So, will critical damage mod sets now be useless?

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..

"CoverlessSkink;c-1623509" wrote:
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.

"crzydroid;c-1623390" wrote:


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.

EDIT: Fixed Math

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.

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.

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. B) 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:

(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.

"B" then end parenthesis should not be smiley face. Too tired to fix. Typing too long.

"crzydroid;c-1624600" wrote:
"B" then end parenthesis should not be smiley face. Too tired to fix. Typing too long.

You truly earned your nick name.
I hope you get paid very well for whatever you do.

"crzydroid;c-1624479" wrote:
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. B) 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:

(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.

So ignoring the non crit damage on the crit damage set is purposeful. The point is not to identify what the overall damage will be. Only how much harder crits will hit.

Crit chance is one of those things that can be safely factored out as it is going to be about the same for both sets when maximizing offense as there will have been no room for it to upgrade with all the offense upgrades.


Likewise, i am calculating % in match damage increase for the offense set regardless of crits. In other words it results in the same % increase regardless of crit or not, though not the same flat damage. Since i am only comparing %s and not flat, this greatly simplifies the equation without sacrificing accuracy.

By only comparing crit damage % increase from the crit set to overall % damage increase from the offense set, I'm factoring out all damage not related to the sets themselves at the earliest possible step to avoid it skewing the results by doing extra math first, and NEVER factoring it back in. It's irrelevant. It can only skew the results.

...kind of like how you pointed out that in match offense can be safely factored out, and the inclusion of that unnecessary constant was skewing my results. Only now, it's you doing it with crit chance and damage not directly coming from the set bonus.

Trying to compare flat damage is excruciating and very easy to get wrong.

If 2 formulas that "should" produce the same results produce different results, the error is likely with the more complicated formula.

Most calculation errors occur with the US because of conversion factors. ...because of extra math.

The point of this question is never really: "Which of my sets of mods should I use?", it's always: "Which one is "the best"?", or "Which should I be farming?"

To answer that question we should assume the best secondaries, which allows factoring out of many variables.

If you're obtaining a different result than I because you're including constants in your formula that I factored out, do you really believe the problem is me not doing extra math with the constants? I don't.

To be clear, I am a chemist. Dimensional analysis is second nature to me. Comparisons and conversions are required to be done constantly. I don't set up equalities or inequalities, I set up ongoing calculations. Taking the time to put it as an equality or inequality usually requires far more setup, extra math, and introduces a lot more chances for things to go wrong.

I'm sorry, but it's your inclusion of these factors that made your math produce an incorrect result, not my factoring them out producing one for me.

Funny thing is all this doesn’t seem to make mods simpler in any way. They are much simpler now as they stand. All this is starting to give me a headache and it hasn’t even begun. Sounds like an epic fail.

See it's like I figured out that the offense set gives an 8.3% increase in offense. So my representation for the offense set is 8.3% Sure I could figure out what he hits for on a crit, how often he crits and what he hits for on a non-crit.

To simplify let's say someone hits for 10k before set bonus is considered. With the offense set, they would hit for 10,830. On a crit they would hit for 19,200 without the offense set and 20793 with it. I can calculate the average damage by using crit chance. let's say 40% so, ((20793 * .4) + (10830 * .6)) - ((19,200 * .4) + (10000 * .6)) = 1135.2 The average damage increase for the offense set would be 1135.2. Now let's see what % of the non offense set damage that is. (19,200 * .4) + (10000 * .6) = 13680.

1135.2 / 13680 = 0.082976... 8.3%. It worked out the same with or without going through all that extra math (not counting a slight variation due to rounding). So the % damage increase is the same regardless of crit chance. This means that we don't have to differentiate between crits and non crits for the offense set since we cover both by using % instead of flat damage.


"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."

No. no this is not an accurate representation of my formula at any point. You are sticking factors into my equation that were already factored out before it hit the paper, like crit chance. It's irrelevant. It is only skewing your results to include it. It is to avoid skewing of results that I made sure to factor it out as early as possible.

The ONLY step of my formula (that's what's great about it, it's only an ongoing calculation that can be solved linearly, not an equality/inequality that requires many many steps) is the one I have shown. It doesn't have multiple steps. It doesn't require doing things in "chunks" as you call it. It is linear, it is quick, it is streamlined, and it is 100% accurate.

This is my formula, what you have shown is avidly not

(1 - (Physical damage listed in panel / physical damage - offense set physical damage) * 100) / (1 - (222/192) * 100)


I don't know if I can explain to you any clearer that you are the one making the mistake that I was making when I first addressed you in this thread... skewing the results by improperly including constants that should be factored out.