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Damage and Armor

 

All damage dealt throughout the game have a certain type. Some are reduced by armor (attacks), some spell resistance (Arc Lightning) and some are seemingly not reduced at all (Laser). Damage does always take the armor type into consideration, but sometimes it just isn't reduced.

All damage has two properties under consideration here: attack type and damage type. It is possible to deal damage with any combination of one attack type and one damage type.

Attack type 


The attack type of an instance of damage determines how it is reduced by the target's armor type. Physical attacks have their attack types determined by a fixed property of the attacking unit; you can see the unit's attack type by hovering the mouse over the attack icon near the bottom of the screen. The types that are used on units in DotA are: Hero, Normal, Piercing, Siege, Chaos, and (rarely) Magic. Damage with these attack types will be reduced by the armor types (see below) which can be read in the tooltip that shows up when you hover the icon. There is another attack type which is only used for abilities, it is called Spells. Damage with this type will be reduced by armor type Hero, and it will also get reduced further by items or abilities giving extra spell resistance. There are also some unique mechanics with attack type Magic (not to be confused with the more common damage type Magic or attack type Spells) used by only one unit in the game: Oblivion attacking an ethereal unit while holding a Deolator, Maelstrom, or Mjollnir. Because of the rarity of this attack type, we will not address it here.


Damage type


Damage type is another field determining if the damage should be even further reduced or blocked. The types used in DotA are: Normal, Enhanced, Magic, and Universal. Normal damage is used by all attacks and a few spells (like Quill Spray). It is blocked by the ethereal state and is the only damage type reduced by armor value (see below). Enhanced damage is used by Cleave and a few spells (like Echo Slam) and is similar to Normal, but is not reduced by armor value. Magic damage is used by the majority of abilities; instead of being blocked by the ethereal state, it is blocked by magic immunity. Finally, Universal damage (used by spells like Doom) is not blocked by ethereal or magic immunity, and affects all units as long as they aren't invulnerable.

The most common ability combination is attack type Spells, damage type Magic, which is reduced by spell resistance and blocked by magic immunity.



Armor

Just like damage, armor consists of two parts as well: Armor type and armor value. The former, armor type, is fixed for each unit (a hero will always have armor type Hero) during the whole game. The used armor types in DotA are: Hero, Unarmoured, Fortified, Light, Medium and Heavy. It is the combination between Armor type and Attack type which determines the primary reduction in damage. Which types are reduced can be seen in the tooltip which appears when you hover the armor type icon ingame (or looking in the table below).

Armor value can be changed while playing by various items and abilities. Some increasee the units' armor value (Plate Mail) and some reduce it (Acid Spray). Only damage with Damage type Normal will get reduced by armor value.

Damage reduction given by armor value is calculated by the following formulas:

Positive armor values:


Damage Reduction = ( 0.06 * armor ) / (1 + 0.06 * armor)


Examples:
10 armor:
( 0.06 * 10 ) / ( 1 + 0.06 * 10 ) = 0.6 / 1.6 = 0.375 = 37.5%
20 armor:
( 0.06 * 20 ) / ( 1 + 0.06 * 20 ) = 1.2 / 2.2 = 0.545 = 54.5%


Negative armor values:



Damage Increase = 1 - 0.94 ^ (-armor)

Examples:
-5 armor:
1 - 0.94 ^ (--5) = 1 - 0.94 ^ 5 = 0.266 = 26.6%
-10 armor:
1 - 0.94 ^ (--10) = 1 - 0.94 ^ 10 = 0.461 = 46.1%


Negative armor has a cap of -20 (71% damage increase). Reducing the armor even more will not change the damage increase.

 

 

Attack type versus Armor Type table

 

--------- Light Medium Heavy Fortified Hero Unarmored
Chaos 100% 100% 100% 40% 100% 100%
Hero 100% 100% 100% 50% 100% 100%
Normal 100% 150% 125% 70% 75% 100%
Pierce 200% 75% 75% 35% 50% 150%
Siege 100% 50% 125% 150% 75% 100%
Spells 100% 100% 100% 100% 75% 100%

 

Armor Stacking

It is generally conceived that armor gets less and less effective the more you have (since the extra damage reduction gets less and less). That a Plate Mail gives you less extra protection from attacks if you already have 20 armor than if you would have only 5. This is false. If one Plate Mail makes the hero survive 3 extra attacks, then 4 Plate Mails will make the hero survive a total of 12 extra attacks before dying. Each Plate Mail gives the same amount of extra protection, which is in this case 3 more attacks before dying.

 


Proof:
Consider a hero with 1000 hp and 0 armor. To kill it one needs to deal at least 1000 damage to it.

If we give the hero 10 armor, which is 37.5% damage reduction, every attack would only deal 62.5% of the original value (100% - 37.5% = 62.5%). To kill it now, one needs to deal 1600 damage (1600 * 0.625 = 1000). You could say that the hero now have 600 more effective hp (EHP).

If we instead give the hero 20 armor, which is 54.5% damage reduction. The damage multiplier is now 45.5%. The damage needed to kill would increase to 2200 (2200 * 0.455 = 1000). The increase in EHP is 1200, twice the amount as given by only 10 armor.


Every armor point adds an additional 6% of your maximum HP to your EHP.



Stacking of damage abilities and armor



Items giving armor or pure damage (not percentage based, critical strikes or others) does stack perfectly with each other. Carrying two Mithril Hammers (+24 damage) will give you a total of +48 damage. The same is true for armor items, having two Plate Mails (+10 armor) gives you a total of +20 armor. There is no cap for how much armor or damage you can have, except that you only can carry 6 items at a time.

There are several different types of abilities which give units bonus damage or armor for a couple of seconds, or whenever they are inside an area. Stacking of such abilities or items follows different rules, but in general they do not stack with other copies of the same ability or item (multiple Ring of Basilius does not give you more than a +2 armor aura).


Damage enhancing abilities, percentage based


Apart from items or abilities giving you a fixed amount of damage, there are some that increases the damage depending on how much you already have. Vengeful Spirit's Command Aura is a good example, increasing nearby friendly units' attack damage by 12/20/28/36% (at level 1/2/3/4). This will only count the unit's base damage plus the primary attribute (in the case of heroes). Damage from any other source will not be counted. So an Ultimate Orb will increase the damage gained by Command Aura, but a Broadsword will not.