen;">7.22</td></tr>
<tr><td>2</td><td style="background-color:lightgreen;">13.05</td><td style="background-color:lightgreen;">15.90</td><td style="background-color:lightgreen;">20.36</td><td> </td><td style="background-color:lightgreen;">16.47</td></tr>
<tr><td>3</td><td> </td><td style="background-color:lightgreen;">24.21</td><td style="background-color:lightgreen;">26.65</td><td style="background-color:lightpink;">27.00</td><td style="background-color:lightgreen;">25.52</td></tr>
<tr><td>4</td><td style="background-color:lightpink;">22.00</td><td style="background-color:lightgreen;">30.90</td><td style="background-color:lightgreen;">35.59</td><td> </td><td style="background-color:lightgreen;">32.84</td></tr>
<tr><td>5</td><td style="background-color:lightpink;">44.00</td><td style="background-color:lightgreen;">40.86</td><td style="background-color:lightgreen;">49.96</td><td> </td><td style="background-color:lightgreen;">44.40</td></tr>
<tr><td>6</td><td> </td><td> </td><td style="background-color:lightgreen;">58.61</td><td style="background-color:lightpink;">60.00</td><td style="background-color:lightgreen;">58.69</td></tr>
<tr><td>7</td><td> </td><td> </td><td style="background-color:lightblue;">60.89</td><td style="background-color:lightgreen;">85.00</td><td style="background-color:lightgreen;">78.62</td></tr>
<tr><td>8</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">65.80</td><td style="background-color:lightpink;">65.80</td></tr>
<tr><td>9</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">126.60</td><td style="background-color:lightpink;">126.60</td></tr>
<tr><td>10</td><td> </td><td> </td><td> </td><td style="background-color:lightblue;">118.64</td><td style="background-color:lightblue;">118.64</td></tr>
<tr><td>11</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">124.67</td><td style="background-color:lightpink;">124.67</td></tr>
<tr><td>12</td><td> </td><td> </td><td style="background-color:lightpink;">146.71</td><td style="background-color:lightpink;">129.33</td><td style="background-color:lightblue;">141.50</td></tr>
<tr><td>13</td><td> </td><td> </td><td style="background-color:lightpink;">175.00</td><td style="background-color:lightpink;">141.43</td><td style="background-color:lightblue;">151.50</td></tr>
<tr><td>14</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">149.00</td><td style="background-color:lightpink;">149.00</td></tr>
<tr><td>15</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">142.00</td><td style="background-color:lightpink;">142.00</td></tr>
<tr><td>16</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>17</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>18</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">178.50</td><td style="background-color:lightpink;">178.50</td></tr>
<tr><td>19</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>20</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">224.50</td><td style="background-color:lightpink;">224.50</td></tr>
<tr><th>Total</th><th>8.28</th><th>25.50</th><th>47.25</th><th>110.69</th><th>43.58</th></tr>
</table></div>
<h3><u>Average Tables</u></h3>
<p>The first thing that jumps out to me here is the obvious relationship between the different types of monster at any given level. If we determine the mathematical relationship between these then determining the hitpoint progression for all of them will be simplified – we can determine any other type based on a single type of the same level.</p>
<p>Consider how RPG designers typically build these tables – they decide on a starting value, a progression and how the adjacent types are derived. It follows that the easiest way to reconstruct a table is to use the same approach.</p>
<p>So we’ll determine an Average progression and build the entire table from there. That will let us ensure that our green and blue data points align closely and that our handful of creatures in the level 14+ region are in the right neighbourhood.</p>
