pDIF caps testing for 1H & 2H weapons

Masamune · 2009-09-28 16:08

Hello everyone,

After i saw the last comment on this page Talk:Level Correction Function and pDIF - FFXIclopedia, the Final Fantasy XI wiki - Characters, items, jobs, and more, i went out for some more testings with different weapons and obtained these results (Note i reused also Kegsay's results) :

Targeted mobs: Wild Rabbits & Tunnel Worms, East Ronfaure; also Gigas(non-MNK) & Weapons Qufim
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 jobs75 with way enough STR and attack to be in capped situation (capped fSTR and cRatio).

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

Spoiler: show

----- 1H Conclusion ----
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 = 2.654
PDIFcritMAX = 3.15

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

Spoiler: show

----- 2H Conclusion ----
PDIFmin = 1.869-1.869
PDIFmax = 2.747-2.758?
PDIFcritMIN = 2.89?
PDIFcritMAX = 3.150

As you can see in those results, i managed to get pDIF caps values matching all tested weapon ranks, unless someone show a screenshot with lower or higher dmg values than those listed (under capped conditions and same DMG rank of course).

Feel free to point any error(s) if i did any in my calculations too.

**Shamaya** · 2009-09-29 00:13

This approach to pDif testing should be pretty straightforward and from what I can see it seems like the right approach, with pretty decent samples. I like how you did multiple weapon ranks--I wouldn't have even considered that if I was testing it, probably.

This is kind of convenient for me coming up right now, as I just did a comparison where knowing the different pDifs (though these are only caps) would be essential (GA/Nin vs Man/Rid vs Swordchucks) (1,2).

Biggest shortcoming of this for general pDif of course is that it is only going into the capped-range (as you already know/stated). Of course it could be equally possible that the pDif curves are very different otherwise, chock-full with different tier points and the like. But for pDif caps this looks to me like valuable data.

I didn't double-check your numbers though and I'm not very good at margin-of-error for samples

Masamune · 2009-09-29 04:22

Well actually, during test on lvl1 weapon, i noticed for example yu get 24 dmg as what "supposed" to be lowest crit on your current parse. Then, on a warpcudgel test, you get 64 for supposed lowest crit. When yu do the simple math 24/9 and 64/24, you'll see both have "large" range of "possible pDIF", hence the idea to use highest possible ranked weapons like an Axe to narrow those pDIF ranges as much as possible. Problem that stopped me is those missing values, just need someone to play "smack-em-all" on rabbits/worms to prove their existence, nothing else.

Next, regarding general pDIF testing i'm not there myself yet, but i think pertinent to show this link : http://www.bluegartr.com/forum/71816...handers-2.html as it is Araelus partial results and some interesting talks with RingThree and VZX. Problem it seems to be outdated maybe they all quit, keeping their secrets in their grave ? :/
But good side of things is, if those capped pDIFs are at least "known", then can conduct rigorous tests on other things like RR/Drake's crit rate@100TP, etc... right now it's so easy to confuse a low crit'd WS with an High Normal dmg one...

**ringthree** · 2009-09-29 10:13

I will try to see if I can find Araelus, he has disappeared for a little while.

Masamune · 2009-09-29 17:09

That would be nice thank you Ringthree, btw don't you have some results yourself to share ? plz.

Edit: Calculations updated: my luck smiled to me tonight and got lowcrit63 on rabbit with a Kaiser Sword(DMG=15), and NormalHigh 59 with same weapon on GigasTrapper@Qufim.

EDIT2: got more missing values, 1H pretty much entirely debunked. Only 3 values to go for 2H... Cleaned the 1st post also for clarity.

**Motenten** · 2009-12-03 06:37

Some testing.

