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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, masteries, and runes. Magic resistance stacks additively.

All champions begin with 30 or 32.1 base magic resistance with the exception of Ivern Ivern and Katarina Katarina. Currently no ranged champion gains magic resistance per level, but most melee champions do except Kassadin Kassadin and Yasuo Yasuo.

Elise Elise, Gnar Gnar, Jayce Jayce, Kayle Kayle and Nidalee Nidalee 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

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.

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 (even if the actual considered damage is of sustained form). Unless champion's resists aren't reduced below zero, it will always be more than or equal to a champion's displayed HP in their health bar and it can be increased by buying items with extra health, armor and magic resistance. 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 HP than MR such that the following inequality will be true: Champion-HP > 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 HP.

If (HP < MR + 100), 1 point of HP will give more effective health than 1 of MR.

If (HP = MR + 100), 1 point of HP 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 HP and MR would be to ensure that you have exactly 100 more HP than MR (this is true regardless of how much HP and MR you actually already have).

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

However, this is only theoretically true if we consider both HP and MR to be equally obtainable resources with simplified mechanism of skill point investment. In reality a player buys these stats for gold instead. As gold value of MR (derived from cost of basic magic resistance item) is currently (as of season six) 6.75 times higher than gold value of HP (derived from cost of basic health item), we theoretically can maximize effective health represented by product of 0.01 × HP × (MR + 100) with gold as input variable by satisfying the following equation: HP = 6.75 × (MR + 100). The graph and conclusions obtained by solving it are mentioned in the analogous section about armor.

Example: Given a theoretical situation where you start off with 0 HP and 0 MR and are given an arbitrary sufficient amount of gold (x ≥ 253.125), which you can either use to increase your HP or MR, the way to maximize your effective health is to buy HP until your HP = 6.75 × (MR + 100) = 6.75 × (0 + 100) = 675, and then split the remaining gold in half, spend half on your HP and half on your MR (as former is 6.75 times cheaper than the latter, it would lead to buying 6.75 times more additional HP than MR and thus naturally reaching equality in the equation above).

Now we just formulated a simple rule of preserving equilibrium (or maximum effective health):

Once equilibrium state is reached, all we need to do to preserve it is to always distribute gold equally into all involved stats for the rest of the game.

... or in our case, always 50% gold into HP and 50% gold into MR.

Again this model is highly simplified and cannot be exactly applied in cases when we are buying any other item than Null-Magic Mantle item.png basic magic resistance item, Negatron Cloak item.png Negatron Cloak or Ruby Crystal item.png basic health item (for example if our decision-making process would involve Giant&#039;s Belt item.png Giant's Belt instead of Ruby Crystal item.png Ruby Crystal, the above model would need to use equilibrium constant 6.84). Even considering the purchase of different MR or HP items with differing gold efficiencies (quite natural expectation under real circumstances) makes use of single constant utterly impossible. Going even further, the continuous model simplifies a discrete character of real shopping, as you cannot really buy 1.125 × Ruby Crystal item.png Ruby Crystals for 450 Gold, so with that much gold you opt to buy either a single Ruby Crystal item.png Ruby Crystal or a single Null-Magic Mantle item.png Null-Magic Mantle, drastically changing the equilibrium constant to 6.0.

However, thankfully to almost linear item stats' gold efficiency a player can use weakened base equilibrium condition in a form: HP ≈ 6.75 × (MR + 100) safely enough to speed up decision-making. The important thing to remember is that there is no reason to hold to it too strictly.

Note: In case of armor only the basic constant 6.75 is slightly changed to 7.5.

This information is strongly theoretical and due to game limitations from champions' base stats, innate abilities and non-linearity of gold value of item stats (gold value of stats differs for different items or is even impossible to be objectively evaluated due to interference of unique item abilities), the real equilibrium function is too complicated to be any useful.

The complexity of this problem provides space for players' intuition to develop and demonstrate their itemization skills. If given sufficient amount of time, each player could perfectly analyze situation at any given moment when he exited the shop and tell what should he buy at that moment for available gold to maximize own effective health. The sheer impossibility of doing such thing in real time creates opportunity to develop the skill. Not only that but often choosing to maximize current effective health leads to suboptimal decision branches in the future. The summary on end game screen about type of fatal damage taken is a key part of this decision process as well.

Instead, broadly speaking, items which provide both HP and MR give a very high amount of effective health against magic damage compared to items which only provide HP 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. Furthermore, these items are among all available items the best ones to distribute their gold value equally among both HP and MR, thus working perfectly for rule of preserving equilibrium.

