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  1. #41
    Sea Torques
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    I know I type like I know a lot, but personally I am not well read into the new stuff and I go largely by this,
    Which is from Masamunai's data, and looks to be an approximate ~1.66 (for my general purposes, an approximation is ok). So I don't know where 1.6 or 1.55 is coming from, unless there is contradictory evidence? Though Masamunai's stuff is usually pretty thorough from what I've seen. Plus, I don't know why the randomizer would matter either, in the case of sample sufficiency or on the other hand side-by-side sample comparisons. I assume the randomizer can proc at a low end multiplier of 1.0 in which case pDif will of course = 'pDifb', so the min remains the same.

  2. #42
    Sea Torques
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    I'm referring to one-handed weapons (he also has a graph for that).

  3. #43
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    Masamunai's testing actually has an error. He gained an fSTR on the lowest level Lesser Colibri, because they have slightly lower VIT than stated by the wiki, and wouldn't fess up to it on the wiki discussion. I even tested for it myself to be sure, while he instead insisted that my model was wrong the whole time.

    Thats likely where the 1.55 came from.

    Another contributing factor is the flooring of final damage. This is a bit of an extreme example, but with base damage 18, 28.8 damage at 1.6 pDIFb is floored to 28 damage which then looks like 1.55 pDIFb instead. Flooring can certainly push you 'under' a minimum.

    Theres also still a strange portion between 5/6 and 10/6 Ratios where the max pDIF multiplier seems to go up to 1.25, but this too he'll have nothing to do with and instead insists that his numbers are perfect and again that my model is wrong. I could also suspect that the target's defense was overestimated.

    The problem then with that 1.66 min pDIFb is that the secondary randomization is almost never 1.0. I have never seen an exact 300 damage crit with Cruadin outside of Campaign. I use it everywhere, camping low NMs and such, just about so I can actively look for such occurrences and monitor my pDIFb easily with that 83+17 damage.

    The minimum is far more difficult to reach than the maximum, because you must roll that 1.6 multiplier and a 1.0 secondary randomization on the same hit. Its not surprising that 1.66 was the lowest found, since its min-pDIFa with a fairly average 3% secondary randomization.

    Crits handle the first part of that themselves when they cap at 3.0, making the maximum appear much more readily (still, someone once postulated that the new pDIF max was Pi, 3.141 XD), needing only to roll maximum on the secondary randomizer to see the peak.

    tl;dr Because crits cap but minimums do not, the minimum pDIFb is much more an extreme approximation and is effectively asymptotic.

    Its really hard to knock people out of math mode and into slightly more abstract thinking. Just the same, everyone swore up and down that 2.76, a 'found' number, was the 2-hander melee pDIF 'cap', when actually its a mathematical limit found by 2.2 * 1.2 * 1.05 (Ratio * pDif multiplier * 2nd Randomization). To make a lame movie quote: Its the difference between knowing the path and walking the path.

    Also please note:
    You're looking for bDmg + fStr: [(your weapon's base damage) + (that base damage, divided by nine; remove the decimal) + 8] * 3.15
    This is when fSTR is capped, so no 'testing' on Kirin folks! Any mob above ~lv50 is suspect on lowish-STR melee, especially crabs which have crazy VIT scaling.

  4. #44
    Sea Torques
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    The 1.66 pDIFa minimum in question is actually corresponding to ratio around 2.09 (2-hander case).

    Also, suppose the secondary randomizer is a continuous uniform random variable and is applied as you say. Then there is practically zero probability of drawing exactly 1.0. But because of flooring, you would see 300 fairly frequently (1 out of every 15 times on average). I'm not proffering an explanation for the mismatch between predicted and actually observed, just pointing out a consequence of the postulated secondary randomizer (the term "randomizer" suggesting that it's considered a uniform R.V., if not necessarily continuous).

    Then again, I guess you would never see 315 damage if the secondary randomizer were a continuous random variable of some sort, so maybe it's discrete, like 1.00-1.05 with increments of 0.001, yet not uniform, but that would still not account for the lack of observed 300s. What is the lowest, maximum (...) crit damage that you've seen?

  5. #45
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    I think I could honestly say that even a <305 crit is rare. 309 is fairly common, and I think I've seen a 304 now and then. I think I've seen a 302, but within memory, never a 300 or a 301. Running on pure anecdote here.