Using Soboro
100 Str and 437 att as sam/dnc w/Hasso

I want a target that can take a lot of hits (make it easier to sample), but that I can cap fStr and cRatio on. Calculated that fStr and cRatio should always be capped vs Savanna Dhalmels (Lvl 34-37).

fStr should be +12
Weapon base is 40

Total weapon damage = 52

Code:

Melee Damage
Player            Melee Dmg   Melee %   Hit/Miss   M.Acc %  M.Low/Hi    M.Avg  #Crit  C.Low/Hi   C.Avg     Crit%
Motenten             120584  100.00 %     939/55   94.47 %    96/141   119.23    218   149/163  158.80   23.22 %

Known max crit: 52 * 3.15 = 163.8 >> 163. Match.

Melee range: 96-141, 46 point spread on 790 non-crit samples. Typical frequency if equally distributed ~= 17, which fairly well matches most sample points (generally 15-20 per point) except for values below 99 and above 138, as well as a few local minimums.

Min melee is 96 == pDiff of 1.846153846154 - 1.865365384615

Masamune's test ended up with a min pDiff ranged to 1.869-1.869. 97 is reachable with that range, and after 500 hits I was expecting that to be the minimum. 96 is slightly below that, and likely a factor of insufficient samples in Masamune's test.

However when we work on trying to predict pDiff ranges from cRatio, we usually assume an even distribution of values. That is not the case with what I saw:

Code:

Melee
       96:    1
       97:    2
       98:    5 -- 1.90, low edge frequency tail
       99:   20
      100:   16
      101:   20
      102:   21
      103:   13
      104:   10 -- 2.0, second lowest outside of edges, distinct minimum
      105:   12
      106:   21
      107:   20
      108:   17
      109:   19
      110:   15
      111:   20
      112:   18
      113:   14
      114:   12 -- 2.20, local minimum
      115:   19
      116:   17
      117:   17
      118:   21
 ^    119:   13 -- median & mean, 2.3, local minimum
      120:   14
      121:   20
      122:   17
      123:    9 -- 2.37, lowest frequency outside of edges
      124:   16
      125:   21
      126:   15
      127:   17
      128:   17
      129:   22
      130:   20
      131:   18
      132:   14
      133:   16
      134:   25
+     135:   30 -- 2.60, maximum
      136:   14
      137:   12
      138:   22
      139:    8 -- 2.68, high edge frequency tail
      140:    9 -- 2.70
      141:    2

We have a few values at each end that have extremely low frequencies compared to the main set. If we consider that the tail edges are an artifact of the alleged 'bonus' factor, then we actually want to look primarily at the main frequency limits of 99-138.

99 pDiff range: 1.903846153846 - 1.923057692308
138 pDiff range: 2.653846153846 - 2.673057692308

Possible full range pDiff spread: 0.7307884615385 - 0.7692115384615

Expected full spread value: 0.75, or +/- 0.375

Center point at that spread would then need to be between 2.278846153846 - 2.298057692308
That doesn't include any of our typically expected limits, with the upper limit on the spread being just a smidge below the 2.30 value.

However, if we consider the possible limit as expressed in fractions of 1024, as so many other things in game are...

Possible cRatio limit value: 2 + 300/1024 == 2.29296875 -- That's within our possible center range.

And we can then express our outer pDiff limits with:
0.375 == 384/1024
Outer limits of 1+940/1024 - 2+684/1024

Applied to base damage of 52, results are: 99.734375 - 138.734375
That's sufficient to match our observed results.

Next, the tails.

There are 3 values in each tail edge, which suggests a symmetric addititional factor.

First estimate: +/- 50/1024, given the supposed 5% bonus.

1+890/1024 = 97.1953125
2+734/1024 = 141.2734375

That's sufficient for the upper limit, but not the lower one.

Second estimate: +/- 60/1024.

1+880/1024 = 96.6875
2+744/1024 = 141.78125

And that matches, giving us a first guess at the outer tail limits.

Given that the frequency declines for the outermost damage values (96 and 141), it's probably not just another flat random amount added in, but some sort of mini bell curve or similar. The non-tail limits are right in line with the other nearby distribution values, though, so the range is probably not higher than +/-60 and then capped inside the normal limits.

