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  1. #101
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    Alright, so I see where I messed up in average bonus that Impetus gives as I was expecting average consecutive hits to =19 @ 95% hit rate, and that you would use 19hits average bonus. Problem lies in the fact that that number is based on the misses being equally spread out, eg. 19hits,1miss,19hits,1miss...etc. That in itself is only 1 possibilty of a much larger number of possible outcomes. It would also result in I think the lowest possible average bonus from an infinite duration Impetus actually >.>

    Quote Originally Posted by pchan View Post
    for H2H, N=300 , 0% base crit rate, 95% accuracy : 16.42%
    for H2H, N=300, 10% base crit rate, 95% accuracy : 26.39% (+16.39%)
    for H2H, N=300, 15% base crit rate, 95% accuracy : 31.37% (+16.37%)
    for H2H, N=300, 20% base crit rate, 95% accuracy : 36.35% (+16.35%)
    for H2H, N=300, 30% base crit rate, 95% accuracy : 46.31% (+16.31%)
    I am generally confused why you posted 0% base crit --> 30% base crit. Aren't your numbers 16.42, 16.39, 16.37, 16.35, 16.31 although different, actually the same result after confidence intervals are factored? The only time as far as I can tell that average bonus should change is when base crit is higher than 50%, thus basically lowering Impetus's +50 cap by means of the total crit cap of 100%.

    Additionally how is it that you get a different number for +crit rate, and + crit damage. They are the same, so there is most likely some problem in your and MDK's formulas. Try a formula that instead of looking for + crit% and +dmg%, looks for average impetus bonus. 1 bonus=+1%crit rate=+1%crit damage=+2 attack=+2 accuracy, so they should all stay in that 1:1:2:2 ratio I am pretty sure.

  2. #102
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    Quote Originally Posted by pchan
    There is a fundamental difference between the two in that crit is a chance to happen and critdmg always happen, also they do not vary independently. Anyway it's easy to input in a simulation and double check it, that is how I found it.
    I should probably clarify. The crit damage bonus itself should be identical to the crit rate bonus on a hit-for-hit basis. However the manifestation of the increase in crit damage is dependent on the distribution of crits, and since the crit rate increases as the number of sequential hits increases, the actual average crit damage results will be weighted towards the higher end even beyond what the crit rate itself is.

    So yeah, the actual output will be the crit rate distribution further weighted upwards, which leads to a higher effective value to be used in the damage calculations.

    [Note: also answers Diasetsu's question on this matter]



    For number of expected hits per cycle:

    Max(N) = ((180*60)/hastedDelay) * AvgHitsPerRound
    Note: using 60 delay/sec since that's what's used in the rest of the spreadsheet.

    Melee time within that period should be on the order of 90% to 95% of all the time, with the remainder primarily being accounted for with weaponskills. Of course the weaponskills themselves provide enough hits to basically compensate for the time used, so probably don't need to tweak anything.

    Average hits per round is already calculated in the spreadsheet, and tends towards 2.5 - 2.7 (mainly depending on whether or not you're subbing /war). Unfortunately the calculated value already accounts for accuracy. We just want total number of swings, since the calculations for Impetus are also accounting for accuracy. Fortunately we should be able to simply divide by the accuracy to factor that out, since there are no secondary complications like Zanshin.

    So as quick examples, unhasted /dnc using Vere would be 116 N; /war with Haste/Marches/Samba would be 287 N. If I use Spharai as /dnc with 0% haste, N is 78.

    Clearly, for the purposes of the spreadsheet, we really don't need to consider the case of N < 50. It's not set up to handle staff or club.

    ... And then I remembered Footwork, which could be as little as 23 N. Meh.

    On the other hand, we -do- need to consider one additional factor that your formula doesn't seem to account for (still trying to work through the math): over-capping crit rate. Suppose, for example, RR+GH atma in Abyssea. Base crit rate is 75%, so Impetus would cap after a mere 25 hits.


    Regarding crit rate influencing the final value: Using your formula, I find the same bonus value at 0% base crit rate; but rather than the average bonus going down with higher crit rate, I'm seeing the average bonus go up (up to 16.726% at 30% base crit rate). I would actually -expect- the average bonus to go down with higher crit rates since you're more likely to run into the crit rate cap.


    Quote Originally Posted by mdkuser
    The program simulates 10,000 impetus, each having 300 attack rounds (so 3 million swings in total). Takes 10min to execute.
    Ugh. While I can certainly appreciate the general usefulness of programs like Maple and Mathematica, the speed really is a killer. If I set my little program to a 5 million swing simulation (since it accounts for both Impetus and non-Impetus time), it takes maybe 10 seconds.


    Need to do some more experimentation with crit damage. Will see if I can get some time to review the formulas provided more deeply.

