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Thread: AP, how exactly does it work?

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    RIFT Guide Writer Gyle's Avatar
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    Default AP, how exactly does it work?

    So with the upcoming changes in 1.4 to Crit, i guess we are going to have to start using some more AP gear. My question is, precisely how is AP figured into the damage calculation? I am not a newby, i just have never really cared until now, stack crit, toss in a little ap here and there to keep a minor balance, but in just my T2 with a few pieces of T3 gear and all +crit epic lessers, my Sabdancer spec puts me at almost the softcap. (yes the +crit skills don't figure in, but Ambidextrous does since it adds DEX right?)

    So for example, with an AP of 551, the mouse over says it adds 55.1 dps. Is that really it? I mean, unless the skill is a finisher, or some other skill that has a +%ap damage written into it like Deadly Strike or Quick Strike. Now, quite obviously it does not merely add 55 damage to each hit, because a skill like Keen Strike that says it his for 80 damage could regularly hit for 2-400 damage without a crit. Since it seems like AP and Crit are the only two stats that make any difference to dps at all, it has to be the AP that is taking the damage of that skill and doubling it or more, but how? As well, it does not seem add precisely 55 Damage Per Second because large AP bonuses i have noticed make very large changes in dps, far greater than the 10% number you read.

    If there is some other post on this somewhere i apologize, i couldn't find it. Please redirect me if this answer is somewhere else.

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    Shield of Telara
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    you will be balancing the stats now. the gear is going to have both on it for the most part anyway as t2 and t3 do. its not going to be that big an issue gear wise. The sourcemachine is going to be the biggest place we start needing to make some adjustments though. I also think that there is a lot of misinformation going around the forums due to misinterpretation of what the caps actually are. (not anyone in particular but generally.)

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    RIFT Guide Writer Gyle's Avatar
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    Not really concerned with how to set up my gear, i think i will be able to get that pretty well correct as i go, thank you though. I am more wondering how AP actually works, HOW is it figured in to the damage calc?

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    Quote Originally Posted by Gyle View Post
    Not really concerned with how to set up my gear, i think i will be able to get that pretty well correct as i go, thank you though. I am more wondering how AP actually works, HOW is it figured in to the damage calc?
    I do not know the exact numbers but this will help you some.

    Keen strike
    A swift attack that deals weapon plus 77 to 80 Physical damage

    The AP affects this portion of the attack. That 55.1 DPS increase you see on the tooltip means these calcs will treat your weapon as x+55.1 actual DPS.

    Skills are normalized to weapon speed and I don't know the actually speed theyre calculated to but let's assume it's 2.0 for a second.

    With a 36 DPS weapon, with 551 AP, we get a 91.1 DPS weapon. Let's take that and remember our weapon only swings once every 2 seconds so we get 182.2 per swing.

    182+77 to 80= 259-263 dmg per keen strike.

    It's gonna be higher than that due to talents but i have no way of knowing how you're specced or anything and this exercise at least illustrates to you why AP can have such a large effect.



    *edit Let's not forget Keen could also be lower than that because its all going to be physical damage which can be reduced by armor of the target. :P
    Last edited by Triscone; 07-16-2011 at 07:44 PM.

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    RIFT Guide Writer Gyle's Avatar
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    That is exactly what i was looking for, thank you.

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    Soulwalker Maliss's Avatar
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    Default Sooo.. maces?

    So the real question is, if your an ability-heavy spec lik 27 dancer 21 NB and 18 assassin, spamming abilities in melee constantly, would you get better DPS (from abilities) with maces?

    THAT is the million dollar question that I've been theory crafting with for weeks.
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    Quote Originally Posted by Maliss View Post
    So the real question is, if your an ability-heavy spec lik 27 dancer 21 NB and 18 assassin, spamming abilities in melee constantly, would you get better DPS (from abilities) with maces?

    THAT is the million dollar question that I've been theory crafting with for weeks.
    No. Your DPS will actually go down, due to the way whetstones are added in. If that weren't the case DPS would be identical.

    1H Weapons are normalized to 2.8s speed (IIRC, got this number in beta 5 when they added normalization in. I don't think it's changed, but could test again).

