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  1. #1
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    Uh oh, Rae's gonna make pDif simple.

    Or: How I learned to stop worrying and love using a variable twicea buncha' times.

    Thread and concepts within, as well as some new concepts I formulated, rolled up as of 1/14/2012

    Making my own thread so as to not hijack Moten's, if as much to keep our systems distinct. I've crammed all of my commentary and elaboration into spoilers to try and keep the post initially concise, but definitely read them before raising questions, contraditctions, or rebuttals. Besides comment titles, raw edits will be in italics.

    Ratio = (Player Attack)/(Mob Defense)

    2-hander Ratio caps at 2.25 (not 2.2, explanation below)
    1-hander Ratio caps at 2.0

    Apply level correction as previously known, cRatio=Ratio-(0.05*dLvl) only for Mob level > Player level else cRatio=Ratio, but in the future it may be found that raw Ratio might be used in place of cRatio in the formula below.

    pDif has two randomizers, Primary and Secondary.

    Primary works upon cRatio and is given as:
    (11/10)*cRatio-0.65+rand*0.85

    How this Primary randomizer was determined
    Spoiler: show
    Primary Multiplier is actually a function of cRatio bounded by:

    Maximum = 1 + ( RAE / cRatio )
    Minimum = 1 - ( LIA / cRatio )

    Where:
    RAE = 0.30+(cRatio-1)/10
    LIA = 0.55-(cRatio-1)/10


    Throw these together and with some algebra, which I'm notoriously averse to, it spits out the combo above

    The method above is simply how RAE and LIA were determined to be fairly static across a range.

    It was found under the working that that Max and Min Intermediate pDif are:
    Max = cRatio+RAE
    Min = cRatio-LIA


    In the case of a critical hit the Primary randomizer changes to:
    ((11/10)*x+0.45+rand*0.75)

    This is effectively a 1.0 bonus inside Primary with some narrowing of Primary's range that looks like a 1.0 bonus at common cRatios as classically reported.


    If Intermediate pDif is now greater than 3.0, it is capped at 3.0.

    There are special rules for particularly low Intermediate pDif, applying to extremely low cRatio (<0.3) crits as well:

    If Intermediate pDif falls below 1.0, it is set to 1.0.

    If Intermediate pDif falls below 0.75, instead add 0.25 to it.

    This predicts the following artifacts in pDif:
    Spoiler: show
    A floor at 1.0 starting below 1.5 cRatio, where cRatio-LIA is now reaching 1.0
    The floor ends below 1.272 (14/11) cRatio, where cRatio-LIA now gets below 0.75, but a spike is retained at 1.0 that are pDifs landing between 0.75 and 1.0
    A ceiling of 1.0 below 0.727~ (8/11) where cRatio+RAE does not reach above 1.0 any more, intead reaching to between 0.75-1.0 which is set to 1.0.
    A continued fall of max pDif below 1.0 at below 0.5 cRatio, where cRatio+RAE+0.25 no longer reaches 1.0.

    Meaning there is an apparent 'floor' at from 1.272 to 1.5 cRatio (cRatio-LIA will not fall below 0.75, so all results below 1.0 get set to 1.0) and an apparent 'ceiling' of 1.0 from 0.5 to 0.727 cRatio (cRatio+RAE will not exceed 1.0, so falls between 0.85 and 1.0 and gets set to 1.0) cRatio.

    Do note that Secondary and final flooring will definitely fudge these a little bit, causing cRatio just below 1.272 to still have apparent 1.0 hits (Masa did break below 1.0 at 1.249 though), and cRatio just above 1.5 to still floor to 1.0 at it's minimum.

    The 0.75 'soft floor' is still a formulated guess and may yet be adjusted. I need better data in the ~1.25 cRatio range, but for now it gives the proper start- and end-points for the 1.0 floor/ceiling effect.[/i]


    This intermediate pDif value is them multiplied by Secondary multiplier, which is randomized between 1.00 and 1.05, averaging 1.025.

    Final pDif is then multiplied by Base Damage for Final Damage which is floored to an integer.

    Mob Weaknesses such as Piercing and certain percentage bonuses like Critical Attack Bonus are applied after flooring of final damage and then re-floored.

    Under this system:
    2.80875 is 2-hander's absolute max pDif at capped 2.25 Ratio.
    2.52 is 1-hander's absolute max pDif at capped 2.0 Ratio.

    However, these value are widely subject to Secondary's ranging.
    2.74185 is the nominal maximum for 2-handers at average Secondary at capped 2.25 Ratio for a small to sane parse size.
    2.46 is the nominal maximum for 1-handers at average Secondary at capped 2.00 Ratio for a small to sane parse size.

    Any value between this 'Average Secondary' and the 'Abolute Maximum' is a valid maximum, which may vary by up to fifteen damage at the upper end for 2-handers depending on parse size and still come up short for large 1-hander parses due to flooring. Put simply: The Absolute Maximum pDif is insanely hard to hit.


    BRACE FOR IMPACT!

    Base Damage calculated as previously known.

    Unsimplified form retained in case a slope needs changing:
    Spoiler: show
    Final (non crit) Damage =
    floor[(Base Damage)*[cRatio-LIA+randx(RAE+LIA)]*[1+randy(0.05)]]

    Where for normal hits:
    RAE = 0.30+(cRatio-1)/10
    LIA = 0.55-(cRatio-1)/10

    randx and randy are randomized between 0 and 1 and are distinct.

