pDIF testing and Damage formulas

[Masamune]

Hello all

Since last test on crit% we completed here @ BG, here i am again this time with pDIF and Damage formulas.

The context is i got a few parses proving current damage formulas from Studio Gobli gives different damage numbers than you would get in game.

So far in this context, i only done one test to determine the caps for 1H & 2H weapons.
But that doesnot tell us at which Ratio one would actually hit those caps.

So i chose a mob not doing Def or VIT increasing moves, having a decent def to cover as much ratios as possible, and who won't rape my face : Lesser Colibris WajaomWoods.

Next i chose weapons. From experience on testing Caps, the higher base DMG the weapon has, the more accurate the division become. So chose the following weapons:
- for 1H : Deae Gratia to cover low Ratios, and Woodville's Axe for the rest.
- for 2H : Subduer then Erlking's Kheten.

I started on 1H test and, through trials and errors, decided to avoid any buffs like Berserk/Defender (except for 2 parses you will see on graph 1H below), same reason for not using Daggers and Polearms. Considering the gears i could use, and the def of those Lcolis, i could neither hit the caps, nor go below Ratio=1.

So after a few parses, i plotted the max and min damages displayed by KParser (included Retaliations) (divided by their respective BaseDMG) on the graph below :

Spoiler: show

http://images1.wikia.nocookie.net/ff...1H_1.0-2.4.jpg

Note: for Ratios from 1.95 and above (1H only), i used Berserk.

BaseDMG used (resp. on lvl63, 64 & 65 Lcolis):
- DeaeGratia: 44, 44, 43
- Woodville's Axe: 59, 59, 58
- Subduer: 97, 97, 96
- Erlking's Kheten: 103, 103, 102

Spoiler: show

http://images1.wikia.nocookie.net/ff...2H_1.4-2.1.jpg

I showed also on those graph the tendancy lines equations, but those only gives you an IDEA of the slopes/integer: remember there is at least one flooring in the calculations process. That means for crit max example, an integer of 1.43 or 1.45 still gives damage numbers matching, same goes for the slopes. But since i used relatively high base DMG weapons, the margin of freedom on those slopes/int should be narrow.

Other important thing is those parses may miss damage numbers, not due to low sample size, but mainly due to LUCK. On some parses, i got surprised to hit 8/12 of expected extreme values, in less than 600hits for a given level of Lcoli. On other parses, after like 3500+hits, i still didnot hit expected values... Sure more sample size would give me more chances, but that's not the cause.

And final important point, are the asumptions i used here:

A) fSTR function is correct: so far only 100% proven proof is the determination of a mob's VIT with 0dmg and DMG1weapon method. Would need to test further using the pDIF=1 range.

B) Only 2 floorings used: one for the fSTR function, and other just in the end of DMG calculations to display a round number. Other than that, there are 0 truncation, roofing or flooring anywhere.

C) the whole concept of the formula is correct, ie a "static" part containing WeaponDMG and fSTR, multiplied then by a randomizer defined by Ratio, and the equations we are searching in this topic. May have other parameters involved like Weapon Delay ?

D) No level correction on mobs lower level than tester.

E) Retaliations don't have any damage boosting (or penalty) factor, and thus should follow same pDIF curves as normal and crit hits.

I leave this topic's voice to BG now.

EDIT: below original data from parses:

Spoiler: show

Each parse contains 3 columns: one for each level of Lesser colibri.

Monster	Exp(no sanction)66	70	72
	Level		63	64	65
	VIT		52	52	55
	Defense		231	235	241

Player	Level		75
	STR		85
	Weapon DMG	50	Woodville Axe
	fSTR		9	9	8
	Base DMG	59	59	58

	Attack		553	553	553	470	470	470	433	433	433	414	414	414	390	390	390	370	370	370
	Ratio		2,394	2,353	2,295	2,035	2,000	1,950	1,874	1,843	1,797	1,792	1,762	1,718	1,688	1,660	1,618	1,602	1,574	1,535
				