    Real Damage = Base Damage + ((Weapon DPS + (Attack Power * Attack Power Coefficient) / 10) * 2.8)
    Solving for Attack Power Coefficient yields:
    Attack Power Coefficient = (-5 * (5 * Base Damage - 5 * Real Damage + 14 * Weapon DPS)) / (7 * Attack Power)
    Now that real damage doesn't take crit into account, but thats easy: Real Damage * Crit Rate * Crit Multiplier + Real Damage = Average Damage
    eg 100 damage attack, 1.5x multiplier, 0.3x crit rate (30%): 100*1.5*0.3+100=145 average damage
    So, after factoring everything for neatness:

    Average Damage = ((7 * Attack Power * Attack Power Coefficient + 5 * (5 * Base Damage + 14 * Weapon DPS)) * (Crit Multiplier * Crit Rate + 1)) / 25

    End simple algebra, time for simple multivariable calculus.
    To find the optimal AP:Crit ratio we want to find the gradient (Partial derivatives as a vector in N-dimensional space.) of the above equation with respect to ∂Attack Power and ∂Crit Rate

    ∂Average Damage/∂Attack Power = (7 * Attack Power Coefficient * (Crit Multiplier * Crit Rate + 1)) / 25
    ∂Average Damag/∂Crit Rate = ((7 * Attack Power * Attack Power Coefficient + 5 * (5 * Base Damage + 14 * Weapon DPS)) * Crit Multiplier) / 25
    Gradient Damage(AP, CritRate) = <(7 * Attack Power Coefficient * (Crit Multiplier * Crit Rate + 1)) / 25, ((7 * Attack Power * Attack Power Coefficient + 5 * (5 * Base Damage + 14 * Weapon DPS)) * Crit Multiplier) / 25>

    The magnitude (Square root of the dot product of the vector with itself) of that vector tells you the rate that your damage increases as you increase AP and Crit at their optimal ratio. The ratio of the terms is that optimal ratio.

    Of course, that's only for one ability. To figure it out across all abilities you have to take a weighted average with the fraction of your total damage done by each ability as the weights. Doing so is left as an exercise to the reader, since your build and rotation will be different from mine.

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    Soulwalker Maliss's Avatar
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    Quote Originally Posted by SoAnIs View Post
    No. Your DPS will actually go down, due to the way whetstones are added in. If that weren't the case DPS would be identical.

    1H Weapons are normalized to 2.8s speed (IIRC, got this number in beta 5 when they added normalization in. I don't think it's changed, but could test again).

    Real Damage = Base Damage + ((Weapon DPS + (Attack Power * Attack Power Coefficient) / 10) * 2.8)
    Solving for Attack Power Coefficient yields:
    Attack Power Coefficient = (-5 * (5 * Base Damage - 5 * Real Damage + 14 * Weapon DPS)) / (7 * Attack Power)
    Now that real damage doesn't take crit into account, but thats easy: Real Damage * Crit Rate * Crit Multiplier + Real Damage = Average Damage
    eg 100 damage attack, 1.5x multiplier, 0.3x crit rate (30%): 100*1.5*0.3+100=145 average damage
    So, after factoring everything for neatness:

    Average Damage = ((7 * Attack Power * Attack Power Coefficient + 5 * (5 * Base Damage + 14 * Weapon DPS)) * (Crit Multiplier * Crit Rate + 1)) / 25

    End simple algebra, time for simple multivariable calculus.
    To find the optimal AP:Crit ratio we want to find the gradient (Partial derivatives as a vector in N-dimensional space.) of the above equation with respect to ∂Attack Power and ∂Crit Rate

    ∂Average Damage/∂Attack Power = (7 * Attack Power Coefficient * (Crit Multiplier * Crit Rate + 1)) / 25
    ∂Average Damag/∂Crit Rate = ((7 * Attack Power * Attack Power Coefficient + 5 * (5 * Base Damage + 14 * Weapon DPS)) * Crit Multiplier) / 25
    Gradient Damage(AP, CritRate) = <(7 * Attack Power Coefficient * (Crit Multiplier * Crit Rate + 1)) / 25, ((7 * Attack Power * Attack Power Coefficient + 5 * (5 * Base Damage + 14 * Weapon DPS)) * Crit Multiplier) / 25>

    The magnitude (Square root of the dot product of the vector with itself) of that vector tells you the rate that your damage increases as you increase AP and Crit at their optimal ratio. The ratio of the terms is that optimal ratio.

    Of course, that's only for one ability. To figure it out across all abilities you have to take a weighted average with the fraction of your total damage done by each ability as the weights. Doing so is left as an exercise to the reader, since your build and rotation will be different from mine.



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  9. #9
    Telaran
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    Thanks for the equations but I'm facing a little problem to put that into use.

    Could you please give one example with an ability and your build please ?

    In your last equation : Gradient Damage(AP, CritRate) = <(7 * Attack Power Coefficient * (Crit Multiplier * Crit Rate + 1)) / 25, ((7 * Attack Power * Attack Power Coefficient + 5 * (5 * Base Damage + 14 * Weapon DPS)) * Crit Multiplier) / 25>


    To solve it I need to find what my attack power coefficient is, reading your other equations :
    Attack Power Coefficient = (-5 * (5 * Base Damage - 5 * Real Damage + 14 * Weapon DPS)) / (7 * Attack Power)

    But then I'd need to find what my real damage for an ability is, using again your equations :
    Real Damage = Base Damage + ((Weapon DPS + (Attack Power * Attack Power Coefficient) / 10) * 2.8)
    To solve that one I'd need the attack power coefficient...Thus I'm kind of stuck.