<p>The other thing I notice thing a number of the creatures seem to be miscategorised, mainly because their XP value seems low for their type. Most importantly the Tough creatures at levels 12 and 13 are probably Solo creatures. The “by HP” table supports this idea and being able to use the average of these two rows should help us build a more accurate table.</p>
<p style="clear:both;"> </p>
<div class="datagrid"><table style="width:300px;">
<tr><th colspan="6">HP Calc Average by XP</th></tr>
<tr><th>Level</th><th>Easy</th><th>Average</th><th>Tough</th><th>Solo</th><th>Total</th></tr>
<tr><td>1</td><td style="background-color:lightgreen;">5.58</td><td style="background-color:lightgreen;">10.50</td><td style="background-color:lightpink;">11.00</td><td> </td><td style="background-color:lightgreen;">7.42</td></tr>
<tr><td>2</td><td style="background-color:lightgreen;">13.85</td><td style="background-color:lightgreen;">16.17</td><td style="background-color:lightgreen;">21.50</td><td> </td><td style="background-color:lightgreen;">17.15</td></tr>
<tr><td>3</td><td> </td><td style="background-color:lightgreen;">25.91</td><td style="background-color:lightgreen;">29.34</td><td style="background-color:lightpink;">27.00</td><td style="background-color:lightgreen;">27.70</td></tr>
<tr><td>4</td><td style="background-color:lightpink;">22.00</td><td style="background-color:lightgreen;">33.63</td><td style="background-color:lightgreen;">37.59</td><td> </td><td style="background-color:lightgreen;">35.21</td></tr>
<tr><td>5</td><td style="background-color:lightpink;">44.00</td><td style="background-color:lightgreen;">45.02</td><td style="background-color:lightgreen;">52.39</td><td> </td><td style="background-color:lightgreen;">47.83</td></tr>
<tr><td>6</td><td> </td><td> </td><td style="background-color:lightgreen;">64.15</td><td style="background-color:lightpink;">66.00</td><td style="background-color:lightgreen;">64.26</td></tr>
<tr><td>7</td><td> </td><td> </td><td style="background-color:lightblue;">70.44</td><td style="background-color:lightgreen;">90.76</td><td style="background-color:lightgreen;">85.38</td></tr>
<tr><td>8</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">90.00</td><td style="background-color:lightpink;">90.00</td></tr>
<tr><td>9</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">130.20</td><td style="background-color:lightpink;">130.20</td></tr>
<tr><td>10</td><td> </td><td> </td><td> </td><td style="background-color:lightblue;">132.86</td><td style="background-color:lightblue;">132.86</td></tr>
<tr><td>11</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">134.00</td><td style="background-color:lightpink;">134.00</td></tr>
<tr><td>12</td><td> </td><td> </td><td style="background-color:lightpink;">163.86</td><td style="background-color:lightpink;">159.33</td><td style="background-color:lightblue;">162.50</td></tr>
<tr><td>13</td><td> </td><td> </td><td style="background-color:lightpink;">183.67</td><td style="background-color:lightpink;">163.71</td><td style="background-color:lightblue;">169.70</td></tr>
<tr><td>14</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">177.25</td><td style="background-color:lightpink;">177.25</td></tr>
<tr><td>15</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">180.00</td><td style="background-color:lightpink;">180.00</td></tr>
<tr><td>16</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>17</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>18</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">214.50</td><td style="background-color:lightpink;">214.50</td></tr>
<tr><td>19</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>20</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">264.50</td><td style="background-color:lightpink;">264.50</td></tr>
<tr><th>Total</th><th>8.55</th><th>27.39</th><th>51.25</th><th>125.16</th><th>47.86</th></tr>
</table></div>
<p>Both the “HP Std” and “HP Calc” tables are promising. In addition the “by HP” and “by XP” divisions both have some interesting variations within them.</p>
