Armor

Armor

 

Changelogs

 

“

▶️ Armored to the teeth! — Clockwerk

”

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

Each point of agility increases a hero's armor by 0.167 or $\tfrac{1}{6}$.

Base armor

Base armor is the part of the main armor that never changes throughout a game. It consists of one fixed value set for each unit individually. The base armor of a unit can be a negative number. Since only heroes have agility, the HUD of all non-hero units shows their base armor.

Heroes

Heroes	Armor
	-3
	-2
	-1
	0
	1
	2
	2.5
	3
	4
	5

Creeps

Units	Armor
Lycan Lane Wolf, Mega Siege Creep, Ranged Creep, Siege Creep, Super Siege Creep	0
Mega Ranged Creep, Super Ranged Creep	1
Flagbearer Creep, Melee Creep	2
Mega Flagbearer Creep, Mega Melee Creep, Super Flagbearer Creep, Super Melee Creep	3

Summons

Summons	Armor
Astral Spirit	0
Familiar	0/2/4
Spirit Bear	0/2/4/6
Fire	0/8/16
Storm	2
Mars Soldier	3
Void	3/4/5
Earth	3/5/7
Warlock Golem	8/12/14

Main armor

Main armor is the armor value shown in white numbers near the shield icon in the HUD, consisting of base armor and the armor granted by a hero's agility. The only way to improve a hero's main armor is to increase its agility, which is gained by leveling up, acquiring certain items, or with the help of certain abilities.

The main armor is defined as

${\text{M}}=\underbrace {b+(A_{current}\times 0.167\times l)} _{\text{Hero Base Armor}}+\underbrace {(A_{bonus}\times 0.167)} _{\text{Bonus Agility}}$

With M being the index of Main Armor, b being the index of Base Armor, A being the index of agility and l being the index of the hero's level.

