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Talk:Level Correction Function and pDIF

what does pDIF stand for? That should be mentioned on this page. --zoogelio-forgot-his-password 19:09, 21 July 2006 (EDT)

the variable was introduced at the first time as pDIF (probably refer to percentage DIFference, but I'm not sure). I can just change it to f(atk/def), but I just like it the old way saying it. A variable is a variable anyway.
on "what is pDIF?" question, I think it's clearly explained on the first sentence on that section--VZX 20:55, 21 July 2006 (EDT)
Well, then "percentage DIFference" should be listed on the page. --zoogelio-forgot-his-password 22:07, 21 July 2006 (EDT)
I've actually always thought about it as "Physical DIFference" as opposed to "Magical DIFference." --Ichthyos 11:42, 24 May 2007 (CDT)

I noticed something interesting the other day while testing Beast Affinity: while Carrie and the EM Steelshell were beating on each other they tended to hit for one number more than others. From the pDIF graph I kind of expected that in the att/def = 0.5-0.8 and 1.5-2.0 ranges, but in this case they had hits both higher and lower than the 'mode' damage. This suggested to me that even in the att/def = 0.8-1.5 range, pDIF = 1 has a higher probability than other values. --Valyana 14:37, 18 August 2006 (EDT)

This is something I have noticed a lot when I use my parser to construct damage frequency charts. Huge spikes of frequency at exactly 1.0 pDIF. --Aurikasura 20:30, 28 October 2006 (EDT)


I have two questions about this, and those questions are <Huh?!> and WTF?!--Unsigned comment left by Alamond


Something seems odd about critical hits adding +1.0 pDIF to your damage. There isn't a mode for critical hits when your attack/defense ratio is around 1.0, but the mode for regular hits (pDIF = 1) shows up 1/3 of the time.

It may be possible that instead of adding +1.0 to your pDIF, a constant value is added to your att/def ratio similar to the level correction thing.--JKL 02:05, 3 May 2007 (CDT)

How is it that this page doesn't include a modification to the formula by your Combat Skill rating? Or is that shown somewhere else?--Mooch 11:18, 24 May 2007 (CDT)

To what modification are you referring? I've never used combat skill in (melee) damage calculations, mostly because "attack" is already shown in the equipment screen. --Ichthyos 11:36, 24 May 2007 (CDT)
Oops, brain had shut off for a bit.--Mooch 15:57, 25 May 2007 (CDT)

Mode[edit]

From looking at the graph, I suspect that in neutral def pDIF=1.00 3/8 of the time, rather than 1/3. When neither max or min pDIF are fixed, the range is 0.8, but in the middle it's only 0.5; I suspect that the other 0.3 of normal range are squeezed into pDIF = 1.00. --Valyana 21:57, 12 August 2007 (CDT)

If this is correct, mean pDIF in the cRatio=5/6-6/5 range could be calculated by (1.2*cRatio+1.2*cRatio-0.5)/2*5/8 + 1*3/8 = cRatio*0.75+0.21875
mean pDIF in the cRatio=1.25-1.5 range would be more complicated, as the mode gets less likely as cRatio rises. I believe that the formula would be 0.9*cRatio*cRatio - 1.5*cRatio + 1.625
note that both formulas give the same result for cRatio = 1.25. --Valyana 23:04, 13 August 2007 (CDT)
(1.2*cRatio+1.2*cRatio-0.5)/2*5/8 + 1*3/8
That means other value than 1.0 is distributed evenly? Are you sure about this?--VZX 01:51, 14 August 2007 (CDT)
Sure? No, it's just a hypothesis, but I would be surprised if the other values were not evenly distributed. --Valyana 08:41, 14 August 2007 (CDT)
Now I think about it again... why mode is getting less likely as cRatio rises from 1.25 to 1.5? and what formula do you use for getting avg on that region? I can't think anything that makes the avg rises quadratically. I thought it's just a simple linear combination of pDIF=1.0 and other range.--VZX 12:51, 24 August 2007 (CDT)
I expect the mode to get less likely between 1.25 and 1.5 as the range between min and max pDIF widens: my mental model is that the server rolls a random number between 0 and 0.8 and adds it to min pDIF for the current cRatio. If this gives a result higher than max pDIF, we get the mode instead. But again, this is just a hypothesis. --Valyana 00:24, 20 September 2008 (UTC)

I've recently test some blue magic coefficient for each spells. Since the physical blue magic also use the same pDIF function. I guess it's still valid to show data from the test.
Here's the ratio of mode/total sample for each level crab:

  • Head Butt:
    • Lv61:14/35 (40%)
    • Lv62:12/39 (30.77%)
    • Lv63:16/39 (41.03%)

--VZX 03:02, 13 August 2007 (CDT)


