Magic resistance

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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 or 32.1 base magic resistance. Currently no ranged champion gains magic resistance per level, but most melee champions do except  and .

, , , and do not gain magic resistance per level because they are not always melee champions due to their variable attack range.

All champions that do gain magic resistance per level gain 1.25 magic resistance per level, reaching 53.4 base magic resistance at level 18.

Damage reduction

Magic Resistance reduces the damage of incoming magical attacks by a percentage. This percentage is determined by the formula: Damage Reduction = Total Magic Resistance / (100 + Total Magic Resistance). For example, a champion with 150 points of magic resistance would receive 60% reduced damage from magical attacks. Incoming magic damage is multiplied by a factor based on the unit's magic resistance(same with armor):

$${\rm Damage\ multiplier}=\begin{cases} {100 \over 100+{\it MR}}, & {\rm if\ }{\it MR} \geq 0\\ 2 - {100 \over 100 - {\it MR}}, & {\rm otherwise} \end{cases}$$

Examples:

• 25 magic resistance → × 0.8 incoming magic damage (20% reduction).
• 100 magic resistance → × 0.5 incoming magic damage (50% reduction).
• −25 magic resistance → × 1.2 incoming magic damage (20% increase).

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 160% 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.

For a more detailed explanation, see this video.

Unlike health, increasing magic resistance makes healings and shields more effective because it requires more raw damage from your enemies to remove the bonus health granted. This is called indirect scaling.

Optimal efficiency (theoretical)

Note: 'Effective Health' describes the amount of raw damage a champion can receive before dying. It will always be more than or equal to a champion's displayed Health in their Health bar and it can be increased by buying items with extra Health, Armor and Magic Resist. In this article, Effective Health will refer to the amount of raw 'Magic Damage' a champion can take.

In almost all circumstances, champions will have a lot more Health than Magic Resistance such that the following inequality will be true: Champion-Health > (Champion-MR + 100).

If this inequality is true, a single point of MR will give more 'Effective Health' to that champion than a single point of Health.

If (Health < MR + 100), 1 point of Health will give more Effective Health than 1 of MR.

If (Health = MR + 100), 1 point of Health will give exactly the same amount of Effective Health as 1 point of MR.

Because of this relationship, theoretically, the way to get the maximum amount of Effective Health from a finite combination of Health and MR is to ensure that you have exactly 100 more Health than MR (this is true regardless of how much Health and MR you actually have).

Example: Given a theoretical situation where you start off with 0 Health and 0 MR and are given an arbitrary number of stat points (x > 100) each of which you can either use to increase your Health or MR by 1 point, the way to maximize your Effective Health is to add points to your health until your Health = (MR + 100) = (0 + 100) = 100, and then split the remaining stat points in half, spend half on your Health and half on your MR.

It's important to note that this information is purely theoretical and due to limitations from the game from champions' base stats and item stats it is incredibly difficult to acquire enough MR to satisfy the conditions given above (to the point where players shouldn't attempt to if they are trying to actually win games).

Instead, broadly speaking, items which provide both Health and MR give a very high amount of Effective Health against Magic Damage compared to items which only provide Health or only provide MR. These items should be purchased when a player is seeking efficient ways to reduce the magic damage they take by a large amount.

Magic Resistance as Scaling

These use the champion's magic resistance to increase the magnitude of the ability. It could involve total or bonus magic resistance. By building magic resistance items, you can receive more benefit and power from these abilities.

Champions

• grants magic resistance equal to 10 / 11.5 / 13 / 14.5 / 16% of his bonus magic resistance to himself and the target ally (in addition to a base amount) for 3 seconds.
• grants him bonus ability power equal to 50% of his total magic resistance.
• grants additional magic resist equal to 20 / 30 / 40 / 50 / 60 + (20% of her bonus magic resistance) for its duration.
• passively grants magic resistance to herself equal to 12% of her total magic resistance, increased to 24% of her total magic resistance while below 40% maximum health.
• takes 40% of the target's magic resistance and gains an equal amount of magic resistance. Half of this magic resistance is stolen on cast, and the next half is taken over 4 seconds. The magic resistance bonus/reduction lasts for another 4 seconds after the drain completes.

