Magic resistance

Magic resistance (or MR) is a stat that all units have, including minions, monsters, and buildings. Increasing magic resistance reduces the magic damage the unit takes. Each champion begins with some magic resistance which may increase with level. You can gain additional magic resistance from abilities, items, masteries, and runes. Magic resistance stacks additively.

All champions begin with 30 base magic resistance. No ranged champions save gain magic resistance per level, but many melee champions do, with 52.5 being the maximum magic resistance possible without items, runes, masteries, or ally buffs.

Damage reduction
Incoming magic damage is multiplied by a factor based on the unit's magic resistance:

$$\pagecolor{Black}\color{White} \text{Damage multiplier} = \begin{cases} \frac{100}{100 + MR} & \text{if MR} \ge 0\\ 2 - \frac{100}{100 - MR} & \text{if MR} \le 0 \end{cases} $$

Examples:
 * 25 magic resistance &rarr; &times;0.8 incoming magic damage (20% reduction).
 * 100 magic resistance &rarr; &times;0.5 incoming magic damage (50% reduction).
 * &minus;25 magic resistance &rarr; &times;1.2 incoming magic damage (20% increase) (This mechanic is outdated. Negative magic resistance does not amplify damage).

Stacking magic resistance
Every point of magic resistance requires a unit to take 1% more of its maximum health in magic damage to be killed. This is called "effective health."
 * Example: A unit with 60 magic resistance has 60% of its maximum health in its effective health, so if the unit has 1000 maximum health, it will take 1600 magic damage to kill it.

What this means: by definition, magic resistance does not have diminishing returns, because each point increases the unit's effective health against magic damage by 1% of its current actual health value whether the unit has 10 magic resistance or 1000 magic resistance.
 * Note: Unlike health, increasing magic resistance also makes healing more effective because it takes more effort to remove the unit's health than it does to restore it.

Champion abilities

 * lays down a cover of smoke for 8 seconds where she gains magic resistance while inside.
 * increases her magic resistance by for 8 seconds.
 * increases an allied champion's magic resistance by for 4 seconds.
 * increases his magic resistance by 0.5 per kill with a maximum of 25.
 * increases his magic resistance by every second he remains in combat. This bonus stacks up to 10 times. Graves is considered in combat if he has dealt or received damage in the last 3 seconds.
 * increases his magic resistance by  for 8 seconds.
 * increases his magic resistance by for 4 seconds.
 * increases her magic resistance by for 3 seconds. The duration of the buff is doubled if any enemies are damaged by the ability.
 * increases his magic resistance by for up to 5 seconds.
 * increases an allied unit's magic resistance by for 6 seconds.
 * grants her magic resistance while in cougar form.
 * increases his magic resistance by for 6 seconds.
 * increases an allied champion's magic resistance by as long as the ball is attached to it.
 * increases his magic resistance by for 6 seconds.
 * passively increases her magic resistance by . This bonus is doubled while she is in dragon form.
 * increases his magic resistance by for 25 seconds.
 * Aura: increases nearby allied champions' magic resistance by while active and persists for two seconds after deactivation.
 * Activation: increases hers and one nearby allied champion's magic resistance by an extra for 3 seconds.
 * increases nearby allied champions' magic resistance by 16.
 * increases his magic resistance by of the target enemy's magic resistance, and doubles the amount over the next 6 seconds.
 * increases his magic resistance by for 4 seconds.
 * grants him magic resistance for each nearby enemy champion.
 * increases his magic resistance by 25 (+ for each enemy champion hit) for 8 seconds.
 * increases his magic resistance by 25 (+ for each enemy champion hit) for 8 seconds.

Masteries

 * increases your champion's magic resistance by.

Runes

 * and runes may also increase magic resistance.

Ways to reduce magic resistance
See magic penetration. Note that magic penetration and magic resistance reduction are different.