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.
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
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.
Lol. The best part about this thread is that you guys are trying to minmax on a game that is COMPLETELY nonhomogeneous. Almost every damage dealer either has some boost to stats that changes how they stack stats (self buffing crit damage, or offense up, or stacking offense of health converting to offense or whatever) in addition to risk/rewards for stacking stats (incurring a taunt for critting, taking an extra attack, clearing debuff on a critical, reducing cooldowns on a critical, inflicting specific debuff on a critical, etc.). That's not even taking into account that for at least 60% of all characters, crit dmg/offense are not your go to set.
The real, honest truth is that every character needs individual consideration, and has best in slot stats that interact with abilities, especially the newer characters.
If you guys want a real hard and fast rule, it's this: use crit damage on characters that yield high crits (wedge, CLS, FOE, Rey, etc). This will naturally spike their peak damage, and make for more interesting and exciting gameplay. Save your good crit dmg sets for them, and use offense on anyone else.
I don't know about the rest of you, but I'm going with "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.)"
And yes I can do the math, but I prefer to just play the game. One of the advantages of not fighting for the top spots I guess.
So many variables like character basics team comp and mod sub stats. Theory crafting is still theory . At the end of the day it’s not about my number is bigger than yours but how you use it.
Finally, I am sorry to point out that while working through your process, I did discover an error in your setup
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).
Incorrect representation of this from the start here. Offense set ratio would be represented by BO + SO / BO CD is represented by CD + SB / CD.
I'm not using any of the same figures in either or these ratios. To represent them with the same variable as you have done is confusing, misleading, and most of all, inaccurate.
In other words, the mere fact that you have used the same variables to represent the parts of my formula for the offense set, and the parts of my formula for the crit damage set means that there is no way you could possibly have found an error in my math with your reasoning.... because you aren't using my math.
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
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.
So somewhere there is a communication error here. I am not talking about any calculations regarding the offense set. That set does provide a constant increase in damage.
I was referring to the fact that you leave the non-crit portion out when relating to the critical damage set. While critical damage sets only affect the crit portion, in comparing them to offense sets, which affect all portions, you need that non-crit portion to tell what value of critical chance will provide more damage overall. As soon as you introduce critical chance into the question, the problem necessarily becomes one of both crit and non-crit damage--for that is what critical chance is: It's that weight which determines how often a hit is a crit and how often it is not. Even if you get more critical damage with a cd set, you will get less non-crit damage than you would have with an offense set. When you then frame the question in terms of what critical chance provides an equal mixture of crit and non-crit for each set, you need the non-crits in there.
I've actually amended the next part of what I was planning on saying in terms of calculations, because I realized you were simply approaching this in a completely different way--while my steps for showing what you did show an answer resulting from an improper combination of fractions, the approach assumes you were thinking of solving for critical chance in the first place. I provided a mathematically equivalent vetsion of your formula (go ahead, try it out), but your question was framed differently.
You took
(1-1.083)/(1-(2.22/1.92))
(Again, this is your formula without the *100--I just put it in decimal form up front, with the result in decimal form as well. Go ahead and try it, and see if you get the same answer).
Anyway, this formula is taking the percent increase in offense set crits vs. non-set over the cd set percent increase in crits over non-set.
The result is is the proportion of increase in crit damage with an offense set to the increase in crit damage with a cd set. It is ONLY concerned with the damage increase for one set over the other ONLY when you crit. This isn't the question we want to answer. It also bears no relationship to crit chance. Crit chance, in this scenario, for all intents and purposes, is 1.00. Either it is actually 1.00, or it is some other non-zero value, but since you are only looking at crits in determining the effectiveness of one set over the other, the value doesn't matter. It doesn't tell us anything about a crit chance breakpoint for which the mixture of crit and non-crit is equal for both sets. It is important to look at this mixture because even as cd sets provide more on a crit, they provide less on a non-crit.
When you solve your equation and come up with 53.12%, that result is completely independent of any level of crit chance, because you are only looking at crits. It does not mean there is a 53.12% crit chance breakpoint. It means an offense set only provides 53.12% of the increase in damage over a cd set for only those instances where you crit. You have provided a perfectly accurate formula for that number, but it is not the question we are asking.
If you are only concerned with crit damage, and a cd set provides more crit damage, then it will ALWAYS be so for crits. But you are not concerned with crit chance in this scenario. When you start asking questions about crit damage breakpoint, you are now concerned with non-crits as well. For that is what critical chance means--it is fundamentally tied to the mixture of crit and non-crit. So it is absolutely vital that both those components be included in any calculation of critical chance. It is also helpful to include the variable of interest in the appropriate place in the equation.
So putting my formula in the same form as yours, you would have
(1-1.083)/(1+1.083*1.92-1.083-2.22)
As you can see, the numerator is the same, but the denominator is different, taking into account the relationships between the sets when the fundamentally important component of non-crit damage is left in. This set up is appropriate to the question we are asking, and finds a crit chance breakpoint of 37%. You will also see that this is mathematically equivalent to the formula I listed above--it is simply a computational form as opposed to a theoretical or definitional one. Those terms are all still there, it's just some of them were pre-calculated, mostly by the game itself. And you can see in my reponses to other posts that I am an advocate of using the game panel offense in practice.
Lol. The best part about this thread is that you guys are trying to minmax on a game that is COMPLETELY nonhomogeneous. Almost every damage dealer either has some boost to stats that changes how they stack stats (self buffing crit damage, or offense up, or stacking offense of health converting to offense or whatever) in addition to risk/rewards for stacking stats (incurring a taunt for critting, taking an extra attack, clearing debuff on a critical, reducing cooldowns on a critical, inflicting specific debuff on a critical, etc.). That's not even taking into account that for at least 60% of all characters, crit dmg/offense are not your go to set.
The real, honest truth is that every character needs individual consideration, and has best in slot stats that interact with abilities, especially the newer characters.
If you guys want a real hard and fast rule, it's this: use crit damage on characters that yield high crits (wedge, CLS, FOE, Rey, etc). This will naturally spike their peak damage, and make for more interesting and exciting gameplay. Save your good crit dmg sets for them, and use offense on anyone else.
Welcome to the discussion.
Yes, it has been a general rule of thumb to put cd sets on characters that crit a lot. But this thread started because of the question as to how the new set bonuses and 6e mods would affect the decision making process.
Since offense sets are multiplicative and crit damage sets are additive, there's a level of crit damage from other sources for which the cd set does not provide as much of an increase relative to the offense set, even for characters who have high or maximum critical chance. This is true under the current system; however, the threshold is unlikely to be reached with current sources of bonuses (maybe Asajj Ventress could reach it after enough deaths).
The new bonus for offense sets, however, decreases that threshold. Simultaneously, slicing a critical damage primary mod to 6e provides mre distance towards reaching the threshold.
The balance to this is that Woodroward pointed out that offense set bonuses only apply to base offense. Therefore, the more offense you add from mods, the more the threshold increases again. Furthermore, those offense values can be sliced as well, further raising that threshold back up.
So the thread is about how, if at all, are the situations where you use one set over the other changed by these new mods.
Of course, as you can see from some of these later responses, some people will just keep on playing the way they play and having fun.
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
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.
So somewhere there is a communication error here. I am not talking about any calculations regarding the offense set. That set does provide a constant increase in damage.
I was referring to the fact that you leave the non-crit portion out when relating to the critical damage set. While critical damage sets only affect the crit portion, in comparing them to offense sets, which affect all portions, you need that non-crit portion to tell what value of critical chance will provide more damage overall. As soon as you introduce critical chance into the question, the problem necessarily becomes one of both crit and non-crit damage--for that is what critical chance is: It's that weight which determines how often a hit is a crit and how often it is not. Even if you get more critical damage with a cd set, you will get less non-crit damage than you would have with an offense set. When you then frame the question in terms of what critical chance provides an equal mixture of crit and non-crit for each set, you need the non-crits in there.
I've actually amended the next part of what I was planning on saying in terms of calculations, because I realized you were simply approaching this in a completely different way--while my steps for showing what you did show an answer resulting from an improper combination of fractions, the approach assumes you were thinking of solving for critical chance in the first place. I provided a mathematically equivalent vetsion of your formula (go ahead, try it out), but your question was framed differently.