Forgot to add another from Delekii's (as 75 BLU) test against Lv75 Steelshell:

--VZX 03:07, 13 August 2007 (CDT)

we really ought to update this with (at the very least) max non-crit and crit pDIF values for 1h and 2h weapons post-2h update. we should also include a note about the suspected 1.0-1.05 random modifier (i can probably get a link to testing from starfox or from some google magic), since it interferes with actually determining the caps (e.g. i've told people that 2h NQ hit pDIF caps at around 2.7, but if 2.7 is the "observed cap", the actual cap would be around 2.571 if the 1.05 random mod exists). i don't want to get too deep into the business of wiki editing, so i'm trying to start this move forward here on the talk page. --Bowser 08:35, 8 August 2008 (UTC)

I did some max crit dmg on lvl 1 mobs and also noticed the max pdif * 1.05 increase. results are posted here http://www.bluegartrls.com/forum/showthread.php?t=62258 --Kroot 15:17, 24 August 2008 (UTC)

calculating an unknown variable using the damage equation[edit]

hey all... i've been trying to calculate the defense of the automaton using the damage equation. i've been going into PVP so i can have a maximum controlled environment for this test. so i know the str and vit values for the attacker and defender, so fStr is easy enough to figure out. i also know the levels (both being capped at 40) so the level correction function = 0. the problem i'm running into is actually deriving the def out of the pdif function. since the only equations posted are min/max... i was wondering how you would go about getting one from the average damage?

New pDIF calculations[edit]

New pDIF Caps Testing[edit]

I put a note into this page letting people know that these equations are outdated. New pDIF cap appears to be 2.7, and crits are over 3.0 now. As far as I know, the new equations have not been found yet. Also, I'm not sure if the new cap just applies to 2 handed weapons, or if the old equations still work for 1 handed weapons, some clarification is required --Wraith Lakshmi 22:45, 11 January 2009 (UTC)

Not sure about other jobs, but on MNK i found that cRatio caps at 2.064 now, and crits caps on 3.15 instead of 3.0 now, the rest remain the same. Always get correct results with those numbers when parsing. --Sedosan 14:09, 27 May 2009 (UTC)


On Lv0 Mobs:

Melee Damage with Warp Cudgel (DMG:15)
Player            Melee Dmg   Melee %   Hit/Miss   M.Acc %  M.Low/Hi    M.Avg  #Crit  C.Low/Hi   C.Avg     Crit%
Kegsay                 5401  100.00 %      101/1   99.02 %     37/58    49.05     21     65/75   70.33   20.79 %
DAMAGE = 24 * pDIF

Melee Damage with Lady Bell (DMG:1)
Player            Melee Dmg   Melee %   Hit/Miss   M.Acc %  M.Low/Hi    M.Avg  #Crit  C.Low/Hi   C.Avg     Crit%
Kegsay                 1954  100.00 %      101/4   96.19 %     14/22    17.70     20     24/28   26.00   19.80 %
DAMAGE = 9 * pDIF

Melee Damage with Brass Rod (DMG:8)
Player            Melee Dmg   Melee %   Hit/Miss   M.Acc %  M.Low/Hi    M.Avg  #Crit  C.Low/Hi   C.Avg     Crit%
Kegsay                 7932  100.00 %     226/11   95.36 %     25/39    31.88     47     42/50   47.34   20.80 %
Note: Tons of hits because M.Hi was suspected to be 39, but took that long to prove it, was 38 before.
DAMAGE = 16 * pDIF

pDIF Max is 2.45 for 1H.
pDIF Min is 1.57~1.58 for 1H.

Theoretical Melee Damage with Martial Wand (DMG:35) using these values:
Min Melee = 72
Max Melee = 112

Melee Damage with Martial Wand (DMG:35)
Player            Melee Dmg   Melee %   Hit/Miss   M.Acc %  M.Low/Hi    M.Avg  #Crit  C.Low/Hi   C.Avg     Crit%
Kegsay                41644  100.00 %     397/19   95.43 %    72/112    93.34    107   122/144  136.21   26.95 %
DAMAGE= 46 * pDIF

Proven. (For pDIF = capped and fSTR = capped) --Kegsay 22:32, 25 August 2009 (UTC)

... Continued these results, since they limited to low ranked weapons, which means large pDIF possibilities revealing wrong with higher ranked weapons damage. Also some of those weapons were missing values, which has been completed below:

Targeted mobs: Wild Rabbits & Tunnel Worms, East Ronfaure; also Gigas(non-MNK) & Weapons Qufim
Tests done under capped conditions,
i.e. with fSTR capped and cRatio=Ratio=capped (no level correction since all mobs lower level than tester).
Rank=~Floor(WeaponDMG/9)
BaseDMG= Floor(WeaponDMG + (Rank+8 ) = Floor(WeaponDMG*(10/9)+8 )
PDIFmin = DamageMIN/BaseDMG
PDIFmax = DamageMAX/BaseDMG
PDIFcritMIN = DamageCritMIN/BaseDMG
PDIFcritMAX = DamageCritMAX/BaseDMG
used triple decimal precision for each pDIF range,
and also various jobs with way enough STR and attack to be in capped situation.