<p>Any of these four tables <i>might</i> provide the data that <i>D&D Next</i> monsters are based upon.</p>
<p>Of course, the best approach is to build all four tables! Then we can reflect on what it took to reproduce the tables and which we believe is the right one.</p>
<p>But before we do that let’s have a look at the graphs...</p>
<p style="clear:both;"> </p>
<h3><u>Graphs</u></h3>
<a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_hp_std_by_hp.png" imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_hp_std_by_hp.png" height="192" width="320" alt="HP Std by HP" /></a>
<a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_hp_std_by_xp.png" imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_hp_std_by_xp.png" height="192" width="320" alt="HP Std by XP" /></a>
<a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_hp_calc_by_hp.png" imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_hp_calc_by_hp.png" height="192" width="320" alt="HP Calc by HP" /></a>
<a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_hp_calc_by_xp.png" imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_hp_calc_by_xp.png" height="192" width="320" alt="HP Calc by XP" /></a>
<p>The very first thing that I noticed with these graphs was… Well to be honest it was the variability of most of the trendlines! But that lead me to consider which trendlines show <i>some</i> kind of stability. And my isn’t that Solo trendline stable! Yes, this is mainly because there are Solo monsters scattered across the levels. And yes, many of these are sparse and we shouldn’t have too much confidence in them. But all in all we should be able to rely on our Solo progression running somewhere near to this trendline.</p>
<p>The Average trendline is also more stable than a first glance leads one to believe. Yes, it gets variable between our two categories (“by HP” and “by XP”), but again we did expect that.</p>
<p>Overall I feel confident that determining a good Average progression and extending this across the adjacent monster types, and ensuring the end result aligns with our green and blue cells is still the best plan.</p>
<p style="clear:both;"> </p>
<h3><u>Choosing Between HP Tables</u></h3>
<p>As previously noted I went ahead and built out all four variations of the hitpoints table. There was a lot of boring “too-ing and fro-ing” that doesn’t bear detailing here.</p>
<p>While almost any numerical table can be built, assuming sufficient computing power, that really isn’t necessary. When we start having to us complex polynomials and sliding variables we are getting well outside the complexity of roleplaying game tables! This simplified matters somewhat and four tables were built with a minimum of fuss.</p>
<p>So how do we decide which one to use? Well, as I said “things aren’t normally that complex”. So when I have to decide between a table that scales using a long decimal point and one that doesn’t. When the simpler one aligns better with the actual observed data. Well that makes the decision pretty easy.</p>
<p>And the upshot of <i>that</i> is that <i>Wizards of the Coast</i> don’t appear to be using a higher value for hitpoints and subtracting “notional hitpoints” from it to allow for resistances, healing and similar... Not in most cases, anyway. Rather they are assuming that creatures at a certain level will have a similar amount of damage mitigation in addition to their hitpoints. Yep, DR just became part of the core mechanics again.</p>
<p style="clear:both;"> </p>
<h3><u>Hitpoints Table</u></h3>
<div class="bluegrid"><table style="width:250px;">
<tr><th>Level</th><th>Easy</th><th>Average</th><th>Hard</th><th>Solo</th></tr>
<tr><td>1</td><td>7.00</td><td>10.00</td><td>13.00</td><td>20.00</td></tr>
<tr><td>2</td><td>10.85</td><td>15.50</td><td>20.15</td><td>31.00</td></tr>
<tr><td>3</td><td>14.70</td><td>21.00</td><td>27.30</td><td>42.00</td></tr>
<tr><td>4</td><td>18.55</td><td>26.50</td><td>34.45</td><td>53.00</td></tr>
<tr><td>5</td><td>22.40</td><td>32.00</td><td>41.60</td><td>64.00</td></tr>
