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### Crit Chance vs Crit Damage -- the MATH

blurrycloud

Senior Member

i would like to know, at what X% CC does CC runes break even with CD?
say include infinity edge.

thats the key question

ceoofdarkness

Senior Member

Hmmm. Why wouldn't my marginal analysis have worked according to your results? Wouldn't taking the partial derivatives and equating the marginal values give accurate results?

Heat n Serve

Senior Member

Quote:
blurrycloud:
i would like to know, at what X% CC does CC runes break even with CD?
say include infinity edge.

thats the key question

Are you blind? I just answered that question.

Quote:
Umbrage:
Unless I misunderstood Quick Sand, he basically answers that - the breakpoint is 50%.

You understood correctly, but it was me, not Quick Sand who only quoted me. Again reading is FUNdamental.

I long for the days when there is a forum staff that can close threads once questions have been answered.

pooyoo

Junior Member

hello ceoofdarkness. i dont know if you remember me, but you posted on my thread when i asked about crit chance runes vs crit damage. im not going to lie... i made a very simple excell spread sheet, and i came up with my conclusion which happens to exactly match up with your results. my first thought was to spread the word, but after reading some posts on the subject i realized no one would really listen... so i decided to just see what the community thought.

you are a very smart person and i commend you

ceoofdarkness

Senior Member

Quote:
pooyoo:
hello ceoofdarkness. i dont know if you remember me, but you posted on my thread when i asked about crit chance runes vs crit damage. im not going to lie... i made a very simple excell spread sheet, and i came up with my conclusion which happens to exactly match up with your results. my first thought was to spread the word, but after reading some posts on the subject i realized no one would really listen... so i decided to just see what the community thought.

you are a very smart person and i commend you

Thank you very much Pooyoo! I am just trying to help people to the best of my ability. The results I derived should be correct from a calculus standpoint, and I will admit to other people who posted in this thread that in college I was an economics and math major, not an engineer.

I appreciate the effort that others in this thread have put into the search for answers regarding the efficiency of crit chance versus crit damage. The reason for my post was more to stir the community and get people actually thinking rather than just guessing and hoping that they were making the right choices than to tell people what to do.

I think a lot of the problem stems from the fact that crit damage runes are twice as costly in general than crit chance runes. People who paid so much more IP for crit damage runes would most likely hate hearing they could do very similar dps with runes that cost half as much money. They want to "get their money's worth" so they believe they received something better than what they actually did.

pooyoo

Junior Member

Quote:
ceoofdarkness:
Thank you very much Pooyoo! I am just trying to help people to the best of my ability. The results I derived should be correct from a calculus standpoint, and I will admit to other people who posted in this thread that in college I was an economics and math major, not an engineer.

I appreciate the effort that others in this thread have put into the search for answers regarding the efficiency of crit chance versus crit damage. The reason for my post was more to stir the community and get people actually thinking rather than just guessing and hoping that they were making the right choices than to tell people what to do.

I think a lot of the problem stems from the fact that crit damage runes are twice as costly in general than crit chance runes. People who paid so much more IP for crit damage runes would most likely hate hearing they could do very similar dps with runes that cost half as much money. They want to "get their money's worth" so they believe they received something better than what they actually did.

well im going to school to be a chemical engineer, so i've taken some pretty advanced math classes, and i can say the math for this problem is quite simple. the early and mid game advantage from crit chance more than makes up for the slight (and very situational) late game advantage crit damage runes give... but we can use this to our advantage on the battlefield and DESTROY THE CRIT DAMAGE RUNE BUYERS!!!
so buy crit damage runes everyone they own

EnronTheGreat

Senior Member

...forgetting of course that some heroes benefit more from crit damage if they have a GUARANTEED crit move. I.E Shaco. That is all. Continue with you tyrnd.. oops er... "hypothetical hero" rune evaluation.

Heat n Serve

Senior Member

The original script I used to find the answer used some old values with runes. I re-ran my methods again and did a better job honing in on the actual break even point. The new script is attached:

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.

At the break even point, if you stack all crit chance or all crit damage, you will have minimal dps (but it's not too far off from maximal dps).

EDIT: It would appear that I got pretty much the same result as Umbrage in the posts above mine. I think it's safe to say that if two people confirm it independently of each other with different methods, then we have our answer. I encourage the OP to edit his original post to reflect these conclusions so that other people can read them. Currently your post does not contain a correct break even point and your conclusions are wrong and misleading.

SquirrelsOnFire

Member

Quote:
Chutzpahnaught:

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.
But when you consider that a full crit chance rune page allows for one less crit chance item to be purchased in order to achieve 100% crit build, the "opportunity cost" of not stacking crit damage goes away because you can purchase and entirely crit damage item, like Infinity Edge.

Shtoogie

Junior Member

Quote:
ceoofdarkness:

Atk:
dDMG/dAtk=(1-CC)+(CC*CD)
CC:
dDMG/dCC=-Atk+(Atk*CD)
Atk(CD-1)
CD:
Atk*CC
So when is it better to stack crit chance over crit damage? We can compare the marginal benefit of each stat to determine this answer.
dDMG/dCC>dDMG/dCD
Atk(CD-1)>Atk(CC)
CD-1>CC
This comparison is considered on margin. CD runes are 2.48% and CC runes are .93% (Marks). Thus is 2.0248-1>.93? 1.0248 is indeed greater than .93. CC runes are better to stack than CD runes disregarding the ease as to which CC is acquired.

Here's your problem. You start by saying that CD and CC are your OVERALL crit damage/chance but when you actually make the comparison this isn't true. Your inequality that you use to prove your result should be 2.0248>0.0093, but even that is a stupid comparison because it shows that if you have 0 crit chance and 0 crit damage to start with, you will want to increase crit chance. Duh.

I won't go into finding the answer the right way because its already been done. Props to Heat N Serve for doing maths the right way. Just thought you might want to know why your conclusion doesn't hold up.