----- 1hand Weapons -----

Rank0: Ibushi Shinai (DMG=1)
BaseDMG= 1*1.11+8 = 9.11 ~ 9
Hit/Miss M.Low/Hi C.Low/Hi
284/14   14/22    23/28
PDIFmin = 14/9 ~ 1.556-1.666
PDIFmax = 22/9 ~ 2.445-2.555
PDIFcritMIN = 23/9 ~ 2.556-2.666
PDIFcritMAX = 28/9 ~ 3.112-3.222

Brass Rod (DMG=8 )
Hit/Miss M.Low/Hi C.Low/Hi
226/11   25/39    42/50
BaseDMG= 8*1.11+8 = 16.88 ~ 16
PDIFmin = 25/16 ~ 1.563-1.624
PDIFmax = 39/16 ~ 2.438-2.499
PDIFcritMIN = 42/16 ~ 2.625-2.687
PDIFcritMAX = 50/16 ~ 3.125-3.187

Rank1: Warp Cudgel / Kaiser Sword (DMG=15)
BaseDMG= 15*1.11+8 = 24.65 ~ 24
Hit/Miss M.Low/Hi C.Low/Hi
562/19   37/59    63/75
PDIFmin = 37/24 ~ 1.542-1.583
PDIFmax = 59/24 ~ 2.459-2.499
PDIFcritMIN = 63/24 ~ 2.625-2.666
PDIFcritMAX = 75/24 ~ 3.125-3.166

Rank2: Garuda Dagger (DMG=19)
BaseDMG= 19*1.11+8 = 29.1 ~ 29
Hit/Miss M.Low/Hi C.Low/Hi
862/50   45/71    76/91
PDIFmin = 45/29 ~ 1.552-1.586
PDIFmax = 71/29 ~ 2.449-2.482
PDIFcritMIN = 76/29 ~ 2.621-2.655
PDIFcritMAX = 91/29 ~ 3.138-3.172

Rank3: Thief Knife (DMG=28 )
BaseDMG= 28*1.11+8 = 39.1 ~ 39
Hit/Miss M.Low/Hi C.Low/Hi
260/16   61/96    103/122
PDIFmin = 61/39 ~ 1.565-1.589
PDIFmax = 96/39 ~ 2.462-2.487
PDIFcritMIN = 103/39 ~ 2.642-2.666
PDIFcritMAX = 122/39 ~ 3.129-3.153

Martial Wand (DMG=35)
Hit/Miss M.Low/Hi C.Low/Hi
397/19   72/112   122/144
BaseDMG= 35*1.11+8 = 46.85 ~ 46
PDIFmin = 72/46 ~ 1.566-1.586
PDIFmax = 112/46 ~ 2.435-2.456 [b]get 113? Can't test since i don't own that weapon[/b]
PDIFcritMIN = 122/46 ~ 2.653-2.673
PDIFcritMAX = 144/46 ~ 3.131-3.152

Rank5: Woodville's Axe (DMG=50)
Hit/Miss M.Low/Hi C.Low/Hi
590/29   98/156   167/198
BaseDMG= 50*1.11+8 = 63.5 ~ 63
PDIFmin = 98/63 ~ 1.556-1.571
PDIFmax = 156/63 ~ 2.477-2.492
PDIFcritMIN = 167/63 ~ 2.651-2.666
PDIFcritMAX = 198/63 ~ 3.143-3.158

1H Conclusions: PDIFmin = 1.566-1.571 PDIFmax = 2.477-2.478? PDIFcritMIN = 2.653-2.655 PDIFcritMAX = 3.143-3.152

Avg pDIFs 1H :

PDIFmin =     1.57
PDIFmax =     2.478
PDIFcritMIN = 2.655
PDIFcritMAX = 3.15

----- 2hand Weapons -----

Rank0: Relic Bhuj (DMG=1)
Hit/Miss M.Low/Hi C.Low/Hi
319/11   16/24    26/28
BaseDMG= 1*1.11+8 = 9.11 ~ 9
PDIFmin = 16/9 ~ 1.778-1.888
PDIFmax = 24/9 ~ 2.667-2.777
PDIFcritMIN = 26/9 ~ 2.889-2.999
PDIFcritMAX = 28/9 ~ 3.112-3.222