    Or, after some algebra (which I'm terrible at):


    Final Damage = Floor([Base Damage] * [(11/10)*cRatio-0.65+rand*0.85] * [1+rand(0.05)])
    And for critical hits:
    Final Damage = Floor([Base Damage] * [(11/10)*cRatio+0.45+rand*0.75] * [1+rand(0.05)])

    Here's a nice handy graph of a random dispersion of my distribution as it stands now with Masa's tendency lines overlaid in Red. Orange is crits with the now modified +1.0 method, while blue is normal hits. The intermediate range where pDif can be above 1.0 and below 0.75 is tricky, and beyond Graph.exe's capability with conditionals (particularly, it rerolls the rand value at every step, making the 'if' function irrelevant), so I instead gave the Secondary-affected max and mins at about the same dispersion as the rest of the graph.



    Where this stands part deux? It needs to be thrown at real data, particularly sub-1.0 cRatio data which needs to be brought forth by certain persons who profess to have it.

    Giant semi-irrelevant comment block
    Spoiler: show
    Secondary
    Spoiler: show
    This Secondary randomization is mostly to perturb capped 3.0 Critical hits and antagonize the crap out of people doing statistical analysis of FFXI's damage. It is most apparent on capped 3.0 criticals but is applied to all damage.


    On the 1.0 floor/spike range
    Spoiler: show
    This was probably some way to make a weapon's base damage 'appear' to a player consistently. With evidence of a 1.0 'spike' being retained, it was clear that some portion of the distribution was being set to 1.0 before Secondary, but then a particularly low pDif was being 'brought up' to intersect 1.0 again, hence the 0.25 bonus on pDif below 0.75.


    These values are based on average Secondary.
    Spoiler: show
    This 'nominal' range was preferred over maximum Secondary because the majority of damage variance comes from the Primary multiplier. Even with thousands of hits, the actual data set for maximum (top 1% or so) Primary value is very small, so Secondary only being partway between average and maximum is very likely. Most maximum damage values fall between 1.025 and 1.05 Secondary.

    This applies more heavily to high cRatio than low cRatio, so the latter was indeed a little too loose. The changeover to non-piecewise Primary solved much of this however.


    2.25 Ratio cap for 2-handers was never actually parsed until now
    Spoiler: show
    2-hander 2.25 Ratio cap comes from personal hard-parsing after Masa's tendency line analysis pointed to it instead of 2.2. I did some shorter parses with a nice tighter cluster than my first attempts with some Last Resort up data. Here is a nice summary of the most important data points.

    Spoiler: show
    720 / 327 2.201
    169 avg, 203 max
    355 hits

    727 / 327 2.223
    170 avg 204 max
    321 hits

    727 / 322 2.257
    174 avg, 207 max
    424 hits

    800+ / 327 2.446
    173 avg, 205 max
    244 hits


    Interestingly, my original 2.2 ratio cap was simply a well intentioned match where the unknown higher Ratio cap offset the unknown lower Primary multiplier:
    Old: 2.2 * 1.2 * 1.05 = 2.772
    New: 2.25 * 1.177~ * 1.05 = 2.7825 See further on.

    Old reports of pDif max are just more accurate.
    Spoiler: show
    Again, max 2-hander pDif reports in the 2.76 to 2.77 range are still valid because of the infinitesimal chance of both Primary and Secondary rolling their maximum values at the same time, followed by up to a point of final damage being lost to flooring. With this new system the 2.76-2.77 reports are actually more accurate because they fall within the 1.025-1.05 range of Secondary.


    On nomenclature.
    Spoiler: show
    In case you're wondering, RAE stands for 'Random Ass Effect' and I've been using it as a variable name for a long time (like, back in 8th Grade programming my Ti-85). LIA stands for 'Lower Increment Alternative' and is certainly not some un-sneaky way to toot my own horn about whose system this is ;D



    Deprecated comments
    Spoiler: show

    These RAE and LIA values are preliminary!
    Spoiler: show
    These RAE breakpoints and values are definitely not final, but determined by Masa's parsed max damage, where up to each break point a RAE value would give max damage in a nominal range between 1.025 and 1.05 secondary, then suddenly jump to some value close to the very extreme (and probabilistically implausible) 1.05 maximum Secondary while the next RAE value chosen would return the parsed max damage to the nominal range. RAE and LIA for cRatio below 1.0 can not be determined for lack of data, but a fair guess below 1.0 cRatio would be 0.3 for RAE, and 0.25 for LIA is fairly certain. LIA may have more breakpoints, but fits a very wide range of data at 0.5 and gives the 'lowballed cRatio average' that gets more apparent at lower cRatios, which I detail in my 'imbalanced multipliers' comment below.

    Since RAE has been modified to a non-piecewise status, it now fits the data even closer than the piecewise arrangement I had before, which simply became a step in the process of determining it.

    On imbalanced multipliers and 'low' averages in parsed data.
    Spoiler: show
    Notice how RAE and LIA are imbalanced towards Primary tending below 1.0, but averages still stay just a little below pDif = cRatio in parsed. This is because of Secondary being imbalanced in the opposite direction.

    For 2.0 cRatio
    (1+0.4/2.0-0.5/2.0) * 1.025 = 0.97375

    For 1.75 cRatio
    (1+0.375/1.75-0.5/1.75) * 1.025 = 0.95178

    This illustrates well a 2.5% 'jump' in average over cRatio I noted while crossing 2.0 cRatio as RAE changed tiers. I noted a similar bump around 2.2 cRatio in Moten's thread that I would plausibly seek as a change in LIA, but I have only my relatively short data to work with.