  3. #103
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    Speaking of limiting the bonus, it seems I left more stuff out of my model code. Went in and properly capped the bonus value at 50 (for the bonus itself) and 100 (for max crit rate). 5 million samples per run (Impetus+non-Impetus), 75 delay (= 144 N), 95% acc, 10% base crit rate:

    Average bonus, unlimited: 16.39
    Average bonus, limited: 15.63

    So there's definitely an impact. Tried again with 30% base crit rate:

    Average bonus, unlimited: 16.37
    Average bonus, limited: 15.60

    In this case there's little, if any, impact from the higher base crit rate. The difference has to be derived from the cap value on Impetus itself.

    Trying again with delay 36 (= 300 N) and 30% crit rate gives:
    Average bonus, unlimited: 17.72-17.76
    Average bonus, limited: 16.59-16.61

    The limited version is still a bit higher than pchan's latest formula estimates.




    Was in the middle of adding in crit damage modelling when I realized this. Will get back to that tomorrow.

  4. #104
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    Ok, was pretty trivial to add, so noting this down now.

    Added an extra field for a crit hit check. This is to verify that the generated average bonus corresponds with the actual average crit rate. Over several 1 million sample runs, they matched to within about 0.05%, so that part looks good.

    After that, I want to sum up the bonuses for all the hits that were actually crits (along with the crit count) in order to see what the average crit damage bonus value is.


    Sample runs (1 mil swings, 75 delay [N=144])

    10% base crit rate:
    Code:
    Limited Bonus model:
    
    Sequences: 32469      Hits: 574020    Avg Seq Length: 17.679017
    Total bonus: 8945423  Avg Bonus: 15.583818
    Total crit count: 146543  Crit rate: 25.529250 (Impetus: 15.529250)
    Crit Dmg bonus: 3419135  Avg Crit Dmg: 23.331957
    0% base crit rate:
    Code:
    Limited Bonus model:
    
    Sequences: 32628      Hits: 573824    Avg Seq Length: 17.586858
    Total bonus: 8915975  Avg Bonus: 15.537822
    Total crit count: 89353  Crit rate: 15.571499 (Impetus: 15.571499)
    Crit Dmg bonus: 2518391  Avg Crit Dmg: 28.184739
    30% base crit rate:
    Code:
    Limited Bonus model:
    
    Sequences: 32397      Hits: 574056    Avg Seq Length: 17.719418
    Total bonus: 8962705  Avg Bonus: 15.612945
    Total crit count: 261316  Crit rate: 45.520994 (Impetus: 15.520994)
    Crit Dmg bonus: 5212008  Avg Crit Dmg: 19.945231

    Very interesting to note that as base crit rate goes up, the value of the crit damage bonus (in terms of relative increase rather than total increase) goes down. It's pretty easy to explain why: With 0% base crit rate, almost all of your crits are at the highest bonus levels because crits are rare at the low bonus levels; with 30% base crit rate you end up with lots of crits occurring when the crit damage bonus is low.

    On the other hand, the total increase in damage from the bonus crit damage is still higher with the higher base crit rate, as evidenced by the "Crit Dmg bonus" value. If you have 3 times as many crits (going from 0% to 30%), even if the average bonus is only 2/3 as large, you still end up with twice the bonus damage.

    In any case, coming up with a formula for the average crit damage bonus granted is likely to be annoying.

  5. #105
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    Quote Originally Posted by Motenten View Post
    On the other hand, we -do- need to consider one additional factor that your formula doesn't seem to account for (still trying to work through the math): over-capping crit rate. Suppose, for example, RR+GH atma in Abyssea. Base crit rate is 75%, so Impetus would cap after a mere 25 hits.
    I suppose you can replace 50,49 and 48 in the formula with the actual cap minus base crit. In case when the base crit rate is > 50% it works as if the bonus cap is C=100-(base critrate). In this case

    50 replaced by min(50, 100-c)
    49 replaced by min(50,100-c) -1
    48 replaced by min(50,100-c)-2

    The difference being that the distinction between the two formula would be N>= or <min(50,100-c). The math behind the formula doesn't depend on 50 being the actual value. I think that would work. Also pointing out that the formula doesn't account for accuracy bonus on impetus, but rather it's fix hit rate. Seing that the bonus to acc is strong after 85% base accuracy, it probably means you still get a high crit and critdmg bonus at those levels.

    I'm confident in getting a formula for the average crit damage bonus and attack.

    PS : for attack I think I brain farted in my simulation (post 92), it seems to be indeed 2x critrate%, no reason to be other wise. You calculate the total damage during an impetus phase, take it's expectation, and compare it to what you would get with the found average critical hit rate and the initial attack value. So on a parse you would see the same damage as if you had say 16.5% crit rate and 33 attack so nvm on this.

  6. #106
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    There was a slight mistake in previous formulas (a 49 somewhere isntead of a 50), giving the new ones.

    First formula : 1<=N<=50
    Code:
    critrate=(N*a^2*c-a+N*a+a^(N+1)-N*a^2+N*c-2*N*a*c)/(-1+a)^2/N
    (unchanged)
    Second formula : N>50
    Code:
    critrate=((49*a+a^51+50*c*a^2-100*c*a-50*a^2+50*c)/(-1+a)^2-(N-50)/(-1+a)*(-a^50*c+a^51*c-50*a^50+49*a^51+c-c*a+a)+(50+c)*a^50*(N-1/(-1+a)*a^N-50+1/(-1+a)*a^50))/N
    (no occurence of 48 anymore).
    It is safe to replace 49 and 50 by min(50,100-c)-1 and min(50,100-c) for when you are in abyssea.


