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    Pyrrhic Kleos Modifier

    Soooooo... I have the flu and can't make sense of my data, but I think I have enough data to refine our understanding of Pyrrhic Kleos. Someone do my thinking for me!

    Here is a link to some of the numbers. After I recorded a dozen or so from each case, I stopped recording individual things and just started updating the max/min.

    Relevant numbers:
    * Minimum 1H Crit pDIF is 2.625
    * Maximum 1H Crit pDIF is 3.15
    * I have Critical Attack Bonus II (7.6~8%, for some reason it always tests at about 7.6 or 7.8% instead of 8% for me)
    * Shamaya/Leonstrife showed that stats other than STR and DEX were not mods, so though I provide them you're free to ignore them

    Edit: Nevermind, fever broke.
    My best fit looks like 30.5% STR/30.5% DEX with 1.355 fTP (91/256)

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    Quote Originally Posted by Byrthnoth View Post
    * I have Critical Attack Bonus II (7.6~8%, for some reason it always tests at about 7.6 or 7.8% instead of 8% for me)
    You mean when testing /w melee hits or ranged crits?

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    Melee hits. With a D55 dagger and 8% Crit Attack Bonus you'd predict a max damage of 187, but the max I observe is 186. I don't know why.

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    Quote Originally Posted by Byrthnoth View Post
    Melee hits. With a D55 dagger and 8% Crit Attack Bonus you'd predict a max damage of 187, but the max I observe is 186. I don't know why.
    Ah okkays... maybe some kind of order of operations thing?

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    Quite possibly, but as far as Masa is concerned there's no rounding in the pDIF equation (except between damage determination and weapon type damage bonus).

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    Melee hits. With a D55 dagger and 8% Crit Attack Bonus you'd predict a max damage of 187, but the max I observe is 186. I don't know why.
    Final damage is floored. Because 55*3.15 is 187.11. You have to land in that 0.11 to get a 187, otherwise you're 186.99 or below and floor to 186. You just don't have enough data and the chances of rolling both pDIF and Secondary that high are next to nil. Your given numbers are mechanically inaccurate, but that demonstrates the disparity well enough.

    Nor enough data on the Kleos testing to even approach a 3.15 pdif. Easy to demonstrate:

    (441/3.15)*2.625 = 367, your low was 380
    (516/3.15)*2.625 = 430, your low was 442

    You're better off taking mean or median and setting them equal to 3.0 pDIF to work anything useful from those numbers.

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    Quote Originally Posted by Raelia View Post
    Final damage is floored. Because 55*3.15 is 187.11. You have to land in that 0.11 to get a 187, otherwise you're 186.99 or below and floor to 186. You just don't have enough data and the chances of rolling both pDIF and Secondary that high are next to nil. Your given numbers are mechanically inaccurate, but that demonstrates the disparity well enough.

    Nor enough data on the Kleos testing to even approach a 3.15 pdif. Easy to demonstrate:

    (441/3.15)*2.625 = 367, your low was 380
    (516/3.15)*2.625 = 430, your low was 442

    You're better off taking mean or median and setting them equal to 3.0 pDIF to work anything useful from those numbers.
    Well.... by your own theory, 3.0 should be the mode of the distribution but not necessarily the median or the mean. I didn't continue to collect anything but max and min really, so all those numbers are inaccessible anyway. Look at the original testing (listed on the page) and tell me that my numbers are somehow less accurate. Then try and play with my numbers and come up with an alternative hypothesis. The tolerance that fits all four sets of data is not very high.

    Also, I guess I should point out that this is hardly the first time I've gone out hitting things with Kila +2s and I'm not the only one to express the suspicion that it's less than a perfect 8% boost.

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    Quote Originally Posted by Byrthnoth View Post
    Also, I guess I should point out that this is hardly the first time I've gone out hitting things with Kila +2s and I'm not the only one to express the suspicion that it's less than a perfect 8% boost.
    I've heard this too, which is why I asked. With ranged hits it's an exact 8% (and it's easy to see it's always an exact integer with crit damage+.) Either melee crit damage+ works different, or more than likely, there's a rounding/truncating that takes place at one or more steps. (Melee damage used to be able to go above 3.0pdif and cap at 3.0 so you could get accurate/exact values fairly easy. Since then it's gone through a few changes, so my guess is one of those changes is what causes the discrepancy.

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    Always truncate at every step unless you are certain you shouldn't (off the top of my head, only things I can think of where you don't are when combining WSC, and the MAB/MDB function). This most likely includes every step of the pDIF function, and most definitely crit damage bonus, since that isn't even part of the pDIF function, but rather a bonus tacked on after.

