Originally Posted by GeneralDirection
No offense intended, but this kind of reminds me of my college textbooks: wordy and not particularly helpful when in search of an ultimate conclusion.
Rather than going through all of the equations above, I see armor penetration is a valuable resource that is extremely hard to obtain. In fact, there are ONLY 3 items in the game which will grant it: Brutalizer/Youmuu's, Black Cleaver, and Last Whisper. As a result, most of the time runes should be assigned to armor penetration as the attack damage items ingame have a much wider variety of options.
I understand your sentiment. However, there are more sources of Apen than just items. You can compare AD runes vs Apen runes, in whatever ratio you prefer. You can also see at what point, if ever, or also how, AD and Apen can outscale each other. This also works for magic pen.
For example, Irelia tends to build only a trinity force, maybe a Frozen Mallet for damage. You can see that AD runes might actually be better for her than Apen runes, because her base attack damage never gets very high. Considering the Crystal Scar aura and masteries, her Apen runes would already be less effective.
It can also be useful in SR, where the line gets fuzzy after a few levels which rune set is better, but that dominant early game is really attractive, and I heard on a stream that a lot of top players are running AD runes on their AD carry. It might be good to know what kind of trade off you are making.
It's not a be all, game-ending equation. Why is it important for players to know that a point of armor/MR is equal to 1% your base health? It's not applicable all the time; it's not even necessary or interesting to 95% of players. But it does allow some calculations about the game, and it's mostly for furthering your understanding of how the game works,
I did mention this is only for people who enjoy math and theorycrafting
. It can be a useful tool for those people, but the rest of people will look at this and not understand a thing, or not care or see any value. I tried to highlight the main points, and I skipped completely over the derivation, so it isn't quite like a textbook, at least not one that I am used to. I like to think of it more as a cheat sheet
Hope that clears it up!
Originally Posted by Alex Dude
this is only meant to be helpful
real equation 2:
total % penetration = 1 - [(1 - % pen from source 1) * (1 - % pen from source 2) * (1 - % pen from source 3) ... etc.]
real equation 3:
effective flat penetration = actual flat penetration * (1 - total % penetration)
I'm not sure what equation 1 is measuring since the units are inconsistent, but it can't be right since it doesn't account for % armor reduction (i.e. Jarvan), flat armor reduction (i.e. Corki), % damage taken reduction, flat damage taken reduction, auto-attack damage reduction, etc (I have no idea how these stack)
Eq. 2 is fine, I just didn't include a third source because there are only one or two instances of a third source of %pen, if any, AFAIK. Although there is the crystal scar aura, so maybe I should have included the potential third source since this is Dominion board. I wanted to write it in an, elegant, concise formula, but I couldn't, so I just figured others would know to reiterate the formula for a third source.
eq 3. has been updated, had the % on the wrong way when I did that oops! Thanks for pointing that out!
The units are fine in Eq. 1. dA and A cancel, leaving units of armor in the numerator which is equal to units of armor from dX.
I highlighted X as current armor because it is meant to be after reduction has been applied, if that hadn't been clear. Essentially, flat pen's value is not dependent on reduction, so reduction of any kind has to be applied first.
% damage and flat damage reduction are extremely rare cases, but are in an interesting point. I believe they would have to be calculated in under X by being converted to an effective armor/MR, but there are only a couple champs in the game who can do this, and that only for a few seconds at a time (Alistar, Maokai ult), and they aren't targets you generally want to focus.
Auto-attack reduction (can only think of Tryndamere's Mocking Shout) is simply applied to base damage, or A in the equation.
Originally Posted by Melvear
Black Cleaver does not, in any way, negate LW or Youmuu's. Reductions and penetration goes hand in hand.
It's true that getting LW and BC isn't a great idea in terms of gold investment, but you'll still end up with more armor pierced.
Let's take targets ate 100, 200 and 300 armor as examples. With only LW, those targets drop to 60, 120 and 180 armor. With BC and LW, they drop to 39, 93 and 153. No negation there.
LW reduces BC, Youmuu's, and any other source of flat pen. % pen in general does this. See above post or eq. 3.
It could be said that % pen and flat pen don't synergize efficiently, but flat pen has better marginal value per point at lower armor/MR (I believe I could prove the general case, but it is apparent in eq. 1 vs AD), so it is a little risky to make a generalization that they don't fit well together. But for the purposes of eq. 1, an "effective flat pen" is necessary.
Hope this answers the comments satisfactorily!