Magic resistance

 Magic Resistance (or MR) is a stat that all units have, including minions, monsters, and structures. 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, and runes. Magic resistance stacks additively.

Gold Value ​​​​

• Magic resistance has a gold value of 18 per point.

Damage reduction

Note: One can include the magic penetration in all the following ideas by enumerating it with a due amount of corresponding negative MR.

Magic resistance reduces the damage of incoming magic damage 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 magic damage. Incoming magic damage is multiplied by a factor based on the unit's magic resistance (same with armor):

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

Examples:

• 25 magic resistance → × 0.8 magic damage (20% reduction).
• 100 magic resistance → × 0.5 magic damage (50% reduction).
• −25 magic resistance → × 1.2 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 healing and shielding more effective because it requires more raw damage from your enemies to remove the bonus health granted. This is called indirect scaling.

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

Self

• Amumu's Tantrum
• Braum's Stand Behind Me
• Galio's Colossal Smash and Shield of Durand
• Garen's Courage
• Leona's Eclipse
• Ornn's Living Forge and Searing Charge
• Poppy's Stubborn to a Fault
• Rammus' Defensive Ball Curl
• Sejuani's Fury of the North

Enemy

• Mordekaiser's Realm of Death
• Rell's Break the Mold
• Trundle's Subjugate

Items

• Gargoyle Stoneplate

Runes

• Aftershock
• Conditioning

Neutral buffs

• Mountainous Vigor

Increasing magic resistance

Items

Item	Cost	Amount	Availability
Abyssal Mask Abyssal Mask	2700	60	All maps
Aegis of the Legion Aegis of the Legion	1500	30	All maps
Banshee's Veil Banshee's Veil	2500	45	All maps
Force of Nature Force of Nature	2900	60	All maps
Forgefire Crest Forgefire Crest	3200	45	All maps
Frostfire Gauntlet Frostfire Gauntlet	3200	25	All maps
Gargoyle Stoneplate Gargoyle Stoneplate	3300	60	All maps
Hexdrinker Hexdrinker	1300	35	All maps
Locket of the Iron Solari Locket of the Iron Solari	2500	30	All maps
Maw of Malmortius Maw of Malmortius	3100	50	All maps
Mercurial Scimitar Mercurial Scimitar	3000	30	All maps
Mercury's Treads Mercury's Treads	1100	25	All maps
Mikael's Blessing Mikael's Blessing	2300	50	All maps
Negatron Cloak Negatron Cloak	900	50	All maps
Null-Magic Mantle Null-Magic Mantle	450	25	All maps
Quicksilver Sash Quicksilver Sash	1300	30	All maps
Reliquary of the Golden Dawn Reliquary of the Golden Dawn	2500	40	All maps
Rimeforged Grasp Rimeforged Grasp	3200	35	All maps
Silvermere Dawn Silvermere Dawn	3000	35	All maps
Spectre's Cowl Spectre's Cowl	1250	25	All maps
Spirit Visage Spirit Visage	2900	40	All maps
Sunfire Aegis Sunfire Aegis	3200	30	All maps
Turbo Chemtank Turbo Chemtank	3200	50	All maps
Turbocharged Hexperiment Turbocharged Hexperiment	3200	65	All maps
Verdant Barrier Verdant Barrier	1200	25	All maps
Wit's End Wit's End	3100	50	All maps

• Demonic Embrace
• Force of Nature
• Gargoyle Stoneplate
• Locket of the Iron Solari ( Reliquary of the Golden Dawn)
• Verdant Barrier

Champion abilities

• Anivia's Rebirth
• Braum's Stand Behind Me
• Gnar's Rage Gene
• Garen's Courage
• Dr. Mundo's Masochism
• Jax's Grandmaster's Might
• Jayce's Transform Mercury Hammer
• Kennen's Slicing Maelstrom
• Leona's Eclipse
• Mordekaiser's Realm of Death
• Nasus' Fury of the Sands
• Olaf's Ragnarok
• Orianna's Command Protect
• Ornn's Living Forge
• Poppy's Stubborn to a Fault
• Rammus' Defensive Ball Curl
• Rell's Break the Mold, Ferromancy: Mount Up and Attract and Repel
• Sejuani's Frost Armor
• Shyvana's Fury of the Dragonborn
• Singed's Insanity Potion
• Trundle's Subjugate

Runes

• Aftershock
• Conditioning
• Shield Bash
• Magic resistance rune shard

Neutral buffs

• Mountainous Vigor

Ways to reduce magic resistance

Main article: magic penetration

Note that magic penetration and magic resistance reduction are different.

List of champions' magic resistance

Main article: List of champions' magic resistance

Most melee champions, along with Graves, Ivern,  Rakan and Urgot, have a base magic resistance of either 32 − 53.25 (based on level).

Most ranged champions, Kassadin, and shapeshifting champions who can become ranged in one of their forms ( Nidalee, Jayce, Elise, Gnar), have base magic resistance of 30 − 38.5 (based on level).

There are a few exceptions:

• Akali with 37 − 58.25 (based on level)
• Cassiopeia with 32 − 40.5 (based on level)
• Garen with 32 − 44.75 (based on level)
• Kayle with 30 − 38.5 (based on level)
• Kled with 28 − 49.25 (based on level)
• Lillia with 32 − 40.5 (based on level)
• Malphite with 28 − 49.25 (based on level)
• Mega Gnar with 33.5 − 101.5 (based on level)
• Nocturne with 32 − 44.75 (based on level)
• Orianna with 26 − 34.5 (based on level)
• Pantheon with 28 − 49.25 (based on level)
• Ryze with 36 − 44.5 (based on level)
• Sylas with 32 − 61.75 (based on level)
• Talon with 39 − 60.25 (based on level)
• Wukong with 28 − 49.25 (based on level)
• Yuumi with 25 − 30.1 (based on level)

Optimal efficiency (theoretical)

Note: Effective burst health, commonly referred to just as 'effective health', describes the amount of raw burst damage a champion can receive before dying in such a short time span that he remains unaffected by any form of health restoration*. Unless champion's resists aren't reduced below zero, it will always be more than or equal to a champion's displayed health in their health bar and can be increased by buying items with extra health, armor and magic resistance. In this section, effective health will refer to the amount of raw 'magical damage' a champion can take.