    Second, minimum pDIF for 1h crits should be 2.58, no? According to what's on wiki, the minimum for regular hits is 1.58 (which I went out and tested briefly; 38 D + 12 fSTR weapon resulted in a 79 damage hit, which shows either 1.59 or 1.58 pDIF), so minimum crit should be 2.58 or 2.59, unless for some reason, crits give more than a 1.0 boost all of a sudden.

    Third, WSC percentages have never ever taken the form of fractions, so 30.5% is very likely incorrect, as the game probably only accepts integers. Most secondary mods are also not unique, in that other WS use the same percentages. Look at a list and you'll see a lot of 30/30, 30/50, 20/20, 50, 35, 32/32 and so on. That's not to say that they can't add new WS with unique mods (Yu is 28/28 DEX/INT, which, unless I missed something, no other WS uses), so while it could be unique, if it doesn't fit well-established patterns, it might be worth taking a second look - doubly so if you have to use an awkward fTP to fit such a limited data set.

    With these things in mind, your values could fit 32/32 STR/DEX, with 1.375 fTP (11/8), which is noticably less awkward, but I'm not particularly confident in this, because the values skew towards the lower end of the spectrum, whereas crits tend to be in the upper end more often. This could be the result of a higher fTP, and lowering it to 1.34375 (43/32), the values fit somewhat better, but for a more proper estimation, we need more data.

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    Crits have given more than a 1.0 boost to pDIF since the 2H update. The minimum for 1H weapons is 2.625 now. Aeolian Edge is also 28/28. Also, it's easy to say that we floor it, but hard to say what we floor it to, and some things in the game look like they're just floating point operations.

    Perhaps the mods are 30%/30% and something is weird with my DEX case. Basically I needed to add 1 base damage to the DEX case while not adding one base damage to the STR case in order to make it match up. Here's my issue:
    * 32/32 with 1.375 fTP puts me a 10-20 damage below the theoretical damage cap on all four cases. Considering how many WSs I did and how many times I hit near but not above my maximum damages, while extending the lower bound several times, it seems very unlikely to me that I could be this far off the cap. You wouldn't be talking about missing the pDIF cap in a sample size of 30, you'd be talking about missing it by a good amount in a sample size of over 120.
    * 30/30 with 1.375 fTP puts me low for the DEX trial by 2 damage points regardless of which order I do my operations in. Considering I wasn't swapping gear for that case (AF3+2 hands stayed on all the time) and the fTP isn't modified by TP (though I always went at exactly 100 with Reverse Flourish), I don't really know how it could be high unless I literally wrote the numbers down wrong (possible I guess, I had a fever). If I boost crit damage from 7.8% to 8% and change the order of operations so it's *mod,1)*.85,1), then it almost fits (509.87, but not 510)
    * 30STR/32DEX with 1.35 fTP works well enough.

    Point is, it isn't 20%STR/30%DEX with 1.5 fTP. I'm willing to tolerate an accuracy of +/- .05 on the fTP and +/- 2% on the mods.

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    Quote Originally Posted by Byrthnoth View Post
    Crits have given more than a 1.0 boost to pDIF since the 2H update.
    Uh... no?

    You know about the 5% randomizer right?

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    Quote Originally Posted by Raelia View Post
    Uh... no?

    You know about the 5% randomizer right?
    Have you seen Masamune's "Distribution Study 1.1.xls"? If you look at his data, there's no way you can conclude that Crits are a simple +1 to cRatio or pDIF before or after the 5% randomizer.

    I mean, apart from genuinely looking at his numbers, you can just look at the graph and go "pDIF min has a plateau at 1.0 cRatio that I don't see in the crit pDIF min" and be done with the whole "pDIF +1" theory. That theory hasn't been accurate since before the 2H patch.

  13. #13
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    Quote Originally Posted by Byrthnoth View Post
    Melee hits. With a D55 dagger and 8% Crit Attack Bonus you'd predict a max damage of 187, but the max I observe is 186. I don't know why.
    On which mob ?
    Asking because if i remember correctly Pyrrhic is multi-hits(?), so would need to test with one-shotting the mob (ideally lvl1 rabbits), and then remove data with main hit missed (1% TP return).