<tr><td>6</td><td>26.25</td><td>37.50</td><td>48.75</td><td>75.00</td></tr>
<tr><td>7</td><td>30.10</td><td>43.00</td><td>55.90</td><td>86.00</td></tr>
<tr><td>8</td><td>33.95</td><td>48.50</td><td>63.05</td><td>97.00</td></tr>
<tr><td>9</td><td>37.80</td><td>54.00</td><td>70.20</td><td>108.00</td></tr>
<tr><td>10</td><td>41.65</td><td>59.50</td><td>77.35</td><td>119.00</td></tr>
<tr><td>11</td><td>45.50</td><td>65.00</td><td>84.50</td><td>130.00</td></tr>
<tr><td>12</td><td>49.35</td><td>70.50</td><td>91.65</td><td>141.00</td></tr>
<tr><td>13</td><td>53.20</td><td>76.00</td><td>98.80</td><td>152.00</td></tr>
<tr><td>14</td><td>57.05</td><td>81.50</td><td>105.95</td><td>163.00</td></tr>
<tr><td>15</td><td>60.90</td><td>87.00</td><td>113.10</td><td>174.00</td></tr>
<tr><td>16</td><td>64.75</td><td>92.50</td><td>120.25</td><td>185.00</td></tr>
<tr><td>17</td><td>68.60</td><td>98.00</td><td>127.40</td><td>196.00</td></tr>
<tr><td>18</td><td>72.45</td><td>103.50</td><td>134.55</td><td>207.00</td></tr>
<tr><td>19</td><td>76.30</td><td>109.00</td><td>141.70</td><td>218.00</td></tr>
<tr><td>20</td><td>80.15</td><td>114.50</td><td>148.85</td><td>229.00</td></tr>
</table></div>
<p>If we take 10 as our starting value for a level 1 Average creature and add 5.5 for each subsequent level we have a progression very close to what our sample data shows. Next we make an Easy worth 70% of an Average, a Tough 130% of Average and Solo worth 200% of Average.<p>
<p>This can be expressed as...
<ul> <li> Average_HP = 4.5 + (level x 5.5)</li>
<li> Easy_HP = Average_HP x 0.7</li>
<li> Tough_HP = Average_HP x 1.3</li>
<li> Solo_HP = Average_HP x 2.0</li>
</ul></p>
<p>This puts us very, very close to our observed data, providing maximum alignment with our blue and green data points...</p>
<p>We are out in a few places though… The amount of data we have to analyse is quite sparse and even our “green data points” are bound to deviate from the underlying proscribed value.</p>
<p>Adjustments seem to be pretty minimal. Regeneration does appear to be factored in (so subtract estimated regeneration per combat from total hitpoints), however resistance does not. Neither do most other forms of damage mitigation. I wouldn’t recommend varying hitpoints by more than +/-2% without being careful to compensate elsewhere.</p>
<p>I could complain here about the low volume of sample data and the uncertainty behind the samples that introduces, but the fact is that this table should work well for most DMs and is quite close to the current crop of monsters.</p>
<p>No, my big concern here is that this is an area where the math is probably wrong. The <i>D&D Next</i> community receives complaints almost daily about the weakness of monsters. And this weakness seems to become more pronounced at higher levels. <i>Wizards of the Coast</i> has generally acknowledged that this is the case and that monster math isn’t finalised yet. They quite rightly indicate that getting the core math correct is a necessary precursor to finalising monster math, since monster math is built upon the character system. Their current stop-gap is to simply adjust monster XP, with the occasional tweak to armor class or hitpoints.</p>
<p>What leads me to believe hitpoints are one of the main areas at fault? Well common sense and history provide some support. Consider the role hitpoints have played in basic monster math revisions in previous editions – most recently in 4th Edition. Hitpoints are one of the major design dials for monsters.</p>
<p>But more to the point the numbers support it. Let’s take a look at that now...</p>
<p style="clear:both;"> </p>
<h3><u>Validation</u></h3>
<p>You might remember back in the <a href="http://surfarcher.blogspot.com/2013/08/d-next-monsters-part-2-class.html">Part 2: Class Development Profiling</a> installment I indicated I’d validate monster hitpoints against PC damage, as the primary comparator, and PC hitpoints, as a secondary comparator. So I expect to see some kind of stable and/or predictable relationship with PC damage output. Since PC hitpoints increase faster than PC damage output I wouldn’t expect to see any constant relationship against it, tho I’d hope to see a trend of steady difference.</p>