    I also have the formula for critical hit damage bonus average (didn't bother builing formula for when you start with a given critical damage, hence there are no valid in abyseea, nor if you cap critical % at 100% with the use of atma because then crit% can cap when crit damage will not)


    First formula : 1<=N<=50
    Code:
    critdamage=-1/(-1+a)^2*(1-a^N*c+3*a^(N+2)-2*a^N*N+4*a^(N+1)*N+2*a^(N+1)*c-N-a^(N+2)*c-a^N-2*c*a+c*a^2-3*a^2+2*a+c-2*a^(N+2)*N-N*a^3+N*a^3*c+N*a-2*a^(N+1)-3*N*a^2*c+3*N*a*c+N*a^2-N*c)*a/(-a+N*a+a^(N+1)+N*a^2*c-2*N*a*c-N*a^2+N*c)
    Second formula : N>50
    Code:
    critdamage=(-1/(-1+a)^4*(-49-a^50*c-97*a^52-101*a^50+198*a^51+2*a^51*c-a^52*c+148*c*a-149*c*a^2+47*a^2+52*a-49*c-50*a^3+50*c*a^3)*a-(N-50)/(-1+a)^2*(-4899*a^51+50*a^50*c-99*a^51*c+2401*a^52+49*a^52*c+2500*a^50-a-c*a-a^2+c*a^2)+50*(50+c)*a^50*(N-1/(-1+a)*a^N-50+1/(-1+a)*a^50))/((49*a+a^51+50*c*a^2-100*c*a-50*a^2+50*c)/(-1+a)^2-(N-50)/(-1+a)*(-a^50*c+a^51*c-50*a^50+49*a^51+c-c*a+a)+(50+c)*a^50*(N-1/(-1+a)*a^N-50+1/(-1+a)*a^50))
    Quick verifications(using corrected formula for crit%)

    N=300 swings ,c=0% crit rate base,a=0.95 accuracy => 29.55% critdmg bonus and 16.59% crit rate
    N=300 swings ,c=15% crit rate base,a=0.95 accuracy => 23.40% critdmg and 31.58% crit rate
    N=300 swings ,c=30% crit rate base,a=0.95 accuracy => 21.21% critdmg and 46.58% crit rate

    PS : the fix in the formula seems to adress motenten's remarks. Also mods should do another thread specific to impetus.

    PPS : Both formula are matching post 104 simulation from Motenten.

  7. #107
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    Ok more and better formula. I fixed another bug happeng when summing stuff around the cap value, doesn't really matther what is is but It's more accurate. My formula are now bigger but account for when critrate will cap at 100 (like in abyssea) and also consider different possible cap values for +critdmg% and + crit% like when you are in abyssea with 75% base crit rate and 30% crit damage. I'm too lazy to build such formula for low values of N like previously so all the following formula are valid as long as N>50.


    Let N=number of swings while impetus is up.
    a=accuracy rate (0.95 for instance)
    c=base crit%,d=base critdmg%
    cap1=min(50+c,100) the crit% bonus cap
    cap2=min(50+d,100) the critdmg% bonus cap
    lambda1=cap1-c the minimal #hits to reach the cap crit% bonus
    lambda2=cap2-d the minimal #hits to reach the cap crit% bonus


    critical % average formula
    this includes base crit rate and gives the value between 0 and 100.
    Code:
    crit%=(c+(lambda1+1)*(-c+a*c-a)/(-1+a)+1/(-1+a)*(-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)/(-1+a)+a^(lambda1+1)*(lambda1+1+c))-1/(-1+a)*(-(-c+a*c-1)*a/(-1+a)+a*(1+c))-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)/(-1+a)+a^(lambda1+1)*cap1+(N-2-lambda1)*(-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)/(-1+a)+(-c+a*c-a)/(-1+a)+a^(lambda1+1)*cap1))/N
    criticaldamage % average formula
    this includes base crit damage % and gives the value between 0 and 100.

