Magic resistance

“

▶️ Thy magic harms me not. — Anti-Mage

”

Magic resistance is a stat that reduces (or increases, if negative) magical damage a unit takes from spells and attacks. Every unit is capable of gaining or losing magic resistance, and most units start with a small amount of base resistance. A hero's magic resistance can be passively increased with talents, certain items, and some abilities. Magic resistance of any unit can also be temporarily increased or reduced with some abilities.

Base magic resistance

Base magic resistance is a value that never changes throughout a game. It consists of one fixed value set for each unit individually. The base magic resistance of a unit can be a negative number.

Heroes

Heroes

Magic resistance

Abaddon, Alchemist, Ancient Apparition, Anti-Mage, Arc Warden, Axe, Bane, Batrider, Beastmaster, Bloodseeker, Bounty Hunter, Brewmaster, Bristleback, Broodmother, Centaur Warrunner, Chaos Knight, Chen, Clinkz, Clockwerk, Crystal Maiden, Dark Seer, Dark Willow, Dazzle, Death Prophet, Disruptor, Doom, Dragon Knight, Drow Ranger, Earth Spirit, Earthshaker, Elder Titan, Ember Spirit, Enchantress, Enigma, Faceless Void, Grimstroke, Gyrocopter, Hoodwink, Huskar, Invoker, Io, Jakiro, Juggernaut, Keeper of the Light, Kunkka, Legion Commander, Leshrac, Lich, Lifestealer, Lina, Lion, Lone Druid, Luna, Lycan, Magnus, Mars, Medusa, Meepo, Mirana, Monkey King, Morphling, Naga Siren, Nature's Prophet, Necrophos, Night Stalker, Nyx Assassin, Ogre Magi, Omniknight, Oracle, Outworld Destroyer, Pangolier, Phantom Assassin, Phantom Lancer, Phoenix, Puck, Pudge, Pugna, Queen of Pain, Razor, Riki, Rubick, Sand King, Shadow Demon, Shadow Fiend, Shadow Shaman, Silencer, Skywrath Mage, Slardar, Slark, Snapfire, Sniper, Spectre, Spirit Breaker, Storm Spirit, Sven, Techies, Templar Assassin, Terrorblade, Tidehunter, Timbersaw, Tinker, Tiny, Treant Protector, Troll Warlord, Tusk, Underlord, Undying, Ursa, Vengeful Spirit, Venomancer, Viper, Visage, Void Spirit, Warlock, Weaver, Windranger, Winter Wyvern, Witch Doctor, Wraith King, Zeus

0.25

Creeps

Units	Magic resistance
Alpha Wolf, Ancient Black Drake, Centaur Conqueror, Centaur Courser, Dark Troll Summoner, Fell Spirit, Ghost, Giant Wolf, Harpy Scout, Harpy Stormcrafter, Hellbear, Hellbear Smasher, Hill Troll, Hill Troll Berserker, Hill Troll Priest, Kobold, Kobold Foreman, Kobold Soldier, Mega Melee Creep, Mega Ranged Creep, Melee Creep, Ogre Bruiser, Ogre Frostmage, Ranged Creep, Satyr Banisher, Satyr Mindstealer, Satyr Tormenter, Super Melee Creep, Super Ranged Creep, Vhoul Assassin, Wildwing, Wildwing Ripper	0%
Ancient Black Dragon, Ancient Granite Golem, Ancient Rock Golem, Ancient Rumblehide, Ancient Thunderhide, Mud Golem, Shard Golem	50%
Roshan	55%
Siege Creep, Super Siege Creep	80%

Summons

Summons	Magic resistance
Astral Spirit, Boar, Earth, Fire, Forged Spirit, Greater Treant, Hawk, Skeleton Warrior, Spirit Bear, Treant	0%
Void	20%
Spiderite, Spiderling, Storm	25%
Undying Zombie, Warlock Golem	33%
Familiar	35%
Necronomicon Archer, Necronomicon Warrior	40%
Eidolon, Wraith King Skeleton	50%
Lycan Lane Wolf, Lycan Wolf	70%

Base magic resistance negation

Natural Order interacts with magic resistance differently. Instead of stacking manipulatively with other sources of magic resistance, it acts as a multiplier for the base magic resistance.

Natural Order is currently the only source of base magic resistance negation and it is defined as

${\text{ActualBaseMagicResistance}}=BaseMagicResistance\times (1-BaseMagicResistanceReduction)$

This means, for heroes with 25% base magic resistance, it reduces magic resistance by 10%/15%/20%/25%, down to 15%/10%/5%/0%.

Base Magic Resistance Negation

• Elder Titan - Natural Order
  
  Base magic resistance negation: 40%/60%/80%/100%
  Aura, affects enemies within range of the Astral Spirit. The reduction is based on the enemies' base magic resistance. The debuff lingers for 1 second.