<p>So imagine my surprise when I paste my proposed hitpoint table into my validation sheet and find a perfect fit… Against PC hitpoint progression!</p>
<p>Yes, the current monster damage progression is completely stable against PC hitpoints! An Average monster of a given level has half the hitpoints of a PC of the same level. How constant is that? Well the average is exactly 0.500 of PC hitpoints with a variance of 0.0002 and a stdev of 0.0141. That’s very, very stable!</p>
<p>This means that Average creatures take progressively more hits to kill, eventually many more than their XP award covers. This isn’t very noticeable at lower levels, where Average monsters are concentrated, and DMs and players using Averages won’t notice an issue. But as players level up the Tough and Solo creatures come progressively into play. But these are quite weak! A Solo has four time the XP of an Average, but Solo creatures at higher levels only have double the hitpoints of an Average creature... An Average creature that doesn’t exist at those levels.</p>
<p>While the table included in this instalment matches the current crop of monsters I consider it faulty and in serious need of correction... Which we’ll tackle a couple of instalments from now.</p>
<p> </p>
<p style="clear:both;"> </p>
<span style="color:lightyellow;"><p>Check back in a couple of days for the next installment <a href="http://surfarcher.blogspot.com/2013/08/d-next-monsters-part-7-damage-analysis.html">Part 7: Damage Analysis</a>...</p></span>
Anonymoushttp://www.blogger.com/profile/02897264071352128421noreply@blogger.com0tag:blogger.com,1999:blog-6511225892793734362.post-17792841244347688812013-08-09T07:00:00.000+09:302013-08-13T07:23:58.398+09:30D&D Next Monsters: Part 5: Attack Bonus Analysis...<span style="color:red;"><p><i>While this blog does <u>not</u> contain material published by Wizards of the Coast it does contain materials summarized and extrapolated from the D&D Next playtest packets. By continuing to read this blog you are consenting to the terms of the Wizards online playtest agreement, which you can view at <a href="http://www.dndnext.com/">dndnext.com</a>.</i></p></span>
<span style="color:lightyellow;"><p><i>In Part 4 Surf broke down Armor Class progression, showing how he approaches the analysis of these simpler linear progressions and finished off by producing an AC Progression table. This time he moves on it’s related neighbour – Attack bonus...</i></p></span>
<p>So looking at Armor Class was interesting, what will we see with monster accuracy? Well, let’s get stuck into it – it should be shorter than last time since we already covered the hows and whys...</p>
<p style="clear:both;"> </p>
<h3><u>High-Level Data</u></h3>
<p>As with Armor Class progression for Attack Bonus is linear and short. It’s also predictably less variable than Armor Class.</p>
<div class="textgrid"><table style="width:125px;float:none;">
<tr><td>Average:</td><td>5.48</td></tr>
<tr><td>Stdev:</td><td>1.64</td></tr>
<tr><td>Var:</td><td>2.69</td></tr>
</table></div>
<p>The standard deviation and variability at each level and data point match up with this, for all our green cells stddev averages 1.05 with most green and blue data points below 1.00. So even more than AC it’s obvious that attack bonus is a linear progression.</p>
<p style="clear:both;"> </p>
<div class="datagrid"><table style="width:300px;">
<tr><th colspan="6">Attack Mod Average by XP</th></tr>
<tr><th>Level</th><th>Easy</th><th>Average</th><th>Tough</th><th>Solo</th><th>Total</th></tr>
<tr><td>1</td><td style="background-color:lightgreen;">3.73</td><td style="background-color:lightgreen;">4.28</td><td style="background-color:lightpink;">5.00</td><td> </td><td style="background-color:lightgreen;">3.94</td></tr>