Personal speculation (just a gut feeling based on the distribution patterns): There are two +/- 30 extra values added in that give a potential to reach +/-60, but cancel out to give a net 0 much of the time. That would give a very small chance of reaching numbers at the far ends of the tails. Note that after running the numbers I don't think this is the exact distribution pattern, but something similar is likely (+/- 40 is another possible pattern).

Comparing with Masamune's Numbers, and using the above values for pDiff min/bonus min:

Relic Bhuj: 17/16, 16 observed
Jupiter Staff: 88/85, 85 observed
Orc Piercer: 116/113, 114 observed
Iron Ram Lance: 163/158, 158 observed
Erlking's Kheten: 209/202, 203 observed

Observed are all within range of predicted. Need to see an actual distribution curve to see whether the base pDiff min is notably distinct, and matches predicted.

And pDiff max/bonus max:

Relic Bhuj: 24/24, 24 observed
Jupiter Staff: 122/125, 126 observed
Orc Piercer: 162/166, 168 observed
Iron Ram Lance: 226/231, 233 observed
Erlking's Kheten: 290/297, 299 observed

The maximums, however, do not quite work out. All but the lowest of the observed values are outside the predicted range. The main outlier is the Orc Piercer, as it hits a peak that's significantly above the requirements for the other weapons:

(in order)
2+744/1024
2+757/1024
2+773/1024
2+759/1024
2+761/1024

All of the others can be reached with a +80 on the bonus portion of the value. Orc Piercer needs +90. With +80, even, I would expect to see a 142 result on the Soboro test, which didn't occur, though I could accept it as an extremely rare result. If the bonus pDiff could reach +90 then the Soboro should be able to hit 143, and that just doesn't seem realistic given the test values. Perhaps only if +80 was at a 0.1% chance and +90 was a 0.01% chance, or similarly unlikely. Perhaps 10 +/-10 bonus totals? Definitely bell curve-like.

At the very least, though, I would like to see whether the normal max pDiffs correspond to the predicted values on the distribution charts (if Masamune still has the parses for these tests). If they do, then we can consider the main portion of the pDiff range worked out.

Next, the crit distributions.

Code:

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

Here we see another artifact-laden distribution. It's clear that the values below 3.0 are an entirely different class of results from the values at 3.0 and up. We can also see that the 3.0-3.15 cannot really be described as the result of a 'possible' random dispersion effect of multiplying by up to 1.05. If it were only a possible addition we would see a much higher spike at 3.0, and reduced frequencies above that. Instead we have 3 points out of 8 on the curve that are at ~32 count, and an overall dispersion that implies a fairly flat constant distribution.

149 is at lowest, 2+887/1024, and at most 2+905/1024. The most likely subtracted values in there are -120/1024 and -128/1024.

Our lowest non-crit value was set at a limit of 1+940/1024, which is reasonably close to what we're seeing here, if given a +1. It's also interesting to note that that's within range of the secondary random dispersion method if it were set to +/-40.

6.4% of all crits are below 3.0. If we use our estimated general pDiff range, 10.8% of non-crits should be below 2.0. That's close enough at these sampling numbers that it could reasonably be considered the results of crits whose pre-crit pDiff was below 2.0.

The remaining ~90% of crits are all distributed within the range of 3.0 to 3.15. It's clear that once the crit cRatio crosses 3.0, pDiff randomness can't reduce it below that point. However it seems impractical at this point to make any guesses as to how the distribution works within that range.

While there's a slight prejudice towards the lower end of the 3.0+ range, overall it looks like you could just consider it a flat random domain between 3.0 and 3.15 once you cross 3.0.

**Mirax** · 2009-12-03 08:12

Wow this is awesome, you guys rock, lemmie know if you need me to do anything.

Masamune · 2009-12-03 08:28

Nice study Motenten.

Just 4 things i would add:

1.Mind proving your Dhalmels test subjects have indeed a VIT and def values low enough to be under capped conditions ?