    On the flooring steps topic, i confirm Raellia saying there is a AT LEAST a flooring in the end of calculations (so it doesnot display decimals in game).
    BUT
    Like you pointed out from my "old" data, can't prove @ 100% at anything before that final flooring... (ie the whole damage formula). That means ANY formula "format" (with or without multiple floorings, with 1, 2 or more randomizers, etc...) can work, as long it fits parsed damage.
    BUT
    As Rena stated, realistically, the game using integers sound an ideal and logical in terms of implementation. So would search for all possible combos of {WSC, fTP, dSTAT if applicable, WSalpha?}, one of them using round sexy numbers. But easier to say than to find :s

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    I did it on L0 rabbits/worms/pugils outside in East Ron.

    Resist trait bullsheeeet... I end up killing a lot of 75-77 BRD mobs when I do Dynamis - Sandy, currently my record is 32 "Resist!"s out of 164 Silence casts, so about a 20% proc rate for Resist Silence job trait.

    Also, I've noticed that Resist Sleep doesn't work against Repose. I assume this was already known, but it's a nifty additional thing. 46 "asleep" vs. 49 casts, 0 "Resist!" Regardless of my mule's shitty divine skill, it's pretty obvious that Repose isn't hit by the Resist Sleep trait.

    9/8: Updated numbers, 20% is holding strong.

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    Original post in this thread:
    Quote Originally Posted by Byrthnoth View Post
    Soooooo... I have the flu and can't make sense of my data, but I think I have enough data to refine our understanding of Pyrrhic Kleos. Someone do my thinking for me!

    Here is a link to some of the numbers. After I recorded a dozen or so from each case, I stopped recording individual things and just started updating the max/min.

    <snip>
    Post in What's Better? thread:
    Quote Originally Posted by Byrthnoth View Post
    40%/40%/1.5 fTP predicts my max damage for the first setup would be 556, unless I'm doing something wrong:
    floor(79*.4*.85) + floor(84*.4*.85) = 54
    43+12+54 = 109
    109*3.15*1.08*1.5 = 556

    Keep in mind that I stopped updating the raw data and stuck to the max/min after a few because I couldn't get the parser to work at the time and got lazy. That's why the lines often end on a max/min. I did at least twice as many WSs as are listed on that page to make my range. It's difficult to get the low end of the range, which was particularly frustrating in the STR Kila +2 case.

    Also, if you think my data is sparse you should look at the methodology that came up with 20% STR/30% DEX/1.5 fTP <_<. I link it from bgwiki.

    I just went back and looked at my PK numbers. They're actually fairly accurate and complete when it comes to covering the range of possible values. For any test with only crits and constant stats, the ratio of max to min should be 1.2, because all that can change is pDIF. Max 1H pDIF is 3.15, min 1H pDIF is 2.625. If I was higher on the min than reality, then I'd end up with a lower ratio than 1.2. If I was lower on the max than reality, I'd end up with a lower ratio than 1.2.

    If you take (Max/Min)/1.2 for the four samples I give, you get no value lower than 95%. Specifically, you get:
    0.967105 0.958618 0.968109 0.972851
    So you can tell that I'm covering most of the possible values. Based on the way we think pDIF works (with the 1~1.05 multiplier), it's more likely that I'm missing values at the low end of the spectrum because I'd have to roll low twice to see them. Thus, I basically chose my mods to fit the high end of the range. They may not be perfect, but they're more accurate than any of the other options given.
    As a follow-on to a discussion in the What's Better thread that referenced this bit of research, here's my analysis for Pyrrhic Kleos:

    You're right, I was only taking the differences, not going back and verifying the values made sense in the final calculation.

    In any case, I think I forgot to scale things down for the crit attack bonus damage. I'd kind of disregarded it as not relevant, since it applied to all samples equally, but it actually increases the range of values, which changes the expected differences, which means the values I'm getting are obviously overestimates.


    The reason I considered the data sparse is because the easiest feature to pinpoint in a decently large sample is the 3.0 pDif value. Overall distribution of a max pDif crit has approximately 50% of all values above 3.0, and 50% below. Since there are 2.5x as many possible values below 3.0 as above, the actual frequency of any given result will be about 2.5x higher for pDifs at 3.0 and above.

    Because of that you can also see that the intervals between samples will tend to be much smaller for the 3.0+ pDifs. The smaller the distribution range (ie: the lower damage the weapon), the easier it is to pick this feature out.


    Trying again.

    Primary range scaling should see approximately 1/3.5 in the 3.0+ range.