Rank3: Jupiter Staff / Zaghnal (DMG=35)
Hit/Miss M.Low/Hi C.Low/Hi
947/39   85/126   132/144
BaseDMG= 35*1.11+8 = 46.85 ~ 46
PDIFmin = 85/46 ~ 1.848-1.869
PDIFmax = 126/46 ~ 2.740-2.760
PDIFcritMIN = 132/46 ~ 2.870-2.891
PDIFcritMAX = 144/46 ~ 3.131-3.152

Rank5: Orc Piercer (DMG=48 )
Hit/Miss M.Low/Hi C.Low/Hi
264/23   114/168  176/192
BaseDMG= 48*1.11+8 = 61.28 ~ 61
PDIFmin = 114/61 ~ 1.869-1.885
PDIFmax = 168/61 ~ 2.755-2.770
PDIFcritMIN = 176/61 ~ 2.886-2.901
PDIFcritMAX = 192/61 ~ 3.148-3.163

Rank7: Iron Ram Lance (DMG=70)
Hit/Miss M.Low/Hi C.Low/Hi
418/21   158/234  245/267
BaseDMG= 70*1.11+8 = 85.7 ~ 85
PDIFmin = 158/85 ~ 1.859-1.870
PDIFmax = 234/85 ~ 2.754-2.764
PDIFcritMIN = 245/85 ~ 2.883-2.894
PDIFcritMAX = 267/85 ~ 3.142-3.152

Rank10: Erlking's Kheten (DMG=91)
Hit/Miss M.Low/Hi C.Low/Hi
869/50   203/300  315/343
BaseDMG= 91*1.11+8 = 109.01 ~ 109
PDIFmin = 203/109 ~ 1.863-1.871
PDIFmax = 300/109 ~ 2.753-2.761
PDIFcritMIN = 315/109 ~ 2.891-2.898
PDIFcritMAX = 343/109 ~ 3.147-3.155

2H Conclusions: PDIFmin = 1.869 PDIFmax = 2.755-2.760 PDIFcritMIN = 2.891 PDIFcritMAX = 3.148-3.152

Avg pDIFs 2H :

PDIFmin =     1.869
PDIFmax =     2.76
PDIFcritMIN = 2.891
PDIFcritMAX = 3.15

Those pDIF caps values match all tested weapons, unless someone show a screenshot with lower or higher dmg values than those listed (under capped conditions and same BaseDMG).

--Masamunai 11:29, October 1, 2009 (UTC)

New pDIF calculation theory[edit]

With Masamunai's pDIF data, I've correlated tons of older data to theory gathered from numerous sites, and posted the current theory on damage calculation to the page. Any discussion and input is welcomed, and I know the verification tags are gonna start flying, but as far as I can tell this theory is 100% valid for every parse I have, and even Masa's data showing a max pDIF of ~2.76 (2.2 * 1.2 * 1.05, 2.77 before truncation losses), and the 3.15 pDIF cap on criticals (and now the only cap on pDIF) --Ranzear 21:27, January 25, 2010 (UTC)

I'm interested in your "tons of older data from numerous sites", can you post them on this page please ? I just posted my current testings results under uncapped pDIFs @ http://www.bluegartrls.com/forum/showpost.php?p=3428312&postcount=1 Regarding what you posted, althought that may match limited data, i don't think the *1.05 theory is valid at all for whole pDIF ranges. Masamunai 14:31, January 26, 2010 (UTC)

You have to understand my interest is only in the model, based on high-end two handed data. Your data fits perfectly still, especially in the link you give. 1.05 is the high end of a second randomizer applied after the main pDIF equation and 3.0 cap, and is obviously intended to add a bit more random factor to crits that hit the 3.0 cap. Its the +5% randomization that creates the apparent 3.15 crit pDIF cap from crits capping at 3.0, and also produces the ~2.77 number if your fMax(pDIF) for 2-handers is used on capped 2.2 ratio and fMAX(pDIF) of 1.2 * cRatio (2.64 * 1.05 = 2.772).

This bluegartr thread @ http://www.bluegartrls.com/forum/showthread.php?t=68018&page=3 (posts by Nameless) was the first suggestion that Ratio was being capped before level correction applied. 2.2 was the 'cRatio cap' determined for non-level-corrected mobs, whereupon decreased pDIF from expectation of Level Correction being overridden by sufficient attack suggests instead that the 2.2 cap is actually on Ratio.

Third post in that same link also details the 1.00-1.05 randomization after initial calculation of pDIF.

