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Why No One Should Ever Buy Crit Dmg - by EnderA

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Crit damage seems great. At first I thought it would be awesome. Then I checked the math. I have not looked back since.

First of all, Crit Damage fully relies on having a chance to crit to do *anything*. That means your item build is locked-in, and your effectiveness is purely late-game. You *have to* go crit chance in order to make it effective, meaning you can't adapt to the game as it progresses.
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Second, only two champions benefit significantly from Crit Damage. Shaco can benefit because he starts at level 1 with a skill that makes him reliably Crit. Ashe's passive gives her somewhat reliable Crits as well, but is still quite conditional - realistically the passive only affects the first attack of any fight.

Third, and probably most convincing, Crit Damage is strictly worse than Armor Penetration, even on the crits.

In Marks, you're trading 17.64 Armor Penetration for 20.07% Crit Damage. In Quints, you're trading 11.73 Armor Penetration for 13.38% Crit Damage. The sum of those is: 29.37 Armor Penetration for 33.45% Crit Damage.

This is how damage is calculated on a crit:

Final Damage = Damage * Crit Damage * (100/(100 + armor - armor pen))

So let's assume the opponent has around 30 armor, perfectly normal early game. Since the amount of damage you're doing is irrelevant to the comparison, let's say it's 100 damage for the sake of simplicity:

With 33.45% Crit Damage: 100 * 2.3345 * (100/130) = 179.58 damage
With 29.37 Armor Pen: 100 * 2 * (100/100.63) = 198.75 damage

That's right, Armor Penetration did more damage on a Crit.

But, you say, people have more than 30 armor. Alright, what if they have 100 armor?

With 33.45% Crit Damage: 100 * 2.3345 * (100/200) = 116.73 damage
With 29.37 Armor Pen: 100 * 2 * (100/170.63) = 117.21 damage

That's right, Armor Penetration did more damage on a Crit. Again.

But, you say, late game people can have a ton of armor. Alright, what if they have 200 armor, and you have an infinity edge?

With 33.45% Crit Damage: 100 * 2.8345 * (100/300) = 94.48 damage
With 29.37 Armor Pen: 100 * 2.5 * (100/270.63) = 92.38 damage

That's right, Armor Penetration almost did more damage on a Crit. Late game.

Convinced yet?
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