    Agi Kila base:
    range: 380~441
    adj. range: 352~409 (57 diff)
    57/3.5 = 16.29
    1/3.5 ~= 16
    3.0 should approximate to 409-16 = about 393 (difficult to approximate from graph, but this is indeed a value I'd consider)
    base damage = 131

    Agi Kila +0.2 fTP:
    range: 439~505
    adj. range: 407~468 (61 diff)
    61/3.5 = 19.37
    1/3.5 ~= 19
    3.0 should approximate to 468-19 = about 449, probably 450 (matches approximations taken from graph)
    base damage = 150, +/-1

    Gain from 0.2 fTP = 19

    1.0 fTP ~= 95

    131/95 = 1.379 (1.375?)

    (since I left the 1.08 in before, this ended up as ~1.49)

    However, the +/- 1 values indicate that the gain from 0.2 fTP could be 20 instead of 19. In that case, 1.0 fTP matches 100 damage, and 131/100 ~= 1.3 fTP. If the difference is 18 instead of 19, final fTP works out to about 1.45.

    I would consider the 1.3 and 1.375 to be the more likely values, but will look at WSC for all three.


    Kila +2 base = 43
    Capped fStr = 12
    total = 55

    Total base damage would be 90, 95 or 100. Therefore WSC has to be a total of 35, 40 or 45 from a base of 79 str & 84 dex.

    If we assume the WSC multipliers are equal for str and dex (not guaranteed, but possible), then we can use their total and get a multiplier:
    35 / 0.85 = 42
    40 / 0.85 = 48
    45 / 0.85 = 53
    79+84 = 163

    42/163 = 25.77%
    48/163 = 29.45%
    53/163 = 32.52%

    So, 25%, 30% or 32.5%



    Multiple stats in WSC are added before flooring.

    Dex sample: +0 str, +56 dex
    Str sample: +52 str, +11 dex

    Str has slightly higher results, but also had higher stats. +7 in raw stat total could end up about +2 in WSC (~30%), and there's a 6 point difference in the max sample seen (2 * 3.15 ~= 6). As such it's not unreasonable to assume that the two stats have equal value, though a 30%/40% split wouldn't show up in this small a variation.

    Continuing (for now) with the assumption that str and dex are equal:

    Dex version:

    79+84+56 = 216
    @25% == 45 WSC
    @30% == 54 WSC
    @32.5% == 59 WSC

    55+45 = 100 * 1.45 = 145
    55+54 = 109 * 1.375 = 149
    55+59 = 114 * 1.3 = 148

    @3.0 - 3.15 (*1.08)
    145: 469-492
    149: 482-506
    148: 479-503

    Max sample: 510
    Estimated 3.0: 492

    Therefore we already know the values are wrong. Base damage with fTP has to be a minimum of 151.

    So let's go back to the fTP tests.

    Rather than taking the range, look at what the potential max is for an estimated 3.0 value:

    +0.2 fTP: We know the 3.0 has to be above the 479 mark, which would only allow a max of 502, when max seen was 505. 483 to 488 range is all possible, as they allow max values between 507 and 512.

    After taking out the 1.08 crit mutiplier, 483 to 488 neatly bracket 150 as the base value for the 3.0 multiplier (483 is base 149.33; 488 is base 150.66). 150 base would have a max value of 509, slighly above the observed 505.

    Base: It cannot use the 414 value for 3.0. 426 works out. After cancelling out the 1.08 crit, 395 allows for a max of 414, when max sample was 409(441). Base value for that would be 131.66, but is almost certainly lower than that. 131 is viable. After applying the 1.08 crit, it would allow for a max value of 444 (max observed was 441). Min value is also within range (131 would allow a min of 343, when min observed was 380(352)).

    Overall, very high likelihood that base is 131 and +0.2 fTP is 150. Therefore we should be using the 19 point spread, which means 95 total base damage without fTP.

    131/95 = 1.3789

    I had approximated that as 1.375, but that would actually not work. 95 * 1.375 = 130. Since the ratio is on the high side, what about 1.4?

    95 * 1.4 = 133, too high
    94 * 1.4 = 131, exact.

    Because of all the rounding going on, 94 base damage is entirely possible. So, once again:

    94 - 55 = 39

    39 comes from 79 str and 84 dex = 163 total (if they're the same multipliers)

    39 / 0.85 = 46 or 47

    46/163 = 28.22%
    47/163 = 28.83%

    If we took 30%, the final value would be 40 instead of 39, putting us back at 95 base damage before fTP.

