### Purpose of crit.chance runes?

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imposer

Junior Member

I've studied effect of runes (but only for one champion: ashe lvl18).
This study was totaly theoretical. I assumed that average damage per second is calculated by next formula:
aSpd * dmg * (1-critChance) + aSpd * dmg * critMulti * critChance

where:
aSpd — attacks per second
dmg — damage per hit

(simpler description of formula:
chance_of_NONcrit * Damage
+
chance_of_crit * Damage * (2+(runes+items)/100)
)

I build a plot of average damage from values of BONUS critChance and BONUS critMulti.
Here is the plot

It's easy to see that critChance has very small influence on final average damage. So why do we have runes with critChance bonus?

Assumed values:
Base damage: 95
Base critChance: 13.35%
Base critMulti: 200% (2 times)
Base attack speed: 1.028

But I'm not sure if average dps is good value to consider. Any ideas?

P.S. I've also written calculator, but it has no gui and no database(Ashe and 2 items only). And have ability to control any bonuses for heroes
P.P.S. Maybe I have done mistakes somewhere BUT I'm sure that my average DPS equals average dps of leaguecraft_builder when same conditions are assumed

EDIT:
Error found. Now I see that critChance have influence

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Sythion

Senior Member

That seems real funky to me. Crit dmg runes of 40% increase damage by 500%?

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IS12082a74128c7e936074b

Senior Member

because you need extra critical chance. you may have a high damage output but you wont be able to just stand there and hit enemies for as long as you need since battles dont last that long for your graph to apply.
also for harrasing. a crit hit is way better than a normal one especially when you are late game and you have high damage output.
Also you can increase the critical damage you make which makes critical hits more usefull.

i may have gotten your post all wrong so correct me if i am off topic.

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Kersei

Senior Member

You messed up your math somewhere, 50% crit damage does not quintuple your dps..

Try this, dps = atkspd * base damage * (1 + crit chance * crit bonus).
crit chance is obviously 0-1.
crit bonus is 1 to start, can go to 1.5 from infinity edge, higher with runes/masteries etc

As you can see, the chance and bonus work together multiplicatively so it's best to get both.

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imposer

Junior Member

Quote:
Originally Posted by Kersei
You messed up your math somewhere, 50% crit damage does not quintuple your dps..
yeap... something is worng )=

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imposer

Junior Member

Oh... sorry..

I've forgotten to reset critMulti bonus every cycle(=

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Rayansaki

Senior Member

In fact, crit damage does jack **** if you don't have the crit chance to back it up. Until about 45% (5 second math) critical chance, the critical chance runes will outperform the critical damage ones. Above that value, crit damage outperforms crit chance.. I find that having a healthy balance of the 2 has the best effect on my main champion (pirate)

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TheOddOne

Recruiter

I forgot the exact number but if I recall correctly, it's around 35% or so crit chance when stacking crit damage will start becoming more useful in terms of damage.

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Kersei

Senior Member

It seems to me that in terms of runes, crit chance > crit damage for standard dps. Since the game has a snowballing effect, the early game boost from crit chance seems to be superior to the crit damage runes.

Exceptions are when characters have a built in crit chance modifier (ashe/shaco).

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Holypope

Senior Member

more correct outgoing damage formula:

base damage + ((base damage * critical chance)*(1 + critical damage bonus)) * attack speed

Example:

100 damage.
10% crit chance
10% crit damage bonus**
2 attack speed

10% crit chance with a 10% bonus to crit damage will equal 111 damage per hit, on average.
2 attack speed will cause 2 attacks to happen per second. 222 dps is the total.

**Crit bonus starts at 100%. If you add 10% via runes, that ups your crit bonus 110% bonus to damage on critical hits.

The key thing to remember is that crit chance, attack speed, and damage all become less efficient as you add more... so the fastest way to a high dps is to make sure your character is balancing them. Crit bonuses don't become more useful than crit chance until much later than most people realize, and even when they do start to become useful, it's a whilee before they pull measurably ahead of crit chance. It's usually more useful to get crit chance, but after about 60% the crit damage starts to do better.

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