Thursday, 12 June 2014

D&D Next Monsters: Part 15: Rebooting The Math: Damage Review

D&D Next Monsters: Part 15: Rebooting The Math: Damage 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

Wherein Surf has a shot at correcting the math in the final playtest's monsters....

OK this took a lot 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.



Scaling Up

D&D Next's 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 Damage (and it's counterpart Hitpoints) 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.

Damage vs PC HP - Actual & Expected
Damage vs PC HP - Actual & Expected

If we divide the average damage of Average monsters by PC Hit Points 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 monster damage gets lower as level increases. 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.

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 Easy, Average, Tough and Solo Damage, telling us how Damage scales out. It also gives us a pretty good idea what Damage should look like for an Average creature at a given level, which tells us something about how Damage scales up.

As you might expect, the existing sequence averages at 0.25 and it's median is 0.25, varying by 0.015. So an Average creature should inflict damage equivalent to 25% of a same-level PC's maximum Hit Points, 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.

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.

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.

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.

Damage Progression: Linear
Damage Progression: Linear

Linear formulae could work here. Obviously a curve that is static at 25% of PC hitpoints might 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.

Damage Progression: Power
Damage Progression: Power

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.

Damage Progression: Poly3
Damage Progression: Poly3

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.


Scaling Out

Monsters in D&D Next appear to scale out with multipliers of about 0.5 for Easy, 1.25 for Tough and 1.50 for Solo creatures. To me this seems a bit on the weak side.


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.

A 20th level Solo creature will deal damage equivalent between 27% and 50% of full PC health, averaging 39%. Now, a Solo 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!

What about a 25th level Solo? It will deal between 39% and 72% of a level 20 PCs full health as damage, averaging 55%. That's a far cry from the 148% damage that four average level 25 monsters would deal!

So to me it's obvious that these multipliers need some updating.

We do need to be careful though, as we could make creatures too overpowering. If we edge the Solo multiplier up to 2.0 the level 25 Solo 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.

What I have gone with for the purposes of this article is 0.6 for Easy, 1.5 for Tough and 2.0 for Solo creatures.

For the reader's convenience I have included a full hitpoints table to the left that corresponds to the derived/power formulas.



  • Damage (derived) ~= (Level x 13 + 4) * (0.0031 x Level + 0.1969)
  • Damage (static linear) = 3.6292 x Level - 0.9125
  • Damage (power) = 3.385 x Level ^ 1.0172
  • Damage (poly3) = 0.0062 x Level ^ 3 - 0.1886 x Level ^ 2 + 4.8052 x Level - 1.8186
  • Easy Damage = Damage x 0.60
  • Hard Damage = Damage x 1.50
  • Solo Damage = Damage x 2.00



Check back Monday for revised monster building tables...