Magic resistance

 Magic Resistance (also Magic Resist), or MR, is one of the two damage resistance subtype stats. It reduces incoming magic damage by a percentage.

• Magic resistance stacks additively.

Every champion has a certain amount of base magic resistance that increases through growth per level. Total magic resistance refers to base plus bonus magic resistance. Bonus magic resistance can be gained from any source other than levels, for example from abilities, buffs, items, runes, and others.

Excluding the intentional outlier of Mega Gnar (whose magic resistance deviates greatly from all other champions' at 115.1), magic resistance values at level 18 range from 43.7 ( Yuumi) to 75.35 ( Sylas).

Gold Value

• Magic resistance has a gold value of 20 per point.

Magic resist formula

Magic resistance determines by how much incoming magic damage is reduced before it applies to the target's health. The incoming pre-mitigation damage is mitigated through magic resist into a reduced amount of post-mitigation damage. This post-mitigation damage equals the actual amount of health deducted from the unit. Also, magic resist reduces an amount of pre-mitigation damage by a percentage; in other words, magic resist can be interpreted as effectively increasing the  nominal health of a unit by a percentage, when receiving magic damage.

To calculate the post-mitigation damage (meaning health deduction) given an amount of incoming magic damage and the target's magic resist, the following formula is used, where:

• $\rm {R}$ is magic resist
• $d_m$ is post-mitigation damage
• $d_r$ is pre-mitigation, or "raw", magic damage

${\rm {post\ mitigation\ damage}}={\rm {magic\ damage}}\times {\begin{cases}{100 \over 100+{\rm {R}}},&{\rm {if\ {\rm {Magic\ Resist}}}}\geq 0\\2-{100 \over 100-{\rm {R}}},&{\rm {otherwise}}\end{cases}}$

Due to the order of operations for resistance penetration and reductions, negative values almost never occur. Therefore, ignoring negative magic resist values, the following simpler formula may be used:

$d_{m}={d_{r} \over 1+{{\rm {R}} \over 100}}$

Solving for raw magic damage instead gives:

$d_{r}=d_{m}\times {\Bigl (}1+{\frac {\rm {R}}{100}}{\Bigr )}$

The second formula proves that magic resistance increases nominal health by a percentage against magic damage; this is called effective health. Every 1 point of magic resist adds 1% to the effective health pool. Also see "Stacking magic resistance" section below.

Examples using 1000 health and 1000 pre-mitigation damage, for the sake of simplicity:

• 25 Magic Resistance
  • 25% effective health increase → 1000 nominal health becomes 1000 × (1 + 25 ÷ 100) = 1000 × 1.25 = 1250 total effective health against magic damage
  • 1000 raw damage ÷ (1 + 25 ÷ 100) = 1000 ÷ 1.25 = 800 post-mitigation damage → 20% total magic damage reduction
• 100 Magic Resistance
  • 100% effective health increase → 1000 nominal health becomes 1000 × (1 + 100 ÷ 100) = 1000 × 2 = 2000 total effective health against magic damage
  • 1000 raw damage ÷ (1 + 100 ÷ 100) = 1000 ÷ 2 = 500 post-mitigation damage → 50% total magic damage reduction
• 200 Magic Resistance
  • 200% effective health increase → 1000 nominal health becomes 1000 × (1 + 200 ÷ 100) = 1000 × 3 = 3000 total effective health against magic damage
  • 1000 raw damage ÷ (1 + 200 ÷ 100) = 1000 ÷ 3 = 333.3 post-mitigation damage → 66.6% total magic damage reduction

Stacking magic resistance

Following the above damage formula, each point of magic resist increases the effective health pool against magic damage by 1%, formally:

${\rm {Effective\ health}}=\left(1+{\frac {\rm {R}}{100}}\right)\times {\rm {Nominal\ health}}$

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.

By definition, magic resist does not give diminishing returns of effective health. Each additional point of magic resist increases the effective health pool (against magic damage) by 1% of your maximum health. This is not changed by any amount of magic resist already held.

If a unit's magic resist is negative due to reduction debuffs, magic resist has increasing returns with respect to itself. This is because negative magic resist cannot reduce effective health to less than 50% of actual health. A unit with -100 magic resist has 66.67% of nominal health (gains −33.33%) of its maximum health as effective health. This is an exotic case with only a select few in-game applications.

For a more detailed explanation, see this video.

Magic resistance as scaling

Effects may benefit from (scale off of) a percentage/ratio, of total magic resistance, or bonus magic resistance.

Champions

Self

• Amumu's Tantrum
• Braum's Stand Behind Me
• Galio's Colossal Smash and Shield of Durand
• Garen's Courage
• K'Sante's Dauntless Instinct, Ntofo Strikes, Path Maker, and All Out
• 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

Self

• Gustwalker Hatchling
• Jak'Sho, The Protean
• Mosstomper Seedling
• Scorchclaw Pup

Runes

Self

• Aftershock
• Conditioning

Neutral buffs

Self

• Mountainous Vigor

Increasing magic resistance

Items

This table is automatically generated based on the data from Module:ItemData/data.