You have another bluegartr thread @ http://www.bluegartrls.com/forum/showthread.php?t=82319 Motenten gives the following crit data: Melee Crits

     149:    1
     150:    2
     151:    3
     153:    2
     154:    3
     155:    3
     156:   32 -- 3.0
     157:   23
     158:   34
     159:   19
     160:   31
     161:   22
     162:   24
     163:   19

Note his 3.0 pDIF as marked. Lower damage is where pDIF was below 2.0 (which is still possible with capped Ratio) and is very sparse. Higher data is strong and a pDIF of 3.15 gives the highest damage parsed, 163. If pDIF ranged as high as 3.77 so readily as the 2.77 'max pDIF' would suggest, then capping after all randomization would not result in this distribution, but all crits being the same. This best suggests that the chart/equation is applied to cRatio, and an additional randomization is applied which was originally postulated to only affect critical hits but also serves to produce the 2.77 maximum pDIF in situations with capped ratio and no level correction

This data also suggests that the range of secondary randomization is instead 1.00 to 1.05.

I think the biggest issue is being stuck with old terms. There isn't yet a name for the intermediate value of pDIF before 1.00-1.05 randomization, its hard to express that as being capped at 3.0 first while discussion still refers to the absolute final value as pDIF.

I'm simply providing a model. If you can find anything wrong with it, please bring it to attention. I feel like I'm getting Burden of Proof shoved in my face. --Ranzear 16:29, January 26, 2010 (UTC)

We are both aiming for a model, so np, but big difference is i feel like you don't seem to try hard enough to actually match theory to available in-game data. 2 examples i don't understand :

a) you wrote "Note his 3.0 pDIF as marked. Lower damage is where pDIF was below 2.0 (which is still possible with capped Ratio)": this data have been with Soboro a 2H weapon. Determined cap for pDIFmin crits 2H have been shown to be around 2.89, at capped Ratio on Ronfaure bunnies. See the contradiction there ? for info, 149/52~2.865 that's not below 2.0 like you saying.
b) If i understood correctly that 0.95-1.05 theory applied on same old pDIF formulas, ok fine let's verify with data i collected on Lesser Colibris and available @ the BG link above. Let's take your example with fMAX(Ratio)=1.2*Ratio, and apply this to the following Ratios:
Ratios: 1.749    1.477
fMAX=   2.0987   1.77261
then let's multiply by 1.05:
fMAX'=  2.2036   1.86124
Resulting max DMG for Normal 2H hits (BaseDMG=103 and 96): DMGmax= floor(fMAX'*BaseDMG)
DMGmax= 226      178
RealDMGparsed= 228 and 182

... don't match ;; (and whole tested range of ratios is unmatching btw...) So where did i misunderstood your theory application ? or is this proof enough to disprove it ? Masamunai 10:43, January 27, 2010 (UTC)

Your 2.89 minimum crit:

  • 1.5 < cRatio ≤ 2 fMin(cRatio) = -0.8 + 1.2 x cRatio

Ratio = 2.2

LC = 0.00

cRatio = 2.2

2.2 * 1.2 - 0.8 = pDIF1.84 + (crit)1.0 = 2.84

This would be multiplied by the secondary randomizer for 2.84-2.98. It is simple to say that absolute minimum critical was not parsed (indeed, even crits below 3.0 were very sparse), because its far more difficult and rare for two different randomizers to roll their minimum at the same time. The issue is that you're still assuming pDIF is capped at all, low or high. It has limits, not caps, and due to the new more thorough randomization these limits can be approached but not often hit like a 'cap'.

The simplest explanation is to calculate pDIF as normal, and then apply 1.00-1.05 for minimum and maximum.

Side note: Its plainly apparent that your one-handed Ratio capped at 2.0. I hadn't seen any one-handed data or speculation until yours, as a DRK player. I'll append this into the article.

I'll pull the full data from your Kheten/Subduer chart, and take a crack at that data:

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
Lv63	Lv64	Lv65
404	404	404
1,719	1,676	1,541
128	123	101
225	217	192

I suspect you may have inadvertently gained 1 fSTR on the 404 attack equipment against level 63 and 64 mobs (section outstanding), due to mis-estimation of their VIT value or just about anything, particularly since fSTR is a function estimated by (dSTR+4)/4. In this case, a final pDIF of 2.2036 and a base damage of 104 would give up to 229.3 damage, and 1.166 * 104 for 225.25, but those decimals are going to be hard to hit (to say: anything up to 228.99 is still 228 damage), while the same equipment on the level 65 mob is correct with 103 damage:

  • L63: Defense 231, Evasion 243, VIT 52, AGI 52
  • L64: Defense 235, Evasion 247, VIT 52, AGI 52
  • L65: Defense 241, Evasion 253, VIT 55, AGI 55

The error you show with the Subduer and 1.477 Ratio, however, does not look like a change in fSTR, indeed with all cRatios less than 1.676. It may be a quirk in our pDIF calculation below cRatio = 10/6 (an estimate, double the breakpoint of 5/6). 182 damage on 96 base gives a 1.8055 value before the secondary randomization, a pDIF multiplier of 1.222. I'm going to stem a guess that there is another segment we're missing for 5/6 < cRatio < 10/6 (an estimate to match your data, which is correct above 1.666) within which x * cRatio is actually higher than for cRatio > 10/6, instead of being assumed to be equal or lower (1.2 * cRatio).

