2011-06-30, 07:17 PM
(This post was last modified: 2011-07-01, 01:52 AM by 2147483647.)
That's the same damage formula with potential bonuses. Since potential bonuses are already floored when you view them in your stat window, it's pointless to build a formula to account for them, since you can just floor everything externally before inserting them into the following formula:
(4*STR+DEX)/(4*WAtk)
It's also impossible to account for flooring, since continuity is a requirement for derivation. Flooring stats externally is actually advantageous when programming, because then you can use those stats for other formulae as well.
I don't really see the need for a precise calculator to be built. If someone is considering a piece of equipment, all he has to do is calculate stats before and after, floor it externally, and then insert it into the formula to find the ratio.
If someone is wondering about "which equipment will give me more damage", the answer is: if (4*STR+DEX) < (4*WAtk), then STR gives more damage, and in any other case, WAtk gives more damage. By how much? Plug it into the very simple equation and find out. Anyone who's passed 8th grade should be able to do this.
Hadriel, the reason your math isn't holding up is that you're using total differentials and abusing the definition of a differential. The following is your work, but I cleaned up some of the symbols:
DMG = (c/100)*(MA)*(4INT+LUK)
∇(DMG) = (c/100)*(4INT+LUK)*Δ(MA) + (c/100)*4*(MA)*Δ(INT) + (c/100)*(MA)*Δ(LUK)
At this stage, you decided that luk should be a constant, making Δ(LUK) = 0. Thus, you simplified:
∇(DMG) = (c/100)*(4INT+LUK)*Δ(MA) + (c/100)*4*(MA)*Δ(INT)
You then suggested taking the ratios of the two terms to yield:
The problem here is that because Δ(INT) and Δ(MA) are differentials, they are supposed to cancel out when you take the limit as Δ(INT) and Δ(MA) both approach 0. This results in the reciprocal of the formula found just by taking individual partial derivatives and dividing them.
Also, LUK isn't negligible. Say that someone (who is ridiculously overpowered) has 2000 INT but only 100 LUK. The ratio of INT to LUK is about 20:1, which is far from "negligible". In fact, it accounts for more than 1% of the total damage, even if you multiply it by 4 (the natural multiplier in the equation).
I'm not sure why you use the Legendre transformation here, but as you probably already know, the Legendre transform is useless when all the variables are known to exact certainty. That's why your transform didn't reveal anything new.
(4*STR+DEX)/(4*WAtk)
It's also impossible to account for flooring, since continuity is a requirement for derivation. Flooring stats externally is actually advantageous when programming, because then you can use those stats for other formulae as well.
I don't really see the need for a precise calculator to be built. If someone is considering a piece of equipment, all he has to do is calculate stats before and after, floor it externally, and then insert it into the formula to find the ratio.
If someone is wondering about "which equipment will give me more damage", the answer is: if (4*STR+DEX) < (4*WAtk), then STR gives more damage, and in any other case, WAtk gives more damage. By how much? Plug it into the very simple equation and find out. Anyone who's passed 8th grade should be able to do this.
Hadriel, the reason your math isn't holding up is that you're using total differentials and abusing the definition of a differential. The following is your work, but I cleaned up some of the symbols:
DMG = (c/100)*(MA)*(4INT+LUK)
∇(DMG) = (c/100)*(4INT+LUK)*Δ(MA) + (c/100)*4*(MA)*Δ(INT) + (c/100)*(MA)*Δ(LUK)
At this stage, you decided that luk should be a constant, making Δ(LUK) = 0. Thus, you simplified:
∇(DMG) = (c/100)*(4INT+LUK)*Δ(MA) + (c/100)*4*(MA)*Δ(INT)
You then suggested taking the ratios of the two terms to yield:
4/100*MA*Δ(INT)
1/100*(4INT+LUK)*Δ(MA)
4*MA*Δ(INT)
(4INT+LUK)*Δ(MA)
1/100*(4INT+LUK)*Δ(MA)
4*MA*Δ(INT)
(4INT+LUK)*Δ(MA)
The problem here is that because Δ(INT) and Δ(MA) are differentials, they are supposed to cancel out when you take the limit as Δ(INT) and Δ(MA) both approach 0. This results in the reciprocal of the formula found just by taking individual partial derivatives and dividing them.
Also, LUK isn't negligible. Say that someone (who is ridiculously overpowered) has 2000 INT but only 100 LUK. The ratio of INT to LUK is about 20:1, which is far from "negligible". In fact, it accounts for more than 1% of the total damage, even if you multiply it by 4 (the natural multiplier in the equation).
I'm not sure why you use the Legendre transformation here, but as you probably already know, the Legendre transform is useless when all the variables are known to exact certainty. That's why your transform didn't reveal anything new.