Allow me to further play into DarthEagames stereotype...
There are currently only 2 places to get Critical Damage from mods: the Critical Damage set bonus, and the Triangle Mod Primary Stat. That means there are four cases to compare [Comparing Triangle Primary w/o CD Set (Purple); Comparing Triangle Primary w/ CD Set (Green); Comparing Set Bonus w/o CD Triangle (Orange); Comparing Set Bonus w/ CD Triangle (Blue)]. For comparison purposes, I assume all other stats are identical (which is obviously unlikely in reality because we don't all have identical mods lying around, but this is a theoretical exercise). The idea is hold everything else constant and compare the item in question to determine which on average gives more damage. I would not consider these numbers definitive by any means, there are many other factors to consider, but it's how the math worked out for me on average damage.
So for the purple case, lets assume we had two identical Triangle mods, except one has Critical Damage as the primary stat, and the other has Offense as the primary stat and you do not have a Critical Damage set bonus. All your other mods and mod bonuses are identical. Currently with 5A mods, if your critical chance is above 17.79%, it is on average better to use a Triangle mod with Critical Damage rather than offense. If we upgraded both of these mods to 6E mods, then your critical chance would have to be higher than 22.52% for the critical damage primary to yield more damage than the offense primary.
The green case repeats the purple case, but assuming you do have a CD set active.
For the orange case, lets assume we had two identical mod sets, except one is a Critical Damage set bonus and the other has an Offense set bonus and you do not have a critical damage primary on the triangle. All of the other stats and bonuses on all your other mods are the same. Currently with 5A mods, if your critical chance is above 40%, it is on average better to use a Critical Damage set than an Offense set. If we upgraded both of these sets to 6E mods, then your critical chance would have to be higher than 66.67% for the critical damage set to yield more damage, otherwise the offense set would be better.
The final blue case repeats the orange case, but assuming you do have a CD triangle.
Woodroward, unless I am misunderstanding how critical damage is applied (which is certainly a possibility, I by no means claim to have perfect knowledge of the game), base offense doesn't matter. To use the saying: a high tide raises all ships. If offense goes up, it increases critical and non-critical damage by the same percentage to their original values. It starts in the equation I used, but actually cancels out (see attached).
So when modding for offense, The game uses your unmodded offense - damage on gear equipped at the current gear level. Reaching the next gear level will let those stats sink in and be affected by mods.
A character's damage is basically their physical/special damage * their ability multiplier.
For example lets use IG88. He has a max base physical damage of around 2900 with 270 of that being from g12/g12+ gear. Lets say we mod him up to 4000 physical damage with primaries and secondaries. An offense set will increase his physical damage by .10 * (2900-270) = 263. 263 is not a 10% increase in damage over 4000 physical damage, it's a 6.5% increase in damage. Just like a 42% increase on top of 180% crit damage is not a 42% increase in damage, it's a 15% increase in damage.
So just like you made a base crit damage to determine the % damage increase for the crit damage actual % in match damage increase, we need a base offense. Since the only primary on the box mod is offense, no character has a base damage that matches what mods see as 100% offense. Right now, base damage is 105.88% offense, and will soon be 108.5% offense. Since we are talking about which of these is better damage, people will be stacking offense on them. So adding in the value of 1 extra offense primary when they could have 3 extra plus 9 secondaries is a conservative way to determine actual values.
So by not having a base offense value, offense appears to be increasing damage more than it is and your results end up skewed towards the offense set being slightly better than it actually is.
Now keep in mind, critical damage is based around what it says in the panel, offense is based around what it says in the panel. Damage is based around what you see in match.The first 2 are just steps on the road to the 3rd. The 3rd is what really matters.
Since we are after determining bigger increase in in-match damage, we need figures for the actual increase. Crit damage will always be the bigger number. The crit chance breakpoint is the % of damage increase that offense gives compared to crit damage. If we don't have a base offense to determine actual damage increase from the offense set and just go with 10/15% , well 10% compared to15% is 67% crit chance, but it's only a 6.5% increase with maxed offense secondaries, and 6.5% compared to 15% is only 43% crit chance.
So if you're interested, here's my formula for comparison of offense mods vs. crit damage mods. It isn't updated for 6e, but it's the most accurate formula for comparing sets of mods I've seen.
Everyone has a compelling argument over which is better and why, but in reality the only blanket rule that you can apply to which mod is better is this: if the group composition gives a 20%+ crit chance bonus that will have large if not constant uptime, crit damage is better.
There are 3 things that most people don't take into account when comparing mods, the first is that what mods consider 100% offense is not what we would consider 100% it is less than that. 105.88% offense is the base that we call 100%.
The other is the fact that as you get more and more offense primaries and secondaries on your gear, the value of the offense set as a % of our in match damage decreases. This means that, in general, offense sets have a higher value early in game, but tend to decrease in value the closer you get to end game.
Finally, stats from gear equipped in the current level do not count towards base stats and must be subtracted before %es are calculated and added back in afterwards for a complete figure.
Bearing all that in mind, it's rather complicated which is better, and it really comes down to the other stats on the mods, and the composition you are using them in (Darth Nihilus leads will always prefer offense mods for instance). So I have come up with a formula that accurately compares a set of crit damage mods and offense mods to see which will result in the highest overall damage increase on average.
The long drawn out but entirely accurate formula on how to compare is as follows: in match effects crit damage set stats offense set stats
100 / ((100 / (186 / 30)) * (100 / (Base offense - Applicable damage from Current gear) * (1 + total %offense from primaries and secondaries: expressed as a decimal) + total flat offense secondaries + Applicable damage from Current gear) / ((Base Offense - Applicable Damage from Current gear) * 105.88 + Applicable damage from current gear)) / ((100/(1 - (Base Offense - Applicable damage from current gear) * (1 + total % offense from primaries and secondaries: expressed as a decimal) + total flat offense + (base offense * .1) + Applicable damage from Current gear) / ((Base offense - Applicable damage from current gear) * 105.88 + Applicable damage from current gear))) - %Crit Chance increase from Buffs and Abilities = Critical chance breakpoint
Applicable damage from current gear is either special or physical damage on gear that you have equipped that you can still examine. Which one to subtract and then re-add depends on which type of damage the character uses.
If the crit damage set of mods you are examining has a crit chance above what the breakpoint is when combined with your character's base crit chance, then it is better than the offense set you were comparing it to as far as total damage output goes. If it is below it, the offense is better. If it is an exact match, then neither is better.
No one really wants to compare sets individually so they leave offense stats on mods out, which is skewed, the range of values should be taken into account that come with calculating the offense and a median value determined. Ignoring them gives lower than the floor value (since every toon has at least one offense primary) which skews the results in favor of offense mods and makes the crit chance breakpoint look higher than it is. I have seen so many people make that mistake, it's not even funny.
