Damage Manipulation

“

▶️ That harms me not.

— Abaddon

”

Damage manipulation is a mechanic that alters damage values, either increasing or reducing it.

Overview[edit]

Damage Manipulation can affect damage but different from Damage Block.

Damage Manipulation has the following properties:

Damage Manipulation can manipulate on both sides, from the dealing unit (outgoing damage) and the receiving unit (incoming damage).
Damage Manipulation can both amplify and reduce damage.
Damage Manipulation always manipulates damage by percentage.
- Especially, Damage Negation is a special kind of Damage Manipulation. It can not generally be considered as a 100% damage reduction.
Damage Manipulation can manipulate negative damage.
- If Damage Manipulation percentage are over 100%, the positive damage can be manipulated to negative damage, and the negative damage also can be manipulated to positive damage.
Damage Manipulation which belongs to the same type can stack additively.
Damage Manipulation which belongs to different types can stack multiplicatively by the priority.

The following Damage Manipulation are shown by the priority.

Outgoing Attack Damage Manipulation (etc. Illusion Outgoing Attack Damage Manipulation) is not shown in this page. For these description please visit Attack Damage.

Main Article: Attack Damage

Outgoing Damage Manipulation[edit]

Outgoing damage manipulation causes the afflicted unit to deal increased or reduced damage.

Spell Damage Amplification[edit]

Driven by MODIFIER_PROPERTY_SPELL_AMPLIFY_PERCENTAGE.

Affects spell damages by percentage and stacks additively, including some damages with HP Removal flag.

Spell Damage Amplification do not apply to damage that is Unaffected by Amplification.

Outgoing Spell Damage Amplification Sources

Outgoing Spell Damage Reduction Sources

Mage Slayer – Mage Slayer

¹ Requires

talent.

^2a Requires

Aghanim's Scepter.

^2b Requires

Aghanim's Shard.

³ Requires selecting the corresponding facet.

The following heroes have a talent that grants them outgoing spell damage amplification.

Bonus	Level 10		Level 15		Level 20		Level 25
Bonus	Left	Right	Left	Right	Left	Right	Left	Right
Spell Amplification

Many items grant their owners a spell damage amplification bonus by giving them a direct bonus. The effects are limited to the item's owner, which must have the item equipped.

Bonus Spell Damage

Item	Value	Item Cost	Cost/Value Point
Kaya	10%	2100	210
Kaya and Sange	12%	4200	350
Meteor Hammer	10%	2850	285
Timeless Enchantment	0.5%	N/A	N/A
Yasha and Kaya	12%	4200	350
Values do not include portions from actives or auras.

Unique Spell Amplification[edit]

Kaya-based items are driven by MODIFIER_PROPERTY_SPELL_AMPLIFY_PERCENTAGE_UNIQUE.

Do not stack each other and only the highest are effective.

Outgoing Universal Damage Manipulation[edit]

Driven by MODIFIER_PROPERTY_TOTALDAMAGEOUTGOING_PERCENTAGE.

Generally affects all types damage by percentage.

Outgoing Universal Damage Manipulation Sources

Aeon Disk - Combo Breaker

Damage Reduction: 100%
Clinkz - Burning Barrage

Attack Damage as Damage:

Incoming Damage Manipulation[edit]

Incoming damage manipulation causes the afflicted unit to take increased or reduced damage depending if it is an enemy or an ally.

armor

Damage Negation[edit]

Damage negation causes entire instances of damage to deal no damage to its target, however, the instance is still registered. This means, if something reacts on damage without having a minimum damage threshold, it still reacts on the negated damage.

The following sources are shown by Damage Negation in different damage types. Generally, there are no priority between them. It means that different Damage Negation is possible to trigger at the same time.

Physical Damage Negation[edit]

Driven by MODIFIER_PROPERTY_ABSOLUTE_NO_DAMAGE_PHYSICAL.

Among them, all Ethereal sources provide Physical Damage Negation.