Personnally, i only checked Catoblepas within Dhalmel family, but results can maybe help you, assuming all Dhalmel type mobs share same family stats:

Spoiler: show

Then, using StudioGobli formulas to determine VIT&AGI, i found matching results with assumptions WAR/war (since they can DoubleAttack) DECC for VIT/AGI/Def/Eva, which gives me following values:

Spoiler: show

So if i use same DECC WAR/war asumption for your tested Dhalmels, i obtain the following stats:

Lvl34 :
- VIT=35
- AGI=37
- Evasion=115
- Defense=132

Lvl35 :
- VIT=35
- AGI=38
- Evasion=119
- Defense=135

Lvl36 :
- VIT=37
- AGI=40
- Evasion=123
- Defense=139

Lvl37 :
- VIT=37
- AGI=40
- Evasion=125
- Defense=141

...assuming their defense/evasion mods from sub /war don't get "trumped" due to to being so low level.

So max expected VIT would be 37, resulting in (with your STR100) an uncapped fSTR=63, but like you calculated fSTR cap with Soboro basedmg40 = 12,

so indeed fSTR will be capped @ 12 on any of those Dhalmels.

However, i don't think anyone figured precisely the cRatio cap for 2Handers (and maybe also 1Handers got ninjaed too?), see 4th point below.

2. Yes i still have my pDIF caps test parses and the Excel sheet that comes with them, but i'm not sure what do you want exactly ?

3. Araelus (and VZX, RingThree) did also some pDIF testings on Lesser Colibris @ http://www.bluegartr.com/forum/71816...handers-2.html but for simplicity i'll just quote directly his results i think relevant to current topic:

Originally Posted by Araelus

STR84, Soboro

Code:

Level	Ratio	dmg min	dmg max	pDIF min	pDIF max	f(min)	        f(max)
63	1.658	57	103	1.163265306	2.102040816	0.701607543	1.267817139
64	1.630	54	102	1.102040816	2.081632653	0.67609866      1.277075247
65	1.589	52	101	1.083333333	2.104166667	0.681770506	1.324208097

Those werenot under capped conditions, but already provides 3 pDIF/Ratio points.

4. Shamaya PMd me some times ago some pDIF results TTaru JP blogger did @ http://translate.google.com/translat...istory_state0=
But since it's poorly translated, i didnot understand at all their methodology... but got at the end of the article this interesting curve:
http://www.bluegartr.com/forum/attac...1&d=1259850398

/em lights the Elmer signal, {Call for Help} /translate Can i have it?

So if i assume x-axis is actually cRatio, i noticed some of my pDIF caps results were matching @ cRatio=2.5.

Then, since you used 437 attack on mobs underlvld (so no lvl correction), cRatio uncapped = 437/141 (taking highest def from tested Dhalmels) = 3.0993.

so indeed cRatio should be capped @ 2.5 on any of those Dhalmels, assuming indeed cRatio cap = 2.5 :s

**eva00r** · 2009-12-03 08:39

Horizontal Axis = Attack/Def ratio
Vertical Axis = PDIF
Red zone = Crit
Green zone = Normal Hit

I think the graph above and raw data from thread starter is somehow conflict, only an exception of 3.15 = max crit PDIF.

**pchan** · 2009-12-03 08:41

The values for normal hits seem uniform, except maybe around the 'maximum', which is not that much more frequent either (sample size issue maybe ? ), and extrem walues. 97% of the mass lies in [98,138], 3% outisde.

The values for critical hit seem uniform for [149,155] and [156,163] and 94% of the mass is in the last interval.

This made me think of magical resists distributions. Under "capped" condition (probably linked to capped cratio), 5% of the hits get extreme values while 95% of the hits are uniform in a given interval.

What could happen is : after the critical hit roll, the game rolls a second time to determine in which interval you are, similarily to how partial resists work. It would be interesting to see if the intervals remain the same for other mobs, still under capped cratio. The intervals for critical hits seems to be simply both 1/2 intervals of the pdif interval.

