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 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.

Total magic resistance is defined as

Magic Resistance = 1 - (1 - Base Magic Resistance) × $\prod _{i=1}^{n}$(1 - Magic Resistance Modifiers _i )

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 123 heroes currently have the same Base Magic Resistance value: 25%

Creeps

Units	Magic resistance
Mega Melee Creep, Mega Ranged Creep, Melee Creep, Ranged Creep, Super Melee Creep, Super Ranged Creep	0%
Lycan Lane Wolf	70%
Siege Creep, Super Siege Creep	80%

Summons

Summons	Magic resistance
Astral Spirit, Earth, Fire, Spirit Bear	0%
Void	20%
Storm	25%
Warlock Golem	33%
Familiar	35%

Base Magic Resistance Negation

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

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%.

Base Magic Resistance Negation Sources

• 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 being one of them. This mechanic is called damage reduction. 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, Magic Resistance Multiplier, Actual Base Magic Resistance, Magic Damage Barrier and Magic Damage Negation Sources (if any). The total or actual magic damage dealt is equal to how much health a target immediately loses as a direct result.

Actual magic damage dealt after magic resistance is defined as

Magic Damage Dealt = (Magical Damage - Magic Damage Barrier - Magic Damage Negations) × (1 - Magic Resistance)

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

Magic Resistance Stacking

Multiple 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. All sources of magic resistance modification stack fully with the exception of Ethereal buffs and debuffs.

Total magic resistance is defined as

Magic Resistance = 1 - (1 - Base Magic Resistance) × $\prod _{i=1}^{n}$(1 - Magic Resistance Modifiers _i )

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

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)

Total Magic Resistance

= 1 - ((1 - 0.25) × (1 - 0.45) × (1 - 0.15))

= 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: -0.35, Decrepify: -0.6

Total Magic Resistance

= 1 - ((1 - 0.25) × (1 + 0.35) × (1 + 0.6))

= -62%

Visage's current magic resistance in this example is -62%. Magic resistance reduction's calculation is highlighted red in this example.

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, and it is defined as the formula above.

Example

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

Magical Damage Taken

= (400 - 300) × (1 - 0.25)

= 75

Anti-Mage will take 75 magical damage in this example.

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.

Magical 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.

Magical Damage Barrier stacking is defined as

Magical Damage Barrier = ${\begin{cases}i-B_{n}&\quad {\text{if }}x\leq B_{n}\\i-(\sum _{i=1}B_{n})&\quad {\text{if }}x>B_{n}\end{cases}}$

With x being the incoming magical damage value, B the source(s) of the magical damage 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: 400, Barrier: 400

Since the incoming magical damage is less than B₁ and B₂:

B₁ ( Flame Guard)

= 400 - 250

= 150

B₂ ( Barrier)

= 400 - 250

= 150

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

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: 400, Barrier: 400

Since the incoming magical damage is more than B₁ and B₂ combined:

Incoming Magical Damage

= 1000 - (400 + 400)

= 200

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, highlighted in blue in this example. Ember Spirit takes the remaining 200 damage before applying magic resistance.

Magical Damage Barrier Sources

Magic Damage Barrier Sources

• Ember Spirit – Flame Guard
• Hood of Defiance – Barrier
• Pipe of Insight – Barrier
• Eternal Shroud – Shroud
• Infused Raindrops – Magical Damage Block

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 123 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 magical damage is defined as

EHP = Σ Current_HP / (1 - Σ Magic Resistance)

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 77.78%, extra EHP whereas one source provides 33.33%.

Examples

Example 1

Anti-Mage at max level has 1540 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

EHP_m

= 1540 / (1 - 0.649375)

= 4392.16

Anti-Mage has 4392.16 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 -62% (or -0.62).

Base hero magic resistance: 0.25

Bonus magic resistance: 0 (None)

Magic resistance reduction: Ancient Seal: 0.35, Decrepify: 0.6

EHP_m

= 2260 / (1 - (-0.62))

= 1395.06

Visage has 1395.06 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 Sources

Magic Resistance Increasing Sources

• Anti-Mage – Counterspell
• Arc Warden – Magnetic Field^2b
• Brewmaster – Drunken Brawler Earth Stance
• Centaur Courser – Cloak Aura
• Dragon Knight – Black Dragon Form^2a
• Glimmer Cape – Glimmer
• Huskar – Berserker's Blood
• Lone Druid – Demolish
• Oracle – Fate's Edict
• Spirit Bear – Demolish
• Meepo – Divided We Stand
• Pipe of Insight – Insight Aura
• Pudge – Flesh Heap
• Vambrace – Switch Attribute
• Viper – Corrosive Skin

¹ Requires talent.

