Crit Chance vs Crit Damage -- the MATH

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ceoofdarkness

Senior Member

12-10-2009

Edited to reflect Heat n Serve's findings concerning the efficiency of stacking crit chance and crit damage runes. He has developed the following findings concerning the break point crit chance levels for when you should use which of the different runes.

The script that he used to develop the findings is attached in his post in one of the subsequent pages.


Quote:
without I.E. (2x crit dmg)
• base < 36.5% => stack more crit chance runes
• base > 36.5% => stack more crit damage runes

with I.E. (2.5x crit dmg)
• base < 56.5% => stack more crit chance runes
• base > 56.5% => stack more crit damage runes

Meaning if your base crit chance from everything excluding runes is greater than the above thresholds, then stacking more crit chance runes will lower your dps. Having more crit damage from items beyond 2.5x will only serve to raise the point at which you reach this threshold of stacking crit chance.

These thresholds are fairly broad, meaning just slightly above or below the threshold, your dps does not differ significantly from the optimal dps.

At the break even point, it is interesting to note that in order to obtain optimal dps, you would need to make a funky combination of crit chance and crit damage runes, rather than stacking all of one or all of the other.


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Ru3y

Junior Member

12-10-2009

before reaching 100% CC, is it better to increase Attack damage or Critical chance? or both at the same time?


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FrankMcCrank

Senior Member

12-11-2009

While crit chance is definitely better early game since a full T3 page is 20% crit so you can reliably crit everything. I find that once mid game comes and you have crit items and whatnot. regardless of the extra 20% crit or not you will have crit streaks when trying to kill heroes and then the extra 50% crit damage will be really nice. From a statistical point of view the 20% crit chance will make you crit more reliably but when playing you won't feel the difference. All you see are crit streaks and how much you crit for.

In the end the difference isn't big unless you are at 100% crit. I always go for what feels the best because if it feels good you will play good.


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BORF

Senior Member

12-11-2009

Would taking armor into account change anything? I'm too tired to think through the math right now but would like to know.


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ceoofdarkness

Senior Member

12-11-2009

Quote:
Originally Posted by BORF View Post
Would taking armor into account change anything? I'm too tired to think through the math right now but would like to know.
Think of the armor an opponent has as a static reduction. No matter which build you choose, he has the same amount of damage reduction from armor. Thus no matter what you choose he reduces the total by a static amount. With this information in hand, you should choose to increase whichever stat increases your dps by the greatest marginal amount.

Quote:
before reaching 100% CC, is it better to increase Attack damage or Critical chance? or both at the same time?
You need to know the current levels of your statistics before you can answer this question. Use the same logic as in my above post to compare marginal damage.
(1-CC)+(CC*CD)>Atk(CD-1)?
Plug in the values of interest and you should receive the results of which you should increase. Remind yourself that this is on margin. If the left side is greater, it's better to stack Atk. Using just the approx values of rune levels it seems that:
(1-.2)+(.2*2.5)>25(2.5-1)?
1.3>37.5
It is far better to stack crit chance marginally before you reach the 100% cap. What I would advise you, from having played 300 games though, is that you need to use your judgment as to which stat to increase. Certain games you will be stomping the opposition and can wait to increase your stats in the most effective ways. Other times you will be having difficulty, the opponents are winning, and it may give you the best results to compromise and increase less efficient stats to try and "even" the game up.


Quote:
While crit chance is definitely better early game since a full T3 page is 20% crit so you can reliably crit everything. I find that once mid game comes and you have crit items and whatnot. regardless of the extra 20% crit or not you will have crit streaks when trying to kill heroes and then the extra 50% crit damage will be really nice. From a statistical point of view the 20% crit chance will make you crit more reliably but when playing you won't feel the difference. All you see are crit streaks and how much you crit for.

In the end the difference isn't big unless you are at 100% crit. I always go for what feels the best because if it feels good you will play good.
All I can tell you is that I definitely notice 20% crit at the start of the game. It is empowering and you crit 1 more out of 5 times. As you begin accumulating more crit chance, you will notice less and less, but in the scheme of things, you will do 20% more damage assuming you only did physical attacks. With a larger sample size, your mean number of crits will average out to the expected value of crits (aka your crit chance). If your crit chance is 20% lower, then as your sample size increases, the probability that you will crit will be 1/5 lower than if you chose the crit chance rune page. This is the central limit theorem.


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Biri Biri

Senior Member

12-11-2009

nearly 25% starting CC is far better then anything else. It will win you a lot of early ganks.


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ceoofdarkness

Senior Member

12-11-2009

Quote:
Originally Posted by Biri Biri View Post
nearly 25% starting CC is far better then anything else. It will win you a lot of early ganks.
My thoughts exactly ^_^


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Charmicarmicarmicat

Senior Member

12-11-2009

Thanks for the post and it confirms my suspicions.

Note: Crit chance seems to be especially important for tryndamere as it also allows himself to heal, and crit damage is perfect on shaco as he has a skill that guarantees a crit.


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Chutzpahnaught

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Recruiter

12-11-2009

your math is bad,

no where did you describe that crit chance has diminishing returns. I.E. for every point of crit chance you have, the successive point is less valuable. The longer a game lasts, the worse crit chance runes become.

They are amazing early game, and really start to lag mid and are useless late game.

Crit damage functions in the opposite manner, becoming stronger as the game progresses.


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ceoofdarkness

Senior Member

12-11-2009

Quote:
Originally Posted by Chutzpahnaught View Post
your math is bad,

no where did you describe that crit chance has diminishing returns. I.E. for every point of crit chance you have, the successive point is less valuable. The longer a game lasts, the worse crit chance runes become.

They are amazing early game, and really start to lag mid and are useless late game.

Crit damage functions in the opposite manner, becoming stronger as the game progresses.
I do not believe my math to be bad. I have not heard about diminishing returns on crit, I'm still relatively new. From all the posts and webpages I checked after I read your post, I have not found any on diminishing returns on crit. If you could post the source for that information, I would appreciate it. Otherwise, I will continue to assume that crit chance is not subject to diminishing returns (it says that it stacks additively on this site).

You are correct that crit chance is better early game than late game and that crit damage gets better end game. I have already said this--I have also shown that the damage that both rune pages produce is approximately equal endgame. What YOU need to realize, however, is that your damage is subject to the above marginal damage formulas. You are not Neo, you are still subject to the laws of math/statistics. Until crit chance = 100%, it is better to stack crit chance than crit damage by the above formula. The marginal formulas above are true all game long, there is no "time" variable present.


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