You took
(1-1.083)/(1-(2.22/1.92))
(Again, this is your formula without the *100--I just put it in decimal form up front, with the result in decimal form as well. Go ahead and try it, and see if you get the same answer).
Anyway, this formula is taking the percent increase in offense set crits vs. non-set over the cd set percent increase in crits over non-set.
The result is is the proportion of increase in crit damage with an offense set to the increase in crit damage with a cd set. It is ONLY concerned with the damage increase for one set over the other ONLY when you crit. This isn't the question we want to answer. It also bears no relationship to crit chance. Crit chance, in this scenario, for all intents and purposes, is 1.00. Either it is actually 1.00, or it is some other non-zero value, but since you are only looking at crits in determining the effectiveness of one set over the other, the value doesn't matter. It doesn't tell us anything about a crit chance breakpoint for which the mixture of crit and non-crit is equal for both sets. It is important to look at this mixture because even as cd sets provide more on a crit, they provide less on a non-crit.
When you solve your equation and come up with 53.12%, that result is completely independent of any level of crit chance, because you are only looking at crits. It does not mean there is a 53.12% crit chance breakpoint. It means an offense set only provides 53.12% of the increase in damage over a cd set for only those instances where you crit. You have provided a perfectly accurate formula for that number, but it is not the question we are asking.
If you are only concerned with crit damage, and a cd set provides more crit damage, then it will ALWAYS be so for crits. But you are not concerned with crit chance in this scenario. When you start asking questions about crit damage breakpoint, you are now concerned with non-crits as well. For that is what critical chance means--it is fundamentally tied to the mixture of crit and non-crit. So it is absolutely vital that both those components be included in any calculation of critical chance. It is also helpful to include the variable of interest in the appropriate place in the equation.
So putting my formula in the same form as yours, you would have
(1-1.083)/(1+1.083*1.92-1.083-2.22)
As you can see, the numerator is the same, but the denominator is different, taking into account the relationships between the sets when the fundamentally important component of non-crit damage is left in. This set up is appropriate to the question we are asking, and finds a crit chance breakpoint of 37%. You will also see that this is mathematically equivalent to the formula I listed above--it is simply a computational form as opposed to a theoretical or definitional one. Those terms are all still there, it's just some of them were pre-calculated, mostly by the game itself. And you can see in my reponses to other posts that I am an advocate of using the game panel offense in practice.
See this is what I'm trying to explain to you. I'm not comparing average damage for the sets. That's a complicated messy waste of time. Instead I'm comparing only the increase each set provides. When does a crit damage set increase the value of a non-crit? It doesn't.
The offense set provides a 8.3% increase on crits and non-crits. The crit damage set provides only a 15% increase on crits. The 1.0 offense and the 1.92 crit damage can be safely factored out of both sets, as it is exactly the same for both. By only comparing the crit % damage increase to the offense % damage increase, I am taking into account all damage immediately, and then immediately factoring out all damage not related to the sets.
The results I am obtaining from this formula are completely independent of any level of crit chance on the mods, because it was factored out. It has no bearing on whether an offense set or a crit damage set can produce more offense at this level of the equation.
In the end this ratio makes a comparison of the actual damage of the offense set to the POTENTIAL damage of the crit chance set.
If an offense set provides a 77% increase in damage 100% of the time compared to an crit damage set that provides 100% damage 77% of the time (because it crit 77% of the time), then they are equal. So the % increase in damage than an offense set provides compared to a crit damage set IS the crit chance breakpoint where a crit damage set becomes better than an offense set. If the result is 1.21, then at 121% crit you'd be better (assuming the damage continued to rise which it doesn't, hence anything over 1 means offense is just better) Anything over 1 means a crit damage set isn't capable of producing more damage than an offense set.
Otherwise, it shows that a crit damage set is CAPABLE of producing more damage than an offense set, but only if it can produce results at that % of the time. This is not in any way a calculation error, it is a massive simplification with 0 loss of accuracy. If you are experiencing different results it is because you are somehow improperly including constants you don't need to, like crit chance, base offense, and base crit damage. For instance this formula right here is incorrect:
(1-1.083)/(1+1.083*1.92-1.083-2.22)
Since you insist upon including things you don't need to. you should at least have the proper format:
(1.083 - 1) / ((1 * 2.22) - (1 * 1.92))
See in your version you are simplifying to just the offense bonus on one side, then adding base offense and base offense and set offense together, multiplying it by a crit with no cd damage set, then subtracting base offense and set offense and subtracting the crit multiplier with a set and triangle. I see why you keep getting a different result than me now. This is not even close to accurate math.
Again, this question is NEVER asking, "which of my mod sets is better?" It is asking, " which set of mods is the best that can be gotten?"
I think I'd like to know which mod set has a higher average damage dealt in a battle.
This can easily be obtained by comparing % damage increases rather than calculating out all the flat values and averaging them. That way is just longer and has far more room for error.
If an offense set provides a 77% increase in damage 100% of the time compared to an crit damage set that provides 100% damage 77% of the time (because it crit 77% of the time), then they are equal. So the % increase in damage than an offense set provides compared to a crit damage set IS the crit chance breakpoint where a crit damage set becomes better than an offense set. If the result is 1.21, then at 121% crit you'd be better (assuming the damage continued to rise which it doesn't, hence anything over 1 means offense is just better) Anything over 1 means a crit damage set isn't capable of producing more damage than an offense set.
This is where you have a missing component. The offense set provides 77% more damage 100% of the time vs. NO SET BONUS. Likewise, the cd set provides 100% more damage 77% of the time vs. NO SET BONUS. You may claim you are not trying to compare offense to cd, but as soon as you start putting them in the same equation (one over the other and determing break points), then you ARE, by definition, COMPARING them. The offense set then no longer provides 77% increase 100% of the time. It provides a 77% increase 23% of the time. The other 77% of the time, it provides a DECREASE in damage (1.77/2=0.885; 0.885 <1).
This is what you are not taking into account. This is actually quite similar in form to a phenomenon known as Simpson's Paradox, for what it's worth.
So this is what I'm trying to show--when comparing the two sets, you are setting up the values wrong because you are leaving out a component of the puzzle. You say you are not comparing the two sets or averages or whatever--fine. But then you need to be clear about what it is you are comparing and what you mean by "critical damage breaking point" and if your question--whatever it may be--is at all interesting to others.
Because when most people say "critical damage breaking point," they mean that point for which the total damage provided by one set is equal to the total damage provided by the other set, holding all else equal. And that is very much so a question of averages, of both crit and non-crit damage.
(1 - (((Offense before mods - offense from currently equipped gear) * (1 + (.15 + .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear ))/ ((Offense before mods - offense from currently equipped gear) * (1 + ( .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear))) / ( 1 - ( 2.22 / 1.92 )) = crit chance breakpoint
If the result is over 1, offense is always better. If it is less than 1, that represents the % of damage the offense set will provide compared to what the crit damage set is capable of, so at that % of crit chance, the crit damage set will have the same average damage. At higher levels it will produce more damage on average.
Since this is determining for max offense secondaries, that leaves not a lot of room for crit chance. 1.5% for each mod + 8 for the 2 set bonus is 17% crit chance added to the character's base. If that will reach or surpass that breakpoint, then crit damage is the best possible damage set.
b Base Offense
z Offense Primary Percent
y flat offense and equipped gear
o Offense from Ingame Bonuses
m Damage Multiplier
c Critical Chance
x total critical damage bonuses from crit damage triangle and in-game abilities
c = (1)/(1.5+2z+(2y/b)-x)
what an ugly thing to say... does this mean we're not friends anymore?
If an offense set provides a 77% increase in damage 100% of the time compared to an crit damage set that provides 100% damage 77% of the time (because it crit 77% of the time), then they are equal. So the % increase in damage than an offense set provides compared to a crit damage set IS the crit chance breakpoint where a crit damage set becomes better than an offense set. If the result is 1.21, then at 121% crit you'd be better (assuming the damage continued to rise which it doesn't, hence anything over 1 means offense is just better) Anything over 1 means a crit damage set isn't capable of producing more damage than an offense set.