    Most interestingly this implies that 1-handers get a +2.3% increase in average damage by hitting capped 2.0 Ratio as opposed to even just 1.999 and bumping RAE up to 0.4, because a 0.375 RAE value cuts the 1-hander 2.0 data too closely.
    [i]With non-piecewise RAE, this notion is false. It was partly indicated by Masa's 1.95 cRatio data which was confounded by a small parse size.

    There is merit in the concept of RAE-LIA approaching 1.0, bringing averages closer and closer to equalling cRatio. It was averages going above equalling cRatio that sparked the notion that RAE was continuing higher than 0.40[/i}


  2. #2
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    Addendum 1: LIA remains 0.5 for crits below 1.25 cRatio. This may entail that LIA doesn't actually change and instead there is a bonus being added.

    Spent a whole Saturday afternoon on this. Now I'm gonna go watch ponies.

  3. #3
    Hydra
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    Quote Originally Posted by Raelia View Post
    Base Damage calculated as previously known.

    Final Damage =
    floor{(Base Damage)*(cRatio)*[(1-LIA/cRatio)+randx((RAE+LIA)/cRatio)]*[1+randy(0.05)]}

    Where:
    cRatio ≥ 2.0, RAE = 0.4, LIA = 0.5
    2.0 > cRatio ≥ 1.5, RAE = 0.375, LIA = 0.5
    1.5 > cRatio ≥ 1.25, RAE = 0.35, LIA = 0.5
    1.25 > cRatio, RAE = 0.325, LIA = 0.25
    randx and randy are randomized between 0 and 1 and are distinct.

    Disagree? Think you can find data this doesn't fit? Think I haven't dug through 100% of Masa's and my own data to hammer this out?
    Spoiler: show
    Final damage formula can be simplified a touch to make it easier when doing calculations.

    floor{(Base Damage)*(cRatio)*[(1-LIA/cRatio)+randx((RAE+LIA)/cRatio)]*[1+randy(0.05)]}

    with cRatio being multiplied through your 1-lia/cratio....

    You end up with
    floor{(Base Damage)*[cRatio-LIA+randx(RAE+LIA)]*[1+randy(0.05)]}

    Which just looks nicer and you don't have to divide make the calculation simple. Unless I am reading something incorrectly.

  4. #4
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    Yep, that works too, I just liked keeping the cRatio, Primary, and Secondary terms separate so the final result was clear. Plus I hate and distrust my algebra.

    I'd even move the middle LIA over just for readability, and you can blow through that term on a calculator now.

    floor{(Base Damage)*[cRatio+randx(RAE+LIA)-LIA]*[1+randy(0.05)]}

    So I suppose that means Intermediate pDif max and min are just cRatio+RAE and cRatio-LIA

  5. #5
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    I can understand wanting to show, never good to skip something where people would be confused. But when using it, it just makes it easier to calculate stuff. As I just did with my ruinator test to see it's attack bonus where I was solving for my attack where I knew the mobs defense, and the numbers you have worked with the numbers I have. As in the max > min attack from the numbers I have.

    Since I assume you have a ton of numbers from just hitting a mob, what was distribution like, like if I am looking for absolute min and max to figure out where I am at on fSTR how many attacks would I need if I were to say have 1.4 cratio? 100, 500, 1000? just a guess don't bother really doing much math, just a guess what you think it would be great.

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    What mob? If you really wanna know for fSTR for such purposes you go to a mob with a known VIT. Most of my 2-hander Ratio cap parsing was on Greater Colibri at the classic birds camp with a 62 damage OA2-4 Scythe. Capped fSTR with this was at only 110 STR on them, so I just stayed (by a fair margin, easily) above that while varying attack anywhere from 2.04 to 2.5+. I'm sure it's worth your while to just reparse on something so well documented if you can just cap your fSTR and still get your attack down around 1.6 or so, which is around 516 or 524 (322 defense if you kill it for 90xp, 327 if you get 100xp).

  7. #7
    Hydra
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    Quote Originally Posted by Raelia View Post
    So I suppose that means Intermediate pDif max and min are just cRatio+RAE and cRatio-LIA
    Yep, that is actually what I first saw when I was reading through your post.

    This is the first formula for pDif that I have seen that actually makes sense in that someone would code this into the game. The numbers are nothing crazy, looks rather simple, I could see this as being the actual formula.

  8. #8
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    Quote Originally Posted by Raelia View Post
    What mob? If you really wanna know for fSTR for such purposes you go to a mob with a known VIT. Most of my 2-hander Ratio cap parsing was on Greater Colibri at the classic birds camp with a 62 damage OA2-4 Scythe. Capped fSTR with this was at only 110 STR on them, so I just stayed (by a fair margin, easily) above that while varying attack anywhere from 2.04 to 2.5+. I'm sure it's worth your while to just reparse on something so well documented if you can just cap your fSTR and still get your attack down around 1.6 or so, which is around 516 or 524 (322 defense if you kill it for 90xp, 327 if you get 100xp).
    Yeah I was just hoping that I could still use the data I have from the mob I was fighting. as it already has a very small window for attack bonus, a window of between 1 and 4 attack. Ends up making it what looks like ether a 150 attack bonus, or a 25% attack bonus. Maybe I will go there for some points as I am running low and fight those mobs again lol.

