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Vayne/Kog'maw/Brand/Amumu's abilities / Madreds blood razor

Are they mitigated by magic resistance?

If so is their damage increased by things like Void Staff / Abyssal Scepter / Sorcerer's shoes?

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Magic resist mitigates magic percentile health damage, such as Kog'Maw's, Brand's and Amumu's respective abilities, and Madred's Bloodrazer/ Kitae's Razer, and their damage can be increased by Void Staff/ Sorcerer's shoes. Vayne's 3 hit of Silver bolts does true damage, which can not be mitigated by armour or Magic Resist or increased by Penetration.

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Most of the percentage health damage abilities/on-hit effects you mentioned are magic damage. Percentage health damage is not a different type of damage, it is simply a different calculation, therefore all magic resistance modifiers and penetration will affect most of the aforementioned abilities.

Vayne, on the other hand, does percentage health in true damage, which ignores resistances.

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Yes, Magic resist and Armor do mitigate the % health damage. The % health is calculated, then it is mitigated by the armor or MR and then applied. This is why you see people get MR to counter Thronmails. Thormail returns 30% of the physical damage done on you back to the attacker as magic damage, so if the attacker gets MR it will negate the thronmail damage.

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