I could be doing the math wrong, but with offense sets increasing to 15%, and critical damage triangles getting the bump to 42% at 6 dot, it seems like cd sets will now very rarely give you more damage than offensive sets. As soon as your critical damage hits 200, then an offense set which gives you +15% offense would then be +30% on a critical hit, right? Which means that even without leader abilities that add to critical damage or critical damage up buffs, a cd of 192 with an offense set would give you ~29% extra damage. So, even in this scenario you’d only get an extra 1% damage on each critical with 15% less on non-criticals. If I did the math right, you’d need to have 96% critical chance for the average damage to break even, more if you factor in critical avoidance and immunity. Maybe useful for Ventress, but I think everyone else that has that hi of cc will have a higher cd as well.
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- 2cz-(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 -0.5-2z-(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+2z+(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 = 0.5899. 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 0.59 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.
where c represents critical chance, z is percent offense bonuses from mod primaries and secondaries, y is flat offense bonuses from mods and equipped gear, b is base offense, and x is critical damage bonuses from mod primaries and in-game abilities,
represents a break-even point for determining whether an offense set (under the new system) or a crtical damage set is better. Positive values in the left hand expression favor offense, and negative values favor cd.
One can solve hypothetical break points for any of the variables by plugging values in for the others. However, since you are limited to the mods you have available, you may just want to record values ontained from your best sets and perform the raw damage calculation to see which would be better.
Crzydroid, you lost me at the simplify step, but I think we started in the same place. However, I was solving for the 6e mods with new bonus values, but you did the old 5a values. So it is interesting that you got over 60% for that whereas commonly accepted rule of thumb for 5a mods has been 40%. Although I wonder if the 40% number had some caveat like "before mods" or something, whereas this number is after mods and all factors.
Woodroward, I did: (Base offense * offense percent increase from primaries and/or set * (1-crit chance)) + (base offense * offense percent increase * crit damage percent * crit chance) And then multiplied by a speed factor, but that bit is irrelevant atm. So for example, (3135 * 1.32 * (1-0.704228)) + (3135 * 1.32 * 1.92 * 0.704228) == (3135 * 1.17 * (1-0.704228)) + (3135 * 1.17 * 2.22 * 0.704228) Where the left side is the offense set bonus (15%) with two offense primaries (8.5%*2) and a crit damage triangle (+42%), and the right side is crit damage set (30%) with two offense primaries (8.5%*2) and crit damage triangle (+42%). The base offense value shown here happens to come from my ventress, and as mentioned I had originally accounted for speed as well, and merely demonstrated that a speed arrow (not to mention secondaries) is very important, but a speed set is not.
Now, I don't know exactly how the game puts all these numbers together, so perhaps I added where I should've multiplied or vice versa, but this was a straightforward interpretation of all of the factors involved (excepting abilities). Also, I left flat offense out of the equation because that depends on your secondaries and is therefore too random to account for in a generalization like this; of course your secondaries will always skew the results of a rule of thumb.
Gingerbreadman, your formula looks just like mine, so my guess is we used different values for the mods; either 5a vs 6e or different number of primaries considered, or maybe you inclued some secondaries, or maybe I missed something.
"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.
"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.
"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.
"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.
"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.
When I say it doesn't modify the crit damage set bonus, I mean it provides the same % damage increase with or without offense up. It provides more flat damage, but % wise, the damage is the same.
Now the offense set actually provides a larger % of damage with offense up than without since the multiplier is increasing the offense provided by the set. It never makes the crit damage set provide more than 30% crit damage, but the amount of offense provided by the offense set actually increases by 50% when offense up is present., or rather it gives the value of %damage increase of the set itself a 1.5x multiplier.
It has to do with the fact that the offense set is more or less additive to the base number, while the crit damage set is only additive to one of the end multipliers. It comes down to order of operations more than anything. The reason this is, is because in match, offense altering abilities are all multiplicative, while crit damage effects are all additive. So the value of the offense set can increase, while the value of the crit damage set can only decrease.
For example (4000 + 263) *1.9 * 1.5 * 1.92 (offense set equation) crit damage: 4000 * 1.9 * 1.5 * (1.92 + .3)
These equations shouldn't be set as a singular equality/inequality. If you did, you could simplify out lots of things... but they are different equations for comparison, so that's not proper math. The idea is to determine different values and then compare them to each other. If the crit damage is greater, we determine what % greater it is and that gives us the amount of crit we need to have before average damage would be higher with the crit damage set. If it isn't greater, then offense is just better. This is a step by step approach, not an equality/inequality. The fact that they would represent different lines on the same graph means they must be treated individually.
