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, 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

Runes

Increasing magic resistance

Items

Item	Cost	Amount	Availability
Abyssal Mask Abyssal Mask	3000	55	All maps
Adaptive Helm Adaptive Helm	2800	55	All maps
Aegis of the Legion Aegis of the Legion	1100	30	All maps
Athene's Unholy Grail Athene's Unholy Grail	2100	30	All maps
Banshee's Veil Banshee's Veil	3000	60	All maps
Chalice of Harmony Chalice of Harmony	800	30	All maps
Circlet of the Iron Solari Circlet of the Iron Solari	2200	75	All maps
Gargoyle Stoneplate Gargoyle Stoneplate	2500	40	All maps
Hexdrinker Hexdrinker	1300	35	All maps
Infernal Mask Infernal Mask	3000	100	All maps
Locket of the Iron Solari Locket of the Iron Solari	2200	60	All maps
Maw of Malmortius Maw of Malmortius	3250	50	All maps
Mercurial Scimitar Mercurial Scimitar	3400	35	All maps
Mercury's Treads Mercury's Treads	1100	25	All maps
Mikael's Crucible Mikael's Crucible	2100	40	All maps
Moonflair Spellblade Moonflair Spellblade	2400	50	Twisted Treeline
Negatron Cloak Negatron Cloak	720	40	All maps
Null-Magic Mantle Null-Magic Mantle	450	25	All maps
Quicksilver Sash Quicksilver Sash	1300	30	All maps
Spectre's Cowl Spectre's Cowl	1200	25	All maps
Spirit Visage Spirit Visage	2800	55	All maps
Wit's End Wit's End	2900	50	All maps
Zeke's Convergence Zeke's Convergence	2250	30	All maps
Zz'Rot Portal Zz'Rot Portal	2700	55	Summoner's Rift, Nexus Blitz

Champion abilities

Runes

Ways to reduce magic resistance

Note that magic penetration and magic resistance reduction are different.

List of champions' magic resistance

Most melee champions, Rakan and 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, 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:

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

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

• One of the biggest amount of magic resistance any champion other than a ​ Jax with ​ Gathering Storm, can obtain is 1752.994415 (which reduces magic damage by 94.603%), being a level 18 Sejuani.

• Base stats: 39.85 MR
• Runes:
  • Conditioning
  • Aftershock
• Items:
  • 1 Infernal Mask
  • 1 Gargoyle Stoneplate near 3 enemy champions
  • 1 Wit's End fully stacked
  • A combination of 3 of the following:
    • Banshee's Veil
    • Locket of the Iron Solari
• Buffs:
  • Sejuani's Fury of the North
  • Braum's Stand Behind Me
  • Orianna's Command Protect
• Braum's bonus MR:
  • Items = 90 + 80 + 70 + 60 × 3 = 420 MR
  • Runes = 8 + 120 = 128 MR
    • Braum's MR = 420 + 128 = 548 bonus MR
    • Stand Behind Me's bonus = 27.5 + 548 × 0.16 = 115.18 bonus MR
• Sejuani's MR:
  • Base stats: 39.85 MR
  • Items = 90 + 80 + 70 + 60 × 3 = 420 MR
  • Runes = 8 + 120 = 128 MR
  • Buffs = 115.18 + 30 = 145.18 MR
  • MR Amplification = 1 + 1.1053 +  0.1053  = 2.2105
    • Sejuani's MR = (39.85 + 420 + 128 + 145.18) × 2.2105 + 132.6316 = 1752.994415 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.