Parses	M.Low		93	92	91	92	92	87	83	81	77	78	76	72	71	69	65	65	63	60
	M.High		145	147	143	147	147	139	138	136	131	133	131	127	127	124	120	121	119	114
	Crit Low	160	157	152	156	157	149	147	148	141	145	142	137	141	137	130	132	130	127
	Crit High	185	185	182	185	185	182	185	185	182	185	185	182	184	185	180	182	179	175
Averages
	Normal		119.78	118.48	117.03	119.78	118.7	114.56	110.55	108.78	104.18	105.71	102.87	98.78	98.69	95.85	92.03	92.41	89.89	87.62
	#Hits		261	492	314	547	548	611	1317	1213	1096	1336	974	1227	851	1277	1376	1296	1177	1003
	Crit		177.19	175.87	170.9	174.52	174.99	169.57	171.41	169.05	162.64	166.25	167.07	161.29	164.01	161.98	154.63	154.82	157.76	149.53
	#Crits		27	69	40	96	103	91	170	154	118	182	140	191	115	174	233	224	174	160
Retaliations
	Low		95	92	93	93	94	88	84	83	77	78	76	73	73	69	65	66	64	60
	High		143	144	141	144	145	140	137	136	131	133	131	126	127	123	120	120	118	114
	Crit Low	146	169	156	160	160	151	150	148	143	144	142	138	138	136	134	135	129	126
	Crit High	185	185	182	184	185	182	185	185	182	185	184	180	181	182	177	178	177	173
	#Retals		93	169	140	157	176	208	466	476	404	433	331	453	279	392	467	255	274	216

Weapon DMG	35	Deae Gratia
fSTR		9	9	8
Base DMG	44	44	43

Attack		322	322	322	301	301	301	284	284	284	254	254	254
Ratio		1,394	1,370	1,336	1,303	1,281	1,249	1,229	1,209	1,178	1,100	1,081	1,054

M.Low		44	44	43	44	44	42	43	42	39	36	35	33
M.High		79	78	74	74	73	70	70	69	66	64	63	60
Crit Low	88	87	83	84	83	79	80	79	76	74	73	70
Crit High	126	125	121	122	121	117	119	118	114	113	112	108
Averages
Normal		58.55	57.26	55.18	55.1	54.02	51.97	52.45	51.26	49.06	47.9	47.04	44.98
#Hits		1230	1335	1521	1440	1672	825	669	601	1087	967	992	1293
Crit		106.61	106.57	101.32	102.88	100.2	98.02	101.09	98.61	94.8	95.88	91.22	90.88
#Crits		177	184	216	246	237	122	128	148	168	134	156	203
Retaliations
Low		44	44	43	-	-	-	-	-	-	-	-	-
High		77	72	73	-	-	-	-	-	-	-	-	-
Crit Low	94	91	87	-	-	-	-	-	-	-	-	-
Crit High	119	122	113	-	-	-	-	-	-	-	-	-
#Retals		124	40	92	0	0	0	0	0	0	0	0	0

Player	Level		75
	STR		97
	fSTR		12	12	11
	Weapon DMG	91	Erlking Kheten							85	Subduer				
	Base DMG	103	103	102							97	97	96

	Attack		482	482	482	435	435	435	404	404	404	356	356	356	337	337	337
	Ratio		2,087	2,051	2,000	1,883	1,851	1,805	1,749	1,719	1,676	1,541	1,515	1,477	1,459	1,434	1,398

Parses	M.Low		172	168	160	148	144	137	131	128	123	101	98	96	97	97	96
	M.High		265	261	254	243	239	231	228	225	217	192	189	182	182	180	173
	Crit Low	280	276	270	260	255	247	245	242	234	211	209	201	203	201	194
	Crit High	324	324	321	324	324	321	324	324	321	294	292	285	286	284	277
Averages
	Normal
	#Hits
	Crit
	#Crits
Retaliations
	Low
	High
	Crit Low
	Crit High
	#Retals

Conclusion :

- for 1-handers,

@  1.05<Ratio<1.25: pDIFmin = ? * Ratio - ?
@  1.25<Ratio<1.5: pDIFmin = 1
@  1.5<Ratio<2: pDIFmin = ? * Ratio - ?

@  1.05<Ratio<2: pDIFmax = ? * Ratio + ?

@  1.05<Ratio<2: pDIFmin Crit = ? * Ratio + ?

@  1.05<Ratio<1.65: pDIFmax Crit = ? * Ratio + ?

- for 2-handers,

@  1.25?<Ratio<1.5: pDIFmin = 1
@  1.5<Ratio<2.25?: pDIFmin = ? * Ratio - ?

@  1.4<Ratio<2.25?: pDIFmax = ? * Ratio + ?

@  1.4<Ratio<2.25?: pDIFmin Crit = ? * Ratio + ?

@  1.4<Ratio<1.65: pDIFmax Crit = ? * Ratio + ?

- Need ideas/help/parses for testing below Ratio<1, ie which mob, which method,... ?