Proposal:

Max pDIF has the following formulas:
Ratio Range Function Value
0 ≤ cRatio < 0.5 fMax(cRatio) = 0.4 + 1.2 x cRatio
0.5 ≤ cRatio ≤ 5/6 fMax(cRatio) = 0.4 + 1.2 x cRatio
5/6 ≤ cRatio ≤ 10/6 fMax(cRatio) = ??? x cRatio, possibly higher than 1.2
10/6 < cRatio ≤ 2.2 fMax(cRatio) = 1.2 x cRatio

Try finding a new fMAX for that cRatio range, I wouldn't be surprised if it was 1.25*cRatio, and don't doubt it being higher. --Ranzear 12:08, January 27, 2010 (UTC)

Sorry pretty much ALL data posted since last year until now prove that : 1. the slopes of old StudioGobli formulas are wrong, and actually lower than 1.2 (and not higher like you say) 2. the caps changed, which have been debunked by my tests and posted on this same very discussion page.

So why not simply admit those formulas are plain outdated and have to work out new equations, matching as much data as possible, and simple ? Honestly, i would suggest you to come to that BG thread instead of flooding that discussion page (and also modifying the main page while it's not even 100% proven, verification tags or not). I'm sure some other dudes than me would understand better what you meant, and will try to actually elaborate your theory with data. Regarding my parse @ 404attack, i just double-checked, no error and i'm sure my STR stayed [email protected] as i was checking almost before engaging each mob. Up to you now, but you can be sure i'll come back here when BG will definitely debunk a 100% proven model.Masamunai 13:09, January 27, 2010 (UTC)


-- I went out to check that level difference is applied after capping cratio. I used monk (292 skill), a D+19 weapon, which is rank 2. Target mobs were qiqirn poulterers in the ruins, they were level 78 and had 72 VIT and 311 defense. DEF was verified using /check command and VIT was verified using the "dmg 1 method", as in, you hit them for only zeros if str=58 and you get some 1s if str=59. This means that fstr is capped and is 10 if you have more than 108 str. Under those conditions, and if cratio caps at 2.0, you expect to see maximum crits of 201 and maximum hits 159 (verified on too weak mobs). I used chaos roll, berserk, 129 STR, dia III, and punched the qiqirns 231 times (I know the sample size is still low). This puts my attack at more than 650 so the ratio is greater than 2.45 (=attack/defense). If the cap was applied after level correction your cratio would be 2.45-3*0.05=2.3 which would then be capped at 2.0. If the cap is applied before level correction, you get a cratio of min(2.0, 2.45)-0.05*3=1.85. Considering that the parse gave a maximum of 151 for non crits and 195 for crits, the second option is likely (just need more sample size obviously to be sure of it).Pchan 16:23, June 8, 2010 (UTC)

  • Done more melee hits with same conditions as above : 368 melee hits with a maximum of 154 now and max crit reached 201 (which is the hard cap for crit with D+19 weapons). This 201 number is expected because you can max crit even if ratio is below 2.0, and the level difference is small. However still no sight of the numbers 155,156,157,158,159.
  • I'm at 500 melee hits now and still no 155,156,157,158,159.Pchan

I'm going to stop you to correct some terms. Ratio is Attack/Defense, and cRatio is Ratio after level correction (c~orrected~Ratio). Referring to cRatio as 'before correction' is improper and a major source of confusion.

I presume I've calculated your base damage with capped fSTR correctly as 64, 32+3+19+10. This gives a capped 3.15 crit 201.6 damage, which you've found precisely. Your 154 damage is a 2.40625 pDIFb, divide out the max 1.05 secondary randomizer for 2.2916 pDIFa, and divide out peak pDIF multiplier of 1.25 for one-handers for and indicated 1.833 cRatio, which indicates level correction after capping Ratio at 2.0. Reverse the process, 64*1.85*1.25*1.05, and you'll find that your max melee should be 155.4, but is fairly unattainable because of the trapezoidal distribution after secondary randomization discussed here: http://www.bluegartr.com/forum/showpost.php?p=3699711&postcount=58 http://www.bluegartr.com/forum/showthread.php?t=90966&page=3