This is where you have a missing component. The offense set provides 77% more damage 100% of the time vs. NO SET BONUS. Likewise, the cd set provides 100% more damage 77% of the time vs. NO SET BONUS. You may claim you are not trying to compare offense to cd, but as soon as you start putting them in the same equation (one over the other and determing break points), then you ARE, by definition, COMPARING them. The offense set then no longer provides 77% increase 100% of the time. It provides a 77% increase 23% of the time. The other 77% of the time, it provides a DECREASE in damage (1.77/2=0.885; 0.885 <1).
This is what you are not taking into account. This is actually quite similar in form to a phenomenon known as Simpson's Paradox, for what it's worth.
So this is what I'm trying to show--when comparing the two sets, you are setting up the values wrong because you are leaving out a component of the puzzle. You say you are not comparing the two sets or averages or whatever--fine. But then you need to be clear about what it is you are comparing and what you mean by "critical damage breaking point" and if your question--whatever it may be--is at all interesting to others.
Because when most people say "critical damage breaking point," they mean that point for which the total damage provided by one set is equal to the total damage provided by the other set, holding all else equal. And that is very much so a question of averages, of both crit and non-crit damage.
No, no. My calculations are not comparing no set bonus. They are ONLY comparing set bonus. I factored out everything EXCEPT the set bonus for comparison.
That's the whole point of comparing only % damage increase for each set bonus. I factored out every single other piece of damage. How could I possibly be comparing the damage without a set bonus when I factored it out before I compared?
The fact that it provides an increase 77% of the time, and a decrease 23% of the time is exactly why it is EVEN. It is the breakpoint. That means even. If it was an increase 77% of the time and equal the rest, it would be an overall increase, but that's not what a breakpoint is. That's where things become even...
((Offense before mods - offense from currently equipped gear) * (1 + (.15 + .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear) / ( 2.22 / 1.92 ) = crit chance breakpoint
If the result is over 1, offense is always better. If it is less than 1, that represents the % of damage the offense set will provide compared to what the crit damage set is capable of, so at that % of crit chance, the crit damage set will have the same average damage. At higher levels it will produce more damage on average.
Since this is determining for max offense secondaries, that leaves not a lot of room for crit chance. 1.5% for each mod + 8 for the 2 set bonus is 17% crit chance added to the character's base. If that will reach or surpass that breakpoint, then crit damage is the best possible damage set.
@Woodroward I'm not following this... Can you format your formula like I did for crzydroid?
Edit-typo
what an ugly thing to say... does this mean we're not friends anymore?
(1-(((Offense before mods - offense from currently equipped gear) * (1 + (.15 + .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear )) / ((Offense before mods - offense from currently equipped gear) * (1 + ( .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear))) / (1 - ( 2.22 / 1.92 ) )= crit chance breakpoint
If the result is over 1, offense is always better. If it is less than 1, that represents the % of damage the offense set will provide compared to what the crit damage set is capable of, so at that % of crit chance, the crit damage set will have the same average damage. At higher levels it will produce more damage on average.
Since this is determining for max offense secondaries, that leaves not a lot of room for crit chance. 1.5% for each mod + 8 for the 2 set bonus is 17% crit chance added to the character's base. If that will reach or surpass that breakpoint, then crit damage is the best possible damage set.
@Woodroward I'm not following this... Can you format your formula like I did for crzydroid?
Edit-typo
Sorry i made a mistake in the representation. Let me correct it.
I can make it somewhat easier but don't ask me to substitute variables for the words they represent. That only makes it more confusing in my opinion. Get so far along, and oh wait, which part does this variable represent again? No, I just say what needs to be put in there.
(1 - (((Panel offense - Offense from currently equipped gear) * 1.54 + 990 + offense from currently equipped gear) / ((Panel offense - Offense from currently equipped gear) * 1.39 + 990 + offense from currently equipped gear)))) / ( 1 - (2.22 / 1.92))
The 1.54 is the % increase for 3 primaries, 3 max secondaries, and the set. The 990 is the flat increase for 6 flat secondaries. the 1.39 is the % offense increase from mods not including the set.
(((Offense before mods - offense from currently equipped gear) * (1 + (.15 + .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear)/ ((Offense before mods - offense from currently equipped gear) * (1 + ( .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear) ) / ( 2.22 / 1.92 ) = crit chance breakpoint
If the result is over 1, offense is always better. If it is less than 1, that represents the % of damage the offense set will provide compared to what the crit damage set is capable of, so at that % of crit chance, the crit damage set will have the same average damage. At higher levels it will produce more damage on average.
Since this is determining for max offense secondaries, that leaves not a lot of room for crit chance. 1.5% for each mod + 8 for the 2 set bonus is 17% crit chance added to the character's base. If that will reach or surpass that breakpoint, then crit damage is the best possible damage set.
@Woodroward I'm not following this... Can you format your formula like I did for crzydroid?
Edit-typo
Sorry i made a mistake in the representation. Let me correct it.
I can make it somewhat easier but don't ask me to substitute variables for the words they represent. That only makes it more confusing in my opinion. Get so far along, and oh wait, which part does this variable represent again? No, I just say what needs to be put in there.
1 - (((Panel offense - Offense from currently equipped gear) * 1.54 + 990 + offense from currently equipped gear) / ((Panel offense - Offense from currently equipped gear) * 1.39 + 990 + offense from currently equipped gear)) / (2.22 / 1.92)
The 1.54 is the % increase for 3 primaries, 3 max secondaries, and the set. The 990 is the flat increase for 6 flat secondaries. the 1.39 is the % offense increase from mods not including the set.
I think both you and crzydroid are adding offense %ages. So I take it the offense % is additive (i.e. Having 2 8. 5% primaries, would be 8.5% + 8.5% instead of multiplicative 1.085 times 1.085 minus 1)?
what an ugly thing to say... does this mean we're not friends anymore?
(((Offense before mods - offense from currently equipped gear) * (1 + (.15 + .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear)/ ((Offense before mods - offense from currently equipped gear) * (1 + ( .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear) ) / ( 2.22 / 1.92 ) = crit chance breakpoint
If the result is over 1, offense is always better. If it is less than 1, that represents the % of damage the offense set will provide compared to what the crit damage set is capable of, so at that % of crit chance, the crit damage set will have the same average damage. At higher levels it will produce more damage on average.
Since this is determining for max offense secondaries, that leaves not a lot of room for crit chance. 1.5% for each mod + 8 for the 2 set bonus is 17% crit chance added to the character's base. If that will reach or surpass that breakpoint, then crit damage is the best possible damage set.
@Woodroward I'm not following this... Can you format your formula like I did for crzydroid?
Edit-typo
Sorry i made a mistake in the representation. Let me correct it.
I can make it somewhat easier but don't ask me to substitute variables for the words they represent. That only makes it more confusing in my opinion. Get so far along, and oh wait, which part does this variable represent again? No, I just say what needs to be put in there.
1 - (((Panel offense - Offense from currently equipped gear) * 1.54 + 990 + offense from currently equipped gear) / ((Panel offense - Offense from currently equipped gear) * 1.39 + 990 + offense from currently equipped gear)) / (2.22 / 1.92)
The 1.54 is the % increase for 3 primaries, 3 max secondaries, and the set. The 990 is the flat increase for 6 flat secondaries. the 1.39 is the % offense increase from mods not including the set.
I think both you and crzydroid are adding offense %ages. So I take it the offense % is additive (i.e. Having 2 8. 5% primaries, would be 8.5% + 8.5% instead of multiplicative 1.085 times 1.085 minus 1)?
Correct. All offense %s on mods are based off of panel damage - damage on currently equipped gear. Chirrut for instance has 3073 physical damage. 185 of that is from G12 gear.
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 damage for a maxed Chirrut with maxed offense once new mods come out.