Increasing magic resistance

Items

Item Cost Amount Availability
2750 60Common
1500 20Common
2250 25Common
2900 20Common
2450 70Common
900 25Common
2700 45Twisted Treeline
2400 45Howling Abyss
1300 35Common
2500 20Summoner's Rift
3250 40Common
3600 35Summoner's Rift, Howling Abyss
1100 25Common
2300 35Summoner's Rift, Howling Abyss
2500 50Howling Abyss
720 40Common
450 25Common
2450 50Howling Abyss
2200 25Black Market Brawlers
1300 30Common
1200 30Common
2800 55Common
1635 25Black Market Brawlers
2500 40Common
2700 55Summoner's Rift

Champion abilities

Note: Only the magic resist buff effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.

• allows her to enter an egg-state for up to 6 seconds upon taking lethal damage. While in this state, she will receive a magic resistance modifier of −40 / −25 / −10 / +5 / +20.
• increases magic resistance by 15 / 17.5 / 20 / 22.5 / 25 + (10 / 11.5 / 13 / 14.5 / 16% bonus magic resistance) to himself and the target ally for 3 seconds.
• increases an allied champion's magic resistance by 30 / 45 / 60 / 75 / 90 for 4 seconds.
• increases his magic resistance by (2 × Gnar's level) when transformed into .
• permanently gains 0.25 bonus magic resistance every time he kills an enemy, up to a maximum of 30.
• increases his magic resistance by 10 / 15 / 20 / 25 / 30 for 4 seconds stacking up to 4 times when shooting pellet, up to 40 / 60 / 80 / 100 / 120 bonus magic resistance.
• increases his magic resistance by 30 / 50 / 70 + (20% AP) for 8 seconds.
• increases his magic resistance by 5 / 15 / 25 / 35.
• increases his magic resistance by 10 / 20 / 30 / 40 / 50 for 4 seconds.
• increases her magic resistance by 20 / 30 / 40 / 50 / 60 + (20% bonus magic resistance) for 3 seconds, deals damage after that time to units around her, and retains the defensive buff for an additional 3 seconds if any enemy is struck by the blast.
•  passively increases his magic resistance by 20 / 30 / 40. He loses the passive while his ability is active.
• increases an allied champion's magic resistance by 10 / 15 / 20 / 25 / 30 as long as the ball is attached to it.
• increases her magic resistance by 12% doubled to 24% while below 40% of her max. health.
• increases his magic resistance by 40 / 60 / 80 / 100 / 120 for 6 seconds.
• lets out a battle roar, damaging enemies increases his magic resist by 10 / 15 / 20 / 25 / 30 for each enemy champion or large monster hit for 4 seconds.
• passively increases her magic resistance by 5 / 10 / 15 / 20. This bonus is doubled while she is in dragon form (20 / 30 / 40).
• increases his magic resistance by 35 / 50 / 80 for 25 seconds.
• immediately steals 20% of the target's magic resistance, and a further 20% over 4 seconds. These magic resistance bonuses lasts for another 4 seconds after the drain completes.
• grants him 4 / 6 / 8 magic resistance for each visible nearby enemy champion.
• increases his magic resistance by 15 / 20 / 25 for each enemy champion hit for 8 seconds.

Masteries

• increases bonus magic resistance and bonus armor by 1 / 2 / 3 / 4 / 5%.
• grants 0.6 / 1.2 / 1.8 / 2.4 / 3 magic resistance and armor for each nearby enemy champion.

Runes

Name Type Tier 1 (Lesser) Tier 2 (Normal) Tier 3 (Greater)
Magic Resist Mark

X X 0.77

205

Seal

0.41

N/A

0.58

1

0.74

205

Glyph

0.74

N/A

1.04

1

1.34

205

Quintessence

2.22

N/A

3.11

1

4

1025

Magic Resist, Scaling

(Magic Resist per level)

Mark

X X 0.07 per level (1.26)

205

Seal

X X 0.1 per level (1.8)

410

Glyph

X X 0.16 per level (2.88)

205

Quintessence

X X 0.37 per level (6.66)

1025

Other

• Disconnecting gives approximately +1000 magic resistance after a delay.