    I suspected increments as well after looking at some Masamunai data, and postulated about it never being 1.00. A 1.01 increment if 303 is the lowest I can get, but then all of my crits would be multiples of 3 and there would only be five values. A 0.005 increment would floor to 301 and give ten values. A 0.001 increment could floor to 300.

    Just now I'm thinking about how they increment other things like Haste in divisions of 256. 16ths of .05 are 0.003125 increments, which floors to 300. 8ths, 0.00625 increments, would floor to 301.

    But I'd rather back up a moment, because I think I've seen in parses that there are about ten values in a set of capped crits (and perhaps an extra or two sneaking in that are uncapped but >3.0 after secondary rand).

    0.005 increments would give:
    301, 303, 304, 306, 307, 309, 310, 312, 313, 315

    But the issue with looking for a pattern like this is the sub-capped-pDIFa's sneaking in with a high secondary randomizer and hitting a non-increment value over 3.00. If we truly could pick out the incrementation, it'd be easy enough to pick out these erroneous values as well.

  6. #46
    Masamune
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    Raelia, if you can give us a measured proof that lvl65 Lesser Colibris have another VIT value than 55, be our guest. Also during those parses, i made sure my STR stayed the same whole time (spellcast //sc d), so hard to fuck up my fSTR...
    Without a proof for that particular VIT value, no use to bash at my ass while i didnot post anything from my parses on official wiki page, since i know none of those regression lines i obtained gives accurate final dmg values for min/max... Same for your "asumption" of "2ndary randomizer"... which has 0 consistent measures to back it up.

    On other hand, I'm agreed on 2 things:
    a) the displayed dmg values on log might be actually floored values, pretty much like TP values not displaying their decimal(s). That doesnot help an exact extrapolation from regression between parses.
    b) If you look closer at the "spike" in dmg frequency distributions i did for Ratio<1.5, they all shows increased frequencies for dmg values within a range of exactly 1-1.05, nowhere else.
    There is also another similar area for crit values, for distributions starting from Ratio>~1.8, you'll notice also an increased frequency for dmg values corresponding to pDIF>3 until cap 3.15. but since this "area" is larger than the one for normal hits, the "spikes" are less noticeable until higher Ratios.
    So can safely say there is "something" going on "on top" of regular dmg formula to induce those observed increased frequencies, maybe some static step function having a 5% width (1-1.05=5% and 3-3.15=5%) convoluted to the regular normal/crit dmg formulas.
    Just proved there is no need for any "2ndary randomizer" there, unless i misunderstood your whole arguements here, @ wiki and at Allak.


    Lastly for Shamaya, regarding the concept of "sufficient" sample sizes, i always thought had just to use the formula for 95% certainty we used for crit% testings to then conclude the Confidence Intervall ?

  7. #47
    Sea Torques
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    It seems 1.55 is more likely a consequence of flooring than testing methodology, so let's just leave it at that. Now, for more speculation.

    Another observation about 1-handed pDIF behavior: it seems that along with a maximum critical pDIF cap of 3.0, there could be a minimum non-critical pDIF floor of 1.0 for certain ranges of attack/defense ratio. So, pDIF of 1.0 shows up more than you would expect. Then, when the secondary randomizer is applied, that could be why you get the observed spike at left endpoint of the observed empirical distribution.

    Now, for lower ranges of attack/defense ratio, the base pDIF distribution could still be uniform. Then, a function could be applied that turns 50% of the randomly selected pDIF values to 1.0 pDIF, which could be why pDIF 1.0 shows up more than expected. Then, when you apply the secondary randomizer, that could be why there is the observed spike sitting in the middle of the observed empirical distribution. Perhaps, as the attack/defense ratio goes lower, the "spike" would shift to the right.


    Finally, I doubt anything in this game is really continuous. As we have already seen for hit rate and critical hit rate, 0.5% increments are not possible, so we probably should consider pDIF and the "secondary randomizer" as being discrete probability distributions in a sense, and I said in the past, the sum of two uniform random variables follows a trapezoidal distribution, which can describe the observed shape of pDIF.

  8. #48
    Masamune
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    Quote Originally Posted by CDF View Post
    It seems 1.55 is more likely a consequence of flooring than testing methodology, so let's just leave it at that. Now, for more speculation.