Stacking

All sources of magic resistance stack multiplicatively. This means a unit's magic resistance value changes less the higher its magic resistance is, and more the lower it is. This prevents a unit from reaching 100% magic resistance by stacking different sources up.

There are several abilities that sets a unit's magic resistance to 100%. E.g. Fate's Edict

Magic resistance multiplier is defined as

$\sum _{MagicResistanceMultiplier}=(1-x)\times \displaystyle \prod _{i=1}^{n}(1-a_{i})\times \displaystyle \prod _{i=1}^{n}(1+r_{i})$

With x being the index of base magic resistance, a being the index of magic resistance sources and r being the index magic resistance reduction sources.

$\sum _{MagicResistanceMultiplier}=(1-BaseMagicResistance)\times (1-Resistance_{1})\times (1-Resistance_{2})\times \dots \times (1+Reduction_{1})\times (1+Reduction_{2})\times \dots$

To get the total magic resistance percentage

${\text{MagicResistance}}=(1-MagicResistanceMultiplier)*100\%$

Actual magic damage dealt after magic resistance is defined as

${\text{ActualMagicDamageDealt}}=(MagicDamage-MagicDamageBarrier)\times MagicResistanceMultiplier$

Magic damage barrier absorbs a set amount of magic damage before it is reduced by magic resistance.

Example 1

Anti-Mage have Level 4 Counterspell and a Cloak. What is his current magic resistance?

Base hero magic resistance: 0.25

Bonus magic resistance: Counterspell: 0.45, Cloak: 0.15

Magic resistance reduction: 0 (None)

$\sum _{MagicResistance}=1-{\Big (}(1-0.25)\times (1-0.45)\times (1-0.15)\times (1+0){\Big )}=64.94\%$

Anti-Mage's current magic resistance in this example is 64.94%.

Example 2

Visage is at max level under the effect of a Level 4 Ancient Seal and a Level 4 Decrepify. What is his current magic resistance?

Base hero magic resistance: 0.25

Bonus magic resistance: 0 (None)

Magic resistance reduction: Ancient Seal: 0.45, Decrepify: 0.6

$\sum _{MagicResistance}=1-{\Big (}(1-0.25)\times (1+0)\times (1+0.45)\times (1+0.6){\Big )}=-74\%$

Visage's current magic resistance in this example is -74%.

Effective HP

The extra damage a unit can take due to magic resistance is known as its extra effective HP (or EHP) for magical damage. Despite each source of magic resistance increasing the magic resistance value less the higher it is and making them seem less effective, each sources increases the unit's effective HP against magical damage by their base value.

A unit with 0% magic resistance has 100% effective HP against magical damage, means magical damage equaling 100% of its health is required to kill it. Most heroes have 0.25 magic resistance by default, making their effective HP against magical damage 133.33%.

Magic resistance	-100%	-75%	-50%	-25%	-10%	0%	10%	25%	50%	75%	100%
Effective HP	500	571	667	800	909	1000	1111	1333	2000	4000	∞

This definition of EHP assumes all damage taken is magical. EHP against physical damage (such as basic hero attacks etc.) is modified by armor.

Effective HP against magical damage is defined as

${\text{EHP}}=\displaystyle {\frac {TotalHealth}{1-MagicResistance\%}}$

Instead of diminishing in effectiveness, multiple sources of resistance are actually more effective stacked than they are individually. Two sources of 25% resistance stacked provides 78% extra EHP whereas one source provides 33%.

Example 1

Anti-Mage at max level has 1400 health with Level 4 Counterspell and a Cloak, how much EHP against magical damage he has?

According to the previous example in magic resistance stacking above, Anti-Mage with Level 4 Counterspell and a Cloak has a magic resistance of 64.94% (or 0.6494).

Base magic resistance: 0.25

Bonus magic resistance: Counterspell: 0.45, Cloak: 0.15

${\text{EHP}}=\displaystyle {\frac {1400}{(1-0.6494)}}=3992.87$

Anti-Mage has 3992.87 EHP against magical damage in this example.

Example 2

Visage has 2260 health at max level. While under the effect of a Level 4 Ancient Seal and Level 4 Decrepify, how much EHP against magical damage he has?

According to the previous example in magic resistance stacking above, Visage who is affected by those two abilities will have a magic resistance of -74% (or -0.74).

Base hero magic resistance: 0.25

Bonus magic resistance: 0 (None)

Magic resistance reduction: Ancient Seal: 0.45, Decrepify: 0.6

${\text{EHP}}=\displaystyle {\frac {2260}{(1--0.74)}}=1298.85$

Visage has 1298.85 EHP against magical damage in this example.

Modifying magic resistance

Several abilites and items have abilities that grant or reduce magic resistance.

