Yuki/Gekko/Kasha Attack bonus Testing

[Nightfyre]

Using fSTR = 11

base damage = 71, WSC = 56, total = 127; 128 vs level 73 Steelshells (fSTR+1)

pDif = 447/360 = ~1.24

pDif w/ Scissor Guard = 447 / 720 = 0.62

No Scissor Guard:

Lowest Wheeling: 439

pDIF = 1.975; ratio range of 2.234-2.313

Highest Wheeling: 638

pDIF = 2.871; ratio range of 2.278-2.393

if 73, pDIF = 2.848; ratio range 2.260-2.373

Apparent ratio range using the 73 figures for highest: 2.260-2.313. Average ratio: 2.287

Suggested defense reduction: 45.3%

Scissor Guard:

Lowest: 234

pDIF = 1.053; range 1.5025-1.544

Highest: 382

pDIF = 1.719; range 1.364-1.4325

Obviously doesn't fit... level 73: pDIF = 1.705; range 1.353-1.421

Apparent ratio range using level 73 data: 1.364-1.421, average 1.393

Suggested defense reduction: ~54%

---

The first set of values falls outside the established Ratio range, which calls for further examination. I've proposed a potential cause for this a few posts down.

Again, thank you for taking the time to test this.

EDIT: While it's a completely meaningless distinction, it's 4am and thus I've no qualms with being pedantic. Might it be more appropriate to say that the other WS with modified pDIF values (which manipulate fTP rather than pDIF, as opposed to WT manipulating pDIF with a constant fTP) ignore defense rather than boost attack?

[Yarko]

assumed 1.05 multiplier yields ratio = 1.289

Hey all, been away from the game for a while now.... I was curious if this mysterious second randomizer has ever been tested and confirmed?

If you take a look at this thread, where Masamune tried to figure out the new pDIF formulas http://www.bluegartr.com/forum/showthread.php?t=87774

pDIFmax and pDIFmin have roughly the same slopes, for 2handers pDIFmin slope is actually higher than pDIFmax one.... unless I'm missing something, that proves there is no such thing as a second 1.00~1.05 randomizer, as pDIFmax slope should be 1.05x greater than pDIFmin slope?

I ripped off the calculation from wiki that says fstr caps at weapon rank + 8. Halberd being rank 6 (damage / 9), again according to wiki, would make it 74 (60 + 6 + 8). Is that wrong? Anyways, yea it's a small sample size, especially for the Scissor Guard portion, but it's a pain in the ass waiting for them to use it. And if it's way off somewhere, I'd be more than happy for someone to show where and why.

fSTR does cap at 14 for Love Halberd, but for it to cap your STR-mob's VIT must be high enough.

In your case, with 137 str and using fSTR formulas on wiki, your fSTR was
floor(137-93+4)/4 = 12 on LV73 crabs
floor(137-94+4)/4 = 11 on LV74 crabs
floor(137-96+4)/4 = 11 on LV75 crabs

So

Base Damage = 60 + 11or12 = 71or72
WSC = floor(floor(137 * .5) * .83) = 56

Did you use a Gorget for your WSs? Or did you have any chance to Double Attack, and if so did you discard those WS numbers? If your fTP was really 1.75, even assuming it was on the lowest level crab, for your highest Wheeling Thrust we'd get:

pDIFmax = 638/1.75/(72+56) = 2.848

which is beyond the pDIFmax cap <_<

[Masamune]

Posted my current pDIF research results on site :
Distributions study v1.1.xls

You can go directly to the last tab "Graphs" where i've put a new 3rd Graph with all pDIF points for 1h AND 2h data, plus the current wiki formulas as a comparison.
Note: i added to wiki pDIFmax and pDIFcritMax 1.05 multiplier, just to show how useless it is.

In short, this last graph basically shows :
- each pDIF curves have different slopes, which means range of dmg values one would see in game vary depending on cRatio.
- pDIF slopes are clearly lower than the "1,2" from Studio Gobli formulas.
- the "floor" for pDIFminCrit doesnot exist anymore.
- 1H and 2H pDIF seems to follow almost same pattern except for capping at a higher cRatio for 2H.
- averages for crits seem to follow nicely pDIF=cRatio, but not for normal hits. This can be explained by the "spike" appearing in frequency charts for cRatio <1,5. Same observation for crit averages @ cRatio>10/6~1,66, but less noticeable. I suspect also for cRatio < 0,5(?) the "spike" will disappear from normal hits frequency charts to reappear on crit ones, modifying their averages.
Note: i'll try when i have some free time to test lower cRatio values, ie for cRatio < 0,8. I hope to find another inflexion point for pDIFmax and pDIFminCrit. I think maybe on PLD/rdm+dagger on Steelshells74, dispelling Scissor Guard + zoning to Cloister to get correct Steelshell level pop.