I'm a history nerd, not a math nerd, sorry (But peace, love, and respect to all my nerd brothers, sisters, and non-binary siblings) so let me make sure I'm getting this straight:
If a character has base 50% crit chance or less, mod for crit damage.
If a character has base 50% crit chance or more, mod for offense.
Does this change for leaders with abilities that increase crit damage (Boba Fett, Jedi Rey, etc)?
I'm a history nerd, not a math nerd, sorry (But peace, love, and respect to all my nerd brothers, sisters, and non-binary siblings) so let me make sure I'm getting this straight:
If a character has base 50% crit chance or less, mod for crit damage.
If a character has base 50% crit chance or more, mod for offense.
Does this change for leaders with abilities that increase crit damage (Boba Fett, Jedi Rey, etc)?
Not exactly.
If your character will have 75% or more crit chance including mods and composition bonuses (R2, crit chance buff, leader bonus), then mod for crit damage, otherwise mod for offense.
Leader abilities than increase critical damage like Boba Fett will raise the crit chance breakpoint because it will reduce the % damage increase from the crit damage set. instead of it being 222/192 = 1.15 a 15% increase in damage it will be a 272/242 = 1.12 a 12% increase in damage.
Since the Offense set gives roughly an 11% increase in damage, that means the crit chance breakpoint under a Boba Fett lead would be 11/12 = .91, 91% crit chance before you'd want to use a crit damage set under a Boba Fett lead.
I'm a history nerd, not a math nerd, sorry (But peace, love, and respect to all my nerd brothers, sisters, and non-binary siblings) so let me make sure I'm getting this straight:
If a character has base 50% crit chance or less, mod for crit damage.
If a character has base 50% crit chance or more, mod for offense.
Does this change for leaders with abilities that increase crit damage (Boba Fett, Jedi Rey, etc)?
Not exactly.
If your character will have 75% or more crit chance including mods and composition bonuses (R2, crit chance buff, leader bonus), then mod for crit damage, otherwise mod for offense.
Leader abilities than increase critical damage like Boba Fett will raise the crit chance breakpoint because it will reduce the % damage increase from the crit damage set. instead of it being 222/192 = 1.15 a 15% increase in damage it will be a 272/242 = 1.12 a 12% increase in damage.
Since the Offense set gives roughly an 11% increase in damage, that means the crit chance breakpoint under a Boba Fett lead would be 11/12 = .91, 91% crit chance before you'd want to use a crit damage set under a Boba Fett lead.
But the Rule of thumb is 75% crit chance.
Was reading through this thread a little too fast, but this last post here seemed to be the most direct and helpful. Thanks.
Excellent, thank you! And thank you as well for explaining precisely how increasing crit damage is a diminishing return--I knew that it did, but didn't understand why.
By my math, the new 6e break even is closer to 70.5% crit chance after all crit chance mods and abilities are factored in (assuming no non-mod crit damage bonuses).
Interestingly, I could not find a situation where the speed set bonus was better than an offense or crit damage set bonus, assuming secondaries are equivalent (e.g. if your speed set mods give you an extra 70 speed over your offense mods, they may be better).
By my math, the new 6e break even is closer to 70.5% crit chance after all crit chance mods and abilities are factored in (assuming no non-mod crit damage bonuses).
Interestingly, I could not find a situation where the speed set bonus was better than an offense or crit damage set bonus, assuming secondaries are equivalent (e.g. if your speed set mods give you an extra 70 speed over your offense mods, they may be better).
Speed in the long run has never been the better choice in terms of damage output, it's about going first in a quick arena match where slight differences in turn order can end up defining a match.
By my math, the new 6e break even is closer to 70.5% crit chance after all crit chance mods and abilities are factored in (assuming no non-mod crit damage bonuses).
I thought maybe my rounding changed the breakpoint to make it higher after reading this, but it actually lowered it.
100 * (1 - 222/192)/ 100 * (1 - 140.5/ 125.5) = 76.494.....
basically, Crit damage with set divided by crit damage with only triangle expressed as a % increase divided by the result of offense with set and primary bonuses divided by offense with primary bonuses expressed as a % increase.
The amount of offense stacked is kind of random, but easily attainable, not including it at all would have raised the crit chance breakpoint even higher.
This is all somewhat sloppy math I'm using because it has to be to make a general conclusion.
In order to have precise math, we'd need to be comparing specific mods on a predetermined character since in order to truly compare, we have to convert flat offense secondaries to % offense secondaries, and that can only be done if we know the (base offense - offense from currently equipped gear) of the character in question.
Thanks for the explanation/clarification Woodroward. You are correct, the formula I was using was definitely simplifying things because of how offense from the mods applies. I think the number you keep quoting of 75% is good general guidance for which set bonus to use. The damage curves between the two sets also look relatively flat where they cross (or flatter than they were), so really I think if you are within 5-10% of that point, you will not see too much difference between them.
You can also modify the formula to treat base offense and G12+/secondary offense separately (I.E. that CD acts on both, but Offense only acts on base). On that basis depending on the amount of offense from G12/secondaries the crossover works out as (assuming Base of 2800):
200 Offense from G12/secondaries = 62%
300 = 59%
400 = 57%
I need someone to check my numbers there, but it looks like the CD+CD combo gets noticeably better the bigger the G12+ and secondary offense contribution.
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.
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.
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.
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.
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.
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.
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.
I understand that generalizing is important, but wouldn’t it be easier to just throw several sets with different mod compositions on whoever you’re modding (without confirming each mod at first, to save credits), then take overall damage=(1-cc)*(total physical damage with mods added) + (cc)(total physical damage with mods)(cd)? Then you have an overall damage value for each set, and you can confirm the combination of mods which give the highest? You could even add in a speed component/factor if the speeds for each set don’t match exactly..
I understand that generalizing is important, but wouldn’t it be easier to just throw several sets with different mod compositions on whoever you’re modding (without confirming each mod at first, to save credits), then take overall damage=(1-cc)*(total physical damage with mods added) + (cc)(total physical damage with mods)(cd)? Then you have an overall damage value for each set, and you can confirm the combination of mods which give the highest? You could even add in a speed component/factor if the speeds for each set don’t match exactly..
I think this is what it boils down to anyway, because you are going to have different secondaries on the mods you have available. If you have buffs that add to critical damage, you may also have to estimate the percentage of the turns those buffs would be on.
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.
I actually use this type of equation to determine the % damage increase that the crit damage set represents, not the crit chance breakpoint. Without figuring out the % damage increase, one can not determine the crit chance breakpoint though.