EDIT: To sum it all up: the more abilities you have that multiply offense in your comp, the greater the value of the offense set. The more abilities that you have for crit damage in your comp, the lower the value of the crit damage set.
I recently discovered the multiplying effect of offense and have developed a strategy to take advantage of it detailed in this thread: https://forums.galaxy-of-heroes.starwars.ea.com/discussion/178283/droids-vs-sion-after-new-mod-updates#latest
IG-88 could potentially get a series of multipliers on his offense fighting against Sion under a Poggle lead. 1.8 from his unique, 1.3 from Poggle lead, 1.5 from offense up and 2.0 from cycle of suffering. This would make the amount of offense he gets from an offense set: 263 * 1.8 * 1.3 * 1.5 * 2 = 1846 offense provided by the offense set in that scenario, Considering that 263 offense is a roughly 11% increase in damage, This makes the offense provided by the set about a 77% increase in damage in that particular composition.
The offense set and crit damage set may both say they are a % increase, but when it comes down to it, the offense set really adds a flat value, while crit damage is always a %. It's because of this difference that the value of one is actually modified by multipliers, and the other is not.
The additive nature of critical damage explains why with high critical damage, the gains from the critical damage set may not be worth the gains from an offense set. But I already detailed that scenario above.
So the critical damage set provides 1.0849 times as much damage as the offense set in your example with in game offense bonuses.
Dropping the offense multipliers out, you have,
(4,000+263)*1.92 = 8,184.96, and
4,000*(1.92+0.3) = 8,880.
It should be no surprise that the critical damage set in this hypothetical example provides 1.0849 times as much damage as the offense set.
The in game offense multipliers here are a constant, therefore all they serve to do is change the scale. Arguing that they cannot be dropped from the equation is like arguing that 30 centimeters is always better than 12 inches.
To explain my inequality better: Taking the two separate lines on a graph and setting them equal to each other yields the point where the lines cross (linear algebra). I have represented this as Offense - CD =0. Since CD is subtracted from Offense, if the value is positive, offense is greater (that section on the graph where the offense line is higher), and if the value is negative, it represents where the offense line is below CD. Using two lines as an example is of course an oversimplification, as it is a multivariate problem and we are therefore discussing two surfaces, or at best, two lines with respect to a single value of a third variable. But the same principal holds.
"The idea is to determine different values and then compare them to each other. If the crit damage is greater, we determine what % greater it is and that gives us the amount of crit we need to have before average damage would be higher with the crit damage set."
This ratio does not seem at all related to critical chance. The average damage would be CD*(CC)+1*(1-CC). The offense set equation would then have a modifier. You would then compare the two lines, as you say.
To simplify things, let's use current set bonus numbers and ignore offense bonuses from other mods. 1.1*1.5 = 1.65, so for the offense set equation, we have 1.65 (c)+1.1 (1-c). The CD set is 1.8 (c) + (1-c). You might brute force these two equations to find that a value of c= 0.4 yields a result of 1.32 for each equation.
Or you could subtract one from the other to obtain -0.15c + 0.1 (1-c)=0, or -0.15c +0.1-0.1c=0, or -0.25c + 0.1 =0. This is what I have done in my calculations above. Solving for c, you would find c=0.4 is the cutoff.
If I understand your method correctly, you would take 1.8/1.65 = 1.09. Since you cannot have greater than 100% cc, I'm guessing you would either go with 9% cc, or perhaps 91% if you reverse the equation, and these seems more consistent with your previous assertions. Neither, of course, would be correct.
In short: The additive nature of critical damage bonuses absolutely affects the determination of which set to use, because of the relative increase vs. the multiplicative increase of the other set. However, it is additive to a MULTIPLIER, and this addition takes place before the in-game offense bonuses are multiplied by that multiplier. Those in game bonuses become a constant, and can be dropped out of the equation since all they do is change the scale, and do not create an interaction effect between the sets (as in game CD additives would).
This is good for us, as I'm no longer entirely sure multiple offense bonuses apply one after the other. Over on bugs forum, it seems that Han gaining a buff against enemy Traya lead (-50% offense) and then firing his second shot (-50% offense) does NOT result in -75% offense, but rather -100% offense. Dev said that was WAI. So I'm not sure anymore that a 1.9 and a 1.5 in game offense bonus would be x*1.9*1.5 (or 2.85x), but might actually be x*(1+0.9+0.5)=2.4x.
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