In almost all circumstances, champions will have more maximum health than magic resistance, thus a single point of magic resistance will give more 'effective health' to a champion than a single point of health. However, if there is a case where max health is below the value of 'magic resistance + 100', the opposite becomes true.

Because of this relationship, theoretically, maximum effective health is attained by ensure that you have exactly 100 more max health than magic resistance, regardless of how much health or magic resistance you actually already have.

Example: Given a theoretical situation where you start off with 1 health and 1 magic resistance and are given an arbitrary sufficient number of stat points (x ≥ 100), each of which you can use to increase either your health or magic resistance by 1 point, the way to maximize your effective health is to add points to your health until your health has 100 more points than magic resistance, then split the remaining stat points in half and share them between your health and magic resistance.

However, this is only theoretically true if we consider both health and magic resistance to be equally obtainable resources with simplified mechanism of skill point investment. In reality a player buys these stats for gold instead. So when attempting to ensure the balance of 'health = magic resistance + 100', consider it through gold value distributed to the stats. Because the gold value of 1 health is roughly 7 times smaller than 1 point of magic resistance (as of V8.7), distribution per point of health or magic resistance should be 12.5% gold into health and 87.5% gold into magic resistance once the 'health = magic resistance + 100' equilibrium is reached.

This model is highly simplified and cannot be exactly applied when buying any other item that aren't purely magic resistance or health oriented as they deviate the equilibrium. Going even further, the continuous model simplifies a discrete character of real shopping, as you cannot really buy 1.125 ×  Ruby Crystals for 450, so you either opt to buy a single Ruby Crystal or a single Null-Magic Mantle, drastically unbalancing the equilibrium.

Broadly speaking, items which provide both health and magic resistance give a very high amount of effective health against magic damage compared to items which only provide health or only provide magic resistance. These items should be purchased when a player is seeking efficient ways to reduce the magic damage they take by a large amount. Furthermore, these items are among all available items the best ones to distribute their gold value equally among both health and magic resistance, thus working perfectly for rule of preserving equilibrium.

Conclusion

This information is strongly theoretical. Due to how there are many variables aside from health, magic resistance and gold value, "true equilibrium" is too complicated and unrealistic to achieve. However, a player can develop their intuition to itemize towards this equilibrium in a timely manner through the experience gained from the multitude of plays they perform.

The important thing to remember is that there is no reason to hold to the equilibrium too strictly, or else you might just lose the fun out of the game.

Trivia

• The old stat icon for magic resistance was a blue recolor of the old stat icon for armor, which seems to based on the old icon of Aegis of the Legion.
• The game internally refers to magic resistance as spellBlock.

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Last updated: July 29, 2020, patch V10.15

Without using Shyvana's Fury of the Dragonborn or Jax's Grandmaster's Might with Gathering Storm which potentially allow for infinite amounts of magic resistance, the largest amount of magic resistance is reached with a level 18 Rammus at 1464 magic resistance (which reduces magic damage by 93.607%).

• Runes:
  • Aftershock
  • Conditioning
  • Shield Bash (triggered with Locket of the Iron Solari)
  • 2 ×  Magic resistance rune shard
• Items:
  • 1 ×  Infernal Mask
  • 1 ×  Gargoyle Stoneplate
  • 4 ×  Locket of the Iron Solari
• Buffs:
  • Rammus' Defensive Ball Curl
  • Braum's Stand Behind Me
  • Orianna's Command Protect
  • 4 ×  Mountainous Vigor

• Braum:
  • Items = 100 + 80 + 60 × 4 = 420 MR
  • Runes = 150 + 9 + 10 + 8 × 2 = 185 MR
  • MR Multiplier = 1 + 0.24 + 0.05 = 1.29
    • Braum's MR = (420 + 185) × 1.29 = 780.45 bonus MR
    • Stand Behind Me's bonus = 26 + 780.45 × 0.12 = 119.654 bonus MR

• Rammus:
  • Base MR = 53.35 MR
  • Items = 100 + 80 + 60 × 4 = 420 MR
  • Runes = 150 + 9 + 10 + 8 × 2 = 185 MR
  • Buffs =  119.654 + 30 + 10 = 159.654 MR
  • MR Multiplier = 1 + 0.5 +  0.24 + 0.05 = 1.79
    • Rammus' MR = (53.35 + 420 + 185 + 159.654) × 1.79 = 1464.22716 MR

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• Prior to Patch 3.10, a level 18 Master Yi with 1 Runic Bulwark, 5 Spirit Visages, 3 points in Resistance, 3 points in Legendary Armor, Creeping Death, Bulwark, Aria of Perseverance, Command Protect, an allied Runic Bulwark aura, a full page of Scaling Magic Resist runes, and Meditate active gave a total of approximately 1004 magic resistance. Switching Mordekaiser for Trundle and having an enemy Trundle with the same setup use Subjugate on Master Yi and the allied Trundle use Subjugate on the enemy Trundle, yielded a total of approximately 1297 magic resistance. This is the highest possible amount of magic resistance, which is 92.8% reduction.
  • If Garen disconnected from the fountain and had the same setup, he will have 2108 magic resistance. This is a 95.5% reduction.
  • NOTE: This calculation does not include the Defender mastery.

Champion statistics