Magic resistance increasing abilities

The following abilities increase magic resistance:

Magic resistance increasing abilities

• Anti-Mage - Counterspell
  
  Magic resistance bonus: 15%/25%/35%/45% ( 35%/45%/55%/65%)
  Passive.
• Centaur Courser - Cloak Aura
  
  Hero magic resistance bonus: 10%
  Non-hero magic resistance bonus: 20%
  Aura, affects nearby allies. The buff lingers for 0.5 seconds.
• Crystal Maiden - Arcane Aura
  
  Magic resistance bonus: 0% ( 6%)
  Self bonus factor: 3
  Self magic resistance bonus: 0% ( 18%)
  Requires a Talent. Aura, affects all allies on the map. Has stronger effect on self. The buff lingers for seconds.
• Dragon Knight - Elder Dragon Form
  
  Magic resistance bonus: 0%/0%/0% ( /40%)
  Only granted on level 4, which requires Aghanim's Scepter.
• Glimmer Cape - Glimmer
  
  Magic resistance bonus: 45%
  Duration: 5
  Affects the target ally. The magic resistance is only applied when fully invisible. It is not applied during the fade time.
• Hellbear - Cloak Aura
  
  Hero magic resistance bonus: 10%
  Non-hero magic resistance bonus: 20%
  Aura, affects nearby allies The buff lingers for 0.5 seconds.
• Oracle - Fate's Edict
  
  Magic resistance bonus: 100%
  Duration: 100%
  Affects the target unit.
• Pipe of Insight - Insight Aura
  
  Magic resistance bonus: 10%
  Aura, affects nearby allies. The buff lingers for 0.5 seconds.
• Pudge - Flesh Heap
  
  Magic resistance bonus: 12%/14%/16%/18%
  Passive.
• Spirit Bear - Demolish
  
  Magic resistance bonus: 33%
  Passive.
• Viper - Corrosive Skin
  
  Magic resistance bonus: 10%/15%/20%/25% ( 15%/20%/25%/30%)
  Passive.

Magic resistance reducing abilities

The following abilities reduce magic resistance:

Magic resistance reducing abilities

• Ancient Apparition - Ice Vortex
  
  Magic resistance reduction: 15%/20%/25%/30% ( 21%/26%/31%/36%)
  Duration: 16
  Aura, affects enemies within the target area. The debuff lingers for 0.5 seconds.
• Ethereal Blade - Ether Blast
  
  Magic resistance reduction: 40%
  Duration: 4
  Affects the target unit. The magic resistance reduction of multiple ethereal effects does not stack, the one with higher value takes priority.
• Ghost Scepter - Ghost Form
  
  Magic resistance reduction: 40%
  Duration: 4
  Affects the caster. The magic resistance reduction of multiple ethereal effects does not stack, the one with higher value takes priority.
• Grove Bow - Magic Amp
  
  Magic resistance reduction: 12%
  Duration: 6
  Affects the attacked enemy.
• Necrophos - Ghost Shroud
  
  Magic resistance reduction: 40%
  Duration: 3/3.5/4/4.5
  Affects the caster. The magic resistance reduction of multiple ethereal effects does not stack, the one with higher value takes priority.
• Pugna - Decrepify
  
  Ally magic resistance reduction: 25%
  Enemy magic resistance reduction: 30%/40%/50%/60%
  Duration: 3.5 ( 5)
  Affects the target unit. The magic resistance reduction of multiple ethereal effects does not stack, the one with higher value takes priority.
• Skywrath Mage - Ancient Seal
  
  Magic resistance reduction: 3/4/5/6 ( )
  Duration:
  Affects the target enemy.
• Viper - Poison Attack
  
  Magic resistance reduction per stack: 6%/8%/10%/12%
  Max stacks: 3%/5%/7%/9%
  Duration: 4
  Affects the attacked enemy.
• Keeper of the Light - Solar Bind
  
  Magic resistance reduction: 15%/20%/25%/30%
  Affects the target enemy.

Magic resistance granting talents

The following heroes have a talent that grants them bonus magic resistance.

Bonus	Level 10		Level 15		Level 20		Level 25
	Left	Right	Left	Right	Left	Right	Left	Right
Magic resistance	+12% +15%	+12% +12% +20%		+15%		+15%		+40%

Besides these, the following heroes have talents which increase the magic resistance of the units they summon

Specific summons magic resistance bonus

• Warlock - Talent by Level 25 Left
  
  80% Magic Resistance for Chaotic Offering Golems:
  

Magic resistance granting items

These items grant bonus magic resistance to the hero who has them equipped.