Hope this post infos will help the topic.

Regards,
Masa

P.S.: regarding the additional 5% randomizer, although it seem to not impact enough the current wiki formulas to fit data, may still have some validity with this:
When looking at the "spike" occuring when pDIF=1 belows to the current cRatio used, one would expect that spike to corresponds to ONE SINGLE dmg frequency. Actually, frequency spike shows a width of exactly 5%, not only for 1<=pDIF<=1,05, but also @ 3<=pDIF<=3,15.

P.S.2: i'm interested to know how do you separate dmg data from a Kparser parse between Scissor guard up and down ?

[Nightfyre]

Hey all, been away from the game for a while now.... I was curious if this mysterious second randomizer has ever been tested and confirmed?

In addition to Masamune's data, running the numbers without it would only raise Ratio further. I do agree that it's odd though, not sure how to approach the discrepancy.

which is beyond the pDIFmax cap <_<

This was the problem I had with the numbers, but I just ran with it. However, it seems I goofed on base D so I'm going to go back and repair that. Still way higher than 2.2, but not much I can do there.

Gorget would increase the max but we could reasonably expect your non-Scissor Guard min to have come from a non-gorget sample... yet Ratio was still very high.

[Nightfyre]

Posting mid-edit so I don't forget about this.

The equation I'm using for the non-Scissor Guard data is listed with a max Ratio of 2.0 on otherwiki, even though 2H ratio caps at 2.2. Given the otherwise unusual data obtained for that set, I think it's likely that the pDIF MIN and pDIF MAX equations are different in the 2.0-2.2 range. A small sample of WS with ~350 attack (basically naked) might provide a better non-SG data set until we verify the pDIF equations for 2.0-2.2.

[Masamune]

... might provide a better non-SG data set until we verify the pDIF equations for 2.0-2.2.

If you look closer @ data i posted above, there are data points in that cRatio range.

[Nightfyre]

I noticed, but it's difficult for me to process as my spreadsheet program reformatted all your graphs along with some other stuff. I'll take another look at it when I get on my other box tonight.

[Doval]

Hey all, been away from the game for a while now.... I was curious if this mysterious second randomizer has ever been tested and confirmed?

A long time ago I stumbled upon the fact that when mobs cap their Attack/Defense ratio, their PDIF is always 4 (even on crits.) After the 2-hander patches, I wanted to use that knowledge to see what kind of DMG mobs have on their weapons (Aegis Schism is -75% Defense, which stacks additively with Berserk bringing you down to precisely 1 Defense always.) Much to my surprise, while the Fomor hit me in the 300-400 range (pretty much what I was expecting,) there was a slight amount of variance in its damage. I never really thought about it that much, but a second randomizer would explain it.

I remember another occasion that I was testing something post-patch (I think I wanted to see if the PDIF ranges had changed) and I noticed it took a very, very large number of swings to see the absolute minimum and maximum damage numbers - I remember that what I thought was my minimum damage got replaced by a lower number after 10-20 minutes of swinging. A second randomizer would help explain that as well, since to see the absolute min/max you'd need to roll the minimum or maximum on both random number generators in the same swing. Skimming over Masamune's data, it seems to coincide with what I saw - the min/max values are very, very rare.

This was all a couple of years ago. Sorry I only have anecdotes to offer.

[Raelia]

A long while ago now Masa pushed me some data that showed the pDIF max multiplier for cRatio of 5/6 to 10/6 matches one hander's upper-end max of 1.25, and actually goes down to 1.2 for values over 10/6.

Nightfyre's numbers tipped me off to something related to this. pDIF multipliers are calculated before the attack bonus is applied, giving you a 1.25 multiplier instead of 1.2

Expecting 2.2-2.31:

pDIFb of 2.871, take out a 1.25 multiplier instead of 1.2, 2.18-2.29

pDIFb of 2.848, take out 1.25 instead of 1.2, 2.16-2.27

I know it sounds convoluted to calculate cRatio twice, but WS attack bonuses have been the last stopgap to my model being accepted, and this is a sensible explanation.