    There must be something I'm missing, but as I read it there are too many variables to solve the equation for an ability.

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    Quote Originally Posted by sagavellius View Post
    Thanks for the equations but I'm facing a little problem to put that into use.

    Could you please give one example with an ability and your build please ?

    In your last equation : Gradient Damage(AP, CritRate) = <(7 * Attack Power Coefficient * (Crit Multiplier * Crit Rate + 1)) / 25, ((7 * Attack Power * Attack Power Coefficient + 5 * (5 * Base Damage + 14 * Weapon DPS)) * Crit Multiplier) / 25>


    To solve it I need to find what my attack power coefficient is, reading your other equations :
    Attack Power Coefficient = (-5 * (5 * Base Damage - 5 * Real Damage + 14 * Weapon DPS)) / (7 * Attack Power)

    But then I'd need to find what my real damage for an ability is, using again your equations :
    Real Damage = Base Damage + ((Weapon DPS + (Attack Power * Attack Power Coefficient) / 10) * 2.8)
    To solve that one I'd need the attack power coefficient...Thus I'm kind of stuck.


    There must be something I'm missing, but as I read it there are too many variables to solve the equation for an ability.
    Take ability A, tooltip says it does 100 damage, so it should crit for 150. Going to a dummy I see it crits for 225. So it does 150 real damage. Say I have 100 AP and a 10 DPS weapon. (-5 * (5 * 100 - 5 * 150 + 14 * 10)) / (7 * 100) = (-5*(500-750+140))/700 = 550/700 ~=0.7857 = Attack Power Coeff.

    In short, get your real damage from a dummy test.

    Example of finishing this calculation, with, say, 50% crit rate:
    Gradient Damage(AP, CritRate) = <(7 * 0.7857 * (1.5 * 0.5 + 1)) / 25, ((7 * 100 * 0.7857 + 5 * (5 * 100 + 14 * 10)) * 1.5) / 25> =< 0.385 , 225 > = < 1, 584>

    Of course real values are quite different from those. AP is worth quite a bit more. Also, with the new soft cap things get easy: Stack crit to 1000 crit rating (for raids), then stack AP.

  11. #11
    Champion of Telara
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    1H Weapons are normalized to 2.8s speed (IIRC, got this number in beta 5 when they added normalization in. I don't think it's changed, but could test again).
    Ability damage calculations normalize AP_DPS (AP_DPS = AP / 10) to a standard delay per attack. From what I've seen, this delay is 1.0.

    I'm not really sure why you're talking about weapon normalization, as it is irrelevant to a discussion of AP's translation if it even exists.

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    Quote Originally Posted by EasymodeX View Post
    Ability damage calculations normalize AP_DPS (AP_DPS = AP / 10) to a standard delay per attack. From what I've seen, this delay is 1.0.

    I'm not really sure why you're talking about weapon normalization, as it is irrelevant to a discussion of AP's translation if it even exists.
    AFAICT that "AP" DPS is added to weapon DPS, then divided by a speed factor to get a total damage. That damage is added to the damage of the skill. I may have the normalizations done wrong, I'll try to test them when I get a chance.

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    weapon speed will matter a lot less with the upcoming patch, with wetstones and spotters order normalized, the only remaining debatable point for faster weapons would be procs like poisons / hellfire blades, and the like

  14. #14
    Qan
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    Quote Originally Posted by SoAnIs View Post
    Attack Power Coefficient = (-5 * (5 * Base Damage - 5 * Real Damage + 14 * Weapon DPS)) / (7 * Attack Power)
    Why is an AP Coefficient equation needed when it's given in the tooltip?
    Keen says nothing, therefore coeff = 1
    Quick Strike says bonus 100%, coeff = 2
    Dusk Strike says bonus 50%, coeff = 1.5

    Quote Originally Posted by SoAnIs View Post
    Now that real damage doesn't take crit into account, but thats easy: Real Damage * Crit Rate * Crit Multiplier + Real Damage = Average Damage
    eg 100 damage attack, 1.5x multiplier, 0.3x crit rate (30%): 100*1.5*0.3+100=145 average damage
    An attack that hits for 100 70% of the time and 150 30% of the time averages out to 115, not 145

    ((Real Damage * (100 - Crit Rate)) + (Crit Damage * Crit Rate)) / 100
    Last edited by Qan; 07-21-2011 at 08:47 PM.
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