"Woodroward;c-1625014" wrote:
See it's like I figured out that the offense set gives an 8.3% increase in offense. So my representation for the offense set is 8.3% Sure I could figure out what he hits for on a crit, how often he crits and what he hits for on a non-crit.
To simplify let's say someone hits for 10k before set bonus is considered. With the offense set, they would hit for 10,830. On a crit they would hit for 19,200 without the offense set and 20793 with it. I can calculate the average damage by using crit chance. let's say 40% so, ((20793 * .4) + (10830 * .6)) - ((19,200 * .4) + (10000 * .6)) = 1135.2 The average damage increase for the offense set would be 1135.2. Now let's see what % of the non offense set damage that is. (19,200 * .4) + (10000 * .6) = 13680.
1135.2 / 13680 = 0.082976... 8.3%. It worked out the same with or without going through all that extra math (not counting a slight variation due to rounding). So the % damage increase is the same regardless of crit chance. This means that we don't have to differentiate between crits and non crits for the offense set since we cover both by using % instead of flat damage.
"Instead, the final step of your calculation essentially takes
(x *(1-c))/(1.083x*(1-c)) + (2.22*c*x)/(1.92*1.083x*c). This is, as you put it, improper math."
No. no this is not an accurate representation of my formula at any point. You are sticking factors into my equation that were already factored out before it hit the paper, like crit chance. It's irrelevant. It is only skewing your results to include it. It is to avoid skewing of results that I made sure to factor it out as early as possible.
The ONLY step of my formula (that's what's great about it, it's only an ongoing calculation that can be solved linearly, not an equality/inequality that requires many many steps) is the one I have shown. It doesn't have multiple steps. It doesn't require doing things in "chunks" as you call it. It is linear, it is quick, it is streamlined, and it is 100% accurate.
This is my formula, what you have shown is avidly not
(1 - (Physical damage listed in panel / physical damage - offense set physical damage) * 100) / (1 - (222/192) * 100)
I don't know if I can explain to you any clearer that you are the one making the mistake that I was making when I first addressed you in this thread... skewing the results by improperly including constants that should be factored out.
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.