The secondary randomizer was shown by someone else on, and is easily proven with, critical hits. Criticals that reach 3.0 pDIF are capped at 3.0 and then a 1.00-1.05 randomizer is applied to make the numbers less boring, making all those capped crits fall into a 3.00 to 3.15 range except the sparse few that can dip below 3.0. Apply it to calculation of regular hits as well and it explains away a lot of discrepancies.

[Masamune]

Interesting anecdote from Doval.

Below the pDIF Chart i made from plugging all 1H and 2H pDIF points i parsed :

http://lh5.ggpht.com/_nmvGKpUuy8I/TD.../pDIFchart.jpg

The brown-colored lines are the wiki pDIF equations, + 5% secondary randomizer applied to pDIFmax for regular and crit'd hits. The other colored lines are the regression lines drawn between all points corresponding to a pDIF "category".
The Cyan lines are the pDIF=cRatio and pDIF=cRatio+1 averages hypothetic, while the light green and pink lines are regression'd averages from data.
This pic have been SSd from The actual Excel sheet available at site in my sig "Distributions Study v1.1", last tab.

One of you can explain me why the secondary randomizer clearly isnot enough to match data @ lower cRatios ? (except for pDIFmin regular hits)
Don't hesitate to point out any miscalculation i might have done, so far i failed to find any that would explain such deviances...

[Raelia]

Separate 1-handed and 2-handed graphs would be vastly more useful. Their pDIF curves are unquestionably different.

[Churchill]

Good to see a Madawc joke.

May he continue to suck.

[Masamune]

Separate 1-handed and 2-handed graphs would be vastly more useful. Their pDIF curves are unquestionably different.

Is this a joke ?
Not only the 1H & 2H pDIF charts are just near each other of this one i posted on same file and same tab, but this one with mixed point clearly show 0 data even near the wiki curves, and the deviation isnot something like 2% but more like 8% at these cRatios (means a dmg difference of about 11DMG leading to even more on WS calculations after).
Thought would be self explanatory o.O

[Amok]

Thought would be self explanatory o.O

It is and it isn't, to me anyway. I had to look at your post then at the chart then back again before I knew what I lines were what. Then I downloaded the sheet from google-code and the labels on the lines made it much clearer.

I'm surprised to see how close the pDIF=cRatio and pDIF=cRatio+1 lines are to the actual measured averages. I had always assumed that the average would always be in the center of the min-max band, but looking at cRatio=1.25 the actual average is very low in the band suggesting that the pDIF floor is applied after everything else. Well I suppose that's also obvious from the fact that the averages for 1H and 2H are the same while only the min and max values differ.

Sorry I'm not posting information and just observations, but I can't help but feel this is important information (the chart, I mean).

[Masamune]

I indeed added averages because of same observations Amok said above.

Personnally i think the real reason inducing such deviation of average for cRatio <1.5, is the boosted frequencies for pDIF=1 dmg values. Same thing can be observed, but less noticeably, near caps.

A possible solution would be to rework new slopes and offsets for wiki formulas then add on top the 5% randomizer to explain the reported anecdotes.
In all cases, it's "vastly and unquestionably" clear that wiki formulas' slopes and offsets need to be reworked. Personnally i already made my own equations from those data, giving me only 1-2DMG differences with data, but that's still not "exact" like magical WSs or nukes equations...

[CDF]

Figuring out magic damage is a joke. Flooring and randomness and poorly characterized fSTR (we "derive" a mob's VIT from the fSTR function and then use that VIT to get fSTR... wut) make it too annoying to make a thorough effort at exactness.

Speculating on the nature of the observed random factor mucking things up some more with respect to physical damage, by visual inspection there is no compelling evidence that the "secondary" random factor is a multiplier, especially considering the "band" of critical pDIF between 218/272 "cRatio" and 390/241.

Suppose that the range of critical pDIF (for any cRatio between 218/272 and 390/241) is really constant (but obviously you can't observe the range without the random factor). If the random factor were really Unif(1.00,1.05) and a multiplier, the band would widen as cRatio increases (being more obvious across a large range of cRatio), but it appears not to widen. The same conclusion is made for non-critical pDIF. 1.05 is a large enough multiplier that you would see something going on.

As a multiplier does not appear to manifest in the observed data, that pretty much leaves an additive factor as the only parsimonious explanation for the random factor. But I choose not to speculate on what value the additive factor takes or if it is even constant for all values of "cRatio."

