Making mathematical sense of champion attributes
iloveyouall2
Member Posts: 17 ★
I tinker with my masteries all the time and one of the things that bugs me is that there is not a predictable way to optimize masteries that impact champion attributes. Specifically I am referring to crit rate, crit damage, and block proficiency. For example, my 5/50 Stark Spidey has a base crit rate of 899 with a corresponding percentage of .31. I interpret this to mean that each attack has a 31% chance to be critical. Using these numbers we should be able to calculate a max crit rate (the rate at which 100% of attacks will be critical) as 2900. (899/x=.31...x=2900) The Lesser Precision mastery adds a max amount of 125pts to your champions critical rate, so it would make sense that by adding 125 to Stark's base rate of 899, we can calculate an improved crit chance of 35%. (899+125=1024...1024/2900=.35). However, 2900 is not a common denominator, (in terms of max crit chance), for all champions. My 5/50 Morningstar has a base crit rate of 381, which, all things being equal, should equate to a crit chance of ~13%. (381/2900=.1314). Instead, she has a crit chance of 16%, and a calculated max crit chance of 2600. This makes it incredibly difficult to compare champions on an apples to apples basis, and even more difficult to predict the impact of masteries. This is important to me because mastery points are limited so it is vital to get as much value as possible out of each and every point.
When comparing Lesser Precision to Lesser Cruelty, Lesser Precision adds a maximum of 125pts to crit rating, improving crit chance by a flat (as opposed to proportionate) 4-5%. However, Lesser Cruelty adds a maximum of 150pts to crit damage, improving damage by 30-60%! Crit damage stats vary widely between champions which allows for a much bigger swing in overall damage output. In this case, you would get a much bigger bang for your mastery buck by investing in Lesser Cruelty rather than Lesser Precision, but there is no way to know this just by reading the description of these masteries!
And the variations are even more dramatic when it comes to Block Proficiency stats. My 5/50 WW2 Cap has a calculated max Block Proficiency (the rate at which blocking would reduce incoming damage to 0) of 7693. (Base stats are 5693bp = 74% reduction in damage...5693/x=.74...x=7693). By contrast, Stark Spidey has a max Block Proficiency of 4167. The Block Proficiency mastery adds 800pts to BP stats, which improves bp by anywhere from 14% to 170% depending on the champ! While in some cases it may be advantageous to have disproportionate effects on different champions, it makes it incredibly difficult and time intensive to try to strategically and predictably improve the performance of your roster through masteries.
Ultimately, my hope is that Kabam will do two things 1) create a common denominator for champion attributes so that we can more easily compare one champion to another, 2) add a percent change description to the masteries that have flat amounts so that we can strategically use our mastery points.
Finally, I am not mentioning diminishing returns as a part of any of my calculations because I don't believe they should come into account since the champion attributes and corresponding masteries are all based on flat amounts rather than percentages. If I am wrong, feel free to correct me.
When comparing Lesser Precision to Lesser Cruelty, Lesser Precision adds a maximum of 125pts to crit rating, improving crit chance by a flat (as opposed to proportionate) 4-5%. However, Lesser Cruelty adds a maximum of 150pts to crit damage, improving damage by 30-60%! Crit damage stats vary widely between champions which allows for a much bigger swing in overall damage output. In this case, you would get a much bigger bang for your mastery buck by investing in Lesser Cruelty rather than Lesser Precision, but there is no way to know this just by reading the description of these masteries!
And the variations are even more dramatic when it comes to Block Proficiency stats. My 5/50 WW2 Cap has a calculated max Block Proficiency (the rate at which blocking would reduce incoming damage to 0) of 7693. (Base stats are 5693bp = 74% reduction in damage...5693/x=.74...x=7693). By contrast, Stark Spidey has a max Block Proficiency of 4167. The Block Proficiency mastery adds 800pts to BP stats, which improves bp by anywhere from 14% to 170% depending on the champ! While in some cases it may be advantageous to have disproportionate effects on different champions, it makes it incredibly difficult and time intensive to try to strategically and predictably improve the performance of your roster through masteries.
Ultimately, my hope is that Kabam will do two things 1) create a common denominator for champion attributes so that we can more easily compare one champion to another, 2) add a percent change description to the masteries that have flat amounts so that we can strategically use our mastery points.
Finally, I am not mentioning diminishing returns as a part of any of my calculations because I don't believe they should come into account since the champion attributes and corresponding masteries are all based on flat amounts rather than percentages. If I am wrong, feel free to correct me.
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https://forums.playcontestofchampions.com/en/discussion/comment/341724#Comment_341724
Look at this thread to figure the formula for flat values to %: https://forums.playcontestofchampions.com/en/discussion/2317/challenger-rating-explained#latest
https://forums.playcontestofchampions.com/en/discussion/2317/challenger-rating-explained
edit: didn't see the post above me
I don't think you understand how diminishing returns work. First of all challenge rating is the challenge rating of the *target* not yourself. In other words, if you are *fighting* a 5/50 then CR is 100. If you are fighting a 4/55 then CR is 110. It doesn't matter what you are. CR reduces your strength based on how strong your opponent is.
If champion A has critical rating of 600 and champion B has a critical rating of 450 then when you use champion A and champion B against the same target champion A will always get a higher rate of scoring critical hits. But if you use champion A against a very high opponent and champion B against a very low opponent it is possible for champion B to end up with a higher critical rate, because how strong your opponent is affects how good you are.
When you say "600 out of a possible 2000" that isn't how the DR math works. The rating is never "out of" something. That's how percentages work, but the reason why DR was implemented was specifically because when you make a score something "out of something" then it is always possible to stack values to reach 100% - when the numerator equals the denominator. In this case, the math is a hyperbolic curve of the form X / (R + X) where no matter how high X gets the denominator is always obviously higher than the numerator and the expression can only approach 1.0 it cannot reach or exceed that.
This kind of math is extremely common in games that use diminishing returns systems. If you are only familiar with proportional math (X out of Y) and not this kind of math it can seem bizarre, but it is actually a reasonable way to implement this kind of system.
You could still make percentages work and have DR at the same time. Giving all champs a common denominator wouldn't negate the ability to decrease the potency of certain affects so that you never reach 1.
All of that being said, do you guys have a better sense for the impact and effectiveness of the mastery tree? Has anyone else used the CR variables etc to determine the pound for pound impact of masteries?
Well, not really. But I don't think we have a common mathematical foundation to discuss that.
Yes and no, mostly no. Because of how DR works, you cannot calculate what impact the masteries will have in general. In general the effect of the masteries is different for different champions because when they stack on different champions their incremental benefit changes. That's fundamental to how diminishing returns work.
Some people have calculated some approximate effects for some masteries in some conditions, with a lot of ifs. But I don't think anyone has collated that all in one place, specifically because of all the ifs.
We have a better incremental understanding of masteries that aren't directly affected by DR. Things like the suicide masteries for example, which affect things health and attack, neither of which are directly affected by DR. And Parry's block bonus on well timed attacks is a specific exception to DR, it grants a flat bonus after DR is calculated (because in 12.0.1 it was changed upon the realization that Parry couldn't function as it should inside of DR).
Is R a constant or adjusted for each champs/stat?
Pretty much from the launch of 12.0 we've known the DR formula. It is this:
Percentage = FlatStat (FlatStat + 1500 + 5 *CR) where CR is the challenge rating of the *target*. Meaning, it is what you face when you're calculating your own stats, and it is you when you are calculating the computer's stats when it attacks you.
So "R" in my example above is 1500 + 5 * CR.