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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, and runes. Magic resistance stacks additively.

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

Runes

Increasing magic resistance

Items

Item Cost Amount Availability
Abyssal Mask item Abyssal Mask3000 Gold55All maps
Adaptive Helm item Adaptive Helm2800 Gold55All maps
Aegis of the Legion item Aegis of the Legion1100 Gold30All maps
Athene's Unholy Grail item Athene's Unholy Grail2100 Gold30All maps
Atma's Reckoning item Atma's Reckoning2900 Gold30Nexus Blitz
Banshee's Veil item Banshee's Veil3000 Gold60All maps
Chalice of Harmony item Chalice of Harmony800 Gold30All maps
Circlet of the Iron Solari item Circlet of the Iron Solari2200 Gold75All maps
Force of Nature item Force of Nature2900 Gold90Nexus Blitz
Gargoyle Stoneplate item Gargoyle Stoneplate2500 Gold40All maps
Hexdrinker item Hexdrinker1300 Gold35All maps
Infernal Mask item Infernal Mask3000 Gold100All maps
Locket of the Iron Solari item Locket of the Iron Solari2200 Gold60All maps
Maw of Malmortius item Maw of Malmortius3250 Gold50All maps
Mercurial Scimitar item Mercurial Scimitar3400 Gold35All maps
Mercury's Treads item Mercury's Treads1100 Gold25All maps
Mikael's Crucible item Mikael's Crucible2100 Gold40All maps
Moonflair Spellblade item Moonflair Spellblade2400 Gold50Twisted Treeline
Negatron Cloak item Negatron Cloak720 Gold40All maps
Null-Magic Mantle item Null-Magic Mantle450 Gold25All maps
Quicksilver Sash item Quicksilver Sash1300 Gold30All maps
Spectre's Cowl item Spectre's Cowl1200 Gold25All maps
Spirit Visage item Spirit Visage2800 Gold55All maps
Stat-Stick of Stoicism item Stat-Stick of Stoicism7237 Gold30Nexus Blitz
Wit's End item Wit's End2900 Gold50All maps
Zeke's Convergence item Zeke's Convergence2250 Gold30All maps
Zz'Rot Portal item Zz'Rot Portal2700 Gold55Summoner's Rift, Nexus Blitz

Champion abilities

Runes

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, RakanSquare Rakan and UrgotSquare Urgot, have a base magic resistance of either 32 − 53.25 (based on level) or 32.1 − 53.35 (based on level).

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

There are a few exceptions:

  • GravesSquare Graves with 30 − 47 (based on level)
  • KayleSquare Kayle with 34 − 42.5 (based on level)
  • OriannaSquare Orianna with 26 − 34.5 (based on level)
  • PykeSquare Pyke with 32 − 57.5 (based on level)
  • SylasSquare Sylas with 36.1 − 57.35 (based on level)
  • TalonSquare Talon with 39 − 60.25 (based on level)
  • YasuoSquare Yasuo with 30 − 51.25 (based on level)
  • YuumiSquare 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 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 Crystal item Ruby Crystals for Gold 450, so you either opt to buy a single Ruby Crystal item Ruby Crystal or a single Null-Magic Mantle item 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

Last updated: March 12, 2018, patch V8.5

  • One of the biggest amount of magic resistance any champion other than a ​JaxSquare Jax with ​Gathering Storm rune Gathering Storm, can obtain is 1752.994415 (which reduces magic damage by 94.603%), being a level 18 SejuaniSquare Sejuani.
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Champion statistics
Offensive Ability power icon Ability power · Attack damage icon Attack damage · Attack speed icon Attack speed · Critical strike chance icon Critical strike chance · Critical strike damage icon Critical strike damage · Armor penetration icon Armor penetration · Magic penetration icon Magic penetration · Life steal icon Life steal · Spell vamp icon Spell vamp · Hybrid penetration icon True damage
Defensive Heal powerHybrid resistances icon Heal and shield power · Health icon Health · Health regeneration icon Health regeneration · Armor icon Armor · Magic resistance icon Magic resistance · Tenacity icon Tenacity · Slow immune icon Slow resist
Utility Cooldown reduction icon Cooldown reduction · Energy icon Energy · Energy regeneration icon Energy regeneration · Mana icon Mana · Mana regeneration icon Mana regeneration
Other Experience icon Experience · Gold icon Gold generation · Movement speed icon Movement speed · Range icon Range
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