  9. #9
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    That was the entire basis. As I said in the other thread: Nobody writes a damage system by mashing their face on the numpad.

    I just happen to dual wield Occam's Razors. Sometimes I switch to Hanlon's for offhand but Tanaka seems to build resistance to it.

  10. #10
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    Quote Originally Posted by darkhorror View Post
    Since I assume you have a ton of numbers from just hitting a mob, what was distribution like, like if I am looking for absolute min and max to figure out where I am at on fSTR how many attacks would I need if I were to say have 1.4 cratio? 100, 500, 1000? just a guess don't bother really doing much math, just a guess what you think it would be great.
    If your cRatio is between ~1.25 and 1.5, the absolute minimum damage will be at exactly 1.0 pDif, and should be fairly easy to spot since you'll always have the full chance at that number, and not a fractional overlap (eg: if base damage was 75 and absolute min was 1.13 pDif, that corresponds to 84.75, which means you'll only have about 25% the chance to hit that number as you would for most other numbers). If your cRatio is between 1.0 and 1.25, absolute minimum will go below 1.0, however it will still generate a high spike at 1.0 (along with a few points higher due to the 1.05 spread), so it's still easy to determine.

    In any case, the number of hits you need to be fairly sure of hitting the 1.0 value is directly proportional to the total base damage. You'd hit it with a warp cudgel (d15) within a few dozen hits at most. With something like an Apocalypse (d154 at 95) it could take up to a few hundred. Figure it's almost certain within 3x as many hits as the total base damage + fStr, and highly probable within 2x as many hits as that.

  11. #11
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    i still dont understand

  12. #12
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    I was trying to figure out what RAE and LIA were acronyms for, until I realized they were just halves of your name (though then you give them after-the-fact definitions at the end of the post)

    I can only assume Primary is evenly distributed.
    For stuff above 1.5 cRatio I agree for most practical purposes, it can be treated as being evenly distributed. However I do commonly see certain oddities in the distribution that I've never been able to properly explain. I usually dismiss them as random quirks, but there's always the possibility that the distribution pattern is a bit more complicated that we expect. [1]

    For stuff below 1.5 cRatio, it's -mostly- evenly distributed, though there are additional factors to consider.


    Primary multiplier =
    (1 - LIA/cRatio) + rand( (RAE+LIA)/cRatio )
    rand is between 0 and 1

    ...

    Primary Multiplier is multiplied by cRatio for an Intermediate pDif.

    It seems over-complicated to divide by cRatio and then multiply by it again. Why not just have:

    Primary Random Spread (PRS) = rand(RAE+LIA)

    which generates a value between 0 and (RAE+LIA), and then have

    Primary Multiplier = cRatio - LIA + PRS

    ?

    Nvm, see you discussed that in later posts..


    Yes I know this has been debated by the regression people, but I attribute any doubt in this to misunderstanding or non-application of Secondary, as it comes after this addition. With this system, flat +1.0 criticals work again. Secondary and just plain Order of Operations are entirely why 1.0 crits don't work in their systems.
    Will leave this up in the air for now since I haven't gone back to look at crits yet.

    This Secondary randomization is mostly to perturb capped 3.0 Critical hits and antagonize the crap out of people doing statistical analysis of FFXI's damage.
    Ayup...


    Final pDif is then multiplied by Base Damage for Final Damage which is truncated to an integer.
    There's the possibility that there's an additional flooring step after the Primary Multiplier is applied, before the Secondary Multiplier. Unfortunately this is a very difficult element to properly prove either way since one could also argue that it just means the calculation to generate the Primary Multiplier is itself wrong.

    I'll note that in my post here, my model would predict a max of 82 if there was not a flooring step between Primary and Secondary, rather than the observed value of 81.


    Disagree? Think you can find data this doesn't fit?
    Well, let's just throw this at the above lesser colibri data and see what shows up. Using your methodology on that data (capped attack and fStr on lesser colibri), we have:

    Total base damage = 33 (d23 weapon + 10 fStr)
    cRatio = 2.0
    Observed low: 51
    Observed high: 81
    (full distribution shown in referenced post)

    cRatio = 2.0, RAE = 0.4, LIA = 0.5

    Predicted low: 2.0 - 0.5 = 1.5
    1.5 * 33 = 49.5

    Predicted high: 2.0 + 0.4 = 2.4
    2.4 * 33 = 79.2 * 1.05 = 83.16 (82.95 if floored after the Primary Multiplier)

    So neither the low nor the high fit the prediction, and being off by more than a full point on both ends indicates that it's not just poor probability chances.



    [1] - Mentioned peculiarities in distribution. Check the lesser colibri damage spread in the above mentioned post and the frequency distribution.

    If you look at the interior frequency values (ie: exclude the outer values at either end that are inordinately affected by the Secondary Multiplier), overall average is 18.4. Average for values 2.0 and higher is 21, average for values below 2.0 is 15.85.

    Here are a few graphs I made years ago when people were first trying to figure out the 1.05 multiplier:




    You'll see that they also have higher frequencies for damages above 2.0 than for damages below 2.0. It would seem to imply that there are actually two Primary Multipliers, one for above cRatio and one for below cRatio, and that the choice of which one to use is not a 50/50 chance, but slightly favors the higher value.