(((Offense before mods - offense from currently equipped gear) * (1 + (.15 + .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear)/ ((Offense before mods - offense from currently equipped gear) * (1 + ( .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear) ) / ( 2.22 / 1.92 ) = crit chance breakpoint
If the result is over 1, offense is always better. If it is less than 1, that represents the % of damage the offense set will provide compared to what the crit damage set is capable of, so at that % of crit chance, the crit damage set will have the same average damage. At higher levels it will produce more damage on average.
Since this is determining for max offense secondaries, that leaves not a lot of room for crit chance. 1.5% for each mod + 8 for the 2 set bonus is 17% crit chance added to the character's base. If that will reach or surpass that breakpoint, then crit damage is the best possible damage set.
@Woodroward I'm not following this... Can you format your formula like I did for crzydroid?
Edit-typo
Sorry i made a mistake in the representation. Let me correct it.
I can make it somewhat easier but don't ask me to substitute variables for the words they represent. That only makes it more confusing in my opinion. Get so far along, and oh wait, which part does this variable represent again? No, I just say what needs to be put in there.
1 - (((Panel offense - Offense from currently equipped gear) * 1.54 + 990 + offense from currently equipped gear) / ((Panel offense - Offense from currently equipped gear) * 1.39 + 990 + offense from currently equipped gear)) / (2.22 / 1.92)
The 1.54 is the % increase for 3 primaries, 3 max secondaries, and the set. The 990 is the flat increase for 6 flat secondaries. the 1.39 is the % offense increase from mods not including the set.
I think both you and crzydroid are adding offense %ages. So I take it the offense % is additive (i.e. Having 2 8. 5% primaries, would be 8.5% + 8.5% instead of multiplicative 1.085 times 1.085 minus 1)?
Correct. All offense %s on mods are based off of panel damage - damage on currently equipped gear. Chirrut for instance has 3073 physical damage. 185 of that is from G12 gear.
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 damage for a maxed Chirrut with maxed offense once new mods come out.
Thank you.
Does crit dmg calculate off of the 3073 physical dmg or the 5622 figure?
what an ugly thing to say... does this mean we're not friends anymore?
(((Offense before mods - offense from currently equipped gear) * (1 + (.15 + .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear)/ ((Offense before mods - offense from currently equipped gear) * (1 + ( .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear) ) / ( 2.22 / 1.92 ) = crit chance breakpoint
If the result is over 1, offense is always better. If it is less than 1, that represents the % of damage the offense set will provide compared to what the crit damage set is capable of, so at that % of crit chance, the crit damage set will have the same average damage. At higher levels it will produce more damage on average.
Since this is determining for max offense secondaries, that leaves not a lot of room for crit chance. 1.5% for each mod + 8 for the 2 set bonus is 17% crit chance added to the character's base. If that will reach or surpass that breakpoint, then crit damage is the best possible damage set.
@Woodroward I'm not following this... Can you format your formula like I did for crzydroid?
Edit-typo
Sorry i made a mistake in the representation. Let me correct it.
I can make it somewhat easier but don't ask me to substitute variables for the words they represent. That only makes it more confusing in my opinion. Get so far along, and oh wait, which part does this variable represent again? No, I just say what needs to be put in there.
1 - (((Panel offense - Offense from currently equipped gear) * 1.54 + 990 + offense from currently equipped gear) / ((Panel offense - Offense from currently equipped gear) * 1.39 + 990 + offense from currently equipped gear)) / (2.22 / 1.92)
The 1.54 is the % increase for 3 primaries, 3 max secondaries, and the set. The 990 is the flat increase for 6 flat secondaries. the 1.39 is the % offense increase from mods not including the set.
I think both you and crzydroid are adding offense %ages. So I take it the offense % is additive (i.e. Having 2 8. 5% primaries, would be 8.5% + 8.5% instead of multiplicative 1.085 times 1.085 minus 1)?
Correct. All offense %s on mods are based off of panel damage - damage on currently equipped gear. Chirrut for instance has 3073 physical damage. 185 of that is from G12 gear.
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 damage for a maxed Chirrut with maxed offense once new mods come out.
Thank you.
Does crit dmg calculate off of the 3073 physical dmg or the 5622 figure?
Crit damage is based off of the figure after offense from mods is included. In this case it would be the 5622-433 number (since the 433 comes from the offense set).
(((Offense before mods - offense from currently equipped gear) * (1 + (.15 + .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear)/ ((Offense before mods - offense from currently equipped gear) * (1 + ( .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear) ) / ( 2.22 / 1.92 ) = crit chance breakpoint
If the result is over 1, offense is always better. If it is less than 1, that represents the % of damage the offense set will provide compared to what the crit damage set is capable of, so at that % of crit chance, the crit damage set will have the same average damage. At higher levels it will produce more damage on average.
Since this is determining for max offense secondaries, that leaves not a lot of room for crit chance. 1.5% for each mod + 8 for the 2 set bonus is 17% crit chance added to the character's base. If that will reach or surpass that breakpoint, then crit damage is the best possible damage set.
@Woodroward I'm not following this... Can you format your formula like I did for crzydroid?
Edit-typo
Sorry i made a mistake in the representation. Let me correct it.
I can make it somewhat easier but don't ask me to substitute variables for the words they represent. That only makes it more confusing in my opinion. Get so far along, and oh wait, which part does this variable represent again? No, I just say what needs to be put in there.
1 - (((Panel offense - Offense from currently equipped gear) * 1.54 + 990 + offense from currently equipped gear) / ((Panel offense - Offense from currently equipped gear) * 1.39 + 990 + offense from currently equipped gear)) / (2.22 / 1.92)
The 1.54 is the % increase for 3 primaries, 3 max secondaries, and the set. The 990 is the flat increase for 6 flat secondaries. the 1.39 is the % offense increase from mods not including the set.
I think both you and crzydroid are adding offense %ages. So I take it the offense % is additive (i.e. Having 2 8. 5% primaries, would be 8.5% + 8.5% instead of multiplicative 1.085 times 1.085 minus 1)?
Correct. All offense %s on mods are based off of panel damage - damage on currently equipped gear. Chirrut for instance has 3073 physical damage. 185 of that is from G12 gear.
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 damage for a maxed Chirrut with maxed offense once new mods come out.
Thank you.
Does crit dmg calculate off of the 3073 physical dmg or the 5622 figure?
Crit damage is based off of the figure after offense from mods is included. In this case it would be the 5622-433 number (since the 433 comes from the offense set).
With my dewy the dunce math, my results are following crzydroid's formula more closely.
what an ugly thing to say... does this mean we're not friends anymore?
(((Offense before mods - offense from currently equipped gear) * (1 + (.15 + .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear)/ ((Offense before mods - offense from currently equipped gear) * (1 + ( .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear) ) / ( 2.22 / 1.92 ) = crit chance breakpoint
If the result is over 1, offense is always better. If it is less than 1, that represents the % of damage the offense set will provide compared to what the crit damage set is capable of, so at that % of crit chance, the crit damage set will have the same average damage. At higher levels it will produce more damage on average.
Since this is determining for max offense secondaries, that leaves not a lot of room for crit chance. 1.5% for each mod + 8 for the 2 set bonus is 17% crit chance added to the character's base. If that will reach or surpass that breakpoint, then crit damage is the best possible damage set.
@Woodroward I'm not following this... Can you format your formula like I did for crzydroid?
Edit-typo
Sorry i made a mistake in the representation. Let me correct it.
I can make it somewhat easier but don't ask me to substitute variables for the words they represent. That only makes it more confusing in my opinion. Get so far along, and oh wait, which part does this variable represent again? No, I just say what needs to be put in there.
1 - (((Panel offense - Offense from currently equipped gear) * 1.54 + 990 + offense from currently equipped gear) / ((Panel offense - Offense from currently equipped gear) * 1.39 + 990 + offense from currently equipped gear)) / (2.22 / 1.92)
The 1.54 is the % increase for 3 primaries, 3 max secondaries, and the set. The 990 is the flat increase for 6 flat secondaries. the 1.39 is the % offense increase from mods not including the set.
