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### Armor Pen vs Crit Dmg: A Quantitative Analysis

MeagerEvil

Junior Member

This is a mathmatical breakdown of the increase in damage that armor penetration runes confer to physical attacks, and a comparison to critical damage runes.

Armor Pen Runes
Marks: 9*1.96= 17.64
Quints: 3*3.91= 11.73
Total: 29.37

What does this mean against different armor values?

Optimal Armor: 30 = (100/130) = 76.923% Damage Before Armor Pen
w/armor pen (100/130-30) = 100% Damage
31.57% Increase in Damage (100/0.76923)

Survivability Armor: 100 = (100/200) = 50% Damage Before Armor Pen
w/armor pen (100/200-30) = 58.8823% Damage
17.76% Increase in Damage (58.8823/50)

Mixed Tank: 200 = (100/300) = 33.33R% Damage Before Armor Pen
w/armor pen (100/300-30) = 37.037% Damage
11.12% Increase in Damage (37.037/33.33)

Full Physical Tank: 300 = (100/400) = 25% Damage Before Armor Pen
w/armor pen (100/400-30) = 27.027% Damage
08.10% Increase in Damage (27.027/25)

Crit Damage Runes:
Marks:9*2.23 = 20.07
Quints:3*4.46 = 13.38
Total: 33.45%

The downside with crit damage is that although it does increase the damage on a crit more then armor pen can, you will either need a very high crit chance in order to make it effective in standing fights (Tryndamere w/ Ult), or be relying on a single super crit to lay a enemy low. (Gangplank w/ Parrrley)

Unfortunately Crit Damage is Applied as a bonus percentage ontop of the 200% crit damage, giving you 233% a 16.66% Increase in damage, making it worse then armor pen as long as the target has armor.

Temlam

Senior Member

don't forget the people who get no armor

xahhfink6

Senior Member

This is entirely wrong...

People, if you are reading this, understand that he is saying that at 30 armor, if you attacked 100 times with crit damage, and crit 94 of them, you would do more damage than if you attacked 100 times with armor pen and crit ZERO of them.

Aka, it proves that crit damage is NEVER better than Armor pen

Senior Member

You do realize Armor Pen applies to the crits too?

MeagerEvil

Junior Member

Quote:
xahhfink6:
This is entirely wrong...

People, if you are reading this, understand that he is saying that at 30 armor, if you attacked 100 times with crit damage, and crit 94 of them, you would do more damage than if you attacked 100 times with armor pen and crit ZERO of them.

Aka, it proves that crit damage is NEVER better than Armor pen

No thats not what i'm saying, assuming an attack did 100 damage, and you made 100 attacks with armor pen and ZERO crits against a target with 200 armor your would do:
100 * 100 * (100/300-30) = 3703 Damage

Making the same 100 attacks with the base 200% crit damage WITHOUT RUNES even 30% of the time
70 * 100 * (100/300) + 30 * 2 * 100 * (100/300) = 4333 Damage

Adding the crit runes brings it to:
70 * 100 * (100/300) + 30* 2.66 * 100 * (100/300) = 4993 Damage

So, with normal attacks criting with armor pen the balance point between the two is at around 33.24% Crit Chance.

And yes, Armor Pen applies to crits that is assumed in the threshold table.

topboy

Senior Member

very nice explanation.

Ps. I got a bit confuse. which is better ? armor pen or crit chance?

Question: I enjoy playing an eve and need some advice. What rune should i give her? She is currently equip with magic pen and dodges tier 3 runes. Should I replace her her dodge with either armor pen or crit chance?
thx

DreamyDays

Senior Member

So...
If you have 30% crit and 30 ArPen, under the same test condition......

(70+30*2)*100*(100/270) = 4814.

But what happens if target has 100 Armor?

ArPen 30
(70+30*2)*100*(100/170) = 7647.

CritDmg
(70+30*2.33)*100*(100/200) = 6995.

Even assuming IE passive & CritDmgMastery....

ArPen 30
(70+30*2.6)*100*(100/170) = 8706.

CritDmg
(70+30*2.93)*100*(100/200) = 7895.

I think you need to diversity your research, and check more extensively.

MeagerEvil

Junior Member

Dreamy. It was my assumption that the 33% crit damage modifier was applied seperate from the crit multiplier, making the crit multiplier 2 * 1.33 = 2.66, and my math above was wrong and it has been corrected.

Senior Member

Can you explain how the math was done wrong in this thread?