    If lambda2<=lambda1
    Code:
    critdmg%=(c*d+(lambda2+1)*(a+a^2-a^2*c-a^2*d+a*d+a*c-2*c*d*a+c*d*a^2+c*d)/(-1+a)^2+(a*d+a*c-3*a+2*(lambda2+1)*a-3-c-d-2*lambda2)/(-3-a+a*c+a*d-d-c-2*lambda2+2*(lambda2+1)*a)/(-1+a)*(-(a+(lambda2+1)^2+a^2+2*(lambda2+1)*a-a^2*c-2*(lambda2+1)^2*a+(lambda2+1)^2*a^2-2*(lambda2+1)*a^2-a^2*d+c*(lambda2+1)+a*d+a*c+d*(lambda2+1)-2*c*d*a+c*d*a^2-2*d*(lambda2+1)*a-2*c*(lambda2+1)*a+a^2*d*(lambda2+1)+a^2*c*(lambda2+1)+c*d)*a^(lambda2+1)/(-1+a)^2+a^(lambda2+1)*(lambda2+1+c)*(lambda2+1+d))+(a+a^2-a^2*c-a^2*d+a*d+a*c-2*c*d*a+c*d*a^2+c*d)/(-1+a)^2-(a*d+a*c-a-3-c-d)/(a*d+a*c-c-d-3+a)/(-1+a)*(-(a+c+d-a*d-2*c*d*a+1+c*d*a^2-a*c+c*d)*a/(-1+a)^2+a*(1+c)*(1+d))-2*(a+(lambda2+1)^2+a^2+2*(lambda2+1)*a-a^2*c-2*(lambda2+1)^2*a+(lambda2+1)^2*a^2-2*(lambda2+1)*a^2-a^2*d+c*(lambda2+1)+a*d+a*c+d*(lambda2+1)-2*c*d*a+c*d*a^2-2*d*(lambda2+1)*a-2*c*(lambda2+1)*a+a^2*d*(lambda2+1)+a^2*c*(lambda2+1)+c*d)*a^(lambda2+1)/(-1+a)^2+a^(lambda2+1)*(lambda2+1+c)*cap2+1/(-1+a)*(-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)*cap2/(-1+a)+a^(lambda1+1)*(lambda1+1+c)*cap2)+(lambda1+1)*(-(a+(lambda2+1)^2+a^2+2*(lambda2+1)*a-a^2*c-2*(lambda2+1)^2*a+(lambda2+1)^2*a^2-2*(lambda2+1)*a^2-a^2*d+c*(lambda2+1)+a*d+a*c+d*(lambda2+1)-2*c*d*a+c*d*a^2-2*d*(lambda2+1)*a-2*c*(lambda2+1)*a+a^2*d*(lambda2+1)+a^2*c*(lambda2+1)+c*d)*a^(lambda2+1)/(-1+a)^2+(-c+a*c-lambda2-1+(lambda2+1)*a-a)*a^(lambda2+1)*cap2/(-1+a)+(a+a^2-a^2*c-a^2*d+a*d+a*c-2*c*d*a+c*d*a^2+c*d)/(-1+a)^2)-1/(-1+a)*(-(-c+a*c-lambda2-2+(lambda2+2)*a-a)*a^(lambda2+2)*cap2/(-1+a)+a^(lambda2+2)*(lambda2+2+c)*cap2)-(lambda2+2)*(-(a+(lambda2+1)^2+a^2+2*(lambda2+1)*a-a^2*c-2*(lambda2+1)^2*a+(lambda2+1)^2*a^2-2*(lambda2+1)*a^2-a^2*d+c*(lambda2+1)+a*d+a*c+d*(lambda2+1)-2*c*d*a+c*d*a^2-2*d*(lambda2+1)*a-2*c*(lambda2+1)*a+a^2*d*(lambda2+1)+a^2*c*(lambda2+1)+c*d)*a^(lambda2+1)/(-1+a)^2+(-c+a*c-lambda2-1+(lambda2+1)*a-a)*a^(lambda2+1)*cap2/(-1+a)+(a+a^2-a^2*c-a^2*d+a*d+a*c-2*c*d*a+c*d*a^2+c*d)/(-1+a)^2)-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)*cap2/(-1+a)+(-c+a*c-lambda2-1+(lambda2+1)*a-a)*a^(lambda2+1)*cap2/(-1+a)+a^(lambda1+1)*cap1*cap2+(N-2-lambda1)*(-(a+(lambda2+1)^2+a^2+2*(lambda2+1)*a-a^2*c-2*(lambda2+1)^2*a+(lambda2+1)^2*a^2-2*(lambda2+1)*a^2-a^2*d+c*(lambda2+1)+a*d+a*c+d*(lambda2+1)-2*c*d*a+c*d*a^2-2*d*(lambda2+1)*a-2*c*(lambda2+1)*a+a^2*d*(lambda2+1)+a^2*c*(lambda2+1)+c*d)*a^(lambda2+1)/(-1+a)^2+(a+a^2-a^2*c-a^2*d+a*d+a*c-2*c*d*a+c*d*a^2+c*d)/(-1+a)^2-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)*cap2/(-1+a)+(-c+a*c-lambda2-1+(lambda2+1)*a-a)*a^(lambda2+1)*cap2/(-1+a)+a^(lambda1+1)*cap1*cap2))/(c+(lambda1+1)*(-c+a*c-a)/(-1+a)+1/(-1+a)*(-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)/(-1+a)+a^(lambda1+1)*(lambda1+1+c))-1/(-1+a)*(-(-c+a*c-1)*a/(-1+a)+a*(1+c))-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)/(-1+a)+a^(lambda1+1)*cap1+(N-2-lambda1)*(-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)/(-1+a)+(-c+a*c-a)/(-1+a)+a^(lambda1+1)*cap1))
    if lambda1=lambda2
    Code:
    critdmg%=(c*d+(lambda2+1)*(a-a^2*c-a^2*d+a*c+a*d-2*c*d*a+c*d*a^2+a^2+c*d)/(-1+a)^2+(a*d-3*a+2*(lambda2+1)*a+a*c-d-3-2*lambda2-c)/(-3+a*c+a*d-c-d-a+2*(lambda2+1)*a-2*lambda2)/(-1+a)*(-(a+2*(lambda2+1)*a-a^2*c-a^2*d+c*(lambda2+1)+d*(lambda2+1)+a*c+a*d-2*(lambda2+1)^2*a+(lambda2+1)^2*a^2-2*(lambda2+1)*a^2-2*c*d*a+c*d*a^2-2*d*(lambda2+1)*a-2*c*(lambda2+1)*a+a^2*d*(lambda2+1)+a^2*c*(lambda2+1)+(lambda2+1)^2+a^2+c*d)*a^(lambda2+1)/(-1+a)^2+a^(lambda2+1)*(lambda2+1+c)*(lambda2+1+d))-(a*d-a+a*c-d-3-c)/(-3+a*c+a*d-c-d+a)/(-1+a)*(-(a+c+d-2*c*d*a-a*d+1-a*c+c*d+c*d*a^2)*a/(-1+a)^2+a*(1+c)*(1+d))-(a+2*(lambda2+1)*a-a^2*c-a^2*d+c*(lambda2+1)+d*(lambda2+1)+a*c+a*d-2*(lambda2+1)^2*a+(lambda2+1)^2*a^2-2*(lambda2+1)*a^2-2*c*d*a+c*d*a^2-2*d*(lambda2+1)*a-2*c*(lambda2+1)*a+a^2*d*(lambda2+1)+a^2*c*(lambda2+1)+(lambda2+1)^2+a^2+c*d)*a^(lambda2+1