I think both you and crzydroid are adding offense %ages. So I take it the offense % is additive (i.e. Having 2 8. 5% primaries, would be 8.5% + 8.5% instead of multiplicative 1.085 times 1.085 minus 1)?
Correct. All offense %s on mods are based off of panel damage - damage on currently equipped gear. Chirrut for instance has 3073 physical damage. 185 of that is from G12 gear.
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 damage for a maxed Chirrut with maxed offense once new mods come out.
Thank you.
Does crit dmg calculate off of the 3073 physical dmg or the 5622 figure?
Crit damage is based off of the figure after offense from mods is included. In this case it would be the 5622-433 number (since the 433 comes from the offense set).
With my dewy the dunce math, my results are following crzydroid's formula more closely.
The 75% breakpoint is for average offense secondaries and primaries rather than maxed. The formula I gave you was for maxed offense secondaries and primaries. The higher these are, the lower the breakpoint will be. If you do the math without counting offense secondaries at all, it ends up around ~90% crit chance as the breakpoint.
With maxed offense secondaries you end up with something close to 55% crit chance as the breakpoint. this will vary a lot depending on how much offense they get from currently equipped gear. Chirrut only has 185 offense from current gear, but Death Trooper has nearly 500 damage from current gear. Because of this, the offense set will always provide a smaller increase for Death Trooper than Chirrut, the end result of which is that he will always have a lower crit chance breakpoint than Chirrut as well.
The rule of thumb is usually used for average. So for average mods, the breakpoint is generally going to be around 75%.
1 - (((Panel offense - Offense from currently equipped gear) * 1.54+ 990 + offense from currently equipped gear) / ((Panel offense - Offense from currently equipped gear) * 1.39 + 990 + offense from currently equipped gear)) / ( 1 - (2.22 / 1.92))
is for max. For average mods, we can take those figures for offense and more or less cut them in half. so it would be
1 - (((Panel offense - Offense from currently equipped gear) * 1.34 + 495 + offense from currently equipped gear) / ((Panel offense - Offense from currently equipped gear) * 1.19 + 495 + offense from currently equipped gear)) / (1 - (2.22 / 1.92))
Let's again use Chirrut as an example: The offense will be (3073 - 185) * 1.34 + 495+ 185 = 4550. The offense set still provides 433 of this damage.
4550/ (4550 - 433) = 1.105 or a 10.5% increase in damage.
10.5 / (1 - (222/192)) * 100
10.5 / 15.6 = 0.67307692307692307692307692307692 or 67% crit, In this example I actually included more secondary offense than when I calculated the 75%, but this is still well over the 50% crit chance breakpoint that can only be reached with amazing mods. 75% is rule of thumb when comparing average sets.
b Base Offense
z Offense Primary Percent
y flat offense and equipped gear
o Offense from Ingame Bonuses
m Damage Multiplier
c Critical Chance
x total critical damage bonuses from crit damage triangle and in-game abilities
c = (1)/(1.5+2z+(2y/b)-x)
I would clarify this by saying the variable z also includes all % based mod secondaries, not just primaries. So if I had a mod primary of 5.88%, and a secondary of 0.88%, z would be 0.0588+0.0088 = 0.0676.
Keep in mind that this formula is based off the new set bonus of 15%. It should allow for either 5e or 6e (or any other) values. For example, for a 5e crit damage primary and no in-game bonuses, x would be 0.36. For 6e, it would be 0.42. If you are looking at a situation where the Crit Damage Up buff is present, add 0.5 to x, etc.
If an offense set provides a 77% increase in damage 100% of the time compared to an crit damage set that provides 100% damage 77% of the time (because it crit 77% of the time), then they are equal. So the % increase in damage than an offense set provides compared to a crit damage set IS the crit chance breakpoint where a crit damage set becomes better than an offense set. If the result is 1.21, then at 121% crit you'd be better (assuming the damage continued to rise which it doesn't, hence anything over 1 means offense is just better) Anything over 1 means a crit damage set isn't capable of producing more damage than an offense set.
This is where you have a missing component. The offense set provides 77% more damage 100% of the time vs. NO SET BONUS. Likewise, the cd set provides 100% more damage 77% of the time vs. NO SET BONUS. You may claim you are not trying to compare offense to cd, but as soon as you start putting them in the same equation (one over the other and determing break points), then you ARE, by definition, COMPARING them. The offense set then no longer provides 77% increase 100% of the time. It provides a 77% increase 23% of the time. The other 77% of the time, it provides a DECREASE in damage (1.77/2=0.885; 0.885 <1).
This is what you are not taking into account. This is actually quite similar in form to a phenomenon known as Simpson's Paradox, for what it's worth.
So this is what I'm trying to show--when comparing the two sets, you are setting up the values wrong because you are leaving out a component of the puzzle. You say you are not comparing the two sets or averages or whatever--fine. But then you need to be clear about what it is you are comparing and what you mean by "critical damage breaking point" and if your question--whatever it may be--is at all interesting to others.
Because when most people say "critical damage breaking point," they mean that point for which the total damage provided by one set is equal to the total damage provided by the other set, holding all else equal. And that is very much so a question of averages, of both crit and non-crit damage.
No, no. My calculations are not comparing no set bonus. They are ONLY comparing set bonus. I factored out everything EXCEPT the set bonus for comparison.
That's the whole point of comparing only % damage increase for each set bonus. I factored out every single other piece of damage. How could I possibly be comparing the damage without a set bonus when I factored it out before I compared?
The fact that it provides an increase 77% of the time, and a decrease 23% of the time is exactly why it is EVEN. It is the breakpoint. That means even. If it was an increase 77% of the time and equal the rest, it would be an overall increase, but that's not what a breakpoint is. That's where things become even...
When you "factored it out before comparing," that is when you compared it. For example, how did you get that the set bonus provides a 77% increase? By comparing it to the non-set portion. If you were truly comparing just the sets to each other, in your earlier example then you would've never had a cd set increase of 1.156. That's the set bonus over (ie, COMPARING TO) non-set bonus (2.22/1.92). If you were comparing to only the offense set, you would have 2.22/1.92*1.083....but that 1.083 is itself a comparison to no set bonus.
The short of it is, you are "factoring out" components that ought not to be factored out. You are comparing incomplete proportions.
Anyway, it seems from your comments that you are inexperienced with using mathematical expressions, and have some revulsion against even attempting to do so. Instead, you claim that the tools mathematicians have used for centuries to solve problems are "improper math," without explaining why. You claim that algebra is needlessly complicated, vaguely hinting that an increase in variables increases likelihood of computational error, but without pointing out where any errors might have occurred. You've "corrected" a formula of mine, not based on mathematical adjustments, but rather on the basis of some conceptual-seeming arrangement of terms during some other step. You also say things like, "You've added in extra constants which can be left out like we discussed before,"--however, as we discussed before, if those terms truly were constants, it would only affect the scale and not the relationships. When I take a proportion, it should yield the same result. You also seem to perhaps show a lack of understanding of how the depiction of a function, such as f (x) [read: "Eff of Ex"] stands in for an entire expression.
I'm trying to point out an omisssion in your set up, but you are refusing to actually have a set up. Instead you are preferring to solve components piecemeal and skip steps as it were in a process that seems to serve your intuition. But in this case, you are supposing you can lop off some chunk that is actually an important piece. I have tried to show you mathematically that you are inadvertantly splitting and combining fractions in an incorrect way by doing this. But you have no interest in looking at math.
So I think this conversation is pretty much finished. I have felt obliged to indulge in this thus far because you have been trying to make arguments that math--which people have been studying since ancient civilizations--somehow does not work. In so much as math is one of the most struggled-with disciplines, I didn't want to leave readers in a place where they didn't know what worked and what didn't.
I feel satisfied, however, that there is now enough in this thread that those who are able and willing to follow the discussion will be well-informed to come up with their own conclusions. Those who cannot follow the conversation will say, "Oh well, stick cd on high crit chance characters and offense otherwise and then just enjoy the game." And that's fine by me.
If there are other questions I will respond in the thread as necessary, but I am done trying to combat false accusations that mathematical problems should not be solved with mathematical tools.