Hero Armor

Hero Base Level 1 Level 15 Level 25 Level 30 Abaddon 0 3.83 6.87 9.03 10.12 Alchemist 0 3.67 7.17 9.67 10.92 Ancient Apparition -1 2.33 7.47 11.13 12.97 Anti-Mage 1 5 11.53 16.2 18.53 Arc Warden 0 3.33 10.33 15.33 17.83 Axe -1 2.33 6.3 9.13 10.55 Bane 1 4.83 10.67 14.83 16.92 Batrider 2 4.5 7.77 10.1 11.27 Beastmaster -1 2 5.73 8.4 9.73 Bloodseeker 2 6 13.23 18.4 20.98 Bounty Hunter 5 8.5 14.57 18.9 21.07 Brewmaster 0 3.17 7.83 11.17 12.83 Bristleback 1 3.83 8.03 11.03 12.53 Broodmother -1 2 8.07 12.4 14.57 Centaur Warrunner -2 0.5 2.83 4.5 5.33 Chaos Knight 2 5 8.27 10.6 11.77 Chen -1 1.5 6.4 9.9 11.65 Clinkz 0 4.17 10.47 14.97 17.22 Clockwerk 1 3.17 8.07 11.57 13.32 Crystal Maiden 0 2.67 6.4 9.07 10.4 Dark Seer 2 5.17 9.37 12.37 13.87 Dark Willow 0 3 6.03 8.2 9.28 Dawnbreaker 2 4.33 8.3 11.13 12.55 Dazzle 0 3.33 6.6 8.93 10.1 Death Prophet 1 3.67 8.33 11.67 13.33 Disruptor 0 2.5 5.77 8.1 9.27 Doom 2 4.5 8 10.5 11.75 Dragon Knight 0 2.67 7.33 10.67 12.33 Drow Ranger 0 3.33 10.1 14.93 17.35 Earth Spirit 0 2.83 8.43 12.43 14.43 Earthshaker 2 4 7.27 9.6 10.77 Elder Titan 0 2.67 6.87 9.87 11.37 Ember Spirit 0 3.67 11.13 16.47 19.13 Enchantress 1 4.17 9.07 12.57 14.32 Enigma 1 3.33 5.67 7.33 8.17 Faceless Void 0 3.17 10.17 15.17 17.67 Grimstroke 0 3 7.43 10.6 12.18 Gyrocopter 2 6.33 13.57 18.73 21.32 Hoodwink 0 4 12.4 18.4 21.4 Huskar -1 0.67 4.17 6.67 7.92 Invoker -1 1.33 5.53 8.53 10.03 Io 1 3.33 7.07 9.73 11.07 Jakiro 1 3.5 6.3 8.3 9.3 Juggernaut 0 5.67 12.2 16.87 19.2 Keeper of the Light 0 2.5 6.23 8.9 10.23 Kunkka 2 4.33 8.07 10.73 12.07 Legion Commander 0 3 6.97 9.8 11.22 Leshrac 0 3.83 10.37 15.03 17.37 Lich -1 1.83 6.5 9.83 11.5 Lifestealer 1 4.17 10.23 14.57 16.73 Lina 0 3.83 9.43 13.43 15.43 Lion 0 2.5 6 8.5 9.75 Lone Druid 0 3.33 8 11.33 13 Luna 2 6 13.93 19.6 22.43 Lycan 0 3 7.2 10.2 11.7 Magnus 1 2.5 7.17 10.5 12.17 Marci 0 3.33 7.53 10.53 12.03 Mars -1 2.33 6.3 9.13 10.55 Medusa -1 2.67 11.07 17.07 20.07 Meepo 4 6.83 11.73 15.23 16.98 Mirana -2 2 7.83 12 14.08 Monkey King 2 5.83 14.47 20.63 23.72 Morphling -2 2 11.1 17.6 20.85 Muerta -1 2.33 8.63 13.13 15.38 Naga Siren 1 4.5 12.2 17.7 20.45 Nature's Prophet 0 2.33 9.8 15.13 17.8 Necrophos 2 4 7.03 9.2 10.28 Night Stalker 2 5 10.13 13.8 15.63 Nyx Assassin 1 4 9.83 14 16.08 Ogre Magi 4 6.33 9.83 12.33 13.58 Omniknight 2 4.5 9.17 12.5 14.17 Oracle 1 3.5 7.47 10.3 11.72 Outworld Destroyer 2.5 6.17 9.9 12.57 13.9 Pangolier 2 5 10.83 15 17.08 Phantom Assassin 1 4.5 12.43 18.1 20.93 Phantom Lancer -1 3.33 9.87 14.53 16.87 Phoenix -1 1 4.5 7 8.25 Primal Beast 2 4.5 6.83 8.5 9.33 Puck -3 0.67 6.5 10.67 12.75 Pudge -1 1.33 4.6 6.93 8.1 Pugna 0 3.5 6.53 8.7 9.78 Queen of Pain 0 3.67 9.5 13.67 15.75 Razor 0 4 10.53 15.2 17.53 Riki 0 5 10.6 14.6 16.6 Rubick 1 4.83 10.67 14.83 16.92 Sand King 1 4.17 8.37 11.37 12.87 Shadow Demon 0 3 8.13 11.8 13.63 Shadow Fiend 1 5.17 13.33 19.17 22.08 Shadow Shaman 3 5.67 9.4 12.07 13.4 Silencer 0 3.67 9.27 13.27 15.27 Skywrath Mage -2 0.17 2.03 3.37 4.03 Slardar 3 5.83 11.43 15.43 17.43 Slark 0 3.5 7 9.5 10.75 Snapfire 1 3.67 6.47 8.47 9.47 Sniper -1 3.5 10.97 16.3 18.97 Spectre 0 4.17 9.07 12.57 14.32 Spirit Breaker 1 3.83 7.8 10.63 12.05 Storm Spirit 1 4.67 10.73 15.07 17.23 Sven -1 2.5 7.63 11.3 13.13 Techies 2 4.33 7.37 9.53 10.62 Templar Assassin 0 3.83 11.3 16.63 19.3 Terrorblade 5 8.67 18 24.67 28 Tidehunter 0 2.5 6 8.5 9.75 Timbersaw 0 2.67 5.7 7.87 8.95 Tinker 2 4.83 8.1 10.43 11.6 Tiny 0 0 0 0 0 Treant Protector -1 1.5 5.7 8.7 10.2 Troll Warlord -1 2.83 10.53 16.03 18.78 Tusk 1 4.83 9.73 13.23 14.98 Underlord 3 5 8.73 11.4 12.73 Undying 1 2.67 5.47 7.47 8.47 Ursa 1 4 10.53 15.2 17.53 Vengeful Spirit 0 3.5 8.4 11.9 13.65 Venomancer 0 4 8.67 12 13.67 Viper -2 1.5 7.8 12.3 14.55 Visage -1 0.83 3.17 4.83 5.67 Void Spirit -1 2.17 7.3 10.97 12.8 Warlock 1 2.67 5 6.67 7.5 Weaver 1 3.83 11.07 16.23 18.82 Windranger 0 3.17 6.43 8.77 9.93 Winter Wyvern 1 3.67 7.17 9.67 10.92 Witch Doctor 0 2.17 5.43 7.77 8.93 Wraith King -1 1.67 5.63 8.47 9.88 Zeus 2 3.83 6.63 8.63 9.63