[Argettio]

So cratio caps at 2.4 for 1h handers, but goes over 2.5 (is that capped?) for 2 handers? Or am I reading it wrong?

[Masamune]

Caps values have been already determined last year : http://wiki.ffxiclopedia.org/wiki/Ta...ction_and_pDIF

Avg pDIFs 1H :
PDIFmin =     1.57
PDIFmax =     2.478
PDIFcritMIN = 2.655
PDIFcritMAX = 3.15

Avg pDIFs 2H :
PDIFmin =     1.869
PDIFmax =     2.76
PDIFcritMIN = 2.891
PDIFcritMAX = 3.15

The goal here isnot caps, but to determine relationship between Ratio and pDIF, and by extension, Damage formulas.

EDIT: guess i misread your sentence Argettio, my bad.
Actually it isnot cRatio, but Ratio because asumption D (no level correction).
Then, yes you misread the graphs: Ratio1H seems to hit caps @ exactly 2, and undetermined for 2H (since i couldnot get high enough attack to test, without Berserk). For CritMax, data definitely shows Ratio caps @ 1.65 for both 1H and 2H.

EDIT2: if you use the tendency lines equations for 2H, then solve for x with the caps values above, you get the following Ratio values:
- pDIFmin Crit : Ratio=2.257
- pDIFmax : Ratio=2.246
- pDIFmin :Ratio=2.259
... which basically means 2H caps @ Ratio=2.25

[Byrthnoth]

cRatio appears to cap at 2 for 1-handers.

If you take the pDIF cap for 2-H players and backsolve the equations for them, you'd get caps at:
pDIF crit min - 2.25 cRatio
pDIF norm max - 2.25 cRatio
pDIF norm min - 2.25 cRatio


But yes, the point I'm taking away from this is that critical hits face further diminishing returns above about 1.65 cRatio.


When it comes to the level correction function, do we know if it's possible to, say, get a cRatio of 2.6 and get corrected down to 2.25?
The other option would be 2.25 being a hard cap on cRatio going into the equations, so if you were fighting a level 80 mob with 2.5 calculated cRatio, you'd still end up having an effective cRatio of 2.0 because it's still FLOOR(cRatio,2.25)-.05*(80-75).

[Argettio]

Caps values have been already determined last year : http://wiki.ffxiclopedia.org/wiki/Ta...ction_and_pDIF

Avg pDIFs 1H :
PDIFmin =     1.57
PDIFmax =     2.478
PDIFcritMIN = 2.655
PDIFcritMAX = 3.15

Avg pDIFs 2H :
PDIFmin =     1.869
PDIFmax =     2.76
PDIFcritMIN = 2.891
PDIFcritMAX = 3.15

The goal here isnot caps, but to determine relationship between Ratio and pDIF, and by extension, Damage formulas.

Ah I didn't realise this has been found.

brb adjusting all my damage calculation spread sheets.

[Hegarty]

Now that we have a perfect DEX>crit chart and know pDIFs and stuff can someone please, please make an excel program where you input DEX (which then calculates dDEX based on a list of mobs given), STR, Attack, Accuracy (and therefore hit %) and Crit hit rate+, that will compare a DEX set up and a STR set up and RR against KJ and Drakesbane against Penta Thrust? I really wanna know what beats when cus I'm not sure if I can get enough DEX on DRG to make it worth it atm.

[Masamune]

But yes, the point I'm taking away from this is that critical hits face further diminishing returns above about 1.65 cRatio.

Those points you are talking about have been actually parsed under Berserk, which led me to stop using any buffs for next parses. i still plotted them to show how bad it can fuck results. i think only buff that would still give correct results is Minuet, but i don't have a mule or friend brd.

When it comes to the level correction function, do we know if it's possible to, say, get a cRatio of 2.6 and get corrected down to 2.25?
The other option would be 2.25 being a hard cap on cRatio going into the equations, so if you were fighting a level 80 mob with 2.5 calculated cRatio, you'd still end up having an effective cRatio of 2.0 because it's still FLOOR(cRatio,2.25)-.05*(80-75).

Best way to answer that is to redo same test on higher level mobs. Just to get you an idea, i tried on Colibris Bhaf (still lvl below75) as war/dnc i got almost raped... so won't try on lvl75+ mobs.

[Masamune]

Now that we have a perfect DEX>crit chart and know pDIFs and stuff can someone please, please make an excel program where you input DEX (which then calculates dDEX based on a list of mobs given), STR, Attack, Accuracy (and therefore hit %) and Crit hit rate+, that will compare a DEX set up and a STR set up and RR against KJ and Drakesbane against Penta Thrust? I really wanna know what beats when cus I'm not sure if I can get enough DEX on DRG to make it worth it atm.

