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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...
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...
High-Level Data
As with Armor Class progression for Attack Bonus is linear and short. It’s also predictably less variable than Armor Class.
| Average: | 5.48 |
| Stdev: | 1.64 |
| Var: | 2.69 |
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.
| Attack Mod Average by XP | |||||
|---|---|---|---|---|---|
| Level | Easy | Average | Tough | Solo | Total |
| 1 | 3.73 | 4.28 | 5.00 | 3.94 | |
| 2 | 4.65 | 4.67 | 4.68 | 4.67 | |
| 3 | 5.00 | 4.90 | 6.00 | 4.97 | |
| 4 | 4.00 | 5.23 | 5.25 | 5.22 | |
| 5 | 6.00 | 5.83 | 6.04 | 5.92 | |
| 6 | 6.72 | 6.50 | 6.71 | ||
| 7 | 6.22 | 7.08 | 6.85 | ||
| 8 | 7.40 | 7.40 | |||
| 9 | 7.20 | 7.20 | |||
| 10 | 7.43 | 7.43 | |||
| 11 | 8.33 | 8.33 | |||
| 12 | 7.29 | 5.00 | 6.60 | ||
| 13 | 9.00 | 7.71 | 8.10 | ||
| 14 | 9.00 | 9.00 | |||
| 15 | 8.00 | 8.00 | |||
| 16 | |||||
| 17 | |||||
| 18 | 8.50 | 8.50 | |||
| 19 | |||||
| 20 | 9.00 | 9.00 | |||
| Total | 4.01 | 5.05 | 5.73 | 7.38 | 5.48 |
Getting Average
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.
Graphical Consideration
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.
Both graphs show the trends are firmly anchored around 4 and head straight towards the neighbourhood of 10.
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.
Let’s see what we can construct to match this.
Attack Table
| Level | Attack |
|---|---|
| 1 | +4 |
| 2 | +4 |
| 3 | +5 |
| 4 | +5 |
| 5 | +5 |
| 6 | +6 |
| 7 | +6 |
| 8 | +6 |
| 9 | +6 |
| 10 | +7 |
| 11 | +7 |
| 12 | +7 |
| 13 | +8 |
| 14 | +8 |
| 15 | +8 |
| 16 | +9 |
| 17 | +9 |
| 18 | +9 |
| 19 | +9 |
| 20 | +10 |
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.
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.
In the end a starting value of 4.00 and a step size of 0.30 is pretty much spot on.
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.
I have a couple of concerns about this progression. First, I’m not convinced Wizards of the Coast 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.
Validation
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).
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).
Again, this gives me a high degree of confidence in the result.
Check back in a couple of days for the next installment Part 6: Hitpoint Analysis...
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