Magic Resistance

Magic resistance is an attribute of heroes, similar to armor. Instead of reducing physical damage, it reduces magical damage. All heroes, except Meepo and Visage, possess 25% magic resistance from their armor type. This percentage is completely independent of their amount of armor. Certain Hero summons, such as Enigma's Eidolons, also possess intrinsic magic resistance.

Magical damage
Magical damage is a special damage type caused mostly by abilities. Unlike physical damage, it is not affected by armor. However, it is affected by magic resistance dealing more or less damage, depending on the unit's current magic resistance. Besides magic resistance, magical damage, just like physical and pure damage, is also affected by damage manipulation.

Mechanics
All Heroes have a basic 25% magic resistance, except for Meepo and his clones, who have 35% and Visage, who has 10%. This means that, by default, for most heroes, all magical damage is reduced by 25%, or only 75% of the ability's damage is dealt. Most non-hero units have a 0% base magic resistance.

Stacking
There are multiple abilities and items which can increase a unit's magic resistance. These bonuses stack diminishingly, means the higher a unit's magic resistance currently is, the lower the effects of another bonus will be, making it impossible to reach 100% magic resistance. It is also possible to reduce a unit's magic resistance with the help of several abilities. These reductions also stack diminishingly, means the higher a unit's magic resistance is, the less effective magic resistance reductions will get.

Example: The following table shows the diminishing effectiveness of multiple on a hero with 25% base magic resistance. As seen in the table, when acquiring 6 hoods, the 6th hood only effectively grants about 3.7% magic resistance, making it about 6 times less effective than the first acquired hood.

Formula for magical damage after magic resistance reductions/amplifications:
 * Actual damage = magical damage × (1 − natural resistance) × (1 − first resistance bonus) × (1 − second resistance bonus) × (1 + first resistance reduction) × (1 + second resistance reduction)

Formula for total magic resistance of a unit (multiply the result by 100 to get the percentage value):
 * Total magic resistance = 1 − (1 − natural resistance) × (1 − first resistance bonus) × (1 − second resistance bonus) × (1 + first resistance reduction) × (1 + second resistance reduction)

100% magic resistance
As one can conclude from the stacking rules above, it is not possible to reach 100% magic resistance. However, there are several abilities which grant 100% magic resistance. Because of the stacking rules, this abilities prevent a unit's magic resistance to be reduced, as the formula will always result in 100%, no matter how big the magic resistance reduction.

Formula example with one magic resistance source being a 100% bonus:
 *  magical damage × (1 − natural resistance) × (1 − 1) × (1 + first resistance reduction) × (1 + second resistance reduction) = 0 total magical damage


 *  (1 − (1 − natural resistance) × (1 − 1) × (1 + first resistance reduction) × (1 + second resistance reduction)) × 100 = 100% magic resistance

Sources of Magic Resistance Bonus

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Sources of Magic Resistance Reduction

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Sources of 100% magic resistance
These abilities grant 100% magic resistance to the affected units, reducing every magical damage they take to 0, and ceasing the effects of magic resistance reductions.


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Magical damage barrier
A magical damage barrier absorbs a set amount of magical damage. It absorbs the damage before it is reduced by magic resistance, unless the resistance is provided by spell immunity.

This means that when for example a hero with a 25% magic resistance and a 300 health damage barrier gets hit by 400 magical damage, the shield will absorb 300 of that. The exceeding 100 are not absorbed and are now reduced by the 25% magic resistance down to 75. So in this scenario, the hero takes 75 damage. This means a barrier is more effective the lower a unit's magic resistance is, similar to how damage block is more effective, the lower the armor is.

Sources of magic damage barriers

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