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    Here we have parses with thousands of hits but only two or three hitting 'maximum' damage and you're gonna tell me out of those three hits Secondary is gonna roll even the top 10% of its range... Riiiiiight.

    Being a point off in the correct direction is exactly what should be seen for Secondary's stinginess in showing you an absolute maximum or minimum. Going past these limits would be a problem, APPROACHING them is exactly what is expected. Can you follow this? If you clamp max and min to observed values it's easy to just blow right past them with a long enough parse. What this requires is prediction and then watching for a nominal value to be reached that approaches that prediction but does not cross it. An infinite parse will give the predicted value, but any finite parse has a very fair chance not to. You are underestimating Secondary as a moderator of the extremes of damage fluctuation.

    In fewer words, stop expecting Secondary to ever 'Push' at the same time Primary 'Pushes', because it's just as likely to 'Pull' instead!

    Your 81 damage high is still within the upper half of Secondary. LIA is still shooting a little low at 0.5 but is definitely a consistent value across a very wide range and your parsed low is at least within Secondary's range too. 0.475 is a little closer, but .45 is too close.

    I'm not going to put too much trust in your flakey 33 base damage one-hander data anymore. You're getting floored by so much it's stacking certain values and you're reading far too much into it. Parse with at least 50 or 100+ base damage so you aren't inducing up to 3.3% error in your final damage measurement to flooring. You're gonna need potentially tens of thousands of hits to see the entire distribution for that matter, so having a much higher base damage gives you much smaller increments such that you don't need an insane parse to at least show the distribution getting closer and closer to the limits given.

    Really though, because of Flooring I can concede that LIA should be a bit tighter. It also pulls predicted averages a little low still too, but LIA should still be greater than RAE for all ranges including 2.0+. It's possible for the predicted low to be 'blown' by flooring but remain legitimate too, so 0.45 is still not out of consideration. Using an extremely low base damage weapon like your Warp Cudgel example is right out though, you're pretty much 'cheating' your minimum damage to an arbitrary low by flooring.

  14. #14
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    While I can't speak for two handed weapons, this formula is rather inaccurate for one handed weapons, by up to about 4-5 points for normal hits, and up to 10 for crits, and this is with fairly high damage one handed weapons, so rounding is not a possible excuse. Neither is sample size, as each data point compared alone is large enough to sufficiently rule out such large inaccuracies.

    Rather noticeably, the disparities between results and your formula grow greater and greater the higher ratio climbs, and ends up at its greatest at cap, and your figures of 2.52 and 1.5 are significantly different from any of the possible pDIF values I have ever seen. 2.478 and 1.57 are the best fits I have seen so far,

    I'd like to ask, do you have any data at all that fits these caps for one handed weapons specifically? Based on previous posts of yours that I vaguely remember, you simply took your two hander formula and applied it to one handers, correct? Even though it might fit two hander data perfectly for all I know, it just does not fit any data I have ever seen for one handers particularly well at all, and I would therefore like to see some sort of proof for one handers specifically, at the very least of 2.0 ratio min/max numbers, because as of right now, I simply cannot find your formula worthy of consideration.

  15. #15
    Chram
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    Here we have parses with thousands of hits but only two or three hitting 'maximum' damage and you're gonna tell me out of those three hits Secondary is gonna roll even the top 10% of its range... Riiiiiight.
    Huh?

    First, I'm not sure what this statement is in response to.

    Second, it doesn't even make any sense. If only 2-3 hits are hitting the "maximum", those -are- the top ~10% or whatever for the secondary modifier, as those 1000-hit runs may be hitting ~20 frequency per normal result.

    If you clamp max and min to observed values it's easy to just blow right past them with a long enough parse.
    You create min/max values that are just barely enough to cover the observed results. If you see results that go beyond that min/max, then you can increase the range. That's perfectly valid since it's possible for a new sample to prove the prediction wrong. You keep making adjustments that provide a prediction that is just barely enough to cover the observed values, and keep iterating for as long as you get data that proves the most recent prediction false.

    Taking min/max values that are -outside- the observed range and then claiming that you didn't see those results because you didn't do enough samples is bad math, as it makes an unfalsifiable claim.

    I'm not going to put too much trust in your flakey 33 base damage one-hander data anymore.
    So because the results are inconvenient to your model, you're going to ignore them? Well, no matter. Let's try Masa's data then.

    Parse file 2010-01-06_470WA_WARdnc_Lcolis.sdf.
    Weapon: Woodville's Axe (d50)
    Str: 85
    dStr: 85-52=33 for lvl 61-62, 85-55=30 for lvl 63
    fStr: 9 for lvl 61-62, 8 for lvl 63 (cf: VZX's fStr chart)
    Att: 376 + Berserk = 470
    Defense: 231, 235, 241 for lvls 61, 62, 63
    cRatio: 2.0, 2.0, 1.950

    Using results for lvls 61 and 62 only, since we just want to look at 2.0 cRatio.

    Total base damage: 50 + 9 = 59


    Samples:
    Lvl 61: 547 non-crits
    Lvl 62: 548 non-crits

    Range:
    Lvl 61: 92 to 147
    Lvl 62: 92 to 147

    Ranges are identical, which should be expected given that fStr and cRatio are identical.

    Another parse: 2010-01-06_533WA_WARdnc_Lcolis.sdf
    Has fewer samples. Same str, higher attack (so 2.0 cRatio on all bird levels).

    Lvl 61: 261 non-crit, range 93-145
    Lvl 62: 492 non-crit, range 92-147

    With ~500 samples, hitting exactly the same range as the other parse.

