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. Currently no ranged champion gains magic resistance per level, but most melee champions do except Kassadin and Yasuo.
Elise, Gnar, Jayce, Kayle and 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
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):
$${\rm Damage\ multiplier}=\begin{cases} {100 \over 100+{\it MR}}, & {\rm if\ }{\it MR} \geq 0\\ 2  {100 \over 100  {\it MR}}, & {\rm otherwise} \end{cases}$$
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 healings and shields 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: ChampionHP > ChampionMR + 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 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 × for 450 , so with that much gold you opt to buy either a single or a single , drastically changing the equilibrium constant to 6.0.
, or (for example if our decisionmaking process would involve instead of , the above model would need to use equilibrium constant 6.84). Even considering the purchase of differentHowever, 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 decisionmaking. 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 nonlinearity 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's 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's Runic Skin grants him bonus ability power equal to 50% total MR.
 Leona's Eclipse grants additional magic resistance equal to 20 / 30 / 40 / 50 / 60 (+ 20% bonus MR) for its duration.
 Poppy's Steadfast Presence passively grants magic resistance to herself equal to 12% total MR, increased to 24% total MR while below 40% maximum HP.
 Trundle's 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 

2750  60  Common  
1500  20  Common  
2250  25  Common  
2900  20  Common  
2450  70  Common  
900  25  Common  
2400  45  Howling Abyss  
1300  35  Common  
2500  20  Summoner's Rift  
3250  40  Common  
3600  35  Common  
1100  25  Common  
2400  35  Summoner's Rift, Howling Abyss  
2500  50  Howling Abyss  
720  40  Common  
450  25  Common  
2450  50  Howling Abyss  
2200  25  Black Market Brawlers  
1300  30  Common  
1200  30  Common  
2800  55  Common  
1635  25  Black Market Brawlers  
2500  40  Common  
2700  55  Summoner'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's Rebirth allows her to enter an eggstate 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's 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's Bulwark increases an allied champion's magic resistance by 30 / 45 / 60 / 75 / 90 for 4 seconds.
 Gnar's Rage Gene increases his magic resistance by (2 × Gnar's level) when transformed into Mega Gnar.
 Garen's Courage permanently gains 0.25 bonus MR every time he kills an enemy, up to a maximum of 30.
 Graves's Quickdraw increases his magic resistance by 10 / 15 / 20 / 25 / 30 for 4 seconds stacking up to 4 times when shooting pellet, up to 40 / 60 / 80 / 100 / 120 bonus MR.
 Jax's Grandmaster's Might increases his magic resistance by 30 / 50 / 70 (+ 20% AP) for 8 seconds.
 Jayce's Transform: Mercury Hammer increases his magic resistance by 5 / 15 / 25 / 35.
 Kennen's Lightning Rush increases his magic resistance by 10 / 20 / 30 / 40 / 50 for 4 seconds.
 Leona's 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.
 Olaf's Ragnarok passively increases his magic resistance by 20 / 30 / 40. He loses the passive while his ability is active.
 Orianna's 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's Steadfast Presence increases her magic resistance by 12%, doubled to 24% while below 40% of her max. HP.
 Rammus's Defensive Ball Curl increases his magic resistance by 40 / 60 / 80 / 100 / 120 for 6 seconds.
 Rengar's 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's 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's Insanity Potion increases his magic resistance by 35 / 50 / 80 for 25 seconds.
 Trundle's 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's Stone Skin grants him 4 / 6 / 8 MR for each visible nearby enemy champion.
 Xin Zhao's Crescent Sweep increases his magic resistance by 15 / 20 / 25 for each enemy champion hit for 8 seconds.
Masteries
 bonus magic resistance and bonus armor by 1 / 2 / 3 / 4 / 5%. increases
 magic resistance and armor for each nearby enemy champion. grants 0.6 / 1.2 / 1.8 / 2.4 / 3
Runes
Name  Type  Tier 1 (Lesser)  Tier 2 (Normal)  Tier 3 (Greater) 

