Wednesday, 9 April 2014

D&D Next Monsters: Part 12: Rebooting The Math: AC Review

D&D Next Monsters: Part 12: Rebooting The Math: AC Review

While this blog does not 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 dndnext.com.

Surf remixes monster Armor Class....

Monster AC was probably the least difficult part of rebooting monster math...

 

Armor Class

Current PC Hit Roll Required
Current PC Hit Roll Required
Derived PC Hit Roll Required
Derived PC Hit Roll Required
Poly2 PC Hit Roll Required
Poly2 PC Hit Roll Required
Poly3 PC Hit Roll Required
Poly2 PC Hit Roll Required

Scaling Up

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 declines 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 Normal creatures with a roll of about 11 or 12.

Is it appropriate for level 1 PCs to only hit level 20 monsters on a 19 or 20? I think so.

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.

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.

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.

 

LevelDerivedPoly2Poly3
1131313
2141414
3151415
4151515
5161616
6161616
7171717
8171717
9181818
10181818
11191919
12191919
13202020
14202020
15202120
16212121
17212121
18222222
19222222
20222322
21232323
22232323
23242424
24242424
25252525

Scaling Out

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.

 

Formulae

To summarise the formulae discussed for the AC reboot...

  • AC (derived) = (9 x Level ^ 0.08) + (Level x 0.368 + 3.798)
  • AC (poly2) = -0.0049 x Level ^ 2 + 0.5959 x Level + 12.681
  • AC (poly3) = 0.0004 x Level ^ 3 - 0.0205 x Level ^ 2 + 0.7453 x Level + 12.445
  • Easy AC = AC - 2
  • Tough AC = AC + 1
  • Solo AC = AC + 2

And to the left you will find a table containing the "scaling up" values for the two key formulae, after appropriate rounding.

 

Check back in a couple of days for the Hit Points review...