    Another observation about 1-handed pDIF behavior: it seems that along with a maximum critical pDIF cap of 3.0, there could be a minimum non-critical pDIF floor of 1.0 for certain ranges of attack/defense ratio. So, pDIF of 1.0 shows up more than you would expect. Then, when the secondary randomizer is applied, that could be why you get the observed spike at left endpoint of the observed empirical distribution.

    Now, for lower ranges of attack/defense ratio, the base pDIF distribution could still be uniform. Then, a function could be applied that turns 50% of the randomly selected pDIF values to 1.0 pDIF, which could be why pDIF 1.0 shows up more than expected. Then, when you apply the secondary randomizer, that could be why there is the observed spike sitting in the middle of the observed empirical distribution. Perhaps, as the attack/defense ratio goes lower, the "spike" would shift to the right.


    Finally, I doubt anything in this game is really continuous. As we have already seen for hit rate and critical hit rate, 0.5% increments are not possible, so we probably should consider pDIF and the "secondary randomizer" as being discrete probability distributions in a sense, and I said in the past, the sum of two uniform random variables follows a trapezoidal distribution, which can describe the observed shape of pDIF.
    Agreed with everything except little correction for :

    The "spike" you see on parses is actually at a constant position: it never moves elsewhere than pDIF=1-1.05, it's the range of dmg values that moves with Ratio. That's why you start to see that spike appearing at Ratio @ 1.5 and below on the very left edge of distribution. Then when Ratio decreases, the spike staying at a constant position while the range of frequencies "moves" towards the left, gives the illusion that the spike moves toward the center of the distribution, to finally go to the right edge of lowest ratio distribution.
    I couldnot test lower ratios as war/dnc or thf/dnc, but i wouldnot be surprised to see that spike disappear around Ratio<~0.7, to see it reappear on crit distributions again.

  9. #49
    Sea Torques
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    Yeah, that was a bad description I gave.

  10. #50
    Masamune
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    mmm realized last posts were derailing topic :s my bad.

    On topic, i honestly think easiest and simplest way to test that belt latent would be to use values we are absolutely sure 100%: the crit cap=3.15x your baseDMG.

    Hardest parts to test on mobs :
    a) on which you are sure to get a capped Ratio (lvl1-15 mobs for example) + constant fSTR (ie constant STR and mob_VIT)
    b) parsing a dmg value higher than 3.15xBaseDMG can take a lot of hits, due to its rarity.
    c) parsing one value higher than 3.15xBaseDMG may not be enough to quantify exact bonus from belt, so might go for even more sample size to get a 95% certainty on highest parsed dmg value being the actual highest "boosted" value.

  11. #51
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    This:
    Quote Originally Posted by Masamune View Post
    Same for your "asumption" of "2ndary randomizer"... which has 0 consistent measures to back it up.
    Followed by:
    Quote Originally Posted by Masamune View Post
    So can safely say there is "something" going on "on top" of regular dmg formula to induce those observed increased frequencies, maybe some static step function having a 5% width (1-1.05=5% and 3-3.15=5%) convoluted to the regular normal/crit dmg formulas.
    Just proved there is no need for any "2ndary randomizer" there, unless i misunderstood your whole arguements here, @ wiki and at Allak.
    I never realized someone could go from blind, mouth-foaming, rageful denial to confirming the exact idea in the course of three paragraphs.

    Yes, Masa, that is exactly what the fuck I was talking about. This is the same treatment you gave the idea on Wiki discussion and it makes me rage so hard that you can't so simply apply it as others in this very thread already have and see it working. That final 5% spread is an independent second randomizer after the standard formula, making the mathematical limits (again, they are not 'caps', I wish that word would disappear from pDIF discussions) much more elusive. There is precisely a need for a revision of the 'known' damage model to accept this new, easily apparent, randomizer.

    As an example. The odds of rolling a 1 on a 20-sided die is 1 in 20. Simple enough to see that limit. If you roll two 20-sided dice and multiply them, your chances of seeing '1' come out are 1 in 400.

    This same effect of having two separate randomizers is what obfuscates trying to bash out the forumula by endless testing. You need to apply some abstract thinking if you care to ever put this to rest.