Magic Resist  Mark  X  X  0.77 
Seal  0.41
N/A  0.58  0.74  
Glyph  0.74
N/A  1.04  1.34  
Quintessence  2.22
N/A  3.11  4  
Magic Resist, Scaling
(Magic Resist per level)  Mark  X  X  0.07 per level (1.26) 
Seal  X  X  0.1 per level (1.8)  
Glyph  X  X  0.16 per level (2.88)  
Quintessence  X  X  0.37 per level (6.66) 
Ways to reduce magic resistance
See magic penetration. Note that magic penetration and magic resistance reduction are different.
List of champions' magic resistance
 66 champions have 30 base magic resistance from level 1 to level 18. These champions are mostly ranged champions, with the exception of Kassadin, and Yasuo.
 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 08/06/2016 on patch 6.11)
 One of the biggest amount of magic resistance any champion can obtain is 1042.53101184 (which reduces magic damage by 91.248%), being a level 18 Poppy.
 Base stats: +53.4 magic resistance
 Runes:
 9 × Scaling Marks of Magic Resistance (+9 × 1.26 magic resistance)
 9 × Scaling Seals of Magic Resistance (+9 × 1.8 magic resistance)
 9 × Scaling Glyphs of Magic Resistance (+9 × 2.88 magic resistance)
 3 × Scaling Quintessences of Magic Resistance (+3 × 6.66 magic resistance)
 Masteries:
 5 points in +5% bonus magic resistance) (
 5 points in +3 × 5 magic resistance) (
 Items:
 6 +6 × 70 magic resistance) (
 Buffs:
 Galio's Bulwark (+90 magic resistance)
 Orianna's Command: Protect (+30 magic resistance)
 +11 magic resistance) (this mastery can not stack) (
 Braum's Stand Behind Me (+110.41792 magic resistance)
 Poppy's Steadfast Presence (+24% total magic resistance)
 Relevant mathematics:
 Braum's bonus magic resistance:
 Items = 420 magic resistance =
 Runes = 1.26 × 9 + 1.8 × 9 + 2.88 × 9 + 6.66 × 3 = 73.44 magic resistance
 Mast. & buffs = 15 magic resistance =
 Bonus magic resistance amplification = = 1.05 = 5% bonus magic resistance
 Braum's bonus magic resistance = (420 + 73.44 + 15) × 1.05 = 533.862 bonus magic resistance
 Stand Behind Me's bonus = 25 + (16% bonus magic resistance)
 Stand Behind Me's bonus = 25 + 85.41792 magic resistance
 Stand Behind Me's bonus = 110.41792 magic resistance
 Poppy's magic resistance:
 Base stats: +53.4 magic resistance
 Items = 420 magic resistance =
 Runes = 1.26 × 9 + 1.8 × 9 + 2.88 × 9 + 6.66 × 3 = 73.44 magic resistance
 Mast. & buffs = 90 + 30 + + 110.41792 = 256.41792 magic resistance +
 Bonus magic resistance amplification = = 1.05 = 5% bonus magic resistance
 Magic resistance amplification = 1.24 = 1.24 = 24% magic resistance
 Poppy's magic resistance = (((420 + 73.44 + 256.41792) × 1.05) + 53.4) × 1.24 = 1042.53101184 magic resistance
 Having an enemy Trundle with the same setup use Subjugate on Poppy will yield a total of 1278.6138409728 magic resistance, which reduces magic damage by 92.746%.
 Poppy's magic resistance = 1042.53101184 magic resistance
 Subjugate's bonus = 40% of enemy's magic resistance
 Subjugate's bonus = 417.012404736
 Trundle's magic resistance:
 Base stats: +53.4 magic resistance
 Items = 420 magic resistance =
 Runes = 1.26 × 9 + 1.8 × 9 + 2.88 × 9 + 6.66 × 3 = 73.44 magic resistance
 Mast. & buffs = 90 + 30 + + 110.41792 + 417.012404736 = 673.430324736 magic resistance +
 Bonus magic resistance amplification = = 1.05 = 5% bonus magic resistance
 Trundle's magic resistance = ((420 + 73.44 + 673.430324736) × 1.05) + 53.4 = 1278.6138409728 magic resistance
 Prior to Patch 3.10, a level 18 Master Yi with 1 , 5 , 3 points in Resistance, 3 points in Legendary Armor, Creeping Death, Bulwark, Aria of Perseverance, Command: Protect, an allied 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.
Champion statistics  

Offensive  
Defensive 

Magical  
Movement 