Bonus armor

Bonus armor is the armor value shown in green numbers with a plus on the left, right below the white armor number on a unit's statistics. Whenever an item or ability shows a +ArmorValue, e.g. Blade Mail +6 Armor, it increases the bonus armor of the affected unit.

Probably the most important difference between main and bonus armor is that illusions only benefit from main armor, although their HUD still shows the bonus armor just like on other heroes, to make them less obvious to the enemy. Some abilities like Marksmanship and Natural Order also only affect main armor.

Modifying armor

A lot of abilites and items have abilities that grant or reduce armor. These changes always affect bonus armor, and never added to the main armor.

Armor increasing abilities

The following abilities increase armor:

Armor increasing abilities

• Ancient Black Dragon - Dragonhide Aura
  
  Armor bonus: 1200
  Aura, affects nearby allies. Multiple instances fully stack. The buff lingers for 3 seconds.
• Axe - Berserker's Call
  
  Armor Bonus: 25
  Duration: 1.8/2.2/2.6/3
  Affects the caster.
• Axe - Battle Hunger
  
  Self Armor Bonus per Affected Enemy:
  Duration: 1.8/2.2/2.6/3
  Affects the caster.
• Crystal Maiden - Freezing Field
  
  Armor bonus: 20
  Duration: 10
  Affects the caster. Lasts until the channeling stops.
• Dragon Knight - Dragon Blood
  
  Armor bonus: 4/7/10/13 ( 16/19/22/25)
  Passive.
• Elder Titan - Astral Spirit
  
  Armor bonus per hero: 1.5/3/4.5/6
  Armor bonus per creep: 0.5
  Duration: 10
  Affects the caster. Bonuses are granted once the spirit rejoins with the caster. Bonuses are based on how many enemies the spirit touched while out.
• Lone Druid - True Form
  
  Armor bonus: 8/10/12
  Duration: 40
  Affects the caster.
• Monkey King - Wukong's Command
  
  Armor bonus: ( )
  Max Duration:
  Affects the caster.
• Ogre Frostmage - Ice Armor
  
  Armor bonus: 4/5/6/8
  Duration: 45
  Affects the target ally.
• Roshan - Strength of the Immortal
  
  Armor bonus per minute: 1
  Passive.
• Slardar - Guardian Sprint
  
  River Armor bonus: 10 ( )
  Requires Aghanim's Scepter. Affects the caster. Passively provided while standing in the river or in a Slithereen Crush puddle.
• Sven - Warcry
  
  Armor bonus: 6/9/12/15
  Duration: 10 ( 14)
  Affects all nearby allied heroes.
• Timbersaw - Reactive Armor
  
  Armor bonus per stack: 0.4/0.5/0.6/0.7
  Max stacks: 15/24/33/42 ( 21/30/39/48)
  Stack duration: 3
  Passive. Gains a stack whenever an attack lands on the hero. The stacks have independent durations.
• Tiny - Grow
  
