Magic resistance

“

▶️ Thy magic harms me not. — Anti-Mage

”

Magic Resistance ( $m$ ) is a stat that reduces (or increases, if negative) magical damage a unit takes from spells and magic 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

All 121 heroes currently have the same Base Magic Resistance value:

$m_{b}=25\%$

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 Abilites

Some abilities negate or ignores a unit's base magic resistance by removing a percentage of the base magic resistance on the target. This magic resistance negation only affects the base magic resistance value of units, other sources of magic resistance are not affected.

Natural Order (and Astral Spirit's Natural Order) interact with magic resistance differently. Instead of stacking multiplicatively with other sources of magic resistance, it acts as a multiplier for the base magic resistance. These two abilities are currently the only two sources of base magic resistance negation, and it is defined as

$m_{A}=m_{b}\times (1-m_{negMu})$

With mb being the Base Magic Resistance Value, mA the Actual Base Magic Resistance and mnegMu the Base Magic Resistance Negation.

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

The following abilities negate base magic resistance:

Base Magic Resistance Negation

• Elder Titan - Natural Order
  
  Radius: 350
  Base Magic Resistance Reduction: 40%/60%/80%/100%
  While Astral Spirit is not summoned, the spirit is hidden and periodically moved along with Elder Titan, so that effectively, it is centered around him.
• Astral Spirit - Natural Order
  
  Radius: 350
  Base Magic Resistance Reduction: 40%/60%/80%/100%
  The effects are provided by an 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.

Pure Damage

Main Articles: Damage Types and HP Removal

Pure Damage is a damage type that is not reduced by Armor or Magic Resistance. It is also not amplified by magical damage amplification abilities, fully ignores Armor and Damage Block. It does not affect invulnerable units.

There are a few sources that can manipulate Pure Damage, with Dispersion is one of them. Pure damage affects units with Spell Immunity (because spell immunity does not block damage), but that does not mean that an ability that deals pure damage is able to target spell immune units.

Total Magic Damage

Calculating the total magic damage of an ability involves using a few multipliers (e.g. Magic Resistance Multiplier, Actual Base Magic Resistance) and Magic Damage Barrier. The total or actual magic damage dealt is equal to how much health a target immediately loses as a direct result.

Actual magic resistance percentage is defined as

$\sum m=(1-\Sigma m_{Mu})*100\%$

With mMu being the Magic Resistance Multiplier.

Actual magic damage dealt after magic resistance is defined as

$m_{DmgA}=(m_{Dmg}-m_{Barrier})\times m_{Mu}$

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

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.

However, there are a few abilities that directly sets a unit's magic resistance to 100%, e.g. Fate's Edict.

Magic resistance multiplier is defined as

$\sum m_{Mu}=(1-m_{A})\times {\Big (}\prod _{i=1}^{n}(1-a_{i})(1+r_{i}){\Big )}$

With mA being the actual base magic resistance, a the magic resistance sources and r the magic resistance reduction sources.

Examples

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)

${\begin{aligned}\sum m&=1-{\big (}\underbrace {(1-0.25)\times (1-0.45)\times (1-0.15)} _{\text{Magic Resistance}}\times (1+0){\big )}\\&=64.94\%\end{aligned}}$

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

${\begin{aligned}\sum m&=1-{\big (}\underbrace {(1-0.25)\times (1-0)} _{\text{Magic Resistance}}\times \underbrace {(1+0.45)\times (1+0.6)} _{\text{Magic Resistance Reduction}}{\big )}\\&=-74\%\end{aligned}}$

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

Effective HP

The total amount of magic damage a unit can take due to magic resistance is known as effective HP (or EHP). 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 magic 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. All 121 have 25% magic resistance by default, making their effective HP against magical damage 133.33%.

Magic Resistance	-100%	-75%	-50%	-25%	0%	25%	50%	75%	100%
Effective HP	500	571	667	800	1000	1333	2000	4000	∞

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

Effective HP against magic damage is defined as

$E_{HP}={\frac {\Sigma _{HP}}{1-m}}$

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%.

Examples

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

${\begin{aligned}E_{HP}&={\frac {\Sigma _{HP}}{1-m}}\\\\&={\frac {1400}{(1-0.6494)}}\\\\&=3992.87\\\end{aligned}}$

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

${\begin{aligned}E_{HP}&={\frac {\Sigma _{HP}}{1-m}}\\\\&={\frac {2260}{(1--0.74)}}\\\\&=1298.85\end{aligned}}$

Visage has 1298.85 EHP against magical damage in this example.

Modifying Magic Resistance

Several abilities 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.
• Arc Warden - Magnetic Field
  
  Effect Radius: 300
  Magic Resistance Bonus: 40%
  Duration: 3.5/4.5/5.5/6.5
  Requires Aghanim's Shard, the effects are provided by an aura. Its buff lingers for 0.1 seconds.
• Centaur Courser - Cloak Aura
  
  Hero Magic Resistance Bonus: 10%
  Non-Hero Magic Resistance Bonus: 20%
  The effects are provided by an aura, affects nearby allies. The buff lingers for 0.5 seconds.
• Crystal Maiden - Arcane Aura
  
  Magic Resistance Bonus: 6%
  Self Bonus Factor: 3
  Requires a Talent. The effects are provided by an aura, affects all allies on the map. Has stronger effect on self. The buff lingers for 0.5 seconds.
• Dragon Knight - Elder Dragon Form
  
  Magic Resistance Bonus: 0%/0%/0% /40%
  Requires Aghanim's Scepter, granted to Black Dragon.
• 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%
  The effects are provided by an aura, affects nearby allies The buff lingers for 0.5 seconds.
• Oracle - Fate's Edict
  
  Enemy Magic Resistance Bonus: 100%
  Ally Magic Resistance Bonus: 100%
  Duration: 3/3.5/4/4.5
  Affects the target unit.
• Pipe of Insight - Insight Aura
  
  Magic Resistance Bonus: 10%
  The effects are provided by an 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.
• Vambrace - Switch Attribute
  
  Strength Magic Resistance Bonus: 10%
  Provided by Vambrace Strength.
• Viper - Corrosive Skin
  
  Magic Resistance Bonus: 10%/15%/20%/25% ( 20%/30%/40%/50%)
  Passive.