    Lvl 63 (base damage 58): 314 samples, range 91-143
    Not as reliable due to sample size, but likewise has a smaller range than predicted.



    Predicted min and max using your formula:

    Min: 2.0 - 0.5 = 1.5 pDif

    59 * 1.5 = 88.5, at least 3.5 lower than observed.

    Your 81 damage high is still within the upper half of Secondary. LIA is still shooting a little low at 0.5 but is definitely a consistent value across a very wide range and your parsed low is at least within Secondary's range too. 0.475 is a little closer, but .45 is too close.
    More than 0.44 should drop the min result below 92. Since you say 0.45 is "too close", that implies I should be seeing a min of 91 at the very least. 0.475 would drop it to potentially as low as 89 (though that would be relatively rare; 90 more likely).

    As I am still not seeing those results, I'm classifying them as "unlikely".


    Max: 2.0 + 0.4 = 2.4, plus secondary mod

    2.4 * 59 = 141.6
    2.4 * 59 * 1.05 = 148.68

    Number of 146 and 147 results:
    Lvl 61: 0 and 1
    Lvl 62: 1 and 1


    Rough expectation of the number of results per number before secondary spread: 547 / (141.6-88.5) = 10.3

    Spread range at upper end: 148.68 - 141.6 = 7.08

    Range of pDif that can generate 148+ results: 140.96 to 141.6
    Percentage of pDif that can generate 148+ results: (141.6 - 140.96) / (141.6 - 88.5) = 1.2%

    Percentage of time that the 1.05 spread can push said potential 148+ results to actual 148: one half of (148.68 - 148) / (148.68 - 141.6) = one half of 9.6% = 4.8%

    1.2% * 4.8% = 1 in 1736 samples.


    Given only ~1100 ~1850 total samples, one can argue that the sample size isn't large enough to expose the result, though it's reaching the point of "quite unlikely".

    I will also note that my own formulations generate results that allow for the possibility of 147 with much lower frequency than actually appear, so my formula likely underpredicts the true max.


    In fewer words, stop expecting Secondary to ever 'Push' at the same time Primary 'Pushes', because it's just as likely to 'Pull' instead!
    Secondary should never "pull". At best it remains neutral, with a 1.0 result.


    Am considering a test setup that I can run tonight for several thousand hits on a total ~d60 weapon and see what shows up.

  16. #16
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    Has anyone tested other cratios using the 1hand and 2hand weapons both using same damage weapon with same STR and same attack? Could it be that 1hand and 2hand have slightly different values for max and/or min? Or is it that the percentage of those other numbers are just very very small and we didn't get enough hits to tell us the true high and low.

    Looks to me like these numbers are close if they are not correct, might just need a slight adjustment, might be good to just test at a few different cratios with same str and weapon. The more data we get the more sure we can be about what we are looking at.

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    Quote Originally Posted by Motenten View Post
    Secondary should never "pull". At best it remains neutral, with a 1.0 result.
    Found your problem. Neutral secondary is 1.025, so 'pull' would be some value between 1.0 and 1.025 which you will not observe in high damage because it just looks like a lower Primary.

    You can pay attention to this response too, and please go back and edit to cut down your posts. Just delete them or trim it down to your point without the excessively spaced math. I don't need your behemoths that do nothing but follow exactly what I'll explain to Rena:

    Quote Originally Posted by Rena View Post
    While I can't speak for two handed weapons, this formula is rather inaccurate for one handed weapons, by up to about 4-5 points for normal hits, and up to 10 for crits, and this is with fairly high damage one handed weapons, so rounding is not a possible excuse. Neither is sample size, as each data point compared alone is large enough to sufficiently rule out such large inaccuracies.
    Would you kindly go back and read the whole goddamn post? I addressed every issue you bring up here. This was constructed from Masa's massive amount of data that makes your probable eyeballing pale in scope. Put simply he has 1-hander data that shows 2.0 ratio to have a 2.491-2.508 maximum depending on flooring, but this is still with only ~2000 hits. I guarantee with a long enough parse with his setup he'd eventually see a 148 hit with 59 base damage, but the margin is so small (148/59/2.52, SqRt that for for what percentile each randomizer needs to roll, then subtract from 1 again and square that for two randomizers, then take the reciprocal for odds, then divide by a simple factor found in the following post to correct for inequal randomizers) this would require 38,500 hits to occur, statistically, for this single data point to show a true maximum.

    (2.0 + 0.4)*1.025=2.46. So long as your maximum hits are in a range between 2.46 and the absolute maximum of 2.52 it is exactly as my model expects. Again you're expecting Secondary to Push at the same time Primary Pushes, when it's just as likely to Pull or stay neutral instead. Can somebody please follow this concept for me.

    You aren't rolling a d20, you're rolling 2d10. Seeing a 20 isn't 1 in 20, it's 1 in 100!

    Or more accurately to this situation, you're rolling a d80 and a d20. Sounds like it would hit 100 pretty easily, right? More like once in 1600 rolls! Whenever you roll an 80 on the first die you're just as likely to roll a 1 as a 20 on the second.

    What part of having two distinct random factors that are unlikely to roll 'high' at the same time is going over people's heads? I feel like I'm posting at FFXIAH here...