When you "factored it out before comparing," that is when you compared it. For example, how did you get that the set bonus provides a 77% increase? By comparing it to the non-set portion. If you were truly comparing just the sets to each other, in your earlier example then you would've never had a cd set increase of 1.156. That's the set bonus over (ie, COMPARING TO) non-set bonus (2.22/1.92). If you were comparing to only the offense set, you would have 2.22/1.92*1.083....but that 1.083 is itself a comparison to no set bonus.
I factored out the non-set portion of the damage before comparing the damage from the sets. You said my final step (more or less) was comparing non-set damage to set damage.
And you are incorrect, the 1.083 is the offense WITH the offense set bonus. A 1 would be no set bonus. Go ahead and multiply the 1 back in there that I factored out and tell me how it affects the equation. I am not factoring things out wrong. You are using offense with the offense set as your base offense across the board resulting in an all around decreased value for the crit damage set.
Look at your math:
(1-1.083)/(1+1.083*1.92-1.083-2.22)
base offense(including mods) - base offense (including mods) with offense set (resulting in a negative number) / Base offense (including mods) + base offense (including mods) with an offense set * crit damage with a triangle - base offense (including mods) with an offense set - crit damage with a triangle and crit damage set.
Now you obviously meant to have one of those minuses be a * instead, but still in that instance you are multiplying your offense set included damage by your crit damage set included damage. There's no way this formula you have given me as representing yours in a similar style to mine is anything anywhere near proper math.
What it is, in my book, is evidence that you are improperly taking constants and multiplying them in in weird places resulting in incorrect comparisons.
If there are other questions I will respond in the thread as necessary, but I am done trying to combat false accusations that mathematical problems should not be solved with mathematical tools.
This isn't even close to what's going on here. I'm complaining about you using abstract math when you could just put your terms in.
As I said, I'm a chemist, I do math constantly. I have an aversion to math that has put variables in where they don't need to be since they represent constants. All that is doing is making me go through extra steps to check the math by plugging in those constants.
You're adding several extra steps in doing so. I provided examples of what I was discussing using math based on concrete things in game. You provided formulas based on conceptualizations without actually doing any math. That's my problem with your attempts to "explain" to me.
I am using mathematical tools myself to show what I am talking about.
There are a number of things that must be assumed to determine which set is capable of producing the greatest damage with ideal secondaries and primaries. To that end we can assume that we have the following stats on our mods:
+30 speed, + 17% crit chance, +990 flat offense + 39% offense, +42% crit damage.
Since we can assume all these secondaries to be what they are for calculation of which is best we can safely factor all these out as soon as we determine what they represent. My equation begins by setting each one of these values as = 1 so they can easily be factored out.
Offense with set is 1.083, what is it without the set? 1
Crit damage with set is 1.156, what is it without the set? 1
Which set will crit more resulting in higher average dps? neither
I can safely factor these things out.
I'm not sure about the debate, but as for numbers, here is my triangulation.
I ran this for an offense set parallel a cd set.
1) assume physical damage
2) add up off % bonuses and multiply by phy dmg
For off set I added 15% extra dmg
For cd set I just added all other % off bonuses
3} the result is my % offense adjusted dmg.
4} For each set I calculated the crit dmg (both with a cd triangle) for the cd set I added it's 30% bonus which I excluded from the offense set. But the offense set still uses 150% cd because even it gets the base cd.
5} For each set I calculated the non-crit dmg
6) I then averaged the crit dmg and non-crit dmg using crit chance.
7) I ran same variables using @crzydroid formula, which I then used as the cc in my formula.
8) the end result, both dmg from off set and cd set were equal, proving to me, crzydroid's formula will find the break-even cc %age.
Just added food for thought. I'm by no means an expert in math, but can get around.
what an ugly thing to say... does this mean we're not friends anymore?
I can't imagine a more convoluted way to design a mod system. Different star levels, with multiple different secondary abilities (on rank up, speed +30, then 2.06% Potency and +90 offense, just for ex.), 5 different spots to place them, and then we have the mod bonuses (ex. 4 speed mods give whatever it is), and you have to pay to put them (or off, can't remember, w/e same same). I mean, could there be anymore moving pieces?? What kind of sadist came up with this idea? You'd have to be a genius like the people above and you'd have to all that work above. Boggles my mind. Great game tho
Replies
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.
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.
The real, honest truth is that every character needs individual consideration, and has best in slot stats that interact with abilities, especially the newer characters.
If you guys want a real hard and fast rule, it's this: use crit damage on characters that yield high crits (wedge, CLS, FOE, Rey, etc). This will naturally spike their peak damage, and make for more interesting and exciting gameplay. Save your good crit dmg sets for them, and use offense on anyone else.
And yes I can do the math, but I prefer to just play the game. One of the advantages of not fighting for the top spots I guess.
Incorrect representation of this from the start here. Offense set ratio would be represented by BO + SO / BO CD is represented by CD + SB / CD.
I'm not using any of the same figures in either or these ratios. To represent them with the same variable as you have done is confusing, misleading, and most of all, inaccurate.
In other words, the mere fact that you have used the same variables to represent the parts of my formula for the offense set, and the parts of my formula for the crit damage set means that there is no way you could possibly have found an error in my math with your reasoning.... because you aren't using my math.
So somewhere there is a communication error here. I am not talking about any calculations regarding the offense set. That set does provide a constant increase in damage.
I was referring to the fact that you leave the non-crit portion out when relating to the critical damage set. While critical damage sets only affect the crit portion, in comparing them to offense sets, which affect all portions, you need that non-crit portion to tell what value of critical chance will provide more damage overall. As soon as you introduce critical chance into the question, the problem necessarily becomes one of both crit and non-crit damage--for that is what critical chance is: It's that weight which determines how often a hit is a crit and how often it is not. Even if you get more critical damage with a cd set, you will get less non-crit damage than you would have with an offense set. When you then frame the question in terms of what critical chance provides an equal mixture of crit and non-crit for each set, you need the non-crits in there.
I've actually amended the next part of what I was planning on saying in terms of calculations, because I realized you were simply approaching this in a completely different way--while my steps for showing what you did show an answer resulting from an improper combination of fractions, the approach assumes you were thinking of solving for critical chance in the first place. I provided a mathematically equivalent vetsion of your formula (go ahead, try it out), but your question was framed differently.
You took
(1-1.083)/(1-(2.22/1.92))
(Again, this is your formula without the *100--I just put it in decimal form up front, with the result in decimal form as well. Go ahead and try it, and see if you get the same answer).
Anyway, this formula is taking the percent increase in offense set crits vs. non-set over the cd set percent increase in crits over non-set.
The result is is the proportion of increase in crit damage with an offense set to the increase in crit damage with a cd set. It is ONLY concerned with the damage increase for one set over the other ONLY when you crit. This isn't the question we want to answer. It also bears no relationship to crit chance. Crit chance, in this scenario, for all intents and purposes, is 1.00. Either it is actually 1.00, or it is some other non-zero value, but since you are only looking at crits in determining the effectiveness of one set over the other, the value doesn't matter. It doesn't tell us anything about a crit chance breakpoint for which the mixture of crit and non-crit is equal for both sets. It is important to look at this mixture because even as cd sets provide more on a crit, they provide less on a non-crit.
When you solve your equation and come up with 53.12%, that result is completely independent of any level of crit chance, because you are only looking at crits. It does not mean there is a 53.12% crit chance breakpoint. It means an offense set only provides 53.12% of the increase in damage over a cd set for only those instances where you crit. You have provided a perfectly accurate formula for that number, but it is not the question we are asking.
If you are only concerned with crit damage, and a cd set provides more crit damage, then it will ALWAYS be so for crits. But you are not concerned with crit chance in this scenario. When you start asking questions about crit damage breakpoint, you are now concerned with non-crits as well. For that is what critical chance means--it is fundamentally tied to the mixture of crit and non-crit. So it is absolutely vital that both those components be included in any calculation of critical chance. It is also helpful to include the variable of interest in the appropriate place in the equation.
