Damage Formula Thread

[Kenji1134]

I have been playing with deriving the damage formula from parse data for about a month now, and basically I have come to a simple conclusion... Its archetype based.
Or more specifically, the formula itself is likely the same, ESPECIALLY if you write it in an expanded form, so you have your Weapon Damage component, Str/Dex/Int/Mind component, Det component, and second order combinations... WD*Int, WD*Det, Int*Det, Det^2, etc... but with a different set of coefficients for each archetype.

Here is the data set I have been building and working with so far:

Data
Class (WD 'A') (Int 'B') (Det 'C') (Parse Pot) ("Untraited")
BLM 8 272 202 0.502409091 0.358863636
BLM 8 305 202 0.5515 0.393928571
BLM 8 325 202 0.587318182 0.419512987
BLM 8 351 202 0.624240909 0.445886364
BLM 8 389 226 0.688059091 0.491470779
BLM 8 416 246 0.737877273 0.527055195
BLM 8 290 213 0.527922 0.377087143
BLM 8 328 238 0.596055 0.425753571
BLM 36 277 202 0.969 0.692142857
BLM 36 310 202 1.06959 0.763992857
BLM 36 330 202 1.11954 0.799671429
BLM 36 356 202 1.20386 0.8599
BLM 36 394 226 1.31427 0.938764286
BLM 36 421 246 1.41968 1.014057143
BLM 36 295 213 1.02556 0.732542857
BLM 36 333 238 1.14481 0.817721429
BLM 69 303 220 1.64099 1.172135714
BLM 69 336 220 1.78894 1.277814286
BLM 69 356 220 1.88979 1.34985
BLM 69 382 220 2.00502 1.432157143
BLM 69 420 244 2.19151 1.565364286
BLM 69 447 264 2.34258 1.673271429
BLM 69 321 231 1.73815 1.241535714
BLM 69 359 256 1.93527 1.382335714
BLM 69 499 286 2.61 1.864285714
BLM 69 452 261 2.35766 1.684042857
BLM 69 458 295 2.43871 1.741935714
BLM 69 467 295 2.48967 1.778335714
BLM 69 461 261 2.42551 1.732507143
BLM 69 471 295 2.50604 1.790028571
BLM 69 467 303 2.49654 1.783242857
BLM 59 451 277 2.12119 1.515135714
MNK 41 404 237 1.11406 1.11406
MNK 5 382 237 0.456889 0.456889
MNK 5 267 202 0.336513 0.336513
PLD 46 341 225 0.999282 0.999282
PLD 5 319 225 0.363854 0.363854
PLD 5 205 202 0.25037 0.25037

My testing methodology is as follows.
Write down the stats and class.
Using ACT to log data, spam a high potency - highly repeatable ability for about 3 minutes, which is roughly 50-70 hits. (I used Blizzard 3, Bootshine, and Fast Blade)
From the ACT data, remove all critical hits, then divide the total damage minus crits by the total number of non-crit hits, and divide again by the potency of the attack... This gives the value in the 5th column, which is the average value of ONE non-crit potency for that class with those stats.

I started doing this for BLM, which is why I have a mountain of BLM data. The "untraited" column is for adjusting that pile of BLM data to try and match the data from other classes.
Now I can construct a model, several models, that match the BLM data points to an average error of under 0.4%... BUT this model fails to match the other class's data. My errors on MNK and PLD tend to range from 3% to 6%. Keep in mind this error is after accounting for the BLM's 1.4 OR 1.43 damage mod, and testing MNK without Fists of Fire or any GL stacks, and testing PLD without any buffs or Oaths up.

So under the same testing conditions, a potency model, and I have tried very many... Valk's, Puro's, various ones using Det-202, using "Stat-Base" and "Stat/Base" where "Base" is determined by taking the stat minus all gear minus allocated points minus racial stat, which leaves how much the Job gives... all 1st order, all 2nd order, mixed-combined 1st and 2nd order... ugh...
Anyway, ranting aside, IT DOES NOT WORK! There is no catch-all equation for all classes...
BUT!
If I use ONLY my BLM data, I get my <0.4% error... Now when I (just recently) took my 6 data points for MNK and PLD... MELEE classes, not CASTERS... I had 0 error. I literally had micro-percent errors... Granted its for 6 datapoints instead of 30, but that is very significant, and leads to a simple, logical conclusion...

There are 2 potency formulas. One for all Casters and a different one for all Melee.

This makes sense since casters do not get an autoattack. So you have the same base formula, but one has greater coefficients to offset the loss of autoattack, while the other has smaller coefficients but has an additional part, likely the same formula with yet a 3rd set of coeffs, which is the autoattack component.

With all of that said, I am going to keep poking at this formula and gathering more data when Im bored, particularly for melee classes, and I should get some WHM data in there too to see how it stacks up against BLM.

Regarding some of the more gritty details, I am doing all of this in Excel using the Data Analysis toolkit's Regression function. I am also modeling the non-linear equation as a super-positioned linear set such that I can use the linear regression function... Basically I am expanding the model and giving each thing a coefficient.
You will notice that at the top of my data I have WD, Int, Det labeled as A, B, C. This is to slightly simplify my model construction. So far the best model I have is as follows:

A+B+C + AB+AC+BC + B^2+C^2 + 0 (no constant intercept)

This is the mixed model that essentially says that WD, Str/Dex/Int/Mind(stat), and Det all have a unique contribution, then (stat) acts on WD, Det acts on WD, and Det acts on (stat), and lastly there is a small, typically negative correction factor for (stat)^2 and Det^2. Note that WD^2 is not included here, simply because in all of my models, WD^2 had the smallest contribution BY FAR and each model was actually MORE accurate without the WD^2 component. I also have typically seen better results when the coefficient was 0, meaning that if all of your stats are 0, your potency is 0, not some small magical value.

So this equation looks ugly as all hell, and even worse when every single term had some monstrous 6-12 digit coefficient attached to it... But this is the most accurate. Given this data, you could combine terms and simplify it down into something more manageable, or remove the term with the significantly lowest contribution and rerun the new model... Eventually you will lose significant accuracy, but even a model such as: A*(B+C) + B*C + B^2 + C^2 + B + C is still very accurate, and much less cumbersome than the "complete" model used above.

That is about all I want to say for the time being. I will continue gathering data and try to work out two solid models for casters and melee... Hopefully the WHM data fits the BLM model, otherwise its going to turn into a huge headache. =)