Physical Damage Negation Hero Sources

Physical Damage Negation Item Sources

Ethereal Blade – Ether Blast
Ghost Scepter – Ghost Form

Pure Damage Negation[edit]

Driven by MODIFIER_PROPERTY_ABSOLUTE_NO_DAMAGE_PURE.

Among them, all Debuff Immunity sources provide Pure Damage Negation.

Do not affect pure damage that pierces Debuff Immunity.

Pure Damage Negation Sources

¹ Requires

talent.

^2a Requires

Aghanim's Scepter.

^2b Requires

Aghanim's Shard.

Universal Damage Negation[edit]

Driven by MODIFIER_PROPERTY_AVOID_DAMAGE.

Affects all types damages.

Some damage with HP Removal can also be negated. However, the trigger situations depend on the ability sources.

Universal Damage Negation Sources

Base Damage Manipulation[edit]

Armor and magic resistance are the most common damage manipulators, affecting incoming physical and magical damage respectively.

For these description please click the link below.

Main Article: Armor

Main Article: Magic Resistance

Incoming Physical Damage Manipulation[edit]

Driven by MODIFIER_PROPERTY_INCOMING_PHYSICAL_DAMAGE_PERCENTAGE.

Only affects physical attack damage and stacks additively.

Incoming Physical Damage Amplification Sources

Attack Damage - Reinforced

Attack Damage Bonus Against Reinforced Units: 0.5
Medusa - Stone Gaze

Physical Damage Amp: ( )

Incoming Physical Damage Reduction Sources

Axe - Counter Helix

Damage Reduction per Stack:
Windranger - Windrun

Damage Reduction:

Generic Incoming Damage Manipulation[edit]

Driven by MODIFIER_PROPERTY_INCOMING_DAMAGE_PERCENTAGE.

Most abilities that affect damage use the generic damage manipulator.

Generic Incoming Damage Manipulation causes the afflicted unit to take increased or reduced damage depending if it is an enemy or an ally. All sources within these lists stack additively with each other.

Therefore, some 100% damage reductions are still possible to receive damage when stacking with other damage amplifications.

Certain damage manipulations can only manipulate specific damage. More information regarding the ability's incoming damage manipulations can be found in their respective ability notes.

Generic Incoming Damage Amplification Sources

Ancient Black Drake - Magic Amplification Aura

Spell Damage Amp: 5%/6%/7%/9%
Beastmaster - Wild Axes

Damage Amp per Stack: 6%/8%/10%/12% ( 8%/10%/12%/14%)
Bounty Hunter - Track

Damage Amp: 8%/12%/16%
Courier - Passive Bonus

Incoming Melee Damage Amplification:
Grimstroke - Soulbind

Bound Units Spell Damage Amp: 25%
Hoodwink - Hunter's Boomerang

Spell Damage Amp: 25%
Undying - Flesh Golem

Damage Amp: 25%/30%/35%
Veil of Discord - Magic Weakness

Spell Damage Amp: 10%

Generic Incoming Damage Reduction Sources

Aeon Disk - Combo Breaker

Damage Reduction: 100%
Bristleback - Bristleback

Rear Damage Reduction: 16%/24%/32%/40% ( 24%/32%/40%/48%)
Side Damage Reduction: 8%/12%/16%/20% ( 12%/16%/20%/24%)
Leshrac - Pulse Nova

Damage Reduction: 10%
Lich - Frost Shield

Attack Damage Reduction: 45%/50%/55%/60% ( 55%/60%/65%/70%)
Luna - Lunar Orbit (Moonshield Facet)

Attack Damage Reduction: 15%/20%/25%/30%
Mars - Bulwark

Front Attack Damage Reduction: 40%/50%/60%/70% ( )
Side Attack Damage Reduction: 20%/25%/30%/35% ( )
Martyr's Plate - Martyrdom

Damage Reduction: 25%
Nyx Assassin - Burrow

Damage Reduction: 40%
Spectre - Dispersion

Damage Reduction: 7%/11%/15%/19% ( 12%/16%/20%/24%)
Underlord - Fiend's Gate

Damage Reduction: 4%/6%/8%/10% ( 9%/11%/13%/15%)
Ursa - Enrage

Damage Reduction: 80%
Winter Wyvern - Winter's Curse

Damage Reduction: 0.5
Buildings - Backdoor Protection

Damage Reduction: 0.5
Protected Illusion Damage Reduction:

Unique Damage Negation[edit]

Driven by MODIFIER_PROPERTY_AVOID_DAMAGE_AFTER_REDUCTIONS.