The reason I say it revolves around the crit chance breakpoint is because of comparing the % damage increase.
Now if the % damage increase is higher in offense than crit damage, it's a no brainer, because offense is constant, and crit damage is only occasional.
But if the % damage increase is higher in crit damage than the offense, it remains to be determined what % of the damage the crit damage set is capable of that the offense set can reach. If the offense set's % increase is 77% of the % damage increase of the crit damage set, then the breakpoint where the one is better than the other is where the crit damage set can provide it's maximum damage increase 77% or more of the time on average, or at 77% crit chance.
To put it in an equation I would take (1 - ((base offense + mod secondary/primary offense + Offense set offense) / (base offense + mod secondary/primary offense))) / (1 - ((crit damage with set and triangle) / (crit damage with triangle))) If the result is greater than 1, offense is just better. If it is less than 1, that is the crit chance percentage at which the crit damage set is better.
In so doing I convert each gain to an in match % damage increase and can then compare those values to determine the relative value and what the final tuning point to be considered is... crit chance.
Because no matter how it turns out, the result will either be: Offense is just better,
or: Crit damage CAN be better, but only if crit chance is....
As for whether in match offense effects affect offense more than crit damage, I must concede the point. I somehow visualized them as separate entities in my head ( I create structures in me head for equations), and my stubbornness didn't allow me to recognize it earlier.
But crit chance breakpoint is more than just a variable in the equation, it is the final one. I have conceded other points, but there's no way that you are even close to correct in saying "This ratio does not seem at all related to critical chance." It's all about the crit chance in the end. By trying to include the crit chance in the equation itself, instead of just making it what you are solving for, you are just muddying the waters and producing an incorrect result.
You are also not correct that comparing the lines is setting them in an equality/inequality. In order to set them in an equality/inequality, you'd have to know if one is greater, less, or they are equal. That's what you are comparing them to find out. In other words you can NOT set them in an equality/inequality until after they have been compared. In this instance, we never do because they end up being different parts of a formula on the same side of the equal/greater than/less than symbol. So this never becomes an equality/inequality.
There are some things that people may be able to outdo me on, but not comparison between offense and crit damage mods. Your math is unfortunately the goofy math here: " 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." This is goofy. It isn't helpful. You're leaving out factors that matter (like offense from mods), but including ones that don't (like the crit multiplier for the offense set).
The offense set provides the same % damage increase whether or not it is a crit. This means that we don't even have to consider crits when determining % damage increase on an offense set, The only important factors to consider are end offense, and all offense - offense from offense set. To use 1.1 as a multiplier representing offense is very disengenuous. It only adds 10% of base offense - damage on current gear. It will never ever ever actually represent 10% of even base offense. It is always less than 10%. If you want to make the offense part of the equation easier, change that % to a flat increase, but definitely don't ignore offense from mods besides the set, that's a pointless piece of math. So to determine the offense % damage increase, the perfectly accurate formula is 1- ((Base offense + mod offense + set offense) / (Base offense + Mod offense))
The perfectly accurate formula for determining what % damage increase the crit damage set is capable of is 1- (crit damage with set and triangle / crit damage with triangle). This is how much it increases the damage of a crit. We have to worry about crits for this side because it only affects crits.
So, if the % increase from the crit damage set registers as more, then that means it CAN be more if you can crit enough to make the % value more.
If offense set % damage increase is 77% of crit damage set % damage increase, then if I crit 77% of time with the crit damage set, it will equal the damage gain from the offense set. If my crit chance is 78% I will actually do more damage with the crit damage set. If it is 76% I will do less.
Trying to find the exact flat numbers is needlessly overcomplicated and leaves much more room for error. Better to create a ratio with only the gains (% gains, not flat gains so as to keep it entirely accurate and simple) and use it to determine the breakpoint, which is based on crit chance.
I'm going to do a simple walkthrough of a character to illustrate exactly how to determine which set is better in general for a character.
Let's use Chirrut as an example.
Chirrut has 3073 physical damage. 185 of that is from G12 gear. This is all the character info I need to determine if crit damage can be better and when it will be if it can.
Using current mod bonuses I can get Chirrut 6 secondaries of about 150 flat offense, 3 primaries of 5.88% offense, and 3 secondaries of 1.5%. So he can end up with an offense of (3073 - 185) * (1 + ((10 + 5.88 + 5.88 + 5.88 + 1.5 + 1.5 + 1.5) / 100) + 900 + 185 = 4900 physical damage we can get him to with mods. This is pretty much as high as he can get currently before in match effects are counted. of his 4900 physical damage, only 288 of it is coming from the offense set. So to determine the % damage increase of the offense set we take 4900 / (4900 - 288) = 1.062
In this instance the actual % increase the offense set provides is 6.2%
Now a crit damage set will provide 216/186 = 1.161 a 16.1% potential increase in damage. Now if I take the offense set damage and divide it by the crit set damage, I can see what % of damage the offense is responsible for compared to the crit damage set.
6.2 / 16.1 = 38.5 %
The offense set provides only 38.5% of the damage the crit damage set does. This means that as long as Chirrut crits at least 38.5% of the time, the crit damage set will be at least equal to the offense set. Chirrut has a base crit chance over 40% though, so at no point would an offense set benefit him over crit damage if offense stats are maxed on the gear under the current system. Now let's reexamine this using the incoming system.
The offense will be (3073 - 185) * (1 + ((15 + 8.5 + 8.5 + 8.5 + 4.5 + 4.5 + 4.5) / 100) + 990 + 185 = 5622 The offense set provides 433 of this physical damage.
5622 / (5622 - 433) = 1,083
The offense set is providing an 8.3% increase in offense with maxed offense in the new lineup.
Under the new system it would take 53.2% crit chance for the crit damage set to be better IF you stack offense on Chirrut in every single nook and cranny. This could actually be reachable since a crit chance set can provide 8% crit in the update, but this is only with absolutely maxed offense. You can bring it down to 53% crit with maxed offense from mods (which greatly decreases the value of the offense set). In general it will be around 75% crit chance as the breakpoint.
Ok, I'm dreading that this reply could potentially be quite lengthy, although perhaps it won't be as drastic as I fear. I then hope we can put this matter to rest, as I can't really keep devoting time to this.
Let's get some minutia out of the way. First, please don't cherry-pick an oversimplied example that was used merely to illustrate a point. Obviously in an actual calculation, I do and have factored in offense bonuses from mods; refer to the calculations in my original post in which I included not only a variable for flat bonuses, but also a variable for percent bonuses separately.