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

  • Braum Braum's Stand Behind Me.png Stand Behind Me grants magic resistance equal to 10 / 11.5 / 13 / 14.5 / 16% bonus MR to himself and the target ally (in addition to a base amount) for 3 seconds.
  • Galio Galio's Runic Skin.png Runic Skin grants him bonus ability power equal to 50% total MR.
  • Leona Leona's Eclipse.png Eclipse grants additional magic resistance equal to 20 / 30 / 40 / 50 / 60 (+ 20% bonus MR) for its duration.
  • Poppy Poppy's Steadfast Presence.png Steadfast Presence passively grants magic resistance to herself equal to 15% total MR, increased to 30% total MR while below 40% maximum HP.
  • Trundle Trundle's Subjugate.png Subjugate 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
Abyssal Scepter item.png Abyssal Scepter2750 Gold60Common
Aegis of the Legion item.png Aegis of the Legion1100 Gold30Common
Athene&#039;s Unholy Grail item.png Athene's Unholy Grail2100 Gold25Common
Banner of Command item.png Banner of Command2200 Gold30Common
Banshee&#039;s Veil item.png Banshee's Veil2450 Gold70Common
Chalice of Harmony item.png Chalice of Harmony800 Gold25Common
Edge of Night item.png Edge of Night3100 Gold35Common
Guardian Angel item.png Guardian Angel2400 Gold45Howling Abyss
Hexdrinker item.png Hexdrinker1300 Gold35Common
Locket of the Iron Solari item.png Locket of the Iron Solari2200 Gold60Summoner's Rift
Maw of Malmortius item.png Maw of Malmortius3250 Gold45Common
Mercurial Scimitar item.png Mercurial Scimitar3600 Gold35Common
Mercury&#039;s Treads item.png Mercury's Treads1100 Gold25Common
Mikael&#039;s Crucible item.png Mikael's Crucible2100 Gold35Summoner's Rift, Howling Abyss
Moonflair Spellblade item.png Moonflair Spellblade2500 Gold50Howling Abyss
Negatron Cloak item.png Negatron Cloak720 Gold40Common
Null-Magic Mantle item.png Null-Magic Mantle450 Gold25Common
Odyn&#039;s Veil item.png Odyn's Veil2450 Gold50Howling Abyss
Quicksilver Sash item.png Quicksilver Sash1300 Gold30Common
Spectre&#039;s Cowl item.png Spectre's Cowl1200 Gold30Common
Spirit Visage item.png Spirit Visage2800 Gold55Common
Wit&#039;s End item.png Wit's End2500 Gold40Common
Zz&#039;Rot Portal item.png Zz'Rot Portal2700 Gold55Summoner's Rift