  Armor bonus: 100/200/300
  Passive.
• Treant Protector - Living Armor
  
  Armor bonus: 15/20/25/30
  Duration:
  Affects the target ally ( all allies within the targeted area).
• Towers - Tower Protection
  
  Armor bonus (tier 1 towers): 3/5/5/5
  Armor bonus (tier 2/3/4 towers): 1/3/3/3
  Aura, affects nearby allies. The buff lingers for 0.5 seconds.
• Troll Warlord - Berserker's Rage
  
  Armor bonus: 4/5/6/7
  Affects the caster. Lasts until toggled off.
• Wildwing Ripper - Toughness Aura
  
  Armor bonus: 1200
  Aura, affects nearby allies. The buff lingers for 3 seconds.

Armor increasing items

• Armlet of Mordiggian - Unholy Strength
  
  Armor bonus: 4
  Affects the caster. Armor is granted after the delay. Lasts until toggled off.
• Assault Cuirass - Assault Aura
  
  Armor bonus: 5
  Aura, affects nearby allies. The buff lingers for 0.5 seconds.
• Buckler - Buckler Aura
  
  Armor bonus: 2
  Aura, affects nearby allies. The buff lingers for 0.5 seconds. Can be toggled to only affect heroes.
• Guardian Greaves - Guardian Aura
  
  Boosted armor bonus: 12
  Aura, affects nearby allied heroes that are below 1.5 health. The buff lingers for 12 seconds.
• Medallion of Courage - Valor
  
  Armor bonus: 6
  Duration: 8
  Affects the target ally.This is an old ability.
• Ring of Aquila - Aquila Aura
  
  Armor bonus: 2
  Aura, affects nearby allies. The buff lingers for 0.5 seconds. Can be toggled to only affect heroes.
• Solar Crest - Shine
  
  Armor bonus: 70
  Duration:
  Affects the target ally.

Armor reducing abilities

Armor Corruption's icon

The following heroes have a talent that causes their attacks to reduce armor of the attacked target. This is also known as Armor Corruption.

The reduction lasts 10 seconds. Multiple sources of Armor Corruption do not stack.

Bonus	Level 10		Level 15		Level 20		Level 25
	Left	Right	Left	Right	Left	Right	Left	Right
Armor Corruption					-4

The following abilities reduce armor:

Armor reducing abilities

• Alchemist - Acid Spray
  
  Armor reduction: 3/4/5/6
  Duration: 15
  Aura, affects enemies within the target area. The debuff lingers for 0.5 seconds.
• Bristleback - Viscous Nasal Goo
  
  Base armor reduction: 1.5/2/2.5/3
  Armor reduction per stack: 15%
  Max stacks: 2/2/3/3 ( 8)
  Hero Duration: 10
  Creep Duration:
  Affects the target enemy. Multiple casts increase the stack count, and refresh the duration of existing stacks.
• Chaos Knight - Reality Rift
  
  Armor reduction: 4/5/6/7
  Duration: 6
  Affects the target enemy.
• Dazzle - Bad Juju
  
  Armor reduction per cast: 20 ( )
  Duration:
  Affects nearby enemies whenever casting a spell. Multiple casts increase the stack count, and refresh the duration of existing stacks.
• Forged Spirit - Melting Strike
  
  Armor reduction per stack: 20 ( )
  Max stacks: 0.8/0.9/1/1.1/1.2/1.3/1.4/1.5 ( )
  Duration: 5
  Passive. Affects the attacked enemy. Multiple attacks increase the stack count, and refresh the duration of existing stacks.
• Lycan - Howl
  
  Armor reduction: 25%/30%/35%/40%
  Duration: 4/5/6/7
  Affects nearby enemies, and all enemies around each Lycan Wolf that is alive.
• Naga Siren - Rip Tide
  
  Armor reduction: 4 ( )
  Duration:
  Passive, has a chance to trigger on attacks. Affects nearby enemies.
• Pangolier - Lucky Shot
  
