Phreak Explains How Armor/Magic Penetration Work

 Earlier today RiotPhreak gave a brief recap on how penetration currently works. Since it seems like a lot of people are still a little confused on how the current calculations work, let's take a look!

Note that they may change this some time in the future, but as far as Season 4 goes, no plans as far as I know.


Penetration Summary

    Percentage based penetration always factors in before flat penetration;
    Flat reduction is calculated before Percentage reduction;
    Reduction is calculated before penetration
    "Penetration" cannot drop resist/armor below 0;
    "Reduction" can drop resist/armor below 0;
    Dropping below 0 is rare, as that means you have more reduction than they have resists not including penetration.

Magic Penetration Calculation Order

    Flat Magic Reduction (Abyssal Scepter, Fiddlesticks Passive)
    Percentage Magic Reduction (Karthus Wall of Pain)
    Percentage Magic Penetration (Void Staff, Xerath's Locus of Power)
    Flat Magic Penetration (Haunting Guise, Sorcerer's Shoes)

Armor Penetration Calculation Order

    Flat Armor Reduction (Nasus Spirit Fire)
    Armor Reduction Percentage (Black Cleaver, Jarvan's Dragon Strike)
    Armor Penetration Percentage (Last Whisper)
    Flat Armor Penetration (Brutalizer)

Here's Phreak's explanation on it, which includes some number examples:

First, % penetration works first. So if I have a Void Staff/Last Whisper, I pretend your MR/Armor is only 65% of what it really is. Then I factor in things like Brutalizer/Sorc Shoes/Haunting Guise. Those things work additively. So for example, if you had 200 MR and I had Void/Sorc/Haunting, Void reduces 200 to 130, then Sorc/Haunting reduce that 130 to 100.

So instead of dealing 1/3 damage (fighting 200 MR) you deal 1/2 damage (fighting 100 MR). Thus, the passives result in you dealing 50% more damage than before.

Note that penetration can only go so far. What I mean is that, if you have exactly 100 flat magic pen, it will only give you at most 100% bonus damage (your opponent has 100 MR). If your opponents have any more or less than 100 magic resist, you will get slightly lower returns.

Example: You have 100 MR, so I deal half damage. With 100 magic pen, I deal full damage, aka double what I would have before. If you have 200 MR, I deal 1/3 damage. I reduce that with my 100 magic pen to 100 MR, and I now deal 1/2 damage, so 50% more than before. If you have 50 MR, I deal 2/3 damage. With 100 magic pen, I deal full damage, or 50% more than before.

I hope those all made sense.
Mathematically this isn't true; they roughly equal out. If you had 80 base armor and bought Thornmail, and I bought Last Whisper, your armor went from 80 to 180, then I reduced it to 117. Obviously we each got some extra stats (damage return, 40 AD), but it's pretty easy to see that while % pen is useful, it does not completely devastate tank items.