So putting my formula in the same form as yours, you would have
(1-1.083)/(1+1.083*1.92-1.083-2.22)
As you can see, the numerator is the same, but the denominator is different, taking into account the relationships between the sets when the fundamentally important component of non-crit damage is left in. This set up is appropriate to the question we are asking, and finds a crit chance breakpoint of 37%. You will also see that this is mathematically equivalent to the formula I listed above--it is simply a computational form as opposed to a theoretical or definitional one. Those terms are all still there, it's just some of them were pre-calculated, mostly by the game itself. And you can see in my reponses to other posts that I am an advocate of using the game panel offense in practice.
Welcome to the discussion.
Yes, it has been a general rule of thumb to put cd sets on characters that crit a lot. But this thread started because of the question as to how the new set bonuses and 6e mods would affect the decision making process.
Since offense sets are multiplicative and crit damage sets are additive, there's a level of crit damage from other sources for which the cd set does not provide as much of an increase relative to the offense set, even for characters who have high or maximum critical chance. This is true under the current system; however, the threshold is unlikely to be reached with current sources of bonuses (maybe Asajj Ventress could reach it after enough deaths).
The new bonus for offense sets, however, decreases that threshold. Simultaneously, slicing a critical damage primary mod to 6e provides mre distance towards reaching the threshold.
The balance to this is that Woodroward pointed out that offense set bonuses only apply to base offense. Therefore, the more offense you add from mods, the more the threshold increases again. Furthermore, those offense values can be sliced as well, further raising that threshold back up.
So the thread is about how, if at all, are the situations where you use one set over the other changed by these new mods.
Of course, as you can see from some of these later responses, some people will just keep on playing the way they play and having fun.
See this is what I'm trying to explain to you. I'm not comparing average damage for the sets. That's a complicated messy waste of time. Instead I'm comparing only the increase each set provides. When does a crit damage set increase the value of a non-crit? It doesn't.
The offense set provides a 8.3% increase on crits and non-crits. The crit damage set provides only a 15% increase on crits. The 1.0 offense and the 1.92 crit damage can be safely factored out of both sets, as it is exactly the same for both. By only comparing the crit % damage increase to the offense % damage increase, I am taking into account all damage immediately, and then immediately factoring out all damage not related to the sets.
The results I am obtaining from this formula are completely independent of any level of crit chance on the mods, because it was factored out. It has no bearing on whether an offense set or a crit damage set can produce more offense at this level of the equation.
In the end this ratio makes a comparison of the actual damage of the offense set to the POTENTIAL damage of the crit chance set.
If an offense set provides a 77% increase in damage 100% of the time compared to an crit damage set that provides 100% damage 77% of the time (because it crit 77% of the time), then they are equal. So the % increase in damage than an offense set provides compared to a crit damage set IS the crit chance breakpoint where a crit damage set becomes better than an offense set. If the result is 1.21, then at 121% crit you'd be better (assuming the damage continued to rise which it doesn't, hence anything over 1 means offense is just better) Anything over 1 means a crit damage set isn't capable of producing more damage than an offense set.
Otherwise, it shows that a crit damage set is CAPABLE of producing more damage than an offense set, but only if it can produce results at that % of the time. This is not in any way a calculation error, it is a massive simplification with 0 loss of accuracy. If you are experiencing different results it is because you are somehow improperly including constants you don't need to, like crit chance, base offense, and base crit damage. For instance this formula right here is incorrect:
(1-1.083)/(1+1.083*1.92-1.083-2.22)
Since you insist upon including things you don't need to. you should at least have the proper format:
(1.083 - 1) / ((1 * 2.22) - (1 * 1.92))
See in your version you are simplifying to just the offense bonus on one side, then adding base offense and base offense and set offense together, multiplying it by a crit with no cd damage set, then subtracting base offense and set offense and subtracting the crit multiplier with a set and triangle. I see why you keep getting a different result than me now. This is not even close to accurate math.
Again, this question is NEVER asking, "which of my mod sets is better?" It is asking, " which set of mods is the best that can be gotten?"
This can easily be obtained by comparing % damage increases rather than calculating out all the flat values and averaging them. That way is just longer and has far more room for error.
This is where you have a missing component. The offense set provides 77% more damage 100% of the time vs. NO SET BONUS. Likewise, the cd set provides 100% more damage 77% of the time vs. NO SET BONUS. You may claim you are not trying to compare offense to cd, but as soon as you start putting them in the same equation (one over the other and determing break points), then you ARE, by definition, COMPARING them. The offense set then no longer provides 77% increase 100% of the time. It provides a 77% increase 23% of the time. The other 77% of the time, it provides a DECREASE in damage (1.77/2=0.885; 0.885 <1).
This is what you are not taking into account. This is actually quite similar in form to a phenomenon known as Simpson's Paradox, for what it's worth.
So this is what I'm trying to show--when comparing the two sets, you are setting up the values wrong because you are leaving out a component of the puzzle. You say you are not comparing the two sets or averages or whatever--fine. But then you need to be clear about what it is you are comparing and what you mean by "critical damage breaking point" and if your question--whatever it may be--is at all interesting to others.
Because when most people say "critical damage breaking point," they mean that point for which the total damage provided by one set is equal to the total damage provided by the other set, holding all else equal. And that is very much so a question of averages, of both crit and non-crit damage.
(1 - (((Offense before mods - offense from currently equipped gear) * (1 + (.15 + .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear ))/ ((Offense before mods - offense from currently equipped gear) * (1 + ( .085 + .085 + .085 + .045 + .045 + .045) + 990 + offense from currently equipped gear))) / ( 1 - ( 2.22 / 1.92 )) = crit chance breakpoint
If the result is over 1, offense is always better. If it is less than 1, that represents the % of damage the offense set will provide compared to what the crit damage set is capable of, so at that % of crit chance, the crit damage set will have the same average damage. At higher levels it will produce more damage on average.
Since this is determining for max offense secondaries, that leaves not a lot of room for crit chance. 1.5% for each mod + 8 for the 2 set bonus is 17% crit chance added to the character's base. If that will reach or surpass that breakpoint, then crit damage is the best possible damage set.
b Base Offense
z Offense Primary Percent
y flat offense and equipped gear
o Offense from Ingame Bonuses
m Damage Multiplier
c Critical Chance
x total critical damage bonuses from crit damage triangle and in-game abilities
c = (1)/(1.5+2z+(2y/b)-x)
No, no. My calculations are not comparing no set bonus. They are ONLY comparing set bonus. I factored out everything EXCEPT the set bonus for comparison.
That's the whole point of comparing only % damage increase for each set bonus. I factored out every single other piece of damage. How could I possibly be comparing the damage without a set bonus when I factored it out before I compared?
The fact that it provides an increase 77% of the time, and a decrease 23% of the time is exactly why it is EVEN. It is the breakpoint. That means even. If it was an increase 77% of the time and equal the rest, it would be an overall increase, but that's not what a breakpoint is. That's where things become even...
@Woodroward I'm not following this... Can you format your formula like I did for crzydroid?
Edit-typo
I can make it somewhat easier but don't ask me to substitute variables for the words they represent. That only makes it more confusing in my opinion. Get so far along, and oh wait, which part does this variable represent again? No, I just say what needs to be put in there.
(1 - (((Panel offense - Offense from currently equipped gear) * 1.54 + 990 + offense from currently equipped gear) / ((Panel offense - Offense from currently equipped gear) * 1.39 + 990 + offense from currently equipped gear)))) / ( 1 - (2.22 / 1.92))
The 1.54 is the % increase for 3 primaries, 3 max secondaries, and the set. The 990 is the flat increase for 6 flat secondaries. the 1.39 is the % offense increase from mods not including the set.
EDIT: fixed formula
I think both you and crzydroid are adding offense %ages. So I take it the offense % is additive (i.e. Having 2 8. 5% primaries, would be 8.5% + 8.5% instead of multiplicative 1.085 times 1.085 minus 1)?
Correct. All offense %s on mods are based off of panel damage - damage on currently equipped gear. Chirrut for instance has 3073 physical damage. 185 of that is from G12 gear.
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 damage for a maxed Chirrut with maxed offense once new mods come out.
Thank you.
Does crit dmg calculate off of the 3073 physical dmg or the 5622 figure?