I would just stop at estimating the slope of average pDIF for all the relevant ranges (which I have already done). And any additive random factor would have no effect on the slopes of anything. The slope of average critical pDIF is greater than 1 (~1.07 until 1.65 cRatio) and the slope of average non-critical pDIF is greater than 1 (~1.16 above 1.5 cRatio)

[Masamune]

Figuring out magic damage is a joke. Flooring and randomness and poorly characterized fSTR (we "derive" a mob's VIT from the fSTR function and then use that VIT to get fSTR... wut)

Indeed, made me lol as well when were 1st doing my calculations inr egards to mob's stats, namely VIT. But actually, i think Studio Gobli used the "square rule", ie for an equation with 2 unknown variables, use 2 different mobs(or more) to validate it. But then that arises another problem: with which pDIF lol ?

Speculating on the nature of the observed random factor mucking things up some more with respect to physical damage, by visual inspection there is no compelling evidence that the "secondary" random factor is a multiplier, especially considering the "band" of critical pDIF between 218/272 "cRatio" and 390/241.

Suppose that the range of critical pDIF (for any cRatio between 218/272 and 390/241) is really constant (but obviously you can't observe the range without the random factor). If the random factor were really Unif(1.00,1.05) and a multiplier, the band would widen as cRatio increases (being more obvious across a large range of cRatio), but it appears not to widen. The same conclusion is made for non-critical pDIF. 1.05 is a large enough multiplier that you would see something going on.

Actually, i observed bolded part when studying each of my parses ranges of dmg values, which made me conclude simply that pDIF slopes couldnot be the same @ 1.2. I admit i didnot think about a 5% randomizer could induce that ?
I would add something else which might be the strongest reason to believe in such "secondary randomizer": the spike in frequency chart observable very clearly @ cRatio <1.5 should corresponds to ONE SINGLE dmg value if there were no multiplier involved. Instead we observe any dmg value falling in the pDIF range of [1-1.05] gets its frequency "boosted", usually 2-3 dmg values. This is also observable but less clearly on criticals for all dmg values falling in the pDIF range [3-3.15].
Funnily, both those ranges [1-1.05] and [3-3.15] = 5%... coïncidence ?

As a multiplier does not appear to manifest in the observed data, that pretty much leaves an additive factor as the only parsimonious explanation for the random factor. But I choose not to speculate on what value the additive factor takes or if it is even constant for all values of "cRatio."

I would just stop at estimating the slope of average pDIF for all the relevant ranges (which I have already done).

Personnally, i stays neutral too because mainly i didnot manage to find a combo of (slopes;offsets)*5% for max pDIF normal and crits matching exactly all dmg values parsed.
Other reasons are crit pDIF min: my parses show very erratic min crit values (possibly due to low samples), but i could fix that soon thanks to Fencer ^^;
... and lower inflexion points for pDIFmax, minCrit and maxCrit... might have to do on Steelshells nearly double the effort i made on Lcolis because of Scissor Guard's unknown duration, so i can't filter damage values properly...
So yes... i just stopped for now at estimating slopes with what i have, and enjoying new content :D

And any additive random factor would have no effect on the slopes of anything. The slope of average critical pDIF is greater than 1 (~1.07 until 1.65 cRatio) and the slope of average non-critical pDIF is greater than 1 (~1.16 above 1.5 cRatio)

Mmmm... found 1 for crits avg (but offset 1.04 ~ 4% or 5%), but agreed for normal hits avg.
Normal hits avg below cRatio 1.5 appears to match nicely the formula: pDIF= 0,8*cRatio+0,2
... as it crosses pDIF = cRatio point and shows clearly how the observed "spikes" in pDIF frequency chart influences averages.

[CDF]

You don't need a multiplier to get the wide "spike." The random factor could be added to pDIF to yield the observed result.

I just don't see the bands widening, which is why an additive factor is more plausible. After plotting the data points that I was interested in (40,607 of them) and regression estimates, I did my own visualization (yes, it is ugly) to examine the shape of the bands:

http://img210.imageshack.us/img210/2808/output.png

I forgot to show what data points are from 1H and what data points are from 2H, but it doesn't really matter that much.

The red "guide lines" are parallel to the estimated regression lines (aside from the one for pDIF = 3.15). Of course, it's not like the slopes are exact (flooring, finite sample sizes and random variability, etc.), but obviously the slopes for critical and non-critical average pDIF are different, so there is no simplistic rule to relate normal pDIF to critical pDIF (like "cRatio +1"), but I wonder whether such rules were ever valid. (The third regression line is just to obtain an estimate of how average critical pDIF increases when attack/defense is high.)