)/(-1+a)^2+a^(lambda2+1)*cap2*cap1+(N-2-lambda2)*(-(a+2*(lambda2+1)*a-a^2*c-a^2*d+c*(lambda2+1)+d*(lambda2+1)+a*c+a*d-2*(lambda2+1)^2*a+(lambda2+1)^2*a^2-2*(lambda2+1)*a^2-2*c*d*a+c*d*a^2-2*d*(lambda2+1)*a-2*c*(lambda2+1)*a+a^2*d*(lambda2+1)+a^2*c*(lambda2+1)+(lambda2+1)^2+a^2+c*d)*a^(lambda2+1)/(-1+a)^2+(a-a^2*c-a^2*d+a*c+a*d-2*c*d*a+c*d*a^2+a^2+c*d)/(-1+a)^2+a^(lambda2+1)*cap2*cap1))/(c+(lambda1+1)*(-c+a*c-a)/(-1+a)+1/(-1+a)*(-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)/(-1+a)+a^(lambda1+1)*(lambda1+1+c))-1/(-1+a)*(-(-c+a*c-1)*a/(-1+a)+a*(1+c))-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)/(-1+a)+a^(lambda1+1)*cap1+(N-2-lambda1)*(-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)/(-1+a)+(-c+a*c-a)/(-1+a)+a^(lambda1+1)*cap1))
    if lambda2>lambda1
    Code:
    critdmg%=(c*d+(lambda1+1)*(a+a^2-a^2*c-a^2*d+a*d+a*c-2*c*d*a+c*d*a^2+c*d)/(-1+a)^2+(a*c+a*d-3*a+2*(lambda1+1)*a-3-d-c-2*lambda1)/(-3-a+a*d+a*c-c-d-2*lambda1+2*(lambda1+1)*a)/(-1+a)*(-(a+(lambda1+1)^2+a^2+2*(lambda1+1)*a-a^2*d-2*(lambda1+1)^2*a+(lambda1+1)^2*a^2-2*(lambda1+1)*a^2-a^2*c+d*(lambda1+1)+a*c+a*d+c*(lambda1+1)-2*c*d*a+c*d*a^2-2*c*(lambda1+1)*a-2*d*(lambda1+1)*a+a^2*c*(lambda1+1)+a^2*d*(lambda1+1)+c*d)*a^(lambda1+1)/(-1+a)^2+a^(lambda1+1)*(lambda1+1+d)*(lambda1+1+c))+(a+a^2-a^2*c-a^2*d+a*d+a*c-2*c*d*a+c*d*a^2+c*d)/(-1+a)^2-(a*d+a*c-a-3-c-d)/(a*d+a*c-c-d-3+a)/(-1+a)*(-(a+c+d-a*d-2*c*d*a+1+c*d*a^2-a*c+c*d)*a/(-1+a)^2+a*(1+c)*(1+d))-2*(a+(lambda1+1)^2+a^2+2*(lambda1+1)*a-a^2*d-2*(lambda1+1)^2*a+(lambda1+1)^2*a^2-2*(lambda1+1)*a^2-a^2*c+d*(lambda1+1)+a*c+a*d+c*(lambda1+1)-2*c*d*a+c*d*a^2-2*c*(lambda1+1)*a-2*d*(lambda1+1)*a+a^2*c*(lambda1+1)+a^2*d*(lambda1+1)+c*d)*a^(lambda1+1)/(-1+a)^2+a^(lambda1+1)*(lambda1+1+d)*cap1+1/(-1+a)*(-(-d+a*d-lambda2-1+(lambda2+1)*a-a)*a^(lambda2+1)*cap1/(-1+a)+a^(lambda2+1)*(lambda2+1+d)*cap1)+(lambda2+1)*(-(a+(lambda1+1)^2+a^2+2*(lambda1+1)*a-a^2*d-2*(lambda1+1)^2*a+(lambda1+1)^2*a^2-2*(lambda1+1)*a^2-a^2*c+d*(lambda1+1)+a*c+a*d+c*(lambda1+1)-2*c*d*a+c*d*a^2-2*c*(lambda1+1)*a-2*d*(lambda1+1)*a+a^2*c*(lambda1+1)+a^2*d*(lambda1+1)+c*d)*a^(lambda1+1)/(-1+a)^2+(-d+a*d-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)*cap1/(-1+a)+(a+a^2-a^2*c-a^2*d+a*d+a*c-2*c*d*a+c*d*a^2+c*d)/(-1+a)^2)-1/(-1+a)*(-(-d+a*d-lambda1-2+(lambda1+2)*a-a)*a^(lambda1+2)*cap1/(-1+a)+a^(lambda1+2)*(lambda1+2+d)*cap1)-(lambda1+2)*(-(a+(lambda1+1)^2+a^2+2*(lambda1+1)*a-a^2*d-2*(lambda1+1)^2*a+(lambda1+1)^2*a^2-2*(lambda1+1)*a^2-a^2*c+d*(lambda1+1)+a*c+a*d+c*(lambda1+1)-2*c*d*a+c*d*a^2-2*c*(lambda1+1)*a-2*d*(lambda1+1)*a+a^2*c*(lambda1+1)+a^2*d*(lambda1+1)+c*d)*a^(lambda1+1)/(-1+a)^2+(-d+a*d-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)*cap1/(-1+a)+(a+a^2-a^2*c-a^2*d+a*d+a*c-2*c*d*a+c*d*a^2+c*d)/(-1+a)^2)-(-d+a*d-lambda2-1+(lambda2+1)*a-a)*a^(lambda2+1)*cap1/(-1+a)+(-d+a*d-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)*cap1/(-1+a)+a^(lambda2+1)*cap2*cap1+(N-2-lambda2)*(-(a+(lambda1+1)^2+a^2+2*(lambda1+1)*a-a^2*d-2*(lambda1+1)^2*a+(lambda1+1)^2*a^2-2*(lambda1+1)*a^2-a^2*c+d*(lambda1+1)+a*c+a*d+c*(lambda1+1)-2*c*d*a+c*d*a^2-2*c*(lambda1+1)*a-2*d*(lambda1+1)*a+a^2*c*(lambda1+1)+a^2*d*(lambda1+1)+c*d)*a^(lambda1+1)/(-1+a)^2+(a+a^2-a^2*c-a^2*d+a*d+a*c-2*c*d*a+c*d*a^2+c*d)/(-1+a)^2-(-d+a*d-lambda2-1+(lambda2+1)*a-a)*a^(lambda2+1)*cap1/(-1+a)+(-d+a*d-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)*cap1/(-1+a)+a^(lambda2+1)*cap2*cap1))/(c+(lambda1+1)*(-c+a*c-a)/(-1+a)+1/(-1+a)*(-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)/(-1+a)+a^(lambda1+1)*(lambda1+1+c))-1/(-1+a)*(-(-c+a*c-1)*a/(-1+a)+a*(1+c))-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)/(-1+a)+a^(lambda1+1)*cap1+(N-2-lambda1)*(-(-c+a*c-lambda1-1+(lambda1+1)*a-a)*a^(lambda1+1)/(-1+a)+(-c+a*c-a)/(-1+a)+a^(lambda1+1)*cap1))
    It matches the simulations in abyssea type environnement so it looks good.

