Damage Formula Thread

[Kenji1134]

I don't understand your data.

BLM 8 272 202 0.502409091 0.358863636

According to what you posted, the .5 column is your "potency-redacted" damage multiplier. The .359 column has the 30% BLM trait removed. However, 0.50241 / 1.3 = 0.3865.

What is the original data for the average damage for those values?

My formula has the result, for that particular line of data, of an expected 104.1 average damage for Blizzard 3 (high potency repeatable attack), with a damage range of [98.9 .. 109.3].

In any case, I'm not a fan of using average values of a population for precise measurements (and then fitting an equation into the measurements).

My method for data collection:

1. Parsed a spammy high potency attack until the maximum value divided by minimum was 1.105-ish. Generally speaking, damage values have a range of 0.95x - 1.05x from RNG. 1.05/.95 = 1.1053. Once that range is achieved, you know you have "good" data.

I included crits, but divided them by 1.5. They were irrelevant for the most part, but they resulted in a new min or max once every 10 data sets or so.

2. Averaged the minimum and maximum. This average should be closer to "real" than the average of the total population of data.

Sho me ur dmg numberz. The averages are fine, too. I simply can't use your column 5/6 values because I don't know how you calculated those.

For the "untraited" column, I divided by 1.4, not 1.3.
The reason for this was that when I was initially leveling BLM, and later WHM, I tried to determine whether the two damage increasing traits stacked, were additive, or multiplicative.
Back then my answer was pretty much "Additive". I recorded my damage on a lvl 39 Ice Sprite at 39, and then at 40, using the same gear, and the difference was about 27-29%.
So I started at 1.1x at 39. If it is additive, I would be at 1.4x, 1.4/1.1 = 1.2727 ~ 30% more.
If its multiplicative then I would see a straight 30% increase, but mine was less, but the difference is small.
If it just replaces the old trait, then I would see 1.3/1.1 = 1.1818 ~ 20%... I had a lot more than 20%, so I am pretty sure it does not replace it.

But TBH it does not really matter. I have tried not adjusting the BLM potency, I have tried dividing by 1.4 and 1.43... the formula does not give a good result for melee classes.

As for getting numbers. I have heard the (max+min)/2 theory, and have tested it. It does work, and the result is very close to just averaging the non-crit damage, OR adjusting the crit damage and averaging everything.
So, here's 100 hits of B3, copied from ACT, using the 69-471-295 setup, which had 2.50604 potency last time. (Potency is calculated by taking whatever your preferred averaging value is and dividing by the potency of the attack spammed, in this case 220 for B3)

DMG Crit? Uncritted
861 TRUE 574
856 TRUE 570.6666667
855 TRUE 570
837 TRUE 558
835 TRUE 556.6666667
824 TRUE 549.3333333
813 TRUE 542
807 TRUE 538
801 TRUE 534
799 TRUE 532.6666667
575 FALSE 575
575 FALSE 575
575 FALSE 575
574 FALSE 574
573 FALSE 573
572 FALSE 572
572 FALSE 572
571 FALSE 571
571 FALSE 571
570 FALSE 570
570 FALSE 570
569 FALSE 569
569 FALSE 569
569 FALSE 569
568 FALSE 568
568 FALSE 568
566 FALSE 566
566 FALSE 566
566 FALSE 566
566 FALSE 566
564 FALSE 564
564 FALSE 564
562 FALSE 562
561 FALSE 561
561 FALSE 561
559 FALSE 559
559 FALSE 559
558 FALSE 558
558 FALSE 558
558 FALSE 558
557 FALSE 557
556 FALSE 556
556 FALSE 556
555 FALSE 555
554 FALSE 554
553 FALSE 553
553 FALSE 553
553 FALSE 553
552 FALSE 552
552 FALSE 552
552 FALSE 552
551 FALSE 551
549 FALSE 549
549 FALSE 549
549 FALSE 549
548 FALSE 548
548 FALSE 548
547 FALSE 547
547 FALSE 547
547 FALSE 547
546 FALSE 546
546 FALSE 546
546 FALSE 546
545 FALSE 545
545 FALSE 545
544 FALSE 544
544 FALSE 544
544 FALSE 544
544 FALSE 544
544 FALSE 544
542 FALSE 542
542 FALSE 542
541 FALSE 541
541 FALSE 541
541 FALSE 541
541 FALSE 541
541 FALSE 541
540 FALSE 540
539 FALSE 539
539 FALSE 539
537 FALSE 537
536 FALSE 536
535 FALSE 535
535 FALSE 535
533 FALSE 533
533 FALSE 533
532 FALSE 532
531 FALSE 531
531 FALSE 531
531 FALSE 531
531 FALSE 531
528 FALSE 528
528 FALSE 528
527 FALSE 527
525 FALSE 525
523 FALSE 523
522 FALSE 522
521 FALSE 521
521 FALSE 521
520 FALSE 520

Average of all (from Uncritted column)
Average 549.9733333
Pot 2.499878788
(0.2% off previous test)

(Min+Max)/2 (again Uncritted column)
Min 520
Max 575
Value 547.5
Pot 2.488636364
(0.7% off previous test), also max/min = 1.10577... a bit less than your desired 1.1053

Removing crits (everything that didnt crit - 90 datapoints)
Average 549.6888889
Pot 2.498585859
(0.3% off previous test)

All accurate to within 1% of the old test. The choice of whether to use the total average, the (min+max)/2 method, or removing crits is up to the person doing the math. I just happened to choose to remove crits simply because I do not particularly like the (min+max)/2 method.
With that method, you can have X hits that dont change or improve the accuracy of your test, then suddenly one magic hit outside the range will change things.
When using an average, EVERY new hit improves your test, rather than waiting out some magical hit that may come in 50 casts, 100 casts, or 1000 casts.

Keep in mind that no matter how you do this, unless you have something like 1000 hits per datapoint, there WILL be some error. As an engineer by trade and a general math guy, <1% for this kind of testing is good enough. Especially since your accuracy cap is based on your smallest unit over your damage, so my min and max uncritted, my smallest unit error is:
100/520 and 100/575 = 0.174% to 0.192%. This is THE lowest error possible due to the unit size... make of that what you will.