Originally Posted by Machinator
This is the formula I have from a while ago. It seems to be accurate compared to the tooltip anyway.
% Reduction = Armor / ( Armor + 467.5 * <Level> - 22168)
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That one's correct for targets over level 60/61. Armour reduction uses the level of the attacker to calculate reduction, and NORM := 467.5*70-22168 = 10557 is the value armour compares to.
So, %Reduction = AC / (AC+NORM), the damage taken is %Damage = NORM / (AC+NORM).
As such, the damage from an amount of PEN armour penetration is
%Damage = ( NORM / ((AC-PEN)+NORM) ) / (NORM / (AC+NORM) ) = (AC+NORM) / ((AC-PEN)+NORM).
The actual damage increase then is
%Increase = %Damage - 1 = PEN / ((AC - PEN) + NORM)
So you see that the percentage increase is higher for lower armoured targets.
1k penetration is a 5.7% increase on an 8k armour target, 6.8% increase on a 5k armour target, 7.9% increase at 3k armour and a 9.5% increase at 1k armour.
This also illustrates how Armour Penetration has increasing returns with itself.
Going from 2k AP to 2.5k AP nets the same increase as going from 1.5k AP to 2k AP,
but going from 1.5k to 2k PEN is a higher increase than going from 1k PEN to 1.5k PEN.