I need to make a better entry in the main article about the secondary randomizer, which is a final 1.00-1.05 multiplier on final damage intended to vary capped 3.0 pDIFa crits. --Ranzear 20:44, June 9, 2010 (UTC)

  • How would you predict the maximum on a too weak mob, with capped ftr ? 64*2.0*1.25*1.05=168. I spent a while and got 159 as maximum on level 15 mobs. ~~ (note : the qiqrns are level 77 or 78, while it's important to understand how the max damage is calculated, it still not contradictory with cap being applied before level correction). Pchan
    • What level 15 mob were you fighting, in particular? Remember that there are two randomizers at work, and both must 'roll high' to see peak damage, which to see the very top 1% would require 10,000 hits just on probability. The difference is with critical hits, where capping 3.0 pDIFa eliminates one randomizer and allows you to see the other at work. --Ranzear 18:48, June 10, 2010 (UTC)

Found some blog with pretty serious entries using high level technics for statistics, in particular one entry regarding melee pDIF based on my Data : http://robonosto.blogspot.com/2010/07/new-melee-pdif.html i got pretty surprised to read he got pretty much same conclusions as me: 2handed and 1handed weapons have still same formulas "format", but different caps and slopes; and more importantly, he also disproved the need for 1-1.05 so called "2ndary randomizer" with simple and straight forward formulas. And finally he also made a possible conclusion that such trapezoidal-like distributions MAY be the result of 2 randomized functions convoluted (either product or sum).
Personnally, on a totally different topic, i have now my war still lvl75 with a Bonesplitter DMG100 and STR100, so might have interesting testing possibilities, but i don't know yet what kind of tests i could do, if someone have an idea i'm open to suggestions...Masamunai 09:40, August 9, 2010 (UTC)

And if you'd actually RTFA, he doesn't refute anything but the name 'secondary randomizer', instead citing the exact same thing that pdif is a function of two separate randomizers to provide the trapezoidal distribution. He also merely states that it is irrelevant to calculating mean pDIF, which is true until you want to deconstruct to raw ratio to verify numbers. --Ranzear 19:36, August 9, 2010 (UTC)

RTFA = ?
I think there is a misunderstanding : yes he citing a function of 2 randomizers BUT NOT as a global multiplier as you explained on this discussion page, but as 2 "true" randomized functions, which either the product or sum would yield not only the variance seen @ extremums but most importantly the spike observed when the pDIF range contains pDIF=1 value (which have a direct impact on averages). See the difference ? a simple randomized multiplier of 1-1.05 wouldNOT yield that. Also a simple randomized multiplier wouldnot explain why min curve (either normal or crits)have different slope than max ones, while 2 independent randomized functions explains that.
Now if you ask which function exactly, honestly main potential candidate i see is the BaseDMG=D+fSTR function, but i might be wrong and could be another 3rd portion to add to the original formula...
Regarding the blog mention about 2 randomizers being irrelevant, it's actually and ONLY to calculate the mean, he said clearly he don't care at all about exactness, implicitly pointing @ max and min values. This discussion page on contrary has those max/min values as MAIN goal. So in my humble opinion, finding that secondary randomized function is actually relevant to this topic.Masamunai 20:28, August 9, 2010 (UTC)

PDIF coefs proposal[edit]

For both 1Handed and 2Handed weapons, i tried correlation tests with all MIN and MAX dmg values (from available data - normal hits) for 1.5<Ratio<2 (27 samples tested) :

I'll use abbreviation SSD standing for "Sum of Squared Deviations" between measured DMG values and estimated DMG values with modelized pDIF coefs, expressed in integer.

pDIF(min) = 1,148348813*Ratio -0,730765574 , R²=99,7535615%, SSD=30 (exact for 1Handed, 2-3dmg difference for some 2Handed samples)

Regarding the correlation tests for max dmg, i tested 3 scenarios :
a) no 2ndary multiplier
b) 5% 2ndary multiplier
c) 5% 2ndary randomizer
Main difference between cases b and c is, like explained in previous post, an additional multiplier just multiply values generated by "main" randomizer, nothing else... while ADDING a 2ndary randomizer to main one lowers frequencies of dmg values in BOTH ends of main randomizer's frequency chart, resulting in the observed testimonies (in other words, gives a trapezoïdal curve).