    Here is some comparison formula/ simulation


    Code:
    N=144 hit, c=10%,d=0%
    C simulation : 15.5961% crit bonus, 23.3031% critdmg bonus
    formula : 15.60982892 and 23.31883956
    N=144 hit, c=0%,d=0%
    C simulation : 15.6092% and 28.2490%
    formula : 15.60982892 and 28.25740146
    N=144 hit, c=30%,d=0%
    C simulation : 15.5997% and 19.9192%
    formula : 15.60982892 and 19.93842317
    c=30%,d=10%,N=300
    my simulation : 16.6087% crit bonus, 21.2273% critdmg bonus
    formula : 16.61250153 21.23356775
    c=75%,d=30%,N=300 (abyssea, RR,GH,SS and cruor buff)
    my simulation : 13.2522% crit bonus, 17.9836% critdmg bonus
    formula : 13.25349170 and 17.99390912
    c=59%, d=81%, N=300(imaginary)
    my simulation : 15.8729% crit bonus, 12.5893% critdmg bonus
    formula : 15.88534993 and 12.59230677

  8. #108
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    I didn't thoroughly look through your simulations to check if it was accounted for, but one thing that may need to be considered is that impetus may be calculated on a per round basis. I am not absolutely certain, but there are times that I've noticed a miss in a sequence of attacks and yet the following attacks of that same attack round still appear to receive a hefty bonus where one would expect it should have reset.