^2a Requires Aghanim's Scepter.

^2b Requires Aghanim's Shard.

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% +12%	+10% +12% +12% +12% +15% +20%		+15%		+15%

With the 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%)
	+10%	32.5%	+7.5%
	+12%	34%	+9%
	+15%	36.25%	+11.25%

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 86%.

Items

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

Magic Resistance Granting Items

Item	Value	Item Cost	Cost/Value Point
Arcanist's Armor	20	N/A	N/A
Bloodthorn	20	6800	340
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	18	1500	83.33
Mage Slayer	20	2400	120
Nether Shawl	20	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
Values may include portions from actives or auras.

Magic Resistance Reducing Sources

Magic Resistance Reducing Sources

• Ancient Apparition – Ice Vortex
• Ceremonial Robe – Ceremonial Aura
• Grove Bow – Magic Amp
• Keeper of the Light – Solar Bind
• Skywrath Mage – Ancient Seal
• Shadow Fiend – Requiem of Souls
• Techies – Proximity Mines
• Viper – Poison Attack

¹ Requires talent.

^2a Requires Aghanim's Scepter.

^2b Requires Aghanim's Shard.

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

Eth = (1 - MAX Ethereal Magic Resistance Reduction)

Ethereal Sources

• Ethereal Blade – Ether Blast
• Ghost Scepter – Ghost Form
• Leshrac – Nihilism
• Necrophos – Ghost Shroud
• Necrophos – Death Seeker
• Pugna – Decrepify

Spell Immunity

Default buff icon
Error sound

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, area of effect, 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.

Version History

Version

Description

7.07

• Fixed magic damage sources from attacks not being blocked by magic damage barrier type abilities (i.e. Barrier, Flame Guard etc.).

Patch History

Patch

Description

24 Mar 2016

• Fixed recasting magic damage barrier abilities not resetting the damage capacity of the magic barrier.

31 Jan 2013

• Update 2
  • Fixed magical damage amplification when a unit drops below 0% magic resistance.

28 Jun 2011

• Fixed magic resistance not stacking properly.

02 Jun 2011

• Fixed various magic resistance rules.

26 May 2011

• Fixed bugs with how magic resistance from base and items were calculated on illusions.

Mechanics Main Stats Armor Attributes ( Strength / Agility / Intelligence) Health & Mana (HP Regen & MP Regen) Magic Resistance Movement Speed Status Resistance Turn Rate Misc Collision Size Gib Type / Shades Legs Vision Abilities Type Active / Passive / Autocast Aura Accuracy / Evasion Channeling Damage Block / Magic Damage Barrier Damage Manipulation Damage Over Time Talents Teleport Targeting Area No Target Point Unit Vector Combinations Casting Cast Range / Motion Buffer Cast Animation (Cast Point + Backswing) Cooldown Reduction (Flat / Current Flat / Percentage) Reset Charge-based Attack Damage Attack Damage Instant Attack Heroes Attack Classes Attack Range (Acquisition Range) Attack Speed (BAT / Interval) Damage Types (Physical / Magical / Pure / Instant Kill) Flags (HP Removal / No-reflection) Projectile Speed Spell Damage (Outgoing / Incoming) Modifiers Bash Cleave / Splash Corruption Critical Strike Lifesteal / Spell Lifesteal Mana Break On-hit Effects Animation Definition Orb Walking Status Effects Disables Cyclone Disabling Orders Forced Movement (Knockback) / Upward Movement Fear Hide Hex Hypnosis Root Leash Stun Sleep Taunt Movement Move Speed Slow Flying Movement Phased / Tree Walk / Unobstructed Movement Other Attack Immune Attack Speed Slow Spell Immunity Invulnerability Invisibility Blind Break Disarm Ethereal Silence Mute Trap Items Mechanics Sharing / Selling Disassemble Recipes Neutral Item Drop