Second, I did notice a computational error in my calculation (though not an error of form). I redid my original calculations in the same way, except writing more legibly, and found I should have had a "-2z" term instead of the previous value. I have amended my original post to reflect this.
Now for the crux of the matter:
I think there are a couple of things going on here. One is that I think you get so set in your method or approach to doing things that you have difficulty seeing when an approach from a different angle is an equally valid setup--furthermore, the fact that you're evaluating the problem in chunks prevents you from seeing where our methods actually end up with the same procedure in the end--or at least, SHOULD...more on that below.
The second thing that I think is going on is that you left out or inadequately described details of your methodology (or perhaps they were buried in much earlier posts) and this lead to confusion on my part. Indeed, while your latest example helped with understanding the process you were undertaking, you actually still explain that process incorrectly with some of your statements.
Finally, I am sorry to point out that while working through your process, I did discover an error in your setup--likely because of your statement that you ignore the non-crit part of the equation when calculating the crit damage set. While you are correct that the set only affects the crit portion, the average damage under a crit set is very much a function of both non-crit and crit damage. To compare the average damage under each set, you need that portion. While you are correct that the offense set provides a 8.3% increase regardless of a crit (this is our earlier discussion that constants can be pulled out front), the increase in average damage is not 15.6%...which is the increase in just the crit portion. Just as adding offense bonuses from mods decreases the actual percentage increase of the offense set, the non-crit portion of the damage calculation decreases the average damage increase from the crit set in comparison to the increase it provides from the crit portion.
Interestingly enough, your final calculation does factor that non-crit portion back in (whether you realize it or not), and your method for finding the crit chance break point as the point where the two ratios become themselves a ratio equal to 1 would seem sound...
EXCEPT for the set up of those two ratios (probably as a result of initially trying to ignore that non-crit portion) results in a situation where you improperly split a fraction. You probably didn't even realize you were doing this, A) because your method of calculating out piecemeal values before setting up the next ration prevented you from realizing you were splitting fractions at all in the first place. Because who DOESN'T LOVE splitting fractions and isn't constantly thinking about them???? It even took a while for me working out your method on paper to realize that's why your step-by-step method was yielding different results than mine.
To be more clear, towards the end of your calculations, you have a situation resulting in ratio that, as a theoretical example, looks something like (a+b)/(c+d). Instead of taking a/(c+d) + b/(c+d), as would be correct, your final calculation essentially takes a/c + b/d, which is very incorrect. Again, you probably didn't realize you were doing this, as you were figuring quantities piecemeal and didn't see this as a problem involving partial fractions in the first place.
The good news is, you don't ACTUALLY have to split into partial fractions. Since you are comparing two values to one another and attempting to find the value of some variable which sets them equal to one another, you set the formula such that the quotient is equal to 1(the Identity of multiplication). You can then multiply both sides of the equation by the denominator. This does result in a situation, however, where the solution to the equation is to subtract like terms from each other--which is what my method was doing anyway when I subtracted one equation from the other and set the difference equal to 0 (the Identity of addition). I'm sorry you have such a grievance over linear equations. But this is simply the way you solve, algebraically, for unknown variables. I think you are focusing on this word, "inequality," and you are making it mean something in your head that it doesn't actually mean. When you compare two things...that's an inequality. When you want to find out when those things result in an EQUALITY, you set them equal to the appropriate Identity for the type of opration you are performing.
So enough with the theoretical, let's begin actually walking through your numbers.
Let's start with the endpoint of your calculations. You correctly determined that an offense set is worth 1.083 times the damage of what is provided without the set. This is a constant that is multiplied through both the crit and non-crit portions, so it therefore also holds true overall. You then determine that a crit damage set provides an increase of 2.22/1.92 = 1.15625 over not having the set. But this is ONLY true for the crit portion of the damage. So when you take 1.15625/1.083=1.0676, that represents the damage increase of the crit damage set over the offense set for the crit portion only . So in order to find the crit chance breaking point, you have to find the value of c (which is now invisible in the way you have this set up, making things difficult) for which this porportional increase would be equal to the proportional increase provided by the offense set over the critical damage set for the non-crit portion...or so you might think.
Here is where the fraction is inadvertently split incorrectly. We have already found the increase provided by the offense set for the non-crit portion: It is the same as that provided over the no-set bonus damage. So 1/1.083=0.92336 represents the loss of the crit damage set to the offense for the non-crit portion. So you intuit to find the value of c for which this ratio equals 1. Even keeping c invisible, you might figure that the bottom ratio only needs to travel 0.07664 to reach 1, and this distance is 53% of the way along the total distance, 1.0676-0.92336. Note that this is the same as 0.083/0.15625, which can be shown mathematically as the result of the ratio of the two ratios presented here. So this later result is how you arrived at the value of c.
But this is where you can see that a fraction was improperly split. And I apologize once again having to delve into the theoretical before getting back to more concrete numbers.
Let's call the the non-set bonus function for the basic damage calculation f (x) = x* (1-c)+x*c*1.92, where c is critical chance, and x is the total final offense number. Note that I am NOT leaving out the bonus offense from mods...I am simply incorporating them now into x so the EXAMPLE is easier to read...when we come back to actual numbers we will deal with those terms.
Why wait on adding them in? Because you have already calculated that the offense set only results in a 1.083 increase in the offense with the values you provided for this example. So we can use this ready value without having to muddle the example by recalculating.
So let us now call the offense set function, o (x) = 1.083x*(1-c)+1.083x*c*1.92.
The critical damage set function will be cd (x) = x*(1-c)+x*c*2.22.
In setting up the ratios the way you did, we are actually winding up with cd (x)/o (x), or,
(x *(1-c)+2.22*c*x)/(1.083x* (1-c)+1.92*1.08x*c).
And here is where the fraction is split. This SHOULD be evaluated as:
thus keeping the whole denominator. Instead, the final step of your calculation essentially takes
(x *(1-c))/(1.083x*(1-c)) + (2.22*c*x)/(1.92*1.083x*c). This is, as you put it, improper math.
I demonstrate all this not to say your approach is somehow wrong. Your approach, conceptually, is a valid one. That is, you want to compare the proportional increase in damage for each of the different sets compared to not set, and then compare those values to one another and find the value of a variable, critical chance, for which this last ratio is equal to 1. I explained all this merely to point out that you made an error in setting up the problem--an error stemming from your assertion that the non-crit portion can be ignored with the crit damage set, even though the non-crit portion absolutely affects the average damage calculation.
Now I will endeavor to show how our two methodologies should actually arrive at the same result. You want to take the increase in damage from offense set over no set: o (x)/f (x). You want to do likewise with crit damage, so cd (x)/f (x). You then want to compare these values to one another, so (cd (x)/f (x))/(o (x)/f (x)). You can see that the two denominators in both the numerator and denominator of the resulting compound fraction actually cancel, by multiplying it by f (x)/f (x) (or 1). You wind up with cd (x)/o (x).
