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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.

The types are split into two parts: Attack type and damage type. They are completly seperate and can be mixed into any combination.

Attack type 


It refers to the type of attack that was made to deal the damage. For units you can see this clearly if you hover the mouse over the attack icon in the bottom of the screen. The types that are used on units in DotA are: Hero, Siege, Chaos, Normal and Piercing. 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 some armor types (Hero armor for example), but it will also get reduced by items or abilities giving extra spell resistance.


Damage type


It's another field determining if the damage should be even further reduced or blocked. The types used in DotA are: Normal, Magic and Universal. Normal is the type for all attacks, and makes the damage gets reduced by armor value (see below). This type is also used for some spells (Quill Spray). Magic is the most common ability damage type which makes the damage not reduced by armor value at all. Instead the damage can be completly blocked by magic immunity. Universal is almost like Magic, with the exception that it isn't blocked by magic immunity.

The most common ability combination is: Attack type Spells, Damage type Magic. Thus, the damage is reduced by spell resistance and blocked by magic immunity.



Armor

Just like attack, 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 Cloud). 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. Command Aura is a good example of that, it increases nearby friendly units' attack damage with 12/20/28/36%. The behaviour of this (and all other percentage based damage increasers/decreasers) is that it will only count damage that are either base damage of the unit, or such damage that is given to it by stats (the primary attribute of heroes). Pure damage by items or abilities will not be counted. Neither will these abilities increase damage given by other of the same type (Command Aura will not benefit from the damage given by Trueshot Aura).