    For example, imagine I have 30 consecutive hits built up on impetus and the next round looks like:
    Nivlakian scores a critical hit! The Mob takes 400 points of damage.
    Nivlakian hits the Mob for 180 points of damage.
    Nivlakian misses the Mob.
    Nivlakian scores a critical hit! The Mob takes 400 points of damage.

    The numbers are made up, but the point is to illustrate how the last hit which crit still appeared to have a significant damage bonus despite the previous hit resetting impetus. One would expect in that case that the damage should have been a more standard critical somewhere close to 300ish damage. I am not certain how much that would alter calculations, but thought it worth mentioning.

  9. #109
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    nvm misunderstood ; However it would not change much I think, and that would definitely increase the bonuses.

  10. #110
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    While I can't say exactly how much it changes things, you are correct in that it recalculates on a per round basis. All hits of a round technically occur at the same time so in a 4 hit attack round, a 3rd hit miss does not actually effect the 4th hit.
    As another example lets say you ALWAYS have 4 attacks per round. After 10 attack rounds or 40 consecutive hits based your bonus would be:

    1st round(hits 1-4)=0,0,0,0 2nd round(hits 4-8 )=4,4,4,4 3rd round(hits 9-12)=8,8,8,8 4th round(13-16)=12,12,12,12
    5th round(17-20)=16,16,16,16 ....... 10th round(hits 37-40)=36,36,36,36

    Which gives a total bonus score of 720 for an average of 18/hit, while a per hit basis would give 780 for an average of 19.5/hit.

    If you had an average of 4hits/round alternating 2hit and 6 hit rounds you'd get a bonus score of 700 for an average of 17.5/hit after 40 consecutive hits.

    To be honest, I don't myself know off the top of my head how to account for this, I suppose that it would have to be compounded somewhere by attacks per round. On top of which you have things like counter which would count effectively as a 1 hit round. Maybe pchan and motenten can figure something out. As I don't believe it should change results too drastically though, it is probably much simpler to stick with what the model is at this point.

  11. #111
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    All it does, imo, is change the acc% rate to make on a per round accuracy rate : if you got 0.95 accuracy and average 2.8 hits per round, the new acc rate is 1-0.05^2.8, and also the bonus would be 2.8% per round ? Might be worth looking more deeply.

  12. #112
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    If you feel like doing another super long parse pchan, you could always dual wield 0dmg clubs mnk/nin to see how it compares. I am temp-deactivated atm or I would just do one myself. Also I might be remembering wrong, but do hits of WS actually add to the bonus counter? I know misses reset it, but I think that maybe they don't. It could be 3 things though I guess:

    1. All hits of WS increase bonus
    2. Only 1st hit of WS can increase bonus
    3. No WS hits increase Bonus

    I'd be grateful if someone could check this as well, I went to go double check and that's when I saw I was deactivated. With not much to do in game atm, I am too cheap to pay for a month to check something that takes 5 minutes of time.

  13. #113
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    shijin spiral on a weak skeletton at 50% HP, 5 tp return with spharai and 9 STP resulted in +6 attack. I think I hit only once during shijin but got the bonus from all hits.

  14. #114
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    So wait, a hit 1 shijin resulted in +6 attack? So it added 3 hits worth of attack?

  15. #115
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    Quick test in Buburimu. Got 100 TP, activated Impetus, and used weaponskill to kill a mob.

    Base attack: 602

    1-hit Howling Fist with Impetus active
    New attack: 604

    Reset Impetus

    2-hit Asuran Fists with Impetus Active
    New attack: 606

    Edit: And in case there's anything wierd with Shijin Spiral:

    Reset Impetus

    1-hit Shijin with Impetus active
    New attack: 604


    It appears to behave normally with weaponskills, only using the hits that landed.

  16. #116
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    Me and mdk checked our attack during dynamis, and they reset a lot during weapon skill. Also attack resets often on normal melee attack so it's impossible that the attack only reset when the whole round misses.

  17. #117
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    I think you misunderstand. It's not that it only resets when a full attack round misses, but that it does not reset for any hits after a miss in the same attack round. Using my example of 4 hit attack rounds with starting attack of 600:

    attack round 1(hit1=600att, hit2= 600att, hit3=600att, hit 4=600att), attack round 2(hit 1=604, hit2=604, hit3=604, hit 4=604), attack round 3(hit1=608, hit2=608, hit3=608, hit4=608 ). Now when misses are thrown in:

    attack round 1(hit1=600, hit2= 600, hit3=600, hit 4=600), attack round 2(hit 1=604, hit2(miss)=604, hit3=604, hit 4=604), attack round 3(hit1=602, hit2=602, hit3=602, hit4=602)

    So it's that the bonus is checked at time of an attack round and whatever that bonus is, is then applied to all hits of that attack round.