<tr><td>2</td><td style="background-color:lightgreen;">4.65</td><td style="background-color:lightgreen;">4.67</td><td style="background-color:lightgreen;">4.68</td><td> </td><td style="background-color:lightgreen;">4.67</td></tr>
<tr><td>3</td><td> </td><td style="background-color:lightgreen;">5.00</td><td style="background-color:lightgreen;">4.90</td><td style="background-color:lightpink;">6.00</td><td style="background-color:lightgreen;">4.97</td></tr>
<tr><td>4</td><td style="background-color:lightpink;">4.00</td><td style="background-color:lightgreen;">5.23</td><td style="background-color:lightgreen;">5.25</td><td> </td><td style="background-color:lightgreen;">5.22</td></tr>
<tr><td>5</td><td style="background-color:lightpink;">6.00</td><td style="background-color:lightgreen;">5.83</td><td style="background-color:lightgreen;">6.04</td><td> </td><td style="background-color:lightgreen;">5.92</td></tr>
<tr><td>6</td><td> </td><td> </td><td style="background-color:lightgreen;">6.72</td><td style="background-color:lightpink;">6.50</td><td style="background-color:lightgreen;">6.71</td></tr>
<tr><td>7</td><td> </td><td> </td><td style="background-color:lightblue;">6.22</td><td style="background-color:lightgreen;">7.08</td><td style="background-color:lightgreen;">6.85</td></tr>
<tr><td>8</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">7.40</td><td style="background-color:lightpink;">7.40</td></tr>
<tr><td>9</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">7.20</td><td style="background-color:lightpink;">7.20</td></tr>
<tr><td>10</td><td> </td><td> </td><td> </td><td style="background-color:lightblue;">7.43</td><td style="background-color:lightblue;">7.43</td></tr>
<tr><td>11</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">8.33</td><td style="background-color:lightpink;">8.33</td></tr>
<tr><td>12</td><td> </td><td> </td><td style="background-color:lightpink;">7.29</td><td style="background-color:lightpink;">5.00</td><td style="background-color:lightblue;">6.60</td></tr>
<tr><td>13</td><td> </td><td> </td><td style="background-color:lightpink;">9.00</td><td style="background-color:lightpink;">7.71</td><td style="background-color:lightblue;">8.10</td></tr>
<tr><td>14</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">9.00</td><td style="background-color:lightpink;">9.00</td></tr>
<tr><td>15</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">8.00</td><td style="background-color:lightpink;">8.00</td></tr>
<tr><td>16</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>17</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>18</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">8.50</td><td style="background-color:lightpink;">8.50</td></tr>
<tr><td>19</td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td>20</td><td> </td><td> </td><td> </td><td style="background-color:lightpink;">9.00</td><td style="background-color:lightpink;">9.00</td></tr>
<tr><th>Total</th><th>4.01</th><th>5.05</th><th>5.73</th><th>7.38</th><th>5.48</th></tr>
</table></div>
<h3><u>Getting Average</u></h3>
<p>If you are new to this game you could be forgiven for assuming that we can create a simple linear progression from 3.94 to 9.00. The sparse data from level 8 makes the second part a bit uncertain. The progression from level 1 to level 7 is a bit better. That would likely get us in the right ballpark. What we will need to do is ensure close alignment in our progression with the green data point values. The blue and pink ones… Well they aren’t quite as reliable and will need to be a rough guide.</p>
<p style="clear:both;"> </p>
<h3><u>Graphical Consideration</u></h3>
<a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_attack_by_hp.png" imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_attack_by_hp.png" height="192" width="320" alt="Attack bonus by HP" /></a>
<a href="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_attack_by_xp.png" imageanchor="1" style="clear:right;float:right;margin-bottom:1em;margin-left:1em;"><img border="0" src="https://googledrive.com/host/0B_Fd4t2Ho8GCRkFVeHNBTnVna28/dnm_attack_by_xp.png" height="192" width="320" alt="Attack bonus by XP" /></a>