Results :
a)pDIF(max) = 1,088856239*Ratio + 0,302514865 , R²=99,7837418%, SSD=22 (exact for some samples, -1dmg difference for most samples)
b) correlation made on (MeasuredMaxDMG/BaseDMG)*(1-5%) (corresponds to what Raellia calls "pDIFa"), then SSD made with INT(BaseDMG*(EstimatedpDIF*(1+5%))) :
pDIF(max) = 1,034413427*Ratio + 0,287389122 , R²=99,7837418%, SSD=42 (exact for 2 samples, -1-4dmg difference for most samples)
c) correlation made on (MeasuredMaxDMG/BaseDMG)-5% , then SSD made with INT(BaseDMG*(EstimatedpDIF+5%)) :
pDIF(max) = 1,088856239*Ratio + 0,252514865 , R²=99,7837418%, SSD=22 (exact for some samples, -1dmg difference for most samples)
Conclusion1: all modelized max dmg values are underestimated, most noticeably in case b.
Conclusion2: case c generates litterally exact same values as case a.

Can conclude safely with the following formulas :
pDIF(min) = 1,14*Ratio - 0,72 capping @ 1.56 for 1H(ratio=2), 1.85 for 2H(ratio=2.25)
pDIF(max) = 1,0888*Ratio + 0,31 capping @ 2.48 for 1H(ratio=2), 2.76 for 2H(ratio=2.25)
Note: 2ndary randomizer is already included in the constant 0.31 for pDIF(max), ie 0.25 from case a +0.05=0.30 (case c) than add 0.01 to make sure to obtain 0 DMG value below observed ones.

Important notes:
- those formulas concerns only the range 1.5<Ratio<caps, and only Normal hits.
- those formulas are approximations, i'm pretty sure noone will get 100% exact formulas that way.
Another way would be to work directly on modelizing the randomizers, each using the basic formula Constant+Floor(Range*RAND()), then convoluted each other to produce a single equation producing both Normal and Crits DMG in one step. Once its shape matching observed frequency charts, would have to correlate Constants and Ranges with Ratio, fSTR and Weapon's D. Then from there it's easy to get MIN & MAX by setting each RAND() to 0 or 1. (and even averages, set @ 0.5 since Excel's RAND() are uniform)
So far, i still fail to reproduce the shape observed @ Ratio<1,5 (with spike @ pDIF=1).Masamunai 19:14, August 26, 2010 (UTC)

I did some test againste even mathc SandSweepers on the test server in the range 0.75 to 1.25 pdif. There is a clear high frequency spike (that amounts for ~30% of the total number of hits) that is lying excatly at the weapon DMG (+ 0~5%). The rest of the distribution is nearly uniform, so I deduced that the distribution of the random hits follows this law : d=(U*T1+(1-U)*DMG)*(1+e), where U,T1,e are independant e is uniform on [0,0.05] (this is the so-called randomizer, appear to be uniform) U is a bernouilly variable of parameter ~0.3 (doesn't seem to vary with ratio in [0.75,1.25]) T1 is uniform on [true min pdif, true max pdif] where the "true" min & max pdif are the values you would get without the randomizer. More info here : http://forum.square-enix.com/ffxi/threads/20989-defense-attack-damage Under 0.75 pdif, it follow the same rules (it seems) because then true max pdif = weapon damage. --Pchan 18:07, February 19, 2012 (UTC) Above 1.5 pdif, it only seems to follow the same rule while U=1, so the bernouilli has a parameter equal to 1 and the low is d=T1*(1+e) so it is not uniform though close to (logarithmic on the edges).--Pchan 18:08, February 19, 2012 (UTC) between 1.25 and 1.5 pdif the lowest values equals the DMG of the weapon and there is a spike with decreasing frequency as r grows to 1.5. The model still holds in this case, and so far it is confirmed that the model holds for 0.5<=r<=1.5 and even r>=1.5 if you assume that that the spike as 0 frequency at this point.--Pchan 10:28, February 22, 2012 (UTC)

PChan, a few things to say about your discoveries:
- can reformulate damage formula in simpler terms with:
FinalDamage = Floor[Floor[ Base Damage * (U*pDIFa + (1-U))] * Rand(1;1.05)]
- can you post in BG Mathy subforum your parses on which you based your Bernouilli parameters, so we can reproduce and check against ours tests please ?
Masamunai 20:05, February 29, 2012 (UTC)

Ok I ajusted the correct pdif range based on the data posted below and the discussion we had on the official forum. Based on hypothesis that the frequency spike occurs with the parameter q=(b-a)_max-(b-a) I find that the slope of the curves is necessarily 10/9 (the real upper value would therefore have 1.05*10/9 as a slope). The formulae I posted come easily from this. (b-a)_max=5/6=0.83.. matches observation and the frequency spike being ~28% around r=1 also mathces observed data. It appear that b is capped prior to 2.0 just like crits at r=0.95 because data suggests that (b-a)=0.79... @ r=2 (using a brew for intsance).--Pchan 10:01, March 26, 2012 (UTC)

This article uses material from the "Talk:Level_Correction_Function_and_pDIF" article on FFXIclopedia and is licensed under the CC-BY-SA License.