  12. #52
    Masamune
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    mmm no sorry if my denial rages you Raelia, but your 2ndary randomizer theory -again if i understood correctly- would apply to the whole damage distribution, after initial calculations, making the dmg values observed at edges of distributions so hard to draw clean regression lines.
    Did i understood correctly ?

    While me CDF and Sham (and certainly others) just pragmatically interprets those "erratic" extremums values to either missing dmg values(since they very rare), or the flooring occuring just before displaying on game log, simple as that and we are sure of nothing since no proof about if there is indeed a flooring or not, just sounds most plausible (+ comparing to the TP formula). That's why i tried to use highest BaseDMG weapons to make that "flooring margin of error" as narrow as possible, and relatively high sample size to try to get as much extremes values as possible, but it's still there making clean regressions still hard to obtain. (NDLR: "Clean regression" means R²>0.999)
    On contrary, obtaining exact same values as observed ones using round pDIF values (like 1 or 3.15) leads us to the obvious: this is a "cap".
    The big difference between us in my opinion is that (i think) you maybe mixed the 2ndary randomizer (to reuse same term as you) we see WITHIN the range of dmg values (not only a edges values) called as "spikes", which applies only in a SMALL PORTION of the affected distribution. This has nothing to do with applying any post-formula randomization on the WHOLE distribution like you seem to theorize...

    Finally, i'm not sure to understand correctly your last sentence, but you can be sure i'm archi-against "abstract thinking" without proof with numbers (and no i'm not idiot enough to do "endless testing"....).

    Hope that clears out any misunderstanding between us.

  13. #53
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    Im thinking a crit hit boost for a kill shot seems a bit unlikely, simply because it would take a lot of coding. The game would wait for a calculated crit hit that would almost kill the enemy then boost dmg to finish it, as a coder that'd be quite the headache.

    Personally I'm going to guess it's either when mob hp is in the yellow/red or during a ws. Though do all the jobs that have fatality belt access also have critting wses? If not then I doubt SE would give a belt that procs crit bonus during ws for jobs that don't even crit in a ws, thus leaving it to be most likely when mob hp is less than a certain amount.

  14. #54
    Sea Torques
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    How I mine for fish?

    But seriously, maybe someone should come up with a list of things that have been reasonably tested already and come up with nothing so other ideas can be tried.

  15. #55
    Masamune
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    maybe Latent activates under Doomed or Cursed or similar debuff effect on ?

  16. #56
    the whitest knight u' know
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    Quote Originally Posted by urat View Post
    Im thinking a crit hit boost for a kill shot seems a bit unlikely, simply because it would take a lot of coding. The game would wait for a calculated crit hit that would almost kill the enemy then boost dmg to finish it, as a coder that'd be quite the headache.
    I mentioned before, I'm almost certain that this type of code already exists in Automatons and their AI's spell choice when their targets have low HP. It knows before their spell even lands whether it will get resisted or not and casts the cheapest one that will reduce its HP to 0.

  17. #57
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    Quote Originally Posted by miokomioko View Post
    I mentioned before, I'm almost certain that this type of code already exists in Automatons and their AI's spell choice when their targets have low HP. It knows before their spell even lands whether it will get resisted or not and casts the cheapest one that will reduce its HP to 0.
    There's a difference between casting a spell that will do close to the right %dmg vs whether or not your weapons next attack wont kill it but when critted and boosted will kill it.

    Also we're talking about some quickly made belt piece vs the entire automatons AI, the entire basis of a whole job that would have had a team of 2-3 people building it for several months.

    One's going to have the leeway to afford quite a bit more coding effort built into it XP

    I'm just saying though it's possible, this type of coding is extremely unlikely to have been implemented in a piece of armor.