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% +12% +15% +20%		+15%		+15% +20%	+30%	+40%

Assuming basic 25% magic resistance and no other sources of magic resistance, the following heroes with bonus magic resistance talents effectively have their magic resistance increased up to:

Heroes	Magic Resistance Talent	Magic Resistance Total	Increased Value
	Basic Magic Resistance (25%)
	+12%	34%	+9%
	+15%	36.25%	+11.25%
	+20%	40%	+15%
	+40%	55%	+30%

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:
  Sets Warlock Golem's magic resistance to 80%. Effectively increasing it by 47%.

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	3250	162.5
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

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
  The effects are provided by an 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
  
  Self 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: 15%
  Duration: 6
  Affects the attacked enemy.
• Keeper of the Light - Solar Bind
  
  Magic Resistance Reduction: 15%/20%/25%/30%
  Duration: 7
  Affects the target enemy.
• Leshrac - Nihilism
  
  Radius: 450
  Enemy Magic Resistance Reduction: 30%
  Duration: 4
  Requires Aghanim's Scepter, the effects are provided by an aura, affects the caster and enemies within radius. The magic resistance reduction of multiple ethereal effects does not stack, the one with higher value takes priority.
• Necrophos - Ghost Shroud
  
  Self 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.
• Nyx Assassin - Vendetta
  
  Enemy Magic Resistance Reduction:
  Magic Resistance Reduction Duration: 20%
  Requires Aghanim's Shard.
• 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: 30%/35%/40%/45% ( 42%/47%/52%/57%)
  Duration: 3/4/5/6
  Affects the target enemy.
• Viper - Poison Attack
  
  Magic Resistance Reduction per Stack: 3%/5%/7%/9%
  Max Stacks: 5 ( 8)
  Duration: 4
  Affects the attacked enemy.

Ethereal

Main Article: Ethereal

Ethereal, sometimes referred to as ghost form, is a type of status effect that makes affected units immune to all physical damage, grants them attack immunity, while also disarming them. It also reduces their magic resistance, causing them to take additional magical damage. Affected units are able to control every other aspect of their character.

The magic resistance reduction of multiple ethereal effects does not stack, the one with higher value takes priority, and it is defined as

$m_{Eth}={\text{max}}\{\;r_{i}\}$

With r being the Magic Resistance Reduction Value.

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.

Actual magic damage dealt after magic resistance is defined as

$m_{DmgA}=(m_{Dmg}-m_{Barrier})\times m_{Mu}$

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

${\begin{aligned}m_{DmgA}&=(m_{Dmg}-m_{Barrier})\times m_{Mu}\\&=(400-300)\times (1-0.25)\\&=75\end{aligned}}$

Anti-Mage will take 75 magical damage.

This means the exceeding 100 magical damage is not absorbed and the damage is reduced by Anti-Mage's base 25% magic resistance to 75 magical damage. In this example, Anti-Mage takes 75 magic 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.

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

$m_{Barrier}={\begin{cases}m_{Dmg}-B_{i}&\quad {\text{if }}m_{Dmg}\leq B_{i}\\m_{Dmg}-(\sum _{i=1}B_{i})&\quad {\text{if }}m_{Dmg}>B_{i}\end{cases}}$

With mDmg being the incoming magical damage value, B the source(s) of the magic barrier value.

Examples

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

$\because m_{Dmg}<B_{1}\quad \&\quad m_{Dmg}<B_{2}$

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

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

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

$\because m_{Dmg}>B_{1}+B_{2}$

${\begin{aligned}m_{Dmg}&=1000-\underbrace {(500+400)} _{\text{Barrier Capacity}}\\&=100\end{aligned}}$

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.

Magic Damage Barrier Granting Abilities

Magic Damage Barrier Granting Abilities

• Ember Spirit - Flame Guard
  
  Barrier Health: 80/220/360/500 ( 360/500/640/780)
  Duration: 11/14/17/20
  Affects the caster.
• Hood of Defiance - Barrier
  
  Barrier Health: 325
  Duration: 12
  Affects the caster.
• 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
  Affects the caster.
• Infused Raindrops - Magical Damage Block
  
  Minimum Damage Threshold: 75
  Magical Damage Blocked: 120
  Number of Charges: 6
  Affects the item bearer. Only triggers on magical damage equal to or greater than 75 before reductions.

Spell Immunity

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Main Article: Spell Immunity

Spell immunity (formerly known as magic immunity) is a modifier which prevents most spells to target the affected unit. This includes single-targeted spells, area spells, passive and active abilities. A unit having 100% magic resistance does not equal to being spell immune. Therefore, Spell Immunity and Magic Resistance are separate and different mechanics.

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 Phased 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