<p>So what jumps out with the graphs is that almost all of the trendline bands align very closely. Yes the “thinness” of some of our data does give us a trendline or two that wanders, but we can ignore that, as long as we check that’s the reason the trendline wanders.</p>
<p>Both graphs show the trends are firmly anchored around 4 and head straight towards the neighbourhood of 10.</p>
<p>Looking at the data points, instead of lines we get a sense that our target is probably on the higher side of the end range.</p>
<p>Let’s see what we can construct to match this.</p>
<p style="clear:both;"> </p>
<h3><u>Attack Table</u></h3>
<div class="bluegrid"><table style="width:125px;">
<tr><th>Level</th><th>Attack</th></tr>
<tr><td>1</td><td>+4</td></tr>
<tr><td>2</td><td>+4</td></tr>
<tr><td>3</td><td>+5</td></tr>
<tr><td>4</td><td>+5</td></tr>
<tr><td>5</td><td>+5</td></tr>
<tr><td>6</td><td>+6</td></tr>
<tr><td>7</td><td>+6</td></tr>
<tr><td>8</td><td>+6</td></tr>
<tr><td>9</td><td>+6</td></tr>
<tr><td>10</td><td>+7</td></tr>
<tr><td>11</td><td>+7</td></tr>
<tr><td>12</td><td>+7</td></tr>
<tr><td>13</td><td>+8</td></tr>
<tr><td>14</td><td>+8</td></tr>
<tr><td>15</td><td>+8</td></tr>
<tr><td>16</td><td>+9</td></tr>
<tr><td>17</td><td>+9</td></tr>
<tr><td>18</td><td>+9</td></tr>
<tr><td>19</td><td>+9</td></tr>
<tr><td>20</td><td>+10</td></tr>
</table></div>
<p>If we take 3.9 at level one and 8.1 at level 13 and make a simple linear progression between them we’ll see that we have a progression of 0.35/level. By comparing this against our averages table we see that we very close to the totals columns for the green cells – in many cases about 0.1-ish away from the value. We can extend this progression down to level 20 and round off the decimal portion, giving us a value of 10.55.</p>
<p>We can tweak this quite easily from here to suit our purposes. Since my handy validation table drives right of my proposed table it’s very easy to seek a series step value that matches our observed data and results in minimal variability against our validation data.</p>
<p>In the end a starting value of 4.00 and a step size of 0.30 is pretty much spot on.</p>
<p>So what can we normally adjust, within the bands of whatever we choose as “normal”? Well as we noted the variance within these numbers is pretty low. I wouldn’t adjust Attack bonus more than +/-1 for most creatures. Say +/-2 for named opponents.</p>
<p>I have a couple of concerns about this progression. First, I’m not convinced <i>Wizards of the Coast</i> have properly anticipated the PCs ability to gain attack bonuses – for example we can expect most parties to have some buffs for every combat by say level 7. My other concern is, again, the lack of clear instruction about magic items – you really need to make sure you apply magic items to creatures before the fight if you are running a game with significant levels of magic. Simply rolling for loot after the fight and deciding if there’s a magic item is going to put your monsters at a disadvantage. Creatures fought should utilise magic items if they are items that have a combat impact.</p>
<p style="clear:both;"> </p>
<h3><u>Validation</u></h3>
<p>The main validation I used here was to subtract the attack bonus for each level from the average AC for PCs at the same level. This gave an average of 9.54 with a variance of 0.188 (stdev 0.434).</p>
<p>As a secondary validation I divided the attack bonus for the level by the average PC attack bonus for the same level. The result of this was an average of 0.89 with a variance of 0.002 (stdev 0.050).</p>
<p>Again, this gives me a high degree of confidence in the result.</p>
<p> </p>
<p style="clear:both;"> </p>
<span style="color:lightyellow;"><p>Check back in a couple of days for the next installment <a hreaf="http://surfarcher.blogspot.com/2013/08/d-next-monsters-part-6-hitpoint-analysis.html">Part 6: Hitpoint Analysis</a>...</p></span>
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