Deals a constant 100% damage reduction, including damage with HP Removal flag.

Only False Promise belongs to this.

Illusion Incoming Damage Manipulation[edit]

Driven by MODIFIER_PROPERTY_INCOMING_DAMAGE_ILLUSION.

Illusion will receive Damage Manipulation when taking damage.

More value information can be found in illusion page.

Main Article: Illusions

Target Dummy Damage Negation[edit]

Target Dummy Damage Negation affects all damages including damage with HP Removal flag.

Armor[edit]

All units, including buildings, have an inherent base armor value and attack class. Any physical damage dealt to a unit is multiplied by the damage multiplier, resulting in either damage reduction or increase depending on the target's armor value.

Damage Multiplier is also used to calculate a unit's Effective HP (EHP). The lower the damage multiplier, the higher the Effective HP of a unit, vice versa.

Armor Formula Base `b`	Armor Formula Factor `f`
1	0.06

For any real-valued armor, the damage multiplier is defined as

Damage Multiplier = 1 - (f x R) / (b + f x | R | )

With D_Mu being the Damage Multiplier and R the armor value.

The damage multiplier limits are 0 and 2, for infinitely positive and negative armor, respectively. Expand the table below for more detailed information on how much positive and negative armor affects damage multiplier.

Examples

Armor (+)	Multiplier	Armor (-)	Multiplier
1	94%	-1	106%
2	89%	-2	111%
3	85%	-3	115%
4	81%	-4	119%
5	77%	-5	123%
6	74%	-6	126%
7	70%	-7	130%
8	68%	-8	132%
9	65%	-9	135%
10	63%	-10	138%
11	60%	-11	140%
12	58%	-12	142%
13	56%	-13	144%
14	54%	-14	146%
15	53%	-15	147%
16	51%	-16	149%
17	50%	-17	150%
18	48%	-18	152%
19	47%	-19	153%
20	45%	-20	155%
21	44%	-21	156%
22	43%	-22	157%
23	42%	-23	158%
24	41%	-24	159%
25	40%	-25	160%
26	39%	-26	161%
27	38%	-27	162%
28	37%	-28	163%
29	36%	-29	164%
30	36%	-30	164%
31	35%	-31	165%
32	34%	-32	166%
33	34%	-33	166%
34	33%	-34	167%
35	32%	-35	168%
36	32%	-36	168%
37	31%	-37	169%
38	30%	-38	170%
39	30%	-39	170%
40	29%	-40	171%
41	29%	-41	171%
42	28%	-42	172%
43	28%	-43	172%
44	27%	-44	173%
45	27%	-45	173%

Stacking[edit]

Armor and magic resistance work separately from other damage manipulators. This means they always stack multiplicatively with any other listed ability.

The effects of incoming and outgoing generic damage manipulators stack additively with themselves. Unique damage manipulators stack multiplicatively with themselves. The three sources of damage manipulation stack multiplicatively with each other after they have been combined with all of their own type.

Many source of damage manipulations have conditions on them like Bristleback where it has damage manipulation only on damage that hits his back or sides, so each damage instance calculates damage manipulation separately. Additionally, outgoing generic damage manipulators do not apply to damage that is Unaffected by Amplification.

The total damage manipulation D_M is defined as

<math>

D_M = \Big( 1 + \sum(\text{Generic Incoming Dmg Manip}) \Big) \times \Big( 1 + \sum(\text{Generic Outgoing Dmg Manip}) \Big) \times \prod(\text{1 + Unique Dmg Manip}) \quad \& \quad D_M \geq 0 </math>

Stacking outgoing damage manipulation stacks in the same way as incoming damage manipulation, i.e. additively. However, since incoming and outgoing manipulations happen at different times with outgoing manipulation calculation happening first, they stack multiplicatively with each other.