I've shown above that for this example, this is
(x *(1-c)+2.22*c*x)/(1.083x* (1-c)+1.92*1.08x*c).
The good news is, we don't ACTUALLY have to split this. Our goal is to determine the value of c for which this ratio equals 1 (meaning the two functions are equal in value). Or if you want to find all c for which one is greater than the other, you could turn the equals sign into one of your dreaded inequality signs (again, I'm not sure what you think is implied by this). So if cd (x)/o (x) = 1, we can simply multiply both sides of the equation by o (x).
So we have x*(1-c) + 2.22cx = 1.083x*(1-c) + 1.92*1.083cx.
With apologies for now having to do algebra like my approach did from the beginning, but this is simply the way you solve for unknowns.
x+1.22cx = 1.083x+0.99636cx
0.22634c = 0.083
c= 0.3667.
Let's now work with all the numbers, which I'm sure is what you are waiting for.
Let's here calculate x as the total culmination of all offense: x=2,888+3*0.085*2,888+3*0.045*2,888+990+185 = 5,189.32.
With an offense set, xo = 2,888*1.15+3*0.85*2,888+3*0.045*2,888+990+185 = 5,622.52.
Note that the slight descrepancy from above is due to rounding error; when I redo the previous example with 1.083688 instead I got about 37.5, and I'm sure carrying to more decimal places in both examples would yield convergent results.
Anyway, you can see how we end up with subtractingthe terms of one side from the other, which is what I did in the beginning after setting the two equations equal to one another.
Now, let's plug these values into my formula from way back:
Although I think we could honestly dump some of the terms in that expression, if, when computing offense bonuses from mods, we take a hand calculation on the non offense set first and then just include it as one term.
But, all of these theoretical discussions are just that, because they assume those other mod bonuses as equal. In practice, as another user pointed out, these will be different based on the mods you have available. So really, you just need to put the sets on, look at the different offense values, and set up cd (x) and o (x) directly, keeping in mind that characters may get crit damage up for a portion of the time. Including the extra mod bonuses is useful for deciding if you want to farm new mods and want to guage how much your offense secondaries would need to be, which is also a variable you could solve for.
In short, are approaches (linear algebra or piecemeal comparison of ratios) should yield the same result, and are both valid conceptualizations of the same problem. However, I felt it dutiful to point out that in setting up your comparisons, your decisiom to ignore non-crit damage as an equalizer resulted in a mathematically unsound comparison, thus throwing off your calculations.
Replies
So when modding for offense, The game uses your unmodded offense - damage on gear equipped at the current gear level. Reaching the next gear level will let those stats sink in and be affected by mods.
A character's damage is basically their physical/special damage * their ability multiplier.
For example lets use IG88. He has a max base physical damage of around 2900 with 270 of that being from g12/g12+ gear. Lets say we mod him up to 4000 physical damage with primaries and secondaries. An offense set will increase his physical damage by .10 * (2900-270) = 263. 263 is not a 10% increase in damage over 4000 physical damage, it's a 6.5% increase in damage. Just like a 42% increase on top of 180% crit damage is not a 42% increase in damage, it's a 15% increase in damage.
So just like you made a base crit damage to determine the % damage increase for the crit damage actual % in match damage increase, we need a base offense. Since the only primary on the box mod is offense, no character has a base damage that matches what mods see as 100% offense. Right now, base damage is 105.88% offense, and will soon be 108.5% offense. Since we are talking about which of these is better damage, people will be stacking offense on them. So adding in the value of 1 extra offense primary when they could have 3 extra plus 9 secondaries is a conservative way to determine actual values.
So by not having a base offense value, offense appears to be increasing damage more than it is and your results end up skewed towards the offense set being slightly better than it actually is.
Now keep in mind, critical damage is based around what it says in the panel, offense is based around what it says in the panel. Damage is based around what you see in match.The first 2 are just steps on the road to the 3rd. The 3rd is what really matters.
Since we are after determining bigger increase in in-match damage, we need figures for the actual increase. Crit damage will always be the bigger number. The crit chance breakpoint is the % of damage increase that offense gives compared to crit damage. If we don't have a base offense to determine actual damage increase from the offense set and just go with 10/15% , well 10% compared to15% is 67% crit chance, but it's only a 6.5% increase with maxed offense secondaries, and 6.5% compared to 15% is only 43% crit chance.
So if you're interested, here's my formula for comparison of offense mods vs. crit damage mods. It isn't updated for 6e, but it's the most accurate formula for comparing sets of mods I've seen.
There are 3 things that most people don't take into account when comparing mods, the first is that what mods consider 100% offense is not what we would consider 100% it is less than that. 105.88% offense is the base that we call 100%.
The other is the fact that as you get more and more offense primaries and secondaries on your gear, the value of the offense set as a % of our in match damage decreases. This means that, in general, offense sets have a higher value early in game, but tend to decrease in value the closer you get to end game.
Finally, stats from gear equipped in the current level do not count towards base stats and must be subtracted before %es are calculated and added back in afterwards for a complete figure.
Bearing all that in mind, it's rather complicated which is better, and it really comes down to the other stats on the mods, and the composition you are using them in (Darth Nihilus leads will always prefer offense mods for instance). So I have come up with a formula that accurately compares a set of crit damage mods and offense mods to see which will result in the highest overall damage increase on average.
The long drawn out but entirely accurate formula on how to compare is as follows:
in match effects
crit damage set stats
offense set stats
100 / ((100 / (186 / 30)) * (100 / (Base offense - Applicable damage from Current gear) * (1 + total %offense from primaries and secondaries: expressed as a decimal) + total flat offense secondaries + Applicable damage from Current gear) / ((Base Offense - Applicable Damage from Current gear) * 105.88 + Applicable damage from current gear)) / ((100/(1 - (Base Offense - Applicable damage from current gear) * (1 + total % offense from primaries and secondaries: expressed as a decimal) + total flat offense + (base offense * .1) + Applicable damage from Current gear) / ((Base offense - Applicable damage from current gear) * 105.88 + Applicable damage from current gear))) - %Crit Chance increase from Buffs and Abilities = Critical chance breakpoint
Applicable damage from current gear is either special or physical damage on gear that you have equipped that you can still examine. Which one to subtract and then re-add depends on which type of damage the character uses.
If the crit damage set of mods you are examining has a crit chance above what the breakpoint is when combined with your character's base crit chance, then it is better than the offense set you were comparing it to as far as total damage output goes. If it is below it, the offense is better. If it is an exact match, then neither is better.