  Armor reduction: 40/80/120/160
  Duration: 2.5/3/3.5/4
  Has a chance to proc on attack, affecting the attacked enemy.
• Razor - Eye of the Storm
  
  Armor reduction per strike: 1
  Max duration: 30
  Strikes the lowest health enemy within range. Does not reduce armor of hit buildings. The armor duration of each strike is based on the storm's remaining duration.
• Shadow Fiend - Presence of the Dark Lord
  
  Armor reduction: 4/5/6/7 ( )
  Aura, affects nearby enemies. The debuff lingers for 2 seconds.
• Slardar - Corrosive Haze
  
  Armor reduction: 100 ( )
  Duration: 10/15/20
  Affects the target enemy.
• Templar Assassin - Meld
  
  Armor reduction: 5/6/7/8 ( 8/9/10/11)
  Duration: 12
  Affects the attacked enemy.
• Tidehunter - Gush
  
  Armor reduction: 4.5 ( )
  Duration:
  Affects the target enemy ( affects all hit enemies).
• Vengeful Spirit - Wave of Terror
  
  Armor reduction: 3/4/5/6 ( 8/9/10/11)
  Duration: 8
  Affects all hit enemies.
• Weaver - The Swarm
  
  Armor reduction per interval: 1 ( 1.5)
  Duration: 16
  Affects all hit enemies. The beetles reduce armor in 1.15/1.0/0.85/0.7 second intervals. The reduction lasts as long as the beetles do.

Armor reducing items

• Assault Cuirass - Assault Aura
  
  Armor reduction: 5
  Aura, affects nearby enemies. The debuff lingers for 0.5 seconds.
• Blight Stone - Lesser Corruption
  
  Armor reduction: 2
  Duration: 8
  Affects the attacked enemy.
• Desolator - Corruption
  
  Armor reduction: 6
  Duration: 7
  Affects the attacked enemy.
• Mask of Madness - Berserk
  
  Armor reduction: 8
  Duration: 6
  Affects the caster.
• Medallion of Courage - Valor
  
  Caster armor reduction: 6
  Target armor reduction: 6
  Duration: 8
  Affects the caster and the target enemy.This is an old ability.
• Orb of Corrosion - Corrosion
  
  Armor reduction: 3
  Duration: 4%
  Affects the attacked enemy.
• Orb of Destruction - Impeding Corruption
  
  Armor reduction: 3
  Duration: 4
  Affects the attacked enemy.
• Solar Crest - Shine
  
  Caster armor reduction: 7
  Target armor reduction: 8
  Duration:
  Affects the caster and the target enemy.
• Stygian Desolator - Greater Corruption
  
  Armor reduction: 10
  Duration: 7
  Affects the attacked enemy.

Armor negating abilities

Some abilities negate a unit's armor by reducing or increasing armor based on the unit's armor, effectively removing a percentage of the armor on the target. This Armor negation only affects the armor value of units, their armor type is unaffected and still reduces damage normally.

The following abilities negate armor:

Armor negating abilities

• Drow Ranger - Marksmanship
  
  Main armor negation: 100%
  Has a chance to completely ignore the target's main armor value on attack, dealing damage as if they had 0 main armor.
• Elder Titan - Natural Order
  
  Main armor negation: 40%/60%/80%/100%
  Aura, affects nearby enemies. The reduction is based on the enemies' main armor. The debuff lingers for 1 second.

Armor granting talents

The following heroes have a talent that grants them bonus armor.

Bonus	Level 10		Level 15		Level 20		Level 25
	Left	Right	Left	Right	Left	Right	Left	Right
Armor	+4	+5 +5

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

Specific summons armor bonus

• Lone Druid - Talent by Level 15 Left
  
  +7 Spirit Bear Armor:
  
• Warlock - Talent by Level 25 Right
  
  +20 Chaotic Offering Golems Armor:
  

Damage multiplier

All units, including buildings, have an inherent base armor value and armor type. 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.