Crit damage is based off of the figure after offense from mods is included. In this case it would be the 5622-433 number (since the 433 comes from the offense set).
With my dewy the dunce math, my results are following crzydroid's formula more closely.
The 75% breakpoint is for average offense secondaries and primaries rather than maxed. The formula I gave you was for maxed offense secondaries and primaries. The higher these are, the lower the breakpoint will be. If you do the math without counting offense secondaries at all, it ends up around ~90% crit chance as the breakpoint.
With maxed offense secondaries you end up with something close to 55% crit chance as the breakpoint. this will vary a lot depending on how much offense they get from currently equipped gear. Chirrut only has 185 offense from current gear, but Death Trooper has nearly 500 damage from current gear. Because of this, the offense set will always provide a smaller increase for Death Trooper than Chirrut, the end result of which is that he will always have a lower crit chance breakpoint than Chirrut as well.
The rule of thumb is usually used for average. So for average mods, the breakpoint is generally going to be around 75%.
1 - (((Panel offense - Offense from currently equipped gear) * 1.54+ 990 + offense from currently equipped gear) / ((Panel offense - Offense from currently equipped gear) * 1.39 + 990 + offense from currently equipped gear)) / ( 1 - (2.22 / 1.92))
is for max. For average mods, we can take those figures for offense and more or less cut them in half. so it would be
1 - (((Panel offense - Offense from currently equipped gear) * 1.34 + 495 + offense from currently equipped gear) / ((Panel offense - Offense from currently equipped gear) * 1.19 + 495 + offense from currently equipped gear)) / (1 - (2.22 / 1.92))
Let's again use Chirrut as an example: The offense will be (3073 - 185) * 1.34 + 495+ 185 = 4550. The offense set still provides 433 of this damage.
4550/ (4550 - 433) = 1.105 or a 10.5% increase in damage.
10.5 / (1 - (222/192)) * 100
10.5 / 15.6 = 0.67307692307692307692307692307692 or 67% crit, In this example I actually included more secondary offense than when I calculated the 75%, but this is still well over the 50% crit chance breakpoint that can only be reached with amazing mods. 75% is rule of thumb when comparing average sets.
Sorry to come in late on this, but looks like you found it.
I would clarify this by saying the variable z also includes all % based mod secondaries, not just primaries. So if I had a mod primary of 5.88%, and a secondary of 0.88%, z would be 0.0588+0.0088 = 0.0676.
Keep in mind that this formula is based off the new set bonus of 15%. It should allow for either 5e or 6e (or any other) values. For example, for a 5e crit damage primary and no in-game bonuses, x would be 0.36. For 6e, it would be 0.42. If you are looking at a situation where the Crit Damage Up buff is present, add 0.5 to x, etc.
When you "factored it out before comparing," that is when you compared it. For example, how did you get that the set bonus provides a 77% increase? By comparing it to the non-set portion. If you were truly comparing just the sets to each other, in your earlier example then you would've never had a cd set increase of 1.156. That's the set bonus over (ie, COMPARING TO) non-set bonus (2.22/1.92). If you were comparing to only the offense set, you would have 2.22/1.92*1.083....but that 1.083 is itself a comparison to no set bonus.
The short of it is, you are "factoring out" components that ought not to be factored out. You are comparing incomplete proportions.
Anyway, it seems from your comments that you are inexperienced with using mathematical expressions, and have some revulsion against even attempting to do so. Instead, you claim that the tools mathematicians have used for centuries to solve problems are "improper math," without explaining why. You claim that algebra is needlessly complicated, vaguely hinting that an increase in variables increases likelihood of computational error, but without pointing out where any errors might have occurred. You've "corrected" a formula of mine, not based on mathematical adjustments, but rather on the basis of some conceptual-seeming arrangement of terms during some other step. You also say things like, "You've added in extra constants which can be left out like we discussed before,"--however, as we discussed before, if those terms truly were constants, it would only affect the scale and not the relationships. When I take a proportion, it should yield the same result. You also seem to perhaps show a lack of understanding of how the depiction of a function, such as f (x) [read: "Eff of Ex"] stands in for an entire expression.
I'm trying to point out an omisssion in your set up, but you are refusing to actually have a set up. Instead you are preferring to solve components piecemeal and skip steps as it were in a process that seems to serve your intuition. But in this case, you are supposing you can lop off some chunk that is actually an important piece. I have tried to show you mathematically that you are inadvertantly splitting and combining fractions in an incorrect way by doing this. But you have no interest in looking at math.
So I think this conversation is pretty much finished. I have felt obliged to indulge in this thus far because you have been trying to make arguments that math--which people have been studying since ancient civilizations--somehow does not work. In so much as math is one of the most struggled-with disciplines, I didn't want to leave readers in a place where they didn't know what worked and what didn't.
I feel satisfied, however, that there is now enough in this thread that those who are able and willing to follow the discussion will be well-informed to come up with their own conclusions. Those who cannot follow the conversation will say, "Oh well, stick cd on high crit chance characters and offense otherwise and then just enjoy the game." And that's fine by me.
If there are other questions I will respond in the thread as necessary, but I am done trying to combat false accusations that mathematical problems should not be solved with mathematical tools.
And you are incorrect, the 1.083 is the offense WITH the offense set bonus. A 1 would be no set bonus. Go ahead and multiply the 1 back in there that I factored out and tell me how it affects the equation. I am not factoring things out wrong. You are using offense with the offense set as your base offense across the board resulting in an all around decreased value for the crit damage set.
Look at your math:
(1-1.083)/(1+1.083*1.92-1.083-2.22)
base offense(including mods) - base offense (including mods) with offense set (resulting in a negative number) / Base offense (including mods) + base offense (including mods) with an offense set * crit damage with a triangle - base offense (including mods) with an offense set - crit damage with a triangle and crit damage set.
Now you obviously meant to have one of those minuses be a * instead, but still in that instance you are multiplying your offense set included damage by your crit damage set included damage. There's no way this formula you have given me as representing yours in a similar style to mine is anything anywhere near proper math.
What it is, in my book, is evidence that you are improperly taking constants and multiplying them in in weird places resulting in incorrect comparisons.
This isn't even close to what's going on here. I'm complaining about you using abstract math when you could just put your terms in.
As I said, I'm a chemist, I do math constantly. I have an aversion to math that has put variables in where they don't need to be since they represent constants. All that is doing is making me go through extra steps to check the math by plugging in those constants.
You're adding several extra steps in doing so. I provided examples of what I was discussing using math based on concrete things in game. You provided formulas based on conceptualizations without actually doing any math. That's my problem with your attempts to "explain" to me.
I am using mathematical tools myself to show what I am talking about.
There are a number of things that must be assumed to determine which set is capable of producing the greatest damage with ideal secondaries and primaries. To that end we can assume that we have the following stats on our mods:
+30 speed, + 17% crit chance, +990 flat offense + 39% offense, +42% crit damage.
Since we can assume all these secondaries to be what they are for calculation of which is best we can safely factor all these out as soon as we determine what they represent. My equation begins by setting each one of these values as = 1 so they can easily be factored out.
Offense with set is 1.083, what is it without the set? 1
Crit damage with set is 1.156, what is it without the set? 1
Which set will crit more resulting in higher average dps? neither
I can safely factor these things out.
I ran this for an offense set parallel a cd set.
1) assume physical damage
2) add up off % bonuses and multiply by phy dmg
For off set I added 15% extra dmg
For cd set I just added all other % off bonuses
3} the result is my % offense adjusted dmg.
4} For each set I calculated the crit dmg (both with a cd triangle) for the cd set I added it's 30% bonus which I excluded from the offense set. But the offense set still uses 150% cd because even it gets the base cd.
5} For each set I calculated the non-crit dmg
6) I then averaged the crit dmg and non-crit dmg using crit chance.
7) I ran same variables using @crzydroid formula, which I then used as the cc in my formula.
8) the end result, both dmg from off set and cd set were equal, proving to me, crzydroid's formula will find the break-even cc %age.
Just added food for thought. I'm by no means an expert in math, but can get around.