    Valid ranges:

    Base:
    Observed: 380-441
    Calculated: 95 * 1.4 * (2.625|3.15) * 1.08 = 376-451 (within scope)
    3.0: 430 (viable)

    +0.2 fTP:
    Observed: 439-505
    Calculated: 95 * 1.6 * (2.625|3.15) * 1.08 = 430-516 (within scope)
    3.0: 492 (viable, if slightly high; may be slightly lower since gorgets may be 100/1024 rather than a true 0.1)

    And for the stat tests:

    Dex:
    Observed: 439-510
    WSC: 79+140 * .3 = 55
    Total base: 55+55 = 110
    Calculated: 110 * 1.4 * (2.625|3.15) * 1.08 = 436-523 (within scope)
    3.0: 498 (viable, if slightly high)

    Str:
    Observed: 442-516
    WSC: 131+95 * .3 = 56
    Total base: 55+56 = 111
    Calculated: 111 * 1.4 * (2.625|3.15) * 1.08 = 438-527 (within scope)
    3.0: 502 (a bit high)



    Overall, the range fits within the scope for all instances. I'm not entirely happy with the 3.0 markers, and would prefer, I think, that the total baseline be 94 instead of 95, but that would require changes in the selected WSC values.... hmm. A thought occurs, will try some math for it.

    Overall results are close enough for now.

    Final verdict (overridden; see post below):

    1.4 fTP
    30% Str
    30% Dex

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    Some slight tweaking:

    Str: 28%
    Dex: 30%


    Base:
    Observed: 380-441
    Calculated: 94 * 1.4 * (2.625|3.15) * 1.08 = 370-444 (within scope)
    3.0: 424 (good)

    +0.2 fTP:
    Observed: 439-505
    Calculated: 94 * 1.6 * (2.625|3.15) * 1.08 = 424-509 (within scope)
    3.0: 486 (good)

    And for the stat tests:

    Dex:
    Observed: 439-510
    WSC: 79*.28 + 140*.3 = 54
    Total base: 55+54 = 109
    Calculated: 109 * 1.4 * (2.625|3.15) * 1.08 = 430-516 (within scope)
    3.0: 492 (good)

    Str:
    Observed: 442-516
    WSC: 131*.28 + 95*.3 = 55
    Total base: 55+55 = 110
    Calculated: 110 * 1.4 * (2.625|3.15) * 1.08 = 436-523 (within scope)
    3.0: 498 (slightly high)

    If fTP is not exactly 1.4, but like 1.399 or whatever, due to /1024 fractions, the str set changes to 433-519 (within scope) and 3.0 at 495 (good).

    New final verdict:

    fTP: 1.4
    Str: 28%
    Dex: 30%

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    Looks good to me. I was uncomfortable with my fTP and knew that the STR and DEX mods were likely not the same, but couldn't get anything I really liked.

    Just out of curiosity, exactly what order do you do your flooring in for mods? I've been just multiplying alpha, mod%, and stat together and flooring it once per stat, then adding the floored numbers together with fSTR and base weapon damage.

    Edit: Oh, one more thing. It think they may have buffed Desperate Flourish's gravity effect. Monsters were moving much slower than I remembered last night.

  18. #18
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    Quote Originally Posted by Byrthnoth
    Just out of curiosity, exactly what order do you do your flooring in for mods? I've been just multiplying alpha, mod%, and stat together and flooring it once per stat, then adding the floored numbers together with fSTR and base weapon damage.
    Examples:
    30% of 145 dex:
    145 * .3 = 43.5, floored to 43
    43 * 0.85 = 36.55, floored to 36

    30% of 145 dex && 28% of 102 str:
    145 * .3 = 43.5
    102 * .28 = 28.56
    43.5 + 28.56 = 72.06, floored to 72
    72 * 0.85 = 61.2, floored to 61

  19. #19
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    Quote Originally Posted by Motenten View Post
    fTP: 1.4
    Str: 28%
    Dex: 30%
    sound weird, from a programmer point of view, to use a 2% difference between stat mods...

    Maybe there is another working combo [fTP, WSCs] ?
    Also, is Byrth really sure about his parsed min/maxs ? asking this because i got same problem with my pDIF tests... and this can change easily the 2% analysis from Motenten.

    EDIT: Shamaya has some tested numbers buried here, leading him to STR20 DEX30 fTP1.5

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    I went back and looked at the logs yesterday. No gear swapping and I found my maxes. It's not TP dependent, so I don't know what else it could be. It's weird to mix a 28% and a 30% mod, but SE has used 28% before on things like Aeolian Edge.

    I don't think I'll be repeating the test any time soon, as it took me several hours over two days. The only reason I had enough patience to do it at the time was because I had the flu and flu medicine.