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

${\text{DamageMultipler}}=1-\displaystyle {\frac {0.06\times MainArmor}{1+0.06\times \vert MainArmor\vert }}$

The damage multiplier limits are 2 and 0, for infinitely negative and positive armor, respectively.

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%

Effective HP

Relationships between effective HP%, damage multiplier and armor

The total amount of physical damage a unit can take due to the armor it has is known as effective HP (or EHP). 16.66 armor adds 100% to EHP. This means a unit with 1000 health and 16.66 armor can take 2000 physical damage. The formula adds 6% EHP per point of armor regardless of the previous armor value.

However, EHP value is of a diminished benefit as a player gaining 1 armor from 0 armor would increase EHP from 100% to 106%, while a player gaining 1 armor from 50 armor would increase EHP from 400% to 406%. On the other hand, the effectiveness of armor is much lower at negative values (refer to graph). Total EHP trends downwards towards 50%, meaning a unit with 1000 health and infinitely low armor would still be able to take 500 physical damage. At this point, losing or gaining 1 armor has essentially no effect.

Armor	-40	-30	-20	-10	0	10	20	30	40
Effective HP	586.21	608.7	647.06	727.27	1000	1600	2200	2800	3400

This definition of EHP assumes all damage taken is physical. EHP against magical damage (such as Lina's or Lion's ultimate) is modified by magic resistance.

Effective HP against physical damage is defined as

${\text{EHP}}=\displaystyle {\frac {CurrentHealth}{DamageMultiplier}}$

Example 1

A Level 25 Sven has a total health of 2293.6 and 11.3 points of armor. What is his effective HP against physical damage?

${\text{DamageMultiplier}}=1-{\frac {0.06\times 11.3}{1+0.06\times \vert 11.3\vert }}=0.595948$

${\text{EHP}}={2293.6 \over 0.595948}=3848.66$

Sven's effective HP against physical damage in this example is 3848.66.

Example 2

The same Level 25 Sven from previous example (has a total health of 2293.6) is affected by a Level 3 Corrosive Haze, and his armor is now . What is his effective HP against physical damage?

Failed to parse (syntax error): {\displaystyle \text{DamageMultiplier Example} = 1 - \frac{0.06 \times (<strong class="error">Expression error: Missing operand for -.</strong>)}{1 + 0.06 \times \vert <strong class="error">Expression error: Unexpected &lt; operator.</strong> \vert} = <strong class="error">Expression error: Unexpected &lt; operator.</strong> }

Failed to parse (syntax error): {\displaystyle \text{EHP} = {2293.6 \over <strong class="error">Expression error: Unexpected &lt; operator.</strong>} = <strong class="error">Expression error: Unexpected &lt; operator.</strong> }

Sven's effective HP against physical damage in this example is .

Armor types

There are several different types of armor, which determine how much damage a unit takes against certain attack damage types. Each of the 3 different armor types either reduces, increases or does not affect the damage from each of the damage types, on top of armor values manipulating them.

Attack damage dealt against armor type is defined as

${\text{AttackDamageDealt}}=OriginalAttackDamage\times DamageMultiplier\times ArmorTypeMultiplier$

This table shows how much damage each armor type reduces against each attack damage type and which unit uses which armor type (units which take a set amount of damage per attack are excluded).

Armor Type	Used by	Attack Damage Type
		Hero	Basic	Pierce	Siege
Hero		100%	75%	50%	100%
Basic		100%	100%	150%	100%
Structure		50%	70%	35%	250%

Example 1

Sven with 100 damage attacks a siege creep which has 0 armor and deals 50 damage to it. The attack type "hero" deals 50% less damage against the armor type "structure" which is the siege creeps' and all buildings' armor type. If the siege creep gained 5 armor, how much the 100 damage attack would deal?

${\text{SiegeCreep DamageMultiplier Example}}=1-{\frac {0.06\times 5}{1+0.06\times \vert 5\vert }}=0.76923$

The siege creep damage multiplier is 0.76923.