  18. #58
    Sea Torques
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    Quote Originally Posted by Masa
    While me CDF and Sham (and certainly others) just pragmatically interprets those "erratic" extremums values to either missing dmg values ...
    ... (*)Lastly for Shamaya, regarding the concept of "sufficient" sample sizes, i always thought had just to use the formula for 95% certainty we used for crit% testings to then conclude the Confidence Intervall?
    I don't know what to believe to be honest. I'm neutral at the moment. In my opinion the randomizer is a good proposal, but I don't really care what is causing the variance. What matters most is that we know the min and max pDif for a given cRatio. And 'nextly', that we know the distribution. I know it's a derail to the fatality belt topic, but,
    Quote Originally Posted by CDF
    so we probably should consider pDIF and the "secondary randomizer" as being discrete probability distributions in a sense, and I said in the past, the sum of two uniform random variables follows a trapezoidal distribution, which can describe the observed shape of pDIF.
    Just to get an idea of what he's talking about, a trapezoidal distribution looks like this,
    http://www.vosesoftware.com/ModelRiskHelp/image88.gif
    This is just a random graph from a random website. So if I'm understanding what you guys are talking about (it's actually a little complicated to me), this is kind of what the distribution of pDif looks like. So 'procs' in the middle area are very common, and procs of the max/min are rare. The second randomizer would just shift the curve to the right, but the shape of the distribution would remain the same. And as Raelia so wonderfully explained, the reason this shape doesn't hold true as far as what we empirically get at the pDif crit cap, is because values above 3 (prior to the theoretical 1.05 randomizer) get floored, making high values very common. But pre-flooring, the shape is still the same, similar to what's shown in the graph above.


    (*)Anyway I really just wanted to respond to Masa's sufficient sample size comment. Testing this sort of thing is, fortunately, much different than the crit rate testing. For that testing, we wanted to find out the shape of the curve and it became a lot of work. But in this case, all we need to find is the max and the min dmg in a given sample. And as we already know the max and min at the pDif crit cap, it makes for a lot of easy testing, for things like latents, effect potency, WSC, and the like. Lemme just make a simplified example,

    Pretend that pDif crit cap min&max are 1.0 & 2.0. Now pretend we are using a base 100 dmg (weapon dmg + capped fStr = 100). Now let's say we're testing fatality belt. We know already that if the latent is not active, the max possible dmg we can have in our sample will be 200 (100 * 2.0) and the minimum possible will be 100 (100 * 1.0). So we've tested for awhile and we can't figure out the latent. And then finally, we find, for example, that in a sample w/ 5 people dead and we suddenly got a proc for 205 dmg. Higher than normally possible. So we found the latent. Now we want to find out its potency. How do we know when we have a sufficient sample and can declare we know the potency %?

    Well, the answer is simple. No matter what, when the highest possible dmg we can deal, divided by the lowest, will be equal to 2. That's because this example's pDif max (2.0) divided by pDif min (1.0), is 2.0/1.0 = 2.

    So if fatality belt were a straight +10% , then when active it would be as if the base dmg were 100*1.10, or 110. The highest dmg possible would be 220, and the lowest 110. Of course, 220/110 = 2. If the belt were +3%, our lowest possible dmg would be 100*1.03 or 103. Highest 206. Still, 206/103 = 2.

    Basically what I'm trying to say, for those that don't know (you included, Masa) is that once we find that the latent is active, we have a sure-fire, easy way to find out exactly how much the potency % increase is. That is, of course, if it were like a separate dmg multiplier in the formula.

  19. #59
    Sea Torques
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    It's not merely that the minimum and maximum are rarely observed; the frequencies of values near the extrema obviously taper off the closer you get to the extrema. I assume that a long time ago, pDIF (itself random) was observed to be uniformly distributed for some cases. Then it makes sense that adding another (supposed uniformly distributed) random factor to pDIF results in the shape we see today (after considering flooring).

  20. #60
    Masamune
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    ok thank you for the explanations for crit dmg enhanced testing sufficiency ^^
    Clearer now in my head.

    Regarding my current pDIF testings, i'm trying to estimate parameters for these type of curves :
    Spoiler: show

    Hand-drawn curves just to "shape" the idea
    http://www.developpez.net/forums/att...ndomizers.jpg/
    ... which led me, with Matlab, to something like :
    http://upload.wikimedia.org/wikipedi...uble_Gauss.png

    ... as functions of (STR-VIT), Ratio and WeaponDMG.
    Regarding the "spike", just have to "insert" a 3rd little curve at a static position corresponding to pDIF=1. Same for crits @ pDIF>3. Both of those "external" curves having a width of 5%.

    Problem for me is i have hard time finding someone who could explain/help me with estimators methods...

    Direct consequence: exact DMGmin and DMGmax functions (same for crits) are still unknown, just have a very rough highly approximated idea...

    EDIT: sorry for big image size, and mistake have to invert "pDIF max" and "pDIF min"

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