Example 1: Spell Damage Manipulation

Spectre has level 4

Dispersion and is affected by level 3

Fiend's Gate,

Magic Weakness and

Ghostship's rum buff. An enemy casted level 4

Bloodrage on himself and has

Kaya. What would the damage manipulation for Spectre be in this scenario?

Incoming Generic Manipulation sources:

Dispersion: -0.19,

Fiend's Gate: -Expression error: Unexpected / operator.,

Magic Weakness: 0.16.

Outgoing Generic Manipulation sources:

Bloodrage: Expression error: Unexpected / operator.,

Kaya: 0.1

Unique Generic Manipulation sources:

Ghostship: -Expression error: Unexpected / operator.

Spell Damage <math>D_M</math>:

<math>\begin{align}

D_M &= \underbrace{(1 - 0.19 - Expression error: Unexpected / operator. + \overbrace{ 0.16 }^\text{Spell Only})}_\text{Generic Incoming} \times \underbrace{(1 + \overbrace{ Expression error: Unexpected / operator. + 0.1 }^\text{Spell Only})}_\text{Generic Outgoing} \times \underbrace{(1 - Expression error: Unexpected / operator.)}_{Unique} \\ &= (Expression error: Unexpected < operator.) \times (Expression error: Unexpected < operator.) \times (Expression error: Unexpected < operator.) \\ &= Expression error: Unexpected < operator.\% \end{align} </math>

Note that Magic Weakness, Bloodrage and Kaya's amplification only apply to spell damage, therefore another calculation will be needed for non-spell damage <math>D_M</math>.

Non-Spell Damage <math>D_M</math>:

<math>\begin{align} D_M &= \underbrace{(1 - 0.19 - Expression error: Unexpected / operator.)}_\text{Generic Outgoing} \times \underbrace{(1)}_\text{Generic Incoming} \times \underbrace{(1- Expression error: Unexpected / operator.)}_\text{Unique} \\ &= (Expression error: Unexpected < operator.) \times (1) \times (Expression error: Unexpected < operator.) \\ &= Expression error: Unexpected < operator.\% \end{align} </math>

In this example,

Spectre would take Expression error: Unexpected < operator.% spell damage and Expression error: Unexpected < operator.% damage from non-spell damage from the enemy in this scenario.

Example 2: Additive Stacking[edit]

All values in this section consider the highest possible level of an ability but exclude talents and aghanim's upgrades unless otherwise mentioned. Examples ignore armor and magic resistance.

Ursa is Enraged and is affected by Flesh Golem.

100% - 80% + = Expression error: Missing operand for +.% damage

Spectre with Dispersion and is affected by Fiend's Gate.

100% - 19% - = Expression error: Missing operand for -.% damage

A hero affected by Winter's Curse and Flesh Golem at the same time.

100% - 2 + = Expression error: Missing operand for +.% damage

Example 3: Other Multiplicative Stacking[edit]

All values in this section consider the highest possible level of an ability but exclude talents and aghanims upgrades unless otherwise mentioned. Examples ignore armor and magic resistance.

Medusa activated Mana Shield and is affected by Flesh Golem.

(100% + ) * (100% - 2.2%) = Expression error: Missing operand for +.% damage

Medusa activated Mana Shield, is affected by Ghostship rum buff and is affected by Flesh Golem.

(100% + ) * (100% - 2.2%) * (100% - %) = Expression error: Missing operand for +.% damage

A Conjure Image illusion (taking 250% damage) affected by Flesh Golem and Fiend's Gate

(100% + - ) * 250% = Expression error: Missing operand for +.% damage

Preventing On-damage Effects[edit]

Many abilities react on damage a unit receives. In some cases, fully negating the damage causes them to not proc. However, some on-damage effects also react on 0 damage so they still may proc even when the proccing damage got negated.

The following abilities and effects do not react on damage when it gets fully negated (reduced to 0):