${\text{AttackDamageDealt Example}}=100\times 0.76923\times 0.5=38.4615$

The armor type multiplier is 0.5 because the attack type "hero" deals 50% less damage against the armor type "structure".

Therefore in this example, Sven's 100 damage attack to the siege creep with 5 armor would be 38.4615. The same attack would deal 76.923 damage to a unit with any other armor type, since attack type hero deals full damage to them.

Trivia

Negative armor damage multiplier for DotA and Dota 2

This graph shows how much more additional damage a target takes when armor debuffs are applied, using the WC3 DotA armor formula.

• In DotA the base magic resistance was bound to the assigned armor. In case of Hero Armor only 75% of the magic damage was applied. Some heroes possessed hidden passive skills to alter their base magic susceptibility albeit Hero Armor to 90% ( Visage) or 65% ( Meepo). Nowadays, in Dota 2 magic resistance works independently from armor.
• In 6.86 Armor types were renamed and some other types were removed.
  • The following armor types were renamed: Unarmored ➜ Soft, Light ➜ Weak, Medium ➜ Basic, Heavy ➜ Strong and Fortified ➜ Structure.
  • Weak and Basic armor types were removed. Units who previously uses the Weak and Basic armor type now use the Soft and Strong armor type respectively.

Negative armor disparity

Amplified damage from negative armor is calculated differently in WC3 DotA than in Dota 2.

Negative armor in WC3 DotA has a cap of -20 armor (71% damage increase). Further reducing the armor does not change the damage increase. Also, the more aggressive damage amplify formula is used resulting in a max damage increase of 71%.

The amplified damage is defined as

$\text{DamageIncrease} = 1 - 0.94^{-a}$

With a being the index of armor.

Comparison table

Armor	WC3 DotA Damage amplification	Dota 2 Damage amplification	Relative difference
0	0.0%	0.0%	N/A
-5	26.6%	23.1%	3.5%
-10	46.1%	37.5%	8.6%
-20	71.0%	54.5%	16.5%
-40	71.0%	70.6%	0.41%
-60	71.0%	78.3%	-7.3%

Recent Changes

Main Article: Armor/Changelogs

References

Mechanics Main Heroes Unit Type (Heroes / Clones / Illusions) Complexity Attributes Table Buyback Level Roles Gold Experience Animations Stats Armor Attributes ( Strength / Agility / Intelligence) / Universal) Health & Mana (HP Regen & MP Regen) Magic Resistance Movement Speed / Slow Resistance Status Resistance Turn Rate Misc Creep Controling Death / Denying Vision Unit Size (Collision Size / Bound Radius / Selection Box / Model Size) Gib Type / Shades Adjectives Buildings Towers / Barracks / Ancient / Fountain Effigy Neutral Buildings (Outposts / Watchers / Twin Gates / Lotus Pools) Abilities Type Active / Passive / Autocast Aura Accuracy / Evasion Channeling Damage Barrier Damage Block 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 Runes Bounty Rune Water Rune Wisdom Rune Power Runes ( Amplify Damage Rune / Arcane Rune / Haste Rune / Illusion Rune / Invisibility Rune / Regeneration Rune / Shield Rune) Misc Random Distribution Transformation 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 / No-Spell-Lifesteal / No-Spell-Amplification) Projectile Speed Spell Damage (Outgoing / Incoming) Modifiers Bash Cleave / Splash Corruption Critical Strike Lifesteal / Spell Lifesteal Mana Break On-hit Effects Misc Damage Instance Animation / Orb Walking Status Effects Disables Cyclone Disabling Orders Forced Movement (Knockback) / Upward Movement Fear (Hypnosis) Hide Hex Root Leash Stun Sleep Taunt Movement Move Speed Slow Flying Movement Phased / Tree Walk / Unobstructed Movement Other Attack Immune / Non-targetable Attack Speed Slow Debuff Immunity Spell Immunity Invulnerability Invisibility Blind Break Disarm Ethereal Silence Mute Trap Dispels Basic Strong Death Items Mechanics Courier Sharing / Selling Disassemble Recipes Neutral Item Drop