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Crit Chance vs Crit Damage -- the MATH

 
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Kelin ?? Senior Member
12-11-2009

There is no diminishing returns.

By the way, a brief look (I actually have to study hehe) at your calculations I didn't see Infinity Edge mentioned.

Anyway, what would really help the community (and I'm at this moment too lazy to make it) is a graph with damage. It's very simple to make, we know the parameters.

Take critical chance as the standard. (0, 5, 10, 15% etc). First make a graph with just the 2 modifier, then with 2.5 (Infinity edge). Then you make a graph with 2 modifier + CD runes, and as last 2.5 modifier + CD runes.


This will show a few things:
- With critical chance runes the infinity edge will be relatively stronger.
- It will show you the point when it's worth to buy infinity edge over + crit chance
- It's easy to just count the amount of + crit chance in your build (and masteries) and see what is useful for your specific strat.

Things that it won't show but definitely matter:
As a carry the rate at which you gather items is very important. We all know that tryn needs about 4 kills to get his first important items. Higher crit chance will give you higher early damage (this will actually show) which gives you better items early on making it even easier to kill (and lvl for that matter) gather more money... snowball effect. With tryn this difference will be enormous because bloodstacks, this won't show in the graph, but it won't be too hard to make a modification for tryn.


I wrote this down with a relatively short thinkprocess so correct me if I am wrong.

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tnemlec ?? Member
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12-11-2009

Altho i am new to this game, i used to be a big theory crafter in WoW, crit chance is always good before u reach a certain threshold. But as some people say, if you dont crit , u wont see crit dmg. What good is it if u have 300% crit dmg, but your crit chance is only 10%. (probably most of u will argue u can get items easily to boost crit)

But, u cant really count how long each game lasts.... sometimes it lasts for 15 mins? sometimes an hour, and according to OP's math, crit chance will def give u an edge early and/ or mid game.

Thus.... ask yourself this, if u are fighting another champion alone, and they have already crit u 3 - 5 times in a row, leaving u to only 20-30% hp left, i think u would start considering running away.....

these crit dmg, (numbers in big red color) have a psychological effect of scaring people... :P

All in all, crit chance will always help u thru-out the game until u reach 100%, but in order to make crit dmg counts, you need to score a crit first. For me, i definitely wouldnt want to wait till late game and farm all the items to do a big crit. just my humble opinion..

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DocDemento ?? Junior Member
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12-11-2009

Question. On an ability such as Decieve which gives 100% crit chance plus extra crit damage. Would it be well worth it to push the crit damage runes when throwing in an ability like that every 9 seconds into a rotation. What's your opinion on that? When I use leaguecraft it don't take in to account the ability for the dps. I am not very sure if his hallucination can crit or not but that would also account for the crit chance's dps.

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Zine ?? Senior Member
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12-11-2009

I have been saying this for a long time, crit chance is the way to go with 2 possible exceptions.

1. Characters who have natural bonuses to crit and will therefore hit 100% very easily (Ashe, Tryn, Shaco).
2. Characters who have attacks where crit damage is calculated differently (Gangplank) and depend on spike damage.

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Max Pita ?? Master Recruiter
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12-11-2009

if u play shaco, get crit dmg is the law

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tnemlec ?? Member
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12-11-2009

Quote:
Originally Posted by Max Pita View Post
if u play shaco, get crit dmg is the law
second that

It really comes to which champ you're using after all.

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Skeptic ?? Junior Member
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12-11-2009

I suddenly feel dumb after reading the OP....Good job though.

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Tikor ?? Senior Member
12-11-2009

This analysis relies on the assumption that one's expected value of damage is the most desirable measure and thus the one the analysis of crit damage vs. crit chance should be measured by.

I say that is false.

What we really want to increase is a conditional probability - not an expected value. Specifically, the relevant measure is the probability of killing a hero given that you only have so much time to swing at him. This problem can be simplified by assuming the hero in question only has x amount of effective hitpoints, only crit damage and crit chance are variable, everything else is static and known thus keeping all the defense forumlas and other offensive stat options out of it, and allowing time to be transferred to swings via a constant attack speed.

With those simplifying assumptions you now have the question:
Does additional crit damage, crit chance or some mix maximize the probability of doing x raw damage given that I only have y swings?

I'll admit this is not an easy problem , even after the simplifying assumptions, but it is the relevant one. Do not let expected value seduce you with its ease of calculation.

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Heat n Serve ?? Senior Member
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12-11-2009

Oh gosh... when economists start trying to analyze LoL, nothing useful can ever come of this. You may as well bring in some philosophers too and we can all hold hands and sing camp songs. You didn't really do math, you did economics and made a whole lot of subjective assumptions.

Most champs that rely on high single crits like Shaco for burst damage are of course going to want crit damage.

The only point that remains up in the air is what combination of crit chance and crit damage gives you the optimal dps for a champ like Teemo or Twitch, for instance, who doesn't have any naturally high crit chance or crit damage ability as a pretense to bias his build. In a full rune page where you have the binary choice of either crit chance or crit damage, you can determine objectively by looking at all combinations of runes by brute force which will give you the optimal dps, regardless of champion attack speed or attack damage.

I have done this using a MATLAB script (attached).

The conclusions are as follows:
EDIT: Script uses out-dated values, here are the new results, click the quote to go see the revised script and discussion.

Quote:
Originally Posted by Heat n Serve View Post
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

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Quick Sand ?? Member
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12-11-2009

Quote:
Originally Posted by Heat n Serve View Post
Oh gosh... when economists start trying to analyze LoL, nothing useful can ever come of this. You may as well bring in some philosophers too and we can all hold hands and sing camp songs. You didn't really do math, you did economics and made a whole lot of subjective assumptions.

Most champs that rely on high single crits like Shaco for burst damage are of course going to want crit damage.

The only point that remains up in the air is what combination of crit chance and crit damage gives you the optimal dps for a champ like Teemo or Twitch, for instance, who doesn't have any naturally high crit chance or crit damage ability as a pretense to bias his build. In a full rune page where you have the binary choice of either crit chance or crit damage, you can determine objectively by looking at all combinations of runes by brute force which will give you the optimal dps, regardless of champion attack speed or attack damage.

I have done this using a MATLAB script (attached).

The conclusions are as follows:
without I.E. (2x crit dmg)
base < 35% => more crit chance runes
base > 35% => more crit damage runes

with I.E. (2.5x crit dmg)
base < 50% => more crit chance runes
base > 50% => 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.

Never send an economist to do an engineer's job. Goodnight.
p.s. The script doesn't do everything, b/c I'm lazy. It was pretty easy for me to import the array into Excel to sort the dps value of each rune combination. Obviously, knowledge of MATLAB is required if you want to play around with this and theory-craft some more.
That's what I'm talking about.

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