    Quote Originally Posted by Rena View Post
    Rather noticeably, the disparities between results and your formula grow greater and greater the higher ratio climbs, and ends up at its greatest at cap, and your figures of 2.52 and 1.5 are significantly different from any of the possible pDIF values I have ever seen. 2.478 and 1.57 are the best fits I have seen so far,
    This is because Secondary's range gets wider as cRatio rises because it is applied to Intermediate pDif, so the range of 1.025-1.05 Secondary causing your purported 'error' gets wider, and even more on critical hits. The probability of rolling much above average Secondary remains the same, it just gets further from absolute maximum pDif. Again, your data is much too short for the trapezoidal distribution already known. I've already addressed that LIA could indeed be a bit tighter, and being 'violated' by a parsed low hit is still valid due it such being caused by flooring.

    Quote Originally Posted by Rena View Post
    Based on previous posts of yours that I vaguely remember, you simply took your two hander formula and applied it to one handers, correct?
    This is certainly not that, and you're getting dangerously close to showing a silly bias because of some previous work that was correct in a single case and more centric on order of operations than modeling all ranges of cRatio and had an obnoxious coincidental parity with 1-hander data at capped Ratio when applied in the same way, which was then incessantly misapplied by certain persons in non capped Ratio cases to 'disprove' it. Such was made invalid by 2-hander Ratio cap being higher than expected anyway.

    If you're gonna come in here with some attitude of 'It's Raelia, he must be wrong' I'd ask you simply to not post. This is an honest request, because such an attitude is not going to help me show you why my model works.

    Quote Originally Posted by darkhorror View Post
    Could it be that 1hand and 2hand have slightly different values for max and/or min? Or is it that the percentage of those other numbers are just very very small and we didn't get enough hits to tell us the true high and low.
    I used both 1-hander and 2-hander data from Masa and they were effectively the same. 2-hander data appears to get 'closer' because of higher base damage getting floored less. This is why I gave Moten a bitching about using low damage weapons, because for example Masa's 2.0 Ratio 59 base damage 147 max could be anywhere from 2.491 to 2.508 final pDif, because a 147.999 still only shows a 147 final damage.

    From my example of Masa's data hitting a 148 with 59 base damage above, it's pretty obvious to me now that people's expectations of 'enough data to show max and min' are a couple magnitudes short. Expecting to see max and min with mere thousands of hits, even my 'tens of thousands' was lowball, is simply asinine now. I find it hil-arious that I get to use the 'Not enough data' argument for once. Everyone repeat it with me now:

    THIRTY EIGHT THOUSAND, FIVE HUNDRED HITS to see your maximum 148 damage with 59 base damage.

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    Separate post for a separate discussion, as well as to have come back with less rageahol in me.
    Quote Originally Posted by Motenten View Post
    More than 0.44 should drop the min result below 92. Since you say 0.45 is "too close", that implies I should be seeing a min of 91 at the very least. 0.475 would drop it to potentially as low as 89 (though that would be relatively rare; 90 more likely).
    With anything less than a couple tens of thousands of hits, you can instead expect your minimum to be around (cRatio-LIA)*1.025, but some portion of the flooring range (Final damage +1) must remain above the absolute cRatio-LIA minimum. I wouldn't call 0.45 'too close' after rethinking it with flooring also considered, but it's easy to check with my simple method of determining probability of a given result for a given margin to hit that result.

    LIA = 0.45
    59*1.55 = 91.45, but then work it backwards with 92/59 = 1.559 and the 0.009 'margin' seems pretty slim given what I've stated about the 0.0115 margin at the top end needing nigh 200k hits to see, this one needs 110k (22k). 92 damage would then have only a 0.026 margin and need 13,805 (2788) hits, Masa hit it three times or more no less, so a 0.45 LIA seems very unlikely to me.

    LIA = 0.475
    59*1.525 = 89.975, the margin to see 89 damage is just 0.0004 (remember: below 90/59 to floor to 89 damage), so this would take about 51 million (10.3 mil) hits to see 89 damage. 90 damage comes at 91/59 and below, still a 0.0173 pDif margin needing 30,645 (6190) hits to see. Masa had only 1848 hits applicable to this figure mind you. 91 damage needs 7807 (1577) hits to see, so only getting 92 as a minimum, needing 3479 (702), on that amount of data is plausible. but still slim since He hit it 3 times, so definitely plausible. This probability analysis is a little harsh mind you, and assumes hitting both percentiles to give the result, but it does give a decent idea of why true max and min pDif are far out of reach for the parses given.

    So with LIA = 0.475, 59*1.525*1.025 gives 92.24 damage, exactly as stated that you might as well expect Secondary to stay average on all but the most extreme parses.

    I do indeed like 0.475 for LIA at 2.0 Ratio.

    Edited to fix subtracting for pDif margin instead of dividing for percentage margin.

    I should probably detail my method and explore some other options:

    For 92 damage to occur with 59 base damage and 0.475 LIA:
    1/(1 - √(2 - (93/59)/1.525))^2 = 1 in 3479 (702) odds.

    For 92 damage to occur with 59 base damage and 0.500 LIA:
    1/(1 - √(2 - (93/59)/1.500))^2 = 1 in 1507 (304) odds, but 59 * 1.5 * 1.025 = 90.7 which lowballs an average Secondary low.