Ways to reduce magic resistance

See magic penetration. Note that magic penetration and magic resistance reduction are different.

List of champions' magic resistance

• 63 champions have 30 base magic resistance from level 1 to level 18. These champions are mostly ranged champions, with the exception of , and .

• 65 champions start with 32.1 base magic resistance at level one, and at 53.4 base magic resistance at level 18. These champion are all melee champions, without exception.

Trivia

(Last updated 08/06/2016 on patch 6.11)

• One of the biggest amount of armor any champion can obtain is 1042.53101184 (which reduces magical damage by 91.248%), being a level 18 .
• Base stats: +53.4 magic resistance
• Runes:
• Masteries:
• 5 points in (+5% bonus magic resistance)
• 5 points in (+3 × 5 magic resistance)
• Items:
• 6 (+6 × 70 magic resistance)
• Buffs:
• (+90 magic resistance)
• (+30 magic resistance)
• (+11 magic resistance) (this mastery can not stack)
• (+110.41792 magic resistance)
• (+24% total magic resistance)
• Relevant mathematics:
• bonus magic resistance:
• Items =  = 420 magic resistance
• Runes =  +  +  +  = 73.44 magic resistance
• Mast. & Buffs =  = 15 magic resistance
• Bonus Magic Resistance Amplification =  = 1.05 = 5% bonus magic resistance
• bonus magic resistance = (420 + 73.44 + 15) × 1.05 = 533.862 bonus magic resistance
• bonus = 25 + (16% bonus magic resistance)
• bonus = 25 + 85.41792
• bonus = 110.41792
• magic resistance:
• Base stats: +53.4 magic resistance
• Items =  = 420 magic resistance
• Runes =  +  +  +  = 73.44 magic resistance
• Mast. & Buffs =  +  +  +  +  = 256.41792 magic resistance
• Bonus Magic Resistance Amplification =  = 1.05 = 5% bonus magic resistance
• Magic Resistance Amplification =  = 1.24 = 24% magic resistance
• magic resistance = (((420 + 73.44 + 256.41792) × 1.05) + 53.4) × 1.24 = 1042.53101184 magic resistance
• Having an enemy with the same setup use on will yield a total of 1278.6138409728 magic resistance, which reduces magical damage by 92.746%.
• magic resistance = 1042.53101184 magic resistance
• bonus = 40% of enemy's magic resistance
• bonus = 417.012404736
• magic resistance:
• Base stats: +53.4 magic resistance
• Items =  = 420 magic resistance
• Runes =  +  +  +  = 73.44 magic resistance
• Mast. & Buffs =  +  +  +  +  +  = 673.430324736 magic resistance
• Bonus Magic Resistance Amplification =  = 1.05 = 5% bonus magic resistance
• magic resistance = ((420 + 73.44 + 673.430324736) × 1.05) + 53.4 = 1278.6138409728 magic resistance

It is still possible to go higher through metagame functions. If a summoner disconnects from the server and is in the fountain, his/her champion will gain 1000 magic resistance. With the same setup as above, a disconnected will have approximately 2042.53101184 magic resist. cannot exceed this. This reduces magical damage by 95.333%.

• Prior to Patch 3.10, a level 18  with 1 , 5 , 3 points in , 3 points in , , , , , an allied  aura, a full page of Scaling Magic Resist runes, and  active gave a total of approximately 1004 magic resist. Switching  for  and having an enemy  with the same setup use  on  and the allied  use  on the enemy , yielded a total of approximately 1297 magic resist. This is the highest possible amount of magic resistance, which is 92.8% reduction.
• If disconnects from the fountain and has the same setup, he will have 2108 magic resist. This is a 95.5% reduction.
• NOTE: This calculation does not include the mastery.