No one really wants to compare sets individually so they leave offense stats on mods out, which is skewed, the range of values should be taken into account that come with calculating the offense and a median value determined. Ignoring them gives lower than the floor value (since every toon has at least one offense primary) which skews the results in favor of offense mods and makes the crit chance breakpoint look higher than it is. I have seen so many people make that mistake, it's not even funny.
If a character has base 50% crit chance or less, mod for crit damage.
If a character has base 50% crit chance or more, mod for offense.
Does this change for leaders with abilities that increase crit damage (Boba Fett, Jedi Rey, etc)?
Not exactly.
If your character will have 75% or more crit chance including mods and composition bonuses (R2, crit chance buff, leader bonus), then mod for crit damage, otherwise mod for offense.
Leader abilities than increase critical damage like Boba Fett will raise the crit chance breakpoint because it will reduce the % damage increase from the crit damage set. instead of it being 222/192 = 1.15 a 15% increase in damage it will be a 272/242 = 1.12 a 12% increase in damage.
Since the Offense set gives roughly an 11% increase in damage, that means the crit chance breakpoint under a Boba Fett lead would be 11/12 = .91, 91% crit chance before you'd want to use a crit damage set under a Boba Fett lead.
But the Rule of thumb is 75% crit chance.
Was reading through this thread a little too fast, but this last post here seemed to be the most direct and helpful. Thanks.
Interestingly, I could not find a situation where the speed set bonus was better than an offense or crit damage set bonus, assuming secondaries are equivalent (e.g. if your speed set mods give you an extra 70 speed over your offense mods, they may be better).
Speed in the long run has never been the better choice in terms of damage output, it's about going first in a quick arena match where slight differences in turn order can end up defining a match.
100 * (1 - 222/192)/ 100 * (1 - 140.5/ 125.5) = 76.494.....
basically, Crit damage with set divided by crit damage with only triangle expressed as a % increase divided by the result of offense with set and primary bonuses divided by offense with primary bonuses expressed as a % increase.
The amount of offense stacked is kind of random, but easily attainable, not including it at all would have raised the crit chance breakpoint even higher.
What formula did you use to get 70.5%?
In order to have precise math, we'd need to be comparing specific mods on a predetermined character since in order to truly compare, we have to convert flat offense secondaries to % offense secondaries, and that can only be done if we know the (base offense - offense from currently equipped gear) of the character in question.
Effective Offense = ((Base offense * offense mods * 100-CC%) + (Base offense * offense mods * (150 + CD mods) * CC%)) /100
You can also modify the formula to treat base offense and G12+/secondary offense separately (I.E. that CD acts on both, but Offense only acts on base). On that basis depending on the amount of offense from G12/secondaries the crossover works out as (assuming Base of 2800):
200 Offense from G12/secondaries = 62%
300 = 59%
400 = 57%
I need someone to check my numbers there, but it looks like the CD+CD combo gets noticeably better the bigger the G12+ and secondary offense contribution.
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.
The expression,
1-1.5c-2cz-(2y/b)c +cx= 0,
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.
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.
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.
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.
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.
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.
Using your own numbers,
(4000+263)*1.9*1.5*1.92 = 23,327.136.
4000*1.9*1.5*(1.92+0.3) = 25,308.
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).
I think this is what it boils down to anyway, because you are going to have different secondaries on the mods you have available. If you have buffs that add to critical damage, you may also have to estimate the percentage of the turns those buffs would be on.
The reason I say it revolves around the crit chance breakpoint is because of comparing the % damage increase.
Now if the % damage increase is higher in offense than crit damage, it's a no brainer, because offense is constant, and crit damage is only occasional.
But if the % damage increase is higher in crit damage than the offense, it remains to be determined what % of the damage the crit damage set is capable of that the offense set can reach. If the offense set's % increase is 77% of the % damage increase of the crit damage set, then the breakpoint where the one is better than the other is where the crit damage set can provide it's maximum damage increase 77% or more of the time on average, or at 77% crit chance.
To put it in an equation I would take (1 - ((base offense + mod secondary/primary offense + Offense set offense) / (base offense + mod secondary/primary offense))) / (1 - ((crit damage with set and triangle) / (crit damage with triangle))) If the result is greater than 1, offense is just better. If it is less than 1, that is the crit chance percentage at which the crit damage set is better.
In so doing I convert each gain to an in match % damage increase and can then compare those values to determine the relative value and what the final tuning point to be considered is... crit chance.
Because no matter how it turns out, the result will either be: Offense is just better,
or: Crit damage CAN be better, but only if crit chance is....
As for whether in match offense effects affect offense more than crit damage, I must concede the point. I somehow visualized them as separate entities in my head ( I create structures in me head for equations), and my stubbornness didn't allow me to recognize it earlier.
But crit chance breakpoint is more than just a variable in the equation, it is the final one. I have conceded other points, but there's no way that you are even close to correct in saying "This ratio does not seem at all related to critical chance." It's all about the crit chance in the end. By trying to include the crit chance in the equation itself, instead of just making it what you are solving for, you are just muddying the waters and producing an incorrect result.
You are also not correct that comparing the lines is setting them in an equality/inequality. In order to set them in an equality/inequality, you'd have to know if one is greater, less, or they are equal. That's what you are comparing them to find out. In other words you can NOT set them in an equality/inequality until after they have been compared. In this instance, we never do because they end up being different parts of a formula on the same side of the equal/greater than/less than symbol. So this never becomes an equality/inequality.
There are some things that people may be able to outdo me on, but not comparison between offense and crit damage mods. Your math is unfortunately the goofy math here: " 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." This is goofy. It isn't helpful. You're leaving out factors that matter (like offense from mods), but including ones that don't (like the crit multiplier for the offense set).
The offense set provides the same % damage increase whether or not it is a crit. This means that we don't even have to consider crits when determining % damage increase on an offense set, The only important factors to consider are end offense, and all offense - offense from offense set. To use 1.1 as a multiplier representing offense is very disengenuous. It only adds 10% of base offense - damage on current gear. It will never ever ever actually represent 10% of even base offense. It is always less than 10%. If you want to make the offense part of the equation easier, change that % to a flat increase, but definitely don't ignore offense from mods besides the set, that's a pointless piece of math. So to determine the offense % damage increase, the perfectly accurate formula is 1- ((Base offense + mod offense + set offense) / (Base offense + Mod offense))
The perfectly accurate formula for determining what % damage increase the crit damage set is capable of is 1- (crit damage with set and triangle / crit damage with triangle). This is how much it increases the damage of a crit. We have to worry about crits for this side because it only affects crits.
