When Parry is better than Dodge
So I was thinking the other day to my self, hmm with the DR curves it might be possible for parry to be better than dodge at some point, so I did some digging and saw that no one did any math on it yet, so here comes...
This is my first ever post so if I mess something up or you think it needs improvement feel free to give feed back!
Based on this article:
I simplified the equations for warriors to:
Ad = C*A/(A+K*C)
Ad = (88.129021*A)/(A+84.25134407) dodge
Ad = (47.03525*A)/(A+44.965699) parry
Then graphed these wonderful equations to see what the DR curve actually looks like:
From here I took the derivative of the functions, because once the slopes of the two curves are equal then adding either dodge or parry adds the same percent, however if the slope of the parry curve at a given points is greater than the slope of the dodge curve then parry is better to stack:
d(Ad(A))/dA = K*(C)^2/(A^2+2*A*K*C + (K*C)^2) by quotient rule.
Adding new terminology here we can balance the parry and dodge equations. Ad will be the dodge before DR and Ap will be the parry before DR, Cd will be the C for dodge, and Cp will be the C for parry.
then we have:
K(Cd)^2/((Ad+KCd)^2) = K(Cp)^2/((Ap+KCp)^2)
after some simplification:
sqrt(K(Cd)^2/K(Cp)^2) = (Ad+KCd)/(Ap+KCp)
sqrt(K(Cd)^2/K(Cp)^2)*KCp - KCd = Ad - sqrt(K(Cd)^2/K(Cp)^2)*Ap
after plugging in all our constants we get:
0 = Ad - 1.874945*Ap
Which means, that if your dodge before DR minus your parry before DR times 1.874945 is equal to 0, then you get the same avoidance from adding parry as dodge. If the number is negative then parry gives you more per point than dodge.
So lets say you're at 15% parry:
Ad = 1.874945*15 = 28.124175
So if you have 15% parry before DR that means that you'd need 28.124175 % dodge before DR before adding parry would give the same as adding dodge.
Edit: it turns out I made a mistake, you cannot simply plug in the rating values as I had before, there is a shift in the 0 point of inflection due to constants that cancel out in the derivative if you do not recalculate the derivative with ratings factored in. The EJ forums realized this and are correct, the end equation including ends up being more complicated, also my above solution only solves for the positive solution of the quadratic (because I square rooted both sides) which is alright because it's the only one we care about (thanks to EJ forums for the equations here).
The real equation after re-calculating the derivative (where rd is the rating for dodge, rp is the rating for parry, P0 is the parry from gear, and D0 is the dodge from gear):
Which simplifies to:
and with numbers:
Which means for my warrior:
The World of Warcraft Armory
at 8.84% dodge, P0 is -0.5269664, which means I shouldnt add any parry at all. However my gear forces me to as it simply comes on it, such is life sometimes.
The graph after accounting for the rating skew ends up being (remember these %'s are before DR):
So simply fallow the X axis for how much dodge from gear you have and see if on the Y axis you have as much parry added from gear as the graph shows, if not, then add more parry to get your best avoidance efficiency.
I'd also like to point out how harsh the parry curve is, it drops of really quick once you get past about 18%
On a side note, after I posed this I found I had been beat to it, but with the same result, and both have pretty graphs lol:
Avoidance Diminishing Returns - Elitist Jerks