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"The order of effects are as follows:
1. Flat Reduction
2. Percentage Reduction
3. Percentage Penetration
4. Flat Penetration
Your armor value is recalculated based on those rules if its base changes while the debuffs are present. All percentage effects stack multiplicatively.
Penetration can only bring the mitigation stat to 0, Reduction can go beyond. Negative mitigation gives you a damage amp equal to the damage reduction you would have gained if you had positive mitigation with the same magnitude.
Armor Penetration is a buff that lets a single champion do more damage to anyone with armor.
Armor Reduction is a debuff that makes a single champion take more damage from physical damage."
This means that NO, Jarvan is NOT going to take 'more damage' from only armor penetration. Building a black cleaver is still useful of course, though.
An idea maybe would to display scores on it to show proof that the build really works otherwise people like I was may be skeptical.
-Alex ( thats my real name btw)
From this guide I made my 3 quinn jungle builds all of which have the same core items of black cleaver, mercs, blade of the ruined king, and frozen mallet. This guide deserves props with my variation in the final 2 items i am 7-0 as quinn jungle averaging 9-15 kills and 1-4 deaths per game and never losing.