Armor Pen vs Crit Dmg: A Quantitative Analysis
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 (100/13030) = 100% Damage 31.57% Increase in Damage (100/0.76923) Survivability Armor: 100 = (100/200) = 50% Damage Before Armor Pen w/armor pen (100/20030) = 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 (100/30030) = 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 (100/40030) = 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. 
don't forget the people who get no armor

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 
You do realize Armor Pen applies to the crits too?

Quote:
100 * 100 * (100/30030) = 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. 
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 
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. 
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.

Can you explain how the math was done wrong in this thread?
http://www.leagueoflegends.com/board...ad.php?t=70173 
Same as above actually, he uses a 2.33 crit damage multiplier, where (I assume) it should be 2 * 1.33 or 2.66 as the total damage is modified by 33% not just added to the crit multiplier percentage. I have searched and found nothing absolute from riot, but it is how I have interpreted the runes, It is extremely hard to verify this math in game. If I find out anything new I will update it.
In fact this seems to be the crux of the issue, how crit damage runes are applied, if they are applied my way, then my math stands and they are useful at a certain crit percentage, however for the sake of argument, if it is applied as additional percentage ontop of the 200% then they are ****ing useless. 100 Internets to anyone who can link a OFFICIAL answer to how crit dmg runes are applied. 
All times are GMT 8. The time now is 05:01 PM. 
(c) 2008 Riot Games Inc