Champion abilities

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

  • Anivia Anivia's Rebirth.png Rebirth 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.
  • Braum Braum's Stand Behind Me.png Stand Behind Me increases magic resistance by 15 / 17.5 / 20 / 22.5 / 25 (+ 10 / 11.5 / 13 / 14.5 / 16% bonus MR) to himself and the target ally for 3 seconds.
  • Galio Galio's Bulwark.png Bulwark increases an allied champion's magic resistance by 30 / 45 / 60 / 75 / 90 for 4 seconds.
  • Gnar Gnar's Rage Gene.png Rage Gene increases his magic resistance by (2 × Gnar's level) when transformed into Mega Gnar Mega Gnar.
  • Garen Garen's Courage.png Courage permanently gains 0.25 bonus MR every time he kills an enemy, up to a maximum of 30.
  • Graves Graves' Quickdraw.png Quickdraw increases his magic resistance by 5 / 7.5 / 10 / 12.5 / 15 for 4 seconds, stacking up to 8 times, up to a maximum of 40 / 60 / 80 / 100 / 120 bonus MR.
  • Jax Jax's Grandmaster&#039;s Might.png Grandmaster's Might increases his magic resistance by 30 / 50 / 70 (+ 20% AP) for 8 seconds.
  • Jayce Jayce's Transform- Mercury Hammer.png Transform: Mercury Hammer increases his magic resistance by 5 / 15 / 25 / 35.
  • Kennen Kennen's Lightning Rush.png Lightning Rush increases his magic resistance by 10 / 20 / 30 / 40 / 50 for 4 seconds.
  • Leona Leona's Eclipse.png Eclipse increases her magic resistance by 20 / 30 / 40 / 50 / 60 (+ 20% bonus MR) 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.
  • Nasus Nasus' Fury of the Sands.png Fury of the Sands increases his magic resistance by 15 / 35 / 55 upon activation and an additional 1 / 2 / 3 upon activation and an additional 1 / 2 / 3 magic resistance per second for 15 seconds up to a maximum of 30 / 65 / 100 magic resistance.
  • Olaf Olaf's Ragnarok.png Ragnarok passively increases his magic resistance by 20 / 30 / 40. He loses the passive while his ability is active.
  • Orianna Orianna's Command- Protect.png Command: Protect increases an allied champion's magic resistance by 10 / 15 / 20 / 25 / 30 as long as the ball is attached to it.
  • Poppy Poppy's Steadfast Presence.png Steadfast Presence increases her magic resistance by 15%, doubled to 30% while below 40% of her max. HP.
  • Rammus Rammus' Defensive Ball Curl.png Defensive Ball Curl increases his magic resistance by 40 / 60 / 80 / 100 / 120 for 6 seconds.
  • Rengar Rengar's Battle Roar.png Battle Roar lets out a battle roar, damaging enemies increases his magic resistance by 10 / 15 / 20 / 25 / 30 for each enemy champion or large monster hit for 4 seconds.
  • Shyvana Shyvana's Dragonborn.png Dragonborn passively increases her magic resistance by 5 / 10 / 15 / 20. This bonus is doubled while she is in dragon form (20 / 30 / 40).
  • Singed Singed's Insanity Potion.png Insanity Potion increases his magic resistance by 35 / 50 / 80 for 25 seconds.
  • Trundle Trundle's Subjugate.png Subjugate immediately steals 20% of the target's magic resistance, and a further 20% over 4 seconds. These magic resistance bonuses last for another 4 seconds after the drain completes.
  • Wukong Wukong's Stone Skin.png Stone Skin grants him 4 / 6 / 8 MR for each visible nearby enemy champion.
  • Xin Zhao Xin Zhao's Crescent Sweep.png Crescent Sweep increases his magic resistance by 15 / 20 / 25 for each enemy champion hit for 8 seconds.

Masteries

  • Tough Skin mastery s4.png Fearless: Grants 10% (+ 2 - 36 (based on level) flat) bonus armor and magic resistance for 2 seconds when damaged by an enemy champion. (9 second cooldown)
  • Legendary Guardian mastery s4.png Legendary Guardian: Grants 0.6 / 1.2 / 1.8 / 2.4 / 3 bonus armor and magic resistance for each nearby enemy champion. (700 range)
  • Siege Commander mastery s2.png Siegemaster: Grants 8 armor and 8 magic resistance when near to an allied tower.
  • Unyielding mastery s4.png Unyielding: Increases bonus armor and magic resistance by 1 / 2 / 3 / 4 / 5%.

Runes

Type Tier 3 % of Highest Price
Magic Resistance
MR mark 3 Mark 0.77 57% 205 IP
MR seal 3 Seal 0.74 55% 205 IP
MR glyph 3 Glyph 1.34 100% 102 IP
MR quint 3 Quintessence 4 100% 1025 IP
Scaling Magic Resistance
Scaling MR mark 3 Mark 0.07 per level
(1.26)
42% 205 IP
Scaling MR seal 3 Seal 0.1 per level
(1.8)
60% 410 IP
Scaling MR glyph 3 Glyph 0.16 per level
(2.88)
100% 205 IP
Scaling MR quint 3 Quintessence 0.37 per level
(6.66)
74% 1025 IP

Ways to reduce magic resistance

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

List of champions' magic resistance

  • 1 champion starts with 30 base magic resistance at level one, and at 51.3 base magic resistance at level 18. This champion is Ivern Ivern.
  • 1 champion starts with 34.1 base magic resistance at level one, and at 55.4 base magic resistance at level 18. This champion is Katarina Katarina.
  • 66 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 13/11/2016 on patch 6.22)

  • One of the biggest amount of magic resistance any champion can obtain is 1092.9760608 (which reduces magic damage by 91.618%), being a level 18 Poppy Poppy.
  • Having an enemy Trundle Trundle with the same setup use Subjugate.png Subjugate on Poppy Poppy will yield a total of 1299.800761536 magic resistance, which reduces magic damage by 92.856%.
  • Poppy Poppy's magic resistance = 1092.9760608 magic resistance
    • Subjugate.png Subjugate's bonus = 0.4 × 1092.9760608 = 437.19042432 magic resistance

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