**Nameless** · 2009-12-03 08:48

alot of the 2hand pdif stuff was talked about in this thread a long while ago, and the numbers kinda match with what you guys have. I hope this helps your research a bit.

http://www.bluegartr.com/forum/showt...t=68018&page=4

I did a bit of a summary on post #94 based on the tests done on post #41 and some other datas through out the thread. Unfortunately for some reason it doesn't match with the data you guys have for cratio lower than 1.8. The numbers do match with what you guys have when cratio is higher than 1.8.

I personally believe some sort of tier is going on here, and I thought we were close in finding out the whole thing but no one ever tested the figures for tier 3 and perhaps tier 4 (if there is one) so we never got a complete conclusion on this.

Masamune · 2009-12-03 09:36

Motenten, from the link Nameless posted above, i stumbled upon a post from Yarko with very similar testing conditions than you @ http://www.bluegartr.com/forum/showp...2&postcount=60

he got a max @ 142 (and min@97), so Soboro real range should be (combining your results and Yarko's):

min=96 , max=142 ?

Originally Posted by Yarko

Done one more test in regards to capped pDIF / pDIF fluctuation using Soboro on WW monsters: lowest hit 97 (4 times), highest hit 142 (2 times), sample size 500 non critical hits.

Base damage for Soboro = 40 + floor(40/9)+8 = 52

pDIF(max): Since damage gets floored, pDIF(max) is
142,000/52 = 2,730 < pDIF(max) < 142,999 = 2,749

Also, i plugged your Soboro results into my excel file which have already other 5 2H weapons min/maxs, to discover:
- your mins normal & crits are much lower than other 5 weapons i tested
- your normal max also lower than other 5 weapons i tested.

i managed to guess the following:
- for pDIF normal max: observing a 143 is enough to match other 5 weapons, -> would reduce pDIFmax=[2.755;2.760]
- for pDIF crit max: observing 163 already matches other 5 weapons, -> no changes, pDIFcrit max=[3.148;3.152]
- for pDIF normal min: your 96 observed is lowest of all weapons, so i would have to go back with OrcPiercer to observe a 113, -> would reduce pDIFmin =[1.863;1.865]
- for pDIF crit min: your 149 observed is lowest of all weapons, so i would have to go back with them to hit even more lower min dmg observed. -> would reduce pDIFcrit min =[2.883;2.884]

**Motenten** · 2009-12-03 11:10

Originally Posted by Masamune

Mind proving your Dhalmels test subjects have indeed a VIT and def values low enough to be under capped conditions ?

Well, you already showed that the fStr is sufficient. Your caculated Def for the highest level dhalmels is 141. A 3.0 cRatio on that would be an attack of 423. Since I had an attack of 437, and as far as we know the cRatio cap must be under 3.0, I would say that it is capped there as well.

Originally Posted by Masamune

Yes i still have my pDIF caps test parses and the Excel sheet that comes with them, but i'm not sure what do you want exactly ?

I'd like to see the frequency distribution from the Offense Details tab. Specifically, I'd like to see if you got the same low frequency tail effects at either end of the hit distribution, and if you did I'd like to see if the limits of the main distribution results match the values predicted in my speculated formula.

Basically, just post the non-crit melee lists for each of those weapons from the Offense Details page.

Originally Posted by Masamune

Araelus (and VZX, RingThree) did also some pDIF testings on Lesser Colibris...

Actually, there was a very interesting picture there. Check post: http://www.bluegartr.com/forum/showp...7&postcount=23

Now, check the graph of the points from my test:

http://img697.imageshack.us/img697/6...lpdifftest.png

While Araelus tried to make a polynomial fit to it, we're both getting the same effect of a large portion of the damage frequencies being relatively stable, but a few low-frequency trailers at either end of the curve.

Originally Posted by Araelus

The more troubling part of my current finding, to my interests, is the extremely low frequency of the results at the upper and lower bounds. 9 instances ad 13 instances out of 9,885 attacks mean it is very rare to see the actual pDIF(min) or (max).

Basicly, he's seeing the same effect I was, but is trying to solve it a different way (either as a single bell curve or as a piecewise quadratic) by actually including those points as part of the base formula.