Check my sig...

also, in your opinion, why did i test crit%=f(dDEX) and now pDIF=g(Ratio) ? (+ an unfinished RagingRush crit%=h(TP) test)

Answer: i was originally wondering exactly same thing you posted, except than begging on a forum, made searches around and ended up testing since either noone tested, or only vague approximations available...

Answer2: RR, and Drakesbane Crit% depending on TP are still unknown.

[Hegarty]

Check my sig...

also, in your opinion, why did i test crit%=f(dDEX) and now pDIF=g(Ratio) ? (+ an unfinished RagingRush crit%=h(TP) test)

Answer: i was originally wondering exactly same thing you posted, except than begging on a forum, made searches around and ended up testing since either noone tested, or only vague approximations available...

Answer2: RR, and Drakesbane Crit% depending on TP are still unknown.

Some people have better things to do than kill hundreds of level 1 mobs or don't even have the time to? Oh, did I mention I don't know how to make excel programs or any kind of pc program? Yeah, "go do it yourself" mentality ftw.

[Hegarty]

Oh and in what way would the comparing be skewed by them giving, for example, +0% or +15%? There would be diminishing returns and a lower average if they give +15%?

[Masamune]

Oh and in what way would the comparing be skewed by them giving, for example, +0% or +15%? There would be diminishing returns and a lower average if they give +15%?

Good question there.

Let's take an example with a 194 dmg displayed on your in game log. Nothing tell us than it's an exact 194 rather than 194.2 or 194.856189. So, assuming it has a hidden floating point nulled by the last floor(), if you use Berserk(25%) that damage becomes :
194 x1.25 = 242.5 -> after flooring = 242
194.2 x 1.25 = 242.75 -> after flooring = 242
194.856 x 1.25 = 243.57 -> after flooring = 243

so when determining pDIF with a "wrong" damage value, you obtain the weird points you can see on the 1H graph @ Ratio>=1.95. So under that doubt, i prefered to stop using Berserk on later parses.

[Byrthnoth]

Still, even with the weirdness via Berserk we can see that Crit Max caps out around 1.65 cRatio. That's what I meant by diminishing returns.

Forgive me for rounding sometimes prz Masa:
Crit Max (1.4 to 1.65): pDIF = .9339*cRatio + 1.6
Crit Max (>1.65): pDIF = 3.15
Crit Min - pDIF = cRatio + .6
Norm Max - pDIF = 1.115*cRatio + .25
Norm Min - pDIF = 1.15*Cratio - .75

.97*cRatio+1.1 = pDIF :: Crit between 1.4 and 1.65 cRatio
.5*cRatio+1.875 = pDIF :: Crit between 1.65 and 2.25 cRatio

1.13*cRatio-.25 = pDIF :: Normal hit between 1.5 and 2.25 cRatio

@ cRatio of 2.25, Crit is worth 3
@ cRatio of 2.25, Normal is worth 2.29
Crit is worth 31% more than a normal hit

@ cRatio of 2, Crit is worth 2.875
@ cRatio of 2, Normal is worth 2
Crit is worth 44% more than a normal hit

@ cRatio of 1.5, Crit is worth 2.55
@ cRatio of 1.5, Normal is worth 1.445
Crit is worth 76% more than a normal hit


This is exactly what I've wanted for the last two years. Christmas is here!
This explains why KJ does comparably or better than RR at high attack values, but RR > KJ with a high crit rate or low attack.

[pchan]

I'm still trying to understand what happens, but from what I gathered from reading the new pdif page on the wiki and this thread :

- The old pdif formula are correct, except that Ratio is calculated differently ?

With Dia III, the attack required to cap that cratio on my monk is the solution of x/(322*0.85)=2.0, which gives 547 ?

And once I cap cratio, additional attack has no effect ?

For crit, anything past the solution of x/(322*0.85)=1.65, which gives 451 attack, is useless ? In other word, in all practical situations, attack doesn't affect crit damage ? o;O

[Masamune]

For both 1H and 2H, i got the following equations (for uncapped pDIFs) with best accuracy i could get vs. the dmg numbers on my parses :

pDIF CritMax = 1.03*Ratio + 1.451 (Accuracy=73.3%for1H, 100%for2H)

pDIF Min = 1.155*Ratio - 0.739 (Accuracy=83.3%for1H, 73.3%for2H)

for pDIFmin Crit and pDIFmax, i didnot manage to find a slope+int giving an accuracy higher than 40%...

