"Woodroward;c-1622891" wrote:
"crzydroid;c-1622880" wrote:
"Woodroward;c-1622872" wrote:
"crzydroid;c-1622663" wrote:
Ok, so I think some of the solutions have ignored the multivariate nature of the problem in favor of the stat of interest (be it cc or whatever). Some of these posts have offered the equation, but I will try to lay it out again here.
Let's call Base offense b, offense primary percent z, flat offense from mods and equipped gear y, offense from in-game bonuses o, damage multiplier m, critical chance c, and total critical damage bonuses from crit damage triangle and in-game abilities x.
If you are lost already, scroll to the bottom.
If I'm not mistaken about game mechanics, unmitigated damage with an offense set would be:
(1.15b +zb+y)om (1-c) + (1.15b+zb+y)omc (1.5+x),
and with a crit damage set instead would be:
(b+zb+y)om (1-c)+(b+zb+y)omc (1.8+x).
The om term is multiplied through every piece, so that drops out in the simplification of the expression. While I can provide the next steps of the simplification and gathering of terms, in order to make this easier to read, I urge you to do it on your own and we can post here if I made a clerical error.
So simplifying those two expressions and setting them equal to one another, I come up with:
1-1.5c- 1.5cz-(2y/b)c+cx =0.
This represents the break even point for determining if an offense or critical damage set would be better in a given situation. If the expression on the left is positive, offense will be better; if negative, cd will be better. Note that this is not a compensatory model--simply increasing one variable, such as cc, will not consistently favor one set across the board. For example, even with a cc of 1.00, for low values of offense from mods but high crit damage bonuses, offense will be better. However, adding more offense from mods and gear can then make cd better again.
Some quick rule of thumb checking: when c =0, we wind up with: 1 =0. The expression will be positive and offense will be better. If c =1.0, we have -0.5-1.5z-(2y/b)+x =0, and we can see that there can be values for which this is positive and favors offense like I explained before, for large positive values of y and z or low values of x, the expression will be negative and favor cd (with no offense bonuses from mods and gear, we would need cd bonuses of greater than 0.5 to favor an offense set).
If we would like to solve for an particular variable, such as cc, we may do so:
c = (-1)/(-1.5-1.5z-(2y/b)+x).
Pulling numbers out of the aether, if we have a base offense of 2500, flat bonuses from gear and mods of 400, two 5.88% primaries, a 36% cd triangle and no in-game cd bonuses, we have c = 0.634. Noting that in moving the offense portions of the equation to the other side of the inequality, we flipped the qualifications for the left hand side (now cc) for favoring one set over the other. So as you would intiut, a critical chance greater than 0.634 would favor a cd set, whereas a cc less than that value would favor offense. This can be checked by plugging these values, along with a cc either above or below the cut-off, into the original equation.
Of course, there remains the problem of for any particular set, offense secondaries from mods will change. So if you're limited in the mods you have to work with, you may just want to see what offense comes out to in each and calculate which would be better.
Simplifying out the in match offense bonuses isn't practical. They don't actually change the value of the crit damage set at all, but they do increase the value of the offense set because of the multiplicative effect they have.
IG-88 is a great example of this. Because he gives himself in in-match offense bonus and bonus crit damage, he currently needs something like 90% crit chance for the crit damage set to be more effective than the offense. Once the new mods come out, he will never prefer a crit damage set under any circumstances.
It's my understanding that in match offense bonuses from abilities multiply against the total offense and not just the base. This means the full effect of the offense bonus is multiplied by the crit damage as well, and becomes a constant throughout the equation, regardless of what set is used. If it's a constant, it can be pulled out with no mathematical bearing on the equation. If IG-88 requires more crit chance, it is likely because of the interactiom of the crit damage boost as I outlined above.
So the reason it affects the offense set and not the crit damage set is because it actually multiplies the offense the offense set provides since it does go off of all the offense and not just the base. However, it doesn't multiply the bonus the crit damage set provides because it is an additive bonus to already present crit damage.
For instance, an offense set on IG88 at maxed gear is about 263 physical damage. An offense up will provide an extra 131 physical damage with the offense set, whereas it doesn't increase the amount of crit damage the set provides at all. The rest of the offense is the same for both and can be safely simplified out.
It absolutely multiplies the crit damage set bonus because while the bonus is additive in terms of how much it adds to crit damage, crit damage itself is a multiplier. So it magnifies the crit damage bonus because of the Distributive Property.
Let's say we have some total offense (x+y). We also have crit damage c and in game offense, z.
On a crit, we'd have (x+y)*z*c, or zcx+zcy.
With an offense set bonus, i, applied to x, we have (ix+y)zc, or izcx+zcy. We can see this is greater than no mod set for positive values of i.
With an additive cd set bonus, j, applied to c, we have,
(x+y)z (c+j), or zcx+zcy+jzx+jzy. This is also greater than no set bonus for positive values of j.
But is (izcx+zcy) greater or less than (zcx+zcy+jzx+jzy)? We can see that z is a constant in all these terms. It has no bearing on the answer to the question. The only thing that matters is weather izcx is greater than (zcx+jzx +jzy). Indeed, taking z out, we are left with comparing icx to (cx+jx+jy). This is the question of interest. The answr to the question is the same regardless of the value of the constant, z.
The full question of course involves critical chance and the proportion that provides...Maybe the cd set provides more damage on a crit than offense, but not so much more that when you average it with the non-offense bonus non-crit damage that it justifies the set over offense. Nevertheless, the constant z would be pulled out of that side of the equation as well.
Constants can always be pulled out of mathematical expressions. That's the way math works.