  18. #118
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    ... That auto-linking is really getting to be obnoxious, isn't it?

  19. #119
    Chram
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    Your formula (the critical % average formula) doesn't appear to be working, pchan.

    What I did:

    First, expanded it out so I could be sure I'm getting all the parentheses in there:

    Code:
    crit%=
    (c+
      (lambda1+1)*
      (-c+a*c-a)/
      (-1+a)+
      1/
      (-1+a)*
      (-
        (-c+a*c-lambda1-1+
          (lambda1+1)*
        a-a)*
        a^(lambda1+1)/
        (-1+a)+
        a^(lambda1+1)*
        (lambda1+1+c)
      )-
      1/
      (-1+a)*
      (-
        (-c+a*c-1)*
        a/
        (-1+a)+
        a*
        (1+c)
      )-
      (-c+a*c-lambda1-1+
        (lambda1+1)*
      a-a)*
      a^(lambda1+1)/
      (-1+a)+
      a^(lambda1+1)*
      cap1+
      (N-2-lambda1)*
      (-
        (-c+a*c-lambda1-1+
          (lambda1+1)*
        a-a)*
        a^(lambda1+1)/
        (-1+a)+
        (-c+a*c-a)/
        (-1+a)+
        a^(lambda1+1)*
      cap1)
    )/N
    Then, using a small chunk of the spreadsheet, entered/calculated values:
    Code:
        AG        AH      AI      AJ
                  base    max     hits to cap
    6   acc       95%     95%     0
    7   crit      12%     62%     50
    8   crit dmg  0%      50%     50
    9   att                       50
    10  hits              144

    Then did a search/replace on the formula you provided, substituting in the appropriate Excel cells:
    Code:
    =
    (ah7+
      (ai7+1)*
      (-ah7+ah6*ah7-ah6)/
      (-1+ah6)+
      1/
      (-1+ah6)*
      (-
        (-ah7+ah6*ah7-ai7-1+
          (ai7+1)*
        ah6-ah6)*
        ah6^(ai7+1)/
        (-1+ah6)+
        ah6^(ai7+1)*
        (ai7+1+ah7)
      )-
      1/
      (-1+ah6)*
      (-
        (-ah7+ah6*ah7-1)*
        ah6/
        (-1+ah6)+
        ah6*
        (1+ah7)
      )-
      (-ah7+ah6*ah7-ai7-1+
        (ai7+1)*
      ah6-ah6)*
      ah6^(ai7+1)/
      (-1+ah6)+
      ah6^(ai7+1)*
      aj7+
      (ai10-2-ai7)*
      (-
        (-ah7+ah6*ah7-ai7-1+
          (ai7+1)*
        ah6-ah6)*
        ah6^(ai7+1)/
        (-1+ah6)+
        (-ah7+ah6*ah7-ah6)/
        (-1+ah6)+
        ah6^(ai7+1)*
      aj7)
    )/ai10

    Then collapsed it all together again to copy into Excel:
    Code:
    =(ah7+(ai7+1)*(-ah7+ah6*ah7-ah6)/(-1+ah6)+1/(-1+ah6)*(-(-ah7+ah6*ah7-ai7-1+(ai7+1)*ah6-ah6)*ah6^(ai7+1)/(-1+ah6)+ah6^(ai7+1)*(ai7+1+ah7))-1/(-1+ah6)*(-(-ah7+ah6*ah7-1)*ah6/(-1+ah6)+ah6*(1+ah7))-(-ah7+ah6*ah7-ai7-1+(ai7+1)*ah6-ah6)*ah6^(ai7+1)/(-1+ah6)+ah6^(ai7+1)*aj7+(ai10-2-ai7)*(-(-ah7+ah6*ah7-ai7-1+(ai7+1)*ah6-ah6)*ah6^(ai7+1)/(-1+ah6)+(-ah7+ah6*ah7-ah6)/(-1+ah6)+ah6^(ai7+1)*aj7))/ai10
    With the above values, the result was 45.53356941.

  20. #120
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    Quote Originally Posted by diasetsu View Post
    If you feel like doing another super long parse pchan, you could always dual wield 0dmg clubs mnk/nin to see how it compares. I am temp-deactivated atm or I would just do one myself. Also I might be remembering wrong, but do hits of WS actually add to the bonus counter? I know misses reset it, but I think that maybe they don't. It could be 3 things though I guess:

    1. All hits of WS increase bonus
    2. Only 1st hit of WS can increase bonus
    3. No WS hits increase Bonus

    I'd be grateful if someone could check this as well, I went to go double check and that's when I saw I was deactivated. With not much to do in game atm, I am too cheap to pay for a month to check something that takes 5 minutes of time.
    He is doing a MNK/NIN parse atm and so far it works as intended ( ie as if yo u were doing 2N attack rounds of 1 hit, instead of N attack rounds with 2 hits): averaging 17.4% critical hit rate, using impetus whenever it's up ( so accounting for impetus up and down).The theoretical values is 17.6% i believe.

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