Armor



Armor ( $$R$$ ) is a stat that reduces (or increases, if negative) physical damage a unit takes from abilities 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 via leveling up, certain items,  talents and some abilities. Armor of any unit can also be temporarily increased or reduced with some abilities.

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

Total armor is defined as



With  being the Total Armor,   the Base Armor,   the Armor Negating Multiplier and   the Bonus Armor (Flat armor values other than  sources).

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.

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, which is gained by leveling up, acquiring certain items, or with the help of certain abilities.

The main armor is defined as



With  being the Main Armor,   being the Base Armor and   the Armor Negating Multiplier.

Bonus Armor
Bonus armor is the armor value shown in green numbers with a plus on the left, right after the white armor number on a unit's statistics. Whenever an armor granting item or armor increasing ability shows a, e.g.   , 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 and  also only affect main armor.

Modifying Armor
A lot of abilities and items have abilities that grant or reduce armor.

These changes mostly affect bonus armor, and never added to the main armor, with, and  being exceptions.

Armor Increasing Abilities
The following abilities increase armor:

Armor Reducing Abilities
The following abilities reduce armor:

Armor Negating Abilities
Some abilities negate or ignores 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 defense class is unaffected and still reduces damage normally.

The following abilities negate base armor:

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

Armor Corruption
Armor Corruption is granted by choosing a Talent, that causes hero attacks to reduce armor of the attacked target.

Damage Multiplier
All units, including buildings, have an inherent base armor value and defense 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.

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

With  being the Damage Multiplier and   the armor value.

The damage multiplier limits are and, 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

Defense Classes
There are several different classes of armor defense (also known as armor type), which determine how much damage a unit takes against certain attack classes. Each of the 3 different defense classes (Hero, Basic, Structure) either reduces, increases, or does not affect the damage from each of the attack classes, on top of armor values manipulating them.

Attack damage dealt against defense class is defined as



With  being the Attack Damage,   being the Defense Class Damage Multiplier and   being the Damage Multiplier.

The following table shows how much damage each defense class reduces against each attack class, and the unit's defense class (units which take a set amount of damage per attack are excluded).

Examples

 * with 100 damage attacks a siege creep which has 0 armor and deals damage to it. If the siege creep gained 5 armor, how much the 100 damage attack would deal?


 * 's Base Armor for this example is.
 * 's Base Armor for this example is.




 * 's Damage Multiplier is undefined.
 * According to the table values, the attack class multiplier is because the attack class "hero" (from ) deals % less damage against the defense class "structure" (to the Siege Creep).




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

Effective HP
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 % to EHP. This means a unit with 1000 health and 16.66 armor can take 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 the attached 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.

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

Effective HP against physical damage is defined as



With  being the Current Health and   the Damage Multiplier.

Examples

 * Example 1:


 * A Level 25 has a total health of  and  points of armor without any items. What is his effective HP against physical damage?


 * 's damage multiplier is in this example.
 * 's damage multiplier is in this example.




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


 * Example 2:


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




 * 's damage multiplier is in this example.




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