So, if the % increase from the crit damage set registers as more, then that means it CAN be more if you can crit enough to make the % value more.
If offense set % damage increase is 77% of crit damage set % damage increase, then if I crit 77% of time with the crit damage set, it will equal the damage gain from the offense set. If my crit chance is 78% I will actually do more damage with the crit damage set. If it is 76% I will do less.
Trying to find the exact flat numbers is needlessly overcomplicated and leaves much more room for error. Better to create a ratio with only the gains (% gains, not flat gains so as to keep it entirely accurate and simple) and use it to determine the breakpoint, which is based on crit chance.
EDIT: Fixed Math
Let's use Chirrut as an example.
Chirrut has 3073 physical damage. 185 of that is from G12 gear. This is all the character info I need to determine if crit damage can be better and when it will be if it can.
Using current mod bonuses I can get Chirrut 6 secondaries of about 150 flat offense, 3 primaries of 5.88% offense, and 3 secondaries of 1.5%. So he can end up with an offense of (3073 - 185) * (1 + ((10 + 5.88 + 5.88 + 5.88 + 1.5 + 1.5 + 1.5) / 100) + 900 + 185 = 4900 physical damage we can get him to with mods. This is pretty much as high as he can get currently before in match effects are counted. of his 4900 physical damage, only 288 of it is coming from the offense set. So to determine the % damage increase of the offense set we take 4900 / (4900 - 288) = 1.062
In this instance the actual % increase the offense set provides is 6.2%
Now a crit damage set will provide 216/186 = 1.161 a 16.1% potential increase in damage. Now if I take the offense set damage and divide it by the crit set damage, I can see what % of damage the offense is responsible for compared to the crit damage set.
6.2 / 16.1 = 38.5 %
The offense set provides only 38.5% of the damage the crit damage set does. This means that as long as Chirrut crits at least 38.5% of the time, the crit damage set will be at least equal to the offense set. Chirrut has a base crit chance over 40% though, so at no point would an offense set benefit him over crit damage if offense stats are maxed on the gear under the current system. Now let's reexamine this using the incoming system.
The offense will be (3073 - 185) * (1 + ((15 + 8.5 + 8.5 + 8.5 + 4.5 + 4.5 + 4.5) / 100) + 990 + 185 = 5622 The offense set provides 433 of this physical damage.
5622 / (5622 - 433) = 1,083
The offense set is providing an 8.3% increase in offense with maxed offense in the new lineup.
Crit damage? 222/192 = 1.156
It's worth 15.6% offense now.
8.3/15.6 = 0.532
Under the new system it would take 53.2% crit chance for the crit damage set to be better IF you stack offense on Chirrut in every single nook and cranny. This could actually be reachable since a crit chance set can provide 8% crit in the update, but this is only with absolutely maxed offense. You can bring it down to 53% crit with maxed offense from mods (which greatly decreases the value of the offense set). In general it will be around 75% crit chance as the breakpoint.
Let's get some minutia out of the way. First, please don't cherry-pick an oversimplied example that was used merely to illustrate a point. Obviously in an actual calculation, I do and have factored in offense bonuses from mods; refer to the calculations in my original post in which I included not only a variable for flat bonuses, but also a variable for percent bonuses separately.
Second, I did notice a computational error in my calculation (though not an error of form). I redid my original calculations in the same way, except writing more legibly, and found I should have had a "-2z" term instead of the previous value. I have amended my original post to reflect this.
Now for the crux of the matter:
I think there are a couple of things going on here. One is that I think you get so set in your method or approach to doing things that you have difficulty seeing when an approach from a different angle is an equally valid setup--furthermore, the fact that you're evaluating the problem in chunks prevents you from seeing where our methods actually end up with the same procedure in the end--or at least, SHOULD...more on that below.
The second thing that I think is going on is that you left out or inadequately described details of your methodology (or perhaps they were buried in much earlier posts) and this lead to confusion on my part. Indeed, while your latest example helped with understanding the process you were undertaking, you actually still explain that process incorrectly with some of your statements.
Finally, I am sorry to point out that while working through your process, I did discover an error in your setup--likely because of your statement that you ignore the non-crit part of the equation when calculating the crit damage set. While you are correct that the set only affects the crit portion, the average damage under a crit set is very much a function of both non-crit and crit damage. To compare the average damage under each set, you need that portion. While you are correct that the offense set provides a 8.3% increase regardless of a crit (this is our earlier discussion that constants can be pulled out front), the increase in average damage is not 15.6%...which is the increase in just the crit portion. Just as adding offense bonuses from mods decreases the actual percentage increase of the offense set, the non-crit portion of the damage calculation decreases the average damage increase from the crit set in comparison to the increase it provides from the crit portion.
Interestingly enough, your final calculation does factor that non-crit portion back in (whether you realize it or not), and your method for finding the crit chance break point as the point where the two ratios become themselves a ratio equal to 1 would seem sound...
EXCEPT for the set up of those two ratios (probably as a result of initially trying to ignore that non-crit portion) results in a situation where you improperly split a fraction. You probably didn't even realize you were doing this, A) because your method of calculating out piecemeal values before setting up the next ration prevented you from realizing you were splitting fractions at all in the first place.
To be more clear, towards the end of your calculations, you have a situation resulting in ratio that, as a theoretical example, looks something like (a+b)/(c+d). Instead of taking a/(c+d) + b/(c+d), as would be correct, your final calculation essentially takes a/c + b/d, which is very incorrect. Again, you probably didn't realize you were doing this, as you were figuring quantities piecemeal and didn't see this as a problem involving partial fractions in the first place.
The good news is, you don't ACTUALLY have to split into partial fractions. Since you are comparing two values to one another and attempting to find the value of some variable which sets them equal to one another, you set the formula such that the quotient is equal to 1(the Identity of multiplication). You can then multiply both sides of the equation by the denominator. This does result in a situation, however, where the solution to the equation is to subtract like terms from each other--which is what my method was doing anyway when I subtracted one equation from the other and set the difference equal to 0 (the Identity of addition). I'm sorry you have such a grievance over linear equations. But this is simply the way you solve, algebraically, for unknown variables. I think you are focusing on this word, "inequality," and you are making it mean something in your head that it doesn't actually mean. When you compare two things...that's an inequality. When you want to find out when those things result in an EQUALITY, you set them equal to the appropriate Identity for the type of opration you are performing.
So enough with the theoretical, let's begin actually walking through your numbers.