My own approach is with the belief that there is a secondary formula applied on top of the flat random distribution that together generates a bell curve effect at either end, and may possibly be somewhat weighted towards the higher values (based both on Masamune's tests and the fact that Araelus saw a general upward slope on the main plot area when trying to use the piecewise formula). My own data shows a 5.5% upward slope on the non-tail values.

He also said that his data was the aggregate of 3 mob levels with slightly varying defenses (would be about +/- 1.5 damage at either end). He said he'd post pics of the separated data later, but apparently dropped the subject before completing it. I would very much like to see those separated plots, though, as they may help confirm the 'walls', and that the long slopes at either end are more the effect of subsets of data as the mobs shift levels.

Originally Posted by Masamune

Shamaya PMd me some times ago some pDIF results TTaru JP blogger

I agree with eva00r on the meaning of the graph, and also believe that it is inaccurate. At the very least, the minimum non-crit pDiff is less than ~2.16 as the graph would indicate.

@Nameless: Potentially useful, but at the moment I'm not trying to determine tiers. I'm working only with capped attack in order to figure out the pDiff range issue. If that can be solved then it will be easier to go back and work on the different tiers later.

@Masamune: Ok, Yarko's data point puts +80 as fully viable for the max secondary variance. From that I'm willing to accept the possibility of reaching 143 (at least +84) as an extremely rare case, but would still like to see it to confirm. That also makes the stacked secondary effects of +/-40 x2 easily possible, though it would still have to be a bit higher to reach 143.

- for pDIF normal max: observing a 143 is enough to match other 5 weapons, -> would reduce pDIFmax=[2.755;2.760]

For that limit range, secondary buffs would need to be able to reach +89 to +94, so setting as +90 as the target limit if my secondary formula idea holds any water.

Masamune · 2009-12-03 11:21

I'm not sure to understand why you interested in frequency, i thought only max and min observable dmg are relevant :s

Sended you my parses + excel file @ your email Mote.

**Motenten** · 2009-12-03 11:23

Min and Max are all that people have been reporting, and it was all that mattered in the old-style formula. However the results I (and Arealus) am seeing indicate that it's more complicated than that.

Masamune · 2009-12-03 11:35

yes i understood what Araelus and you meant by "more complicated", but my question is actually "How does this matter ?" since what poeple interested is obtaining something resembling to that japanese curve so can calculate dmg from it, so why care about frequencies of dmg between bounds?

i mean that not caring about frequencies would allow much more freedom to find a matching formula.

**Byrthnoth** · 2009-12-03 11:47

If there's a possibility of the distribution being uneven, then it does matter because the value you actually care about is your average pDIF value, which will be skewed away from (Max+Min)/2 if the distribution is asymmetric.

**Motenten** · 2009-12-03 11:49

"How does this matter?" I don't know the answer to that question. At this point, noone knows the answer, and that's the problem. I'm trying to explore a path that looks like it has some interesting potential. Your parses can provide data to either further support it or to refute it. Either way, it's important to know.

Ignoring the frequencies doesn't give you more freedom, it just gives you a different set of restrictions. You only get the pretty curve after doing the work to figure out what makes the curve exist in the first place.

Masamune · 2009-12-03 11:57

Originally Posted by Byrthnoth

If there's a possibility of the distribution being uneven, then it does matter because the value you actually care about is your average pDIF value, which will be skewed away from (Max+Min)/2 if the distribution is asymmetric.

yes that's 1st answer to my question i thought, but Araelus and Mote results pretty much show both a symetric curve bell-like or 3 piece-wise, so... (min+max)/2 shouldnot be that much skewed ?

Anyways i'll let you guys care about that matter, i'll just watch how it turns out :s

**Mojo** · 2009-12-03 12:14

(min+max)/2 would be a good approximation for an average pDIF when dMax and dMin are both increasing at the same rate (from the data we have so far), but fails when either one of them is 0 (which occurs on most parts of the pDIF function.) So if you really want a good average, understanding the distribution of pDIF is crucial.

Thread: pDIF caps testing for 1H & 2H weapons

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