Magic resistance granting items

Item	Value	Item cost	Cost per value point
Cloak	15	500	33.33
Cloak of Flames	10	N/A	N/A
Eternal Shroud	20	3300	165
Glimmer Cape	15	1950	130
Hood of Defiance	20	1500	75
Mage Slayer	20	3450	172.5
Nether Shawl	25	N/A	N/A
Pipe of Insight	30	3475	115.83
Titan Sliver	16	N/A	N/A
Trickster Cloak	20	N/A	N/A
Vambrace (Strength)	10	N/A	N/A

Magical damage barrier

Magical damage barriers absorb a flat amount of magical damage, no matter whether it comes from abilities (magical spell damage) or attacks (magical attack damage). The barrier absorbs the damage before it is reduced by magic resistance.

Example 1

Anti-Mage has a 300 health damage barrier, and gets hit by 400 magical damage. How much actual magical damage will he take?

Base magic resistance: 0.25

${\text{ActualMagicDamageDealt}}=(400-300)\times 0.75=75$

Anti-Mage will take 75 magical damage.

This means the exceeding 100 magical damage is not absorbed and the damage is reduced by 25% magic resistance to 75 magical damage. In this example, Anti-Mage takes 75 damage. This means a barrier is more effective the lower a unit's magic resistance is, similar to how damage block is more effective, the lower the armor is.

Magic damage barrier stacking

Multiple sources of magical damage barriers work independently and do not stack, when a unit is affected by multiple magical damage barriers, all of them deplete at the same time.

However, if a unit is affected by multiple barriers receive a damage instance that is greater than all barriers individually, the damage gets blocked as if the barriers were one barrier with combined capacity.

Magic damage barrier stacking is defined as

${\text{MagicDamageBarrier}}={\begin{cases}n-b_{i}&\quad {\text{if }}n\leq b\\n-(\sum _{i=1}b_{i})&\quad {\text{if }}n>b\end{cases}}$

With n being the incoming magical damage value, b being the index of sources of magic barrier value.

Example 1

Ember Spirit is affected by Level 4 Flame Guard and Barrier of Pipe of Insight. He then takes 250 magical damage. Both magical damage barriers will lose 250 capacity.

Barrier capacity: Flame Guard: 500, Barrier: 400

$\because IncomingMagicDamage\leq \sum {MagicDamageBarrier}$

$MagicBarrier_{1}=500-250=250$

$MagicBarrier_{2}=400-250=150$

Since incoming magical damage is less than all individual barriers. Both Flame Guard and Barrier will now have 250 and 150 remaining magic barrier capacity respectively.

Example 2

Ember Spirit is affected by Level 4 Flame Guard and Barrier of Pipe of Insight. He then takes 1000 magical damage.

Barrier capacity: Flame Guard: 500, Barrier: 400

$\because IncomingMagicDamage>\sum {MagicDamageBarrier}$

$\therefore IncomingMagicDamage=1000-(500+400)=100$

Since incoming magical damage is greater than the sum of both barriers, both Flame Guard and Barrier are depleted, and magical damage is blocked as if the barriers were one barrier with combined capacity. Ember Spirit takes the remaining 100 damage before applying magic resistance.

Sources of magic damage barriers

• Ember Spirit - Flame Guard
  
  Barrier Health: 80/220/360/500 ( 360/500/640/780)
  Duration: 8/12/16/20
  
• Hood of Defiance - Barrier
  
  Barrier Health: 325
  Duration: 12
  
• Pipe of Insight - Barrier
  
  Barrier Health: 400
  Duration: 12
  Affects allies and structures within a 1200 radius on cast.
• Eternal Shroud - Shroud
  
  Magical Damage Absorbed: 400
  Duration: 12
  

Mechanics Stats Armor Attributes (Strength / Agility / Intelligence) Collision size Health (Health regeneration) Magic resistance Mana (Mana regeneration) Movement speed Status resistance Turn rate Vision Attack Attack animation Attack damage Attack modifier (Bash / Cleave & Splash / Critical strike / Lifesteal / Mana break) Attack range Attack speed Cast animation Cast range Damage types Motion buffer range Projectile speed Spell damage Spell lifesteal Abilities Abilities Aura Channeling Cooldown Damage block Damage manipulation Damage over time Evasion Talents Teleport Status effects Attack immunity Break Cyclone Disable Disarm Ethereal Fear Forced movement Hex Hide Hypnosis Invisibility Invulnerability Leash Root Silence Sleep Slow Spell immunity Stun Taunt World Experience Gold Glyph of Fortification Map (Minimap) River Scan Runes Time of day Trees Gameplay Creep control techniques Denying Disjoint Dispel Ganking Harassment Hero complexity Initiating Item passive stacking Item sharing Jungling Lane Pushing Random distribution Roles Trap Units Ancient creeps Buildings Couriers Creep-heroes Heroes Illusions Lane creeps Neutral creeps Roshan Summons & Wards