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**kayman37**:

first off endrA may i say that i greatly respect what you're trying to accomplish here. education and utilization of rescources to help people not waste their time is very honorable.

actually what koss smith was trying to tell you is that the formula for final damage is not 100/(100+armor)*crit damage*base damage (which for our purposes you used 100 base damage which we'll keep because it's easy) it is total armor/(100+ total armor)*crit damage*base damage as stated in the champion statistics (http://www.leagueoflegends.com/learn/champion_statistics). I can' t seem to find a patch where they say that they converted it to your formula, if you can find it can you please link it?

so under the "correct" formula:

with 33.45% Crit Damage: 100 * 2.3345 * (100/200) = 116.725 damage

With 29.37 Armor Pen: 100 * 2 * (70.63/170.63) = 82.7873 damage

so crit damage is 29% beter on a crit... so you still need a high crit rate to make it plausible, but either are still decent runes to go with, depending on your char. (sure makes the crit damage rune nerf in v1.0.0.74 (http://www.leagueoflegends.com/board/showthread.php?t=58247) make a lot more sense..

edit: added the "correct" formula so peeps dont have to goto the page and look it up

The formula you found is damage *reduction*, not final damage modifier. So for example, if you have 0 armor, you'd reduce the damage by 0.

While armor penetration is very alluring, there is one item that makes all the mathematics go a bit awry. That item is last whisper. The reason why this item screws with the math is because it has a percentage armor penetration rather than a set number of armor penetrated, which means that it's effectiveness is increased if you do not have armor penetration runes by the order that armor reduction is applied (percentages come last). The combination of critical damage and last whisper is very potent indeed.

The correct formula for total damage is actually:

Total damage = Attack * Crit damage - Attack * Crit damage * armor/(100 + armor)

Which simplifies to:

Total damage = Attack * Crit damage * (1 - Armor / 100 + armor)

= Attack * Crit damage * ( (100 + armor - armor)/(100 + armor) )

= Attack * Crit damage * 100/(100 + armor)

Which we can see is the formula ender gave....except.....one thing about armor penetration - I am not quite so sure that it modifies as a direct negative from armor in the way that is listed. I don't see any help files relating to the way armor penetration effects, but it seems to me that armor reduction effects would not be the same as armor penetration effects, which would be the case by the equations used in this thread.

My guess, without proof, would be armor penetration value is the maximum number of damage that is delt without any armor reduction. So for example, someone with 100 damage with 20 armor penetration attacking a player with 100 armor would deal 60 damage instead of 50 if that armor penetration were 0. This would make it a distinct statistic from armor reduction.