Item	Cost	Amount	Availability
Abyssal Mask Abyssal Mask	2650	45	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Aegis of the Legion Aegis of the Legion	1100	25	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Banshee's Veil Banshee's Veil	3000	40	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Cloak of Starry Night Cloak of Starry Night	0	100	Arena
Cruelty Cruelty	0	30	Arena
Eleisa's Miracle Eleisa's Miracle	0	65	Arena
Force of Nature Force of Nature	2800	55	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Gargoyle Stoneplate Gargoyle Stoneplate	0	65	Arena
Hexdrinker Hexdrinker	1300	25	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Hollow Radiance Hollow Radiance	2800	40	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Jak'Sho, The Protean Jak'Sho, The Protean	3200	45	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Kaenic Rookern Kaenic Rookern	2900	80	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Lightning Rod Lightning Rod	0	30	Arena
Locket of the Iron Solari Locket of the Iron Solari	2200	25	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Maw of Malmortius Maw of Malmortius	3100	40	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Mercurial Scimitar Mercurial Scimitar	3200	40	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Mercury's Treads Mercury's Treads	1300	20	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Negatron Cloak Negatron Cloak	850	45	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Null-Magic Mantle Null-Magic Mantle	400	20	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Quicksilver Sash Quicksilver Sash	1300	30	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Radiant Virtue Radiant Virtue	0	35	Arena
Reverberation Reverberation	0	35	Arena
Spectre's Cowl Spectre's Cowl	1250	35	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Spirit Visage Spirit Visage	2700	50	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Talisman of Ascension Talisman of Ascension	0	0	Arena
The Golden Spatula The Golden Spatula	0	40	Arena
Unending Despair Unending Despair	2800	25	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Verdant Barrier Verdant Barrier	1600	25	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Vigilant Wardstone Vigilant Wardstone	2300	30	Classic Summoner's Rift 5v5
Watchful Wardstone Watchful Wardstone	1100	15	Classic Summoner's Rift 5v5
Wit's End Wit's End	2800	45	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Zeke's Convergence Zeke's Convergence	2300	25	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid

Item passives

• Force of Nature
• Hullbreaker *
• Jak'Sho, The Protean
• Terminus

Champion abilities

• Anivia's Rebirth
• Braum's Stand Behind Me
• Briar's Hematomania
• Gnar's Rage Gene
• Garen's Courage
• Gwen's Hallowed Mist
• Hecarim's Spirit of Dread
• Jax's Grandmaster-At-Arms
• 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
• Pantheon's Empowered Aegis Assault
• Poppy's Stubborn to a Fault
• Rammus' Defensive Ball Curl
• Rell's Break the Mold and Ferromancy: Mount Up
• Sejuani's Frost Armor
• Shyvana's Fury of the Dragonborn
• Singed's Insanity Potion
• Trundle's Subjugate

Runes

• Aftershock
• Conditioning
• Unflinching
• Magic resistance rune shard

Neutral buffs

• Mountainous Vigor

Reducing magic resistance

Main article: magic penetration

Magic resist can be negated by magic penetration and magic resistance reduction, treated as negative values in damage calculations. The calculation then uses the effective magic resist values after the reduction; the actual damage formulae are not changed.

Magic resist vs. Health

Note: The following information similarly applies to armor. As of season six, the base equilibrium line for magic resist is a function:

health = 6.75 × (magic resist + 100)

while the line for armor is a bit shifted up and more steep:

health = 7.5 × (armor + 100)

It can be helpful to understand the equilibrium between maximum health and magic resist, which is represented in the graph on the right. The equilibrium line represents the point at which your champion will have the highest effective health against that damage type, while the smaller lines represent the baseline progression for each kind of champion from level 1-18 without items. You can also see that for a somewhat brief period in the early game health is the most gold efficient purchase, however this assumes the enemy team will only have one type of damage. The more equal the distribution of physical damage/magic damage in the enemy team, the more effective will buying health be.

There are many other factors which can effect whether you should buy more magic resist or health, such as these key examples:

• Unlike HP, increasing magic resist also makes healing more effective because it takes more effort to remove the unit's HP than it does to restore it.
• HP helps you survive both magic damage and physical damage. Against a team with mainly burst or just low damage, HP can be more efficient than resistances.
• Percentage magic resist reduction in the enemy team tilts the optimal health:magic resist ratio slightly in the favor of HP.
• Whether or not the enemy is capable of delivering true damage or percent health damage, thus reducing the value of magic resist and health stacking respectively.
• The presence of resist or HP steroids built into your champion's kit, such as in Leona's Eclipse or Cho'Gath's Feast.
• Against sustained damage vamp and healing abilities can be considered as contributing to your maximum HP (while being mostly irrelevant against burst damage).
• The need to prioritize specific items mainly for their other qualities (regardless of whether or not they contribute towards the ideal balance between HP and resists).

List of champions' magic resistance

Main article: List of champions' magic resistance

Most melee champions, along with Graves, Ivern, and Urgot, have a base magic resistance of 32 − 66.85 (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 − 52.1 (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