Let's start with the endpoint of your calculations. You correctly determined that an offense set is worth 1.083 times the damage of what is provided without the set. This is a constant that is multiplied through both the crit and non-crit portions, so it therefore also holds true overall. You then determine that a crit damage set provides an increase of 2.22/1.92 = 1.15625 over not having the set. But this is ONLY true for the crit portion of the damage. So when you take 1.15625/1.083=1.0676, that represents the damage increase of the crit damage set over the offense set for the crit portion only . So in order to find the crit chance breaking point, you have to find the value of c (which is now invisible in the way you have this set up, making things difficult) for which this porportional increase would be equal to the proportional increase provided by the offense set over the critical damage set for the non-crit portion...or so you might think.
Here is where the fraction is inadvertently split incorrectly. We have already found the increase provided by the offense set for the non-crit portion: It is the same as that provided over the no-set bonus damage. So 1/1.083=0.92336 represents the loss of the crit damage set to the offense for the non-crit portion. So you intuit to find the value of c for which this ratio equals 1. Even keeping c invisible, you might figure that the bottom ratio only needs to travel 0.07664 to reach 1, and this distance is 53% of the way along the total distance, 1.0676-0.92336. Note that this is the same as 0.083/0.15625, which can be shown mathematically as the result of the ratio of the two ratios presented here. So this later result is how you arrived at the value of c.
But this is where you can see that a fraction was improperly split. And I apologize once again having to delve into the theoretical before getting back to more concrete numbers.
Let's call the the non-set bonus function for the basic damage calculation f (x) = x* (1-c)+x*c*1.92, where c is critical chance, and x is the total final offense number. Note that I am NOT leaving out the bonus offense from mods...I am simply incorporating them now into x so the EXAMPLE is easier to read...when we come back to actual numbers we will deal with those terms.
Why wait on adding them in? Because you have already calculated that the offense set only results in a 1.083 increase in the offense with the values you provided for this example. So we can use this ready value without having to muddle the example by recalculating.
So let us now call the offense set function, o (x) = 1.083x*(1-c)+1.083x*c*1.92.
The critical damage set function will be cd (x) = x*(1-c)+x*c*2.22.
In setting up the ratios the way you did, we are actually winding up with cd (x)/o (x), or,
(x *(1-c)+2.22*c*x)/(1.083x* (1-c)+1.92*1.08x*c).
And here is where the fraction is split. This SHOULD be evaluated as:
(x*(1-c))/(1.083x* (1-c)+1.92*1.08x*c) + (2.22*c*x)/(1.083x* (1-c)+1.92*1.08x*c),
thus keeping the whole denominator. Instead, the final step of your calculation essentially takes
(x *(1-c))/(1.083x*(1-c)) + (2.22*c*x)/(1.92*1.083x*c). This is, as you put it, improper math.
I demonstrate all this not to say your approach is somehow wrong. Your approach, conceptually, is a valid one. That is, you want to compare the proportional increase in damage for each of the different sets compared to not set, and then compare those values to one another and find the value of a variable, critical chance, for which this last ratio is equal to 1. I explained all this merely to point out that you made an error in setting up the problem--an error stemming from your assertion that the non-crit portion can be ignored with the crit damage set, even though the non-crit portion absolutely affects the average damage calculation.
Now I will endeavor to show how our two methodologies should actually arrive at the same result. You want to take the increase in damage from offense set over no set: o (x)/f (x). You want to do likewise with crit damage, so cd (x)/f (x). You then want to compare these values to one another, so (cd (x)/f (x))/(o (x)/f (x)). You can see that the two denominators in both the numerator and denominator of the resulting compound fraction actually cancel, by multiplying it by f (x)/f (x) (or 1). You wind up with cd (x)/o (x).
I've shown above that for this example, this is
(x *(1-c)+2.22*c*x)/(1.083x* (1-c)+1.92*1.08x*c).
The good news is, we don't ACTUALLY have to split this. Our goal is to determine the value of c for which this ratio equals 1 (meaning the two functions are equal in value). Or if you want to find all c for which one is greater than the other, you could turn the equals sign into one of your dreaded inequality signs (again, I'm not sure what you think is implied by this). So if cd (x)/o (x) = 1, we can simply multiply both sides of the equation by o (x).
So we have x*(1-c) + 2.22cx = 1.083x*(1-c) + 1.92*1.083cx.
With apologies for now having to do algebra like my approach did from the beginning, but this is simply the way you solve for unknowns.
x+1.22cx = 1.083x+0.99636cx
0.22634c = 0.083
c= 0.3667.
Let's now work with all the numbers, which I'm sure is what you are waiting for.
Let's here calculate x as the total culmination of all offense: x=2,888+3*0.085*2,888+3*0.045*2,888+990+185 = 5,189.32.
With an offense set, xo = 2,888*1.15+3*0.85*2,888+3*0.045*2,888+990+185 = 5,622.52.
In now comparing cd (x)/o (x), we have
(5,189.32*(1-c) + 5,189.32*2.22c)/(5,622.52*(1-c)+5,622.52*1.92c).
Setting this equal to 1, then multiplying both sides by the denominator and distributing, we have
5,189.32-5,189.32c+11,520.29c = 5,622.52 - 5,622.52c + 10,795.2384c
=
6,330.97c-5,172.718c = 5,622.52-5,189.32
=
1,158.252c = 433.2
c=0.374.
Note that the slight descrepancy from above is due to rounding error; when I redo the previous example with 1.083688 instead I got about 37.5, and I'm sure carrying to more decimal places in both examples would yield convergent results.
Anyway, you can see how we end up with subtractingthe terms of one side from the other, which is what I did in the beginning after setting the two equations equal to one another.
Now, let's plug these values into my formula from way back:
c= 1/ (1.5+2*(0.85*3+0.45*3)+(2*(990+185)/2888)-0.42) = 1/2.6737 = 37.4.
Although I think we could honestly dump some of the terms in that expression, if, when computing offense bonuses from mods, we take a hand calculation on the non offense set first and then just include it as one term.
But, all of these theoretical discussions are just that, because they assume those other mod bonuses as equal. In practice, as another user pointed out, these will be different based on the mods you have available. So really, you just need to put the sets on, look at the different offense values, and set up cd (x) and o (x) directly, keeping in mind that characters may get crit damage up for a portion of the time. Including the extra mod bonuses is useful for deciding if you want to farm new mods and want to guage how much your offense secondaries would need to be, which is also a variable you could solve for.
In short, are approaches (linear algebra or piecemeal comparison of ratios) should yield the same result, and are both valid conceptualizations of the same problem. However, I felt it dutiful to point out that in setting up your comparisons, your decisiom to ignore non-crit damage as an equalizer resulted in a mathematically unsound comparison, thus throwing off your calculations.
You truly earned your nick name.
I hope you get paid very well for whatever you do.