    Why is this method harsh in simple terms? It's like working with two d20s instead of a d16 and a d4 just to be faster to calculate. 1/20th squared is 1 in 400 as opposed to (1/16*1/4)^2 which is only 1 in 64. So there is a bit of a flaw in it when the two randomizers are inequal. With a 0.475 LIA Secondary's range is 2/35ths the factor that Primary is, so it's more like rolling a d284 and a d16 to see 300: 1 in 4544 as opposed to two d150s giving 1 in 22,500, and this scales the same to 1/2840*1/160 vs (1/1500)^2 (2250000/454,400) so my estimates are probably off by a simple factor of 4.95, giving 1 in 700 odds for 0.475 LIA to show 92 damage with 59 base, but still only knocking the 148 max damage odds to 1 in 38,000. I have edited the prior post to reflect this, and inserted italicized alternative numbers in the data of this post as it doesn't change any conclusions besides making them a little slimmer.

    With this correction, 0.475 LIA is very viable.

  19. #19
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    This is certainly not that, and you're getting dangerously close to showing a silly bias because of some previous work that was correct in a single case and more centric on order of operations than modeling all ranges of cRatio and had an obnoxious coincidental parity with 1-hander data at capped Ratio when applied in the same way, which was then incessantly misapplied by certain persons in non capped Ratio cases to 'disprove' it. Such was made invalid by 2-hander Ratio cap being higher than expected anyway.

    If you're gonna come in here with some attitude of 'It's Raelia, he must be wrong' I'd ask you simply to not post.
    First of all, you can drop the persecution complex, as it has absolutely nothing to do with any personal feelings regarding you (of which I had none in particular), I asked because I recalled you stating somewhere that you did not care about one handers, and wanted clarification as to how you came to your conclusions.

    Would you kindly go back and read the whole goddamn post? I addressed every issue you bring up here. This was constructed from Masa's massive amount of data that makes your probable eyeballing pale in scope. Put simply he has 1-hander data that shows 2.0 ratio to have a 2.491-2.508 maximum depending on flooring, but this is still with only ~2000 hits. I guarantee with a long enough parse with his setup he'd eventually see a 148 hit with 59 base damage, but the margin is so small (About 0.46% of total pDif, so subtract 0.0046 from 1, SqRt that for for what percentile each randomizer needs to roll, then subtract from 1 again and square that for two randomizers, then take the reciprocal for odds) this would require 188,600 hits to occur, statistically. This is larger than the entirety of his data, plus my data, plus Moten's data... For a single data point to show a true maximum.
    My data set of 'probable eyeballing' (and I must applaud you on your hypocrisy there; accusing others of bias, yet repeatedly showing your own biases that anybody criticizing you does not have sufficient evidence to support reasonable doubt, without even trying to find out if such is really the case) that I used to compare to your theory is a combined data set for high ratio of almost 20,000 hits, a sample size large enough, I would think, to rule out point differences greater than 1 to 2 points of damage. For an example though, we can take a look at Masamune's data that you linked to; minimum damage for a 58 and 59 level weapon, using your formula, should be 87 and 88, yet the lowest observed at capped ratio is 91, over a combined 2162 hits. You linked me to this dataset, but it doesn't support your minimum, nor minimum crit damage formulae at all. What other data do you have that does support it? If not, what is your reasoning for using this particular formula?

    Also, using your own formula to show the probability of a particular number happening to validate the lack of evidence for said number, suggesting this validates your theory, effectively making falsification of your theory impossible through impracticality is amusingly circular. Show data that supports it, or adjust the formula to account for inaccuracies.

    Definitely would like to see more of your supposed data regarding min pDIF at 2.0 ratio for both crits and non-crits though, because that is the largest, most obvious flaw.

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    Quote Originally Posted by Rena View Post
    Definitely would like to see more of your supposed data regarding min pDIF at 2.0 ratio for both crits and non-crits though, because that is the largest, most obvious flaw.
    Prior post addressed LIA definitely being 0.475. A 'flaw' never negates a whole system, despite the attitude around here so far wanting to call out otherwise.

    I just feel like I'm having to viciously beat it into people, in other threads and now this one, that they are very unlikely see min and max in any sane parse.

    What's the base damage on your 20,000 hits? If I go with 70 base damage just for example, your 2.478 can be as high as 2.486 before flooring and you still see 173 damage maximum, and this is being generous that you somehow read 173.5 damage. The margin to see 174 damage gives about 1 in 4335 hits (and only for this paricular base damage), and that's still only to show a 'parsed' 2.486 max pDif. 1 in 12.7k hits will give you 175 damage, but that still only looks like 2.50 final pDif. Flooring is a huge portion of not seeing 'max' damage (actually, 70 damage looks like a pretty good candidate to hit at least a 2.50 final pDif in only 12k hits because of this... 1 in 157k hits would give 176 damage for 2.514 pDif if you got lucky, so now to find a D56 weapon!).

    Now let's go to a decent 2-hander, 334 damage on 121 base is 2.760 and one in 13k hits, 335 damage is 2.768 and one in 29k hits, 336 damage is the 'maximum' given by 2.7825, but then only reads back as 2.777 due to flooring and is one in over 200k hits. Can you see why flooring can cause the majority of undershoot for max pDif? Can you see how common reports of 2.76-2.77 max 2-hander pDif came about? Even if you get lucky and hit that infinitesimal top end margin for 336 damage you only see 2.777!

    Working my method backwards from 20,000 hits, you're not likely to see any higher than 2.504 before flooring.

    All I want is a better argument than 'It's not exact!' That's all I'm hearing so far from two different people, even after I assert that 'exact' would be wrong.

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