[Byrthnoth]

Attack still affects minimum critical hit damage above 1.65 adjusted cRatio. It just stops affecting the maximum critical hit damage so you see a lower average increase in critical hit damage.

edit: I guess I don't understand what I'm looking at Masa. It looks like your data for Crit min and max has a linear fit with a very high R^2 value?

[pchan]

Attack still affects minimum critical hit damage above 1.65 adjusted cRatio. It just stops affecting the maximum critical hit damage so you see a lower average increase in critical hit damage.

edit: I guess I don't understand what I'm looking at Masa. It looks like your data for Crit min and max has a linear fit with a very high R^2 value?

I thought there was recently a thread showing that the distribution of critical pdif tends to be near the cap unlike normal hit where it's almost uniform.

[Byrthnoth]

Oh, I thought what we took from that was that both kinds of hits were fairly uniformly distributed with the extremes being uncharacteristically rare (possibly due to rounding).

Bah, I'll sort this out when I get home from work tonight, lol.

[Masamune]

I'm still trying to understand what happens, but from what I gathered from reading the new pdif page on the wiki and this thread :

- The old pdif formula are correct, except that Ratio is calculated differently ?

it's one of the main asumptions i did (asumption C). Maybe another way can work also or even better ?

With Dia III, the attack required to cap that cratio on my monk is the solution of x/(322*0.85)=2.0, which gives 547 ?

And once I cap cratio, additional attack has no effect ?

For crit, anything past the solution of x/(322*0.85)=1.65, which gives 451 attack, is useless ? In other word, in all practical situations, attack doesn't affect crit damage ? o;O

There sorry i didnot understood anything :s

[Masamune]

I thought there was recently a thread showing that the distribution of critical pdif tends to be near the cap unlike normal hit where it's almost uniform.

Yep, from Motenten. But here i don't care at all about distribution of dmg between the extreme values. i only looked upon the extreme values, nothing else. IMO, distribution of dmg can be looked at, but only after such basic damage testings have been set once and for all, not the other way around. Same goes for testing about Y/G/K attack boost etc...

There is also another main asumptions that may need to be tested also: fSTR function.

[Yarko]

For both 1H and 2H, i got the following equations (for uncapped pDIFs) with best accuracy i could get vs. the dmg numbers on my parses :

pDIF CritMax = 1.03*Ratio + 1.451 (Accuracy=73.3%for1H, 100%for2H)

pDIF Min = 1.155*Ratio - 0.739 (Accuracy=83.3%for1H, 73.3%for2H)

for pDIFmin Crit and pDIFmax, i didnot manage to find a slope+int giving an accuracy higher than 40%...

First of all nice tests and interesting results.

I refuse to think they added formulas with so many decimals, the formulas must be a bit easier.

Crit Max (1.4 to 1.65): pDIF = .9339*cRatio + 1.6
Crit Max (>1.65): pDIF = 3.15
Crit Min - pDIF = cRatio + .6
Norm Max - pDIF = 1.115*cRatio + .25
Norm Min - pDIF = 1.15*Cratio - .75

^ is what I was thinking the formulas are too, except maybe a slope of 1 for all crit equations (so Crit max (1.4 to 1.65) pDIF = cRatio + 1.6) and the slope of norm max /norm min must be the same (both 1.15?).
This is quite interesting, as it seems that crits don't simply add 1 to pDIF value as it was believed, but rather have their own equations with a different slope.

Looking at it from a programmer point of view:
the pDIF formulas seem to be all in the format of a * Ratio + q

the "a" variable (slope) is most likely not randomized (but probably changes depending on the value of Ratio), while q is the random variable that makes damage vary. Making both of them random variables would be useless, and I guess SE would do something like that only if they really really wanted to make sure the equations were uncrackable.

the "a" variable could well be a fraction, and thus be decimal. It could be quite complicated to find out the exact value of it. The randomized q variable, though, probably has a lower and upper limit which don't have more than 2 decimals (e.g. qmax = 0.25; qmin = -0.75).
In this case, assuming the random variable q can assume any value between qmax and qmin with the same probability, avg pDIF value would be
a * Ratio + (qmax + qmin)/2

When analysing different DDs/setups/etc avg damage is what matters, so finding out how that works would be more useful than finding out the exact min/max's themselves imo.

Can you look at your parses and backsolve avg pDIF values using (avg norm hit dmg parsed)/(base damage) and (avg crit damage parsed)/(base damage) please?
And maybe add it to the graphs too. That would be quite helpful.