Armor is a stat shared by all units, including monsters, and buildings. Increasing armor reduces the physical damage the unit takes. Each champion begins with some armor which increases with level ( Thresh being the only exception). You can gain additional armor from abilities, items, and runes. Armor stacks additively.

Excluding Thresh whose base armor does not scale with levels, base armor ranges from 68. 04 ( Orianna) to 130 ( Pyke) at level 18.

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Damage reduction

Note: One can include the armor penetration in all the following ideas by enumerating it with a due amount of corresponding negative armor.

Incoming physical damage is multiplied by a factor based on the unit's armor:

$ \pagecolor{Black}\color{White}{\rm Damage\ multiplier}=\begin{cases}{100 \over 100+{\it Armor}}, & {\rm if\ }{\it Armor} \geq 0\\2 - {100 \over 100 - {\it Armor}}, & {\rm otherwise}\end{cases} $

Examples:

25 armor → × 0.8 incoming physical damage (20% reduction, + 25% effective health).

× + 100 armor → × 0.5 incoming physical damage (50% reduction, +100% effective health).

× -25 armor → × 1.2 incoming physical damage (20% increase, -16.67% effective health).

Stacking armor

Every point of armor requires a unit to take 1% more of its maximum health in physical damage to be killed. This is called effective health:

$ \pagecolor{Black}\color{White}{\rm Effective\ health} = \left(1 + \frac{{Armor}}{100}\right)\times{\rm Nominal\ health} $

Example: A unit with 60 armor has 60% more of its maximum health in effective health, so if the unit has 1000 maximum health, it will take 1600 physical damage to kill it.

What this means: by definition, armor does not have diminishing returns in regard of effective hitpoints, because each point increases the unit's effective health against physical damage by 1% of its current actual health whether the unit has 10 armor or 1000 armor. However, health and armor have increasing returns with respect to each other.

Example: A unit starts with 1000 health and 100 armor giving it 2000 effective health. Now, it increases its nominal health from 1000 to 2000, thereby increasing its effective health from 2000 to 4000. Increasing the unit's armor by 100 at both nominal health levels would yield +1000 effective health and +2000 effective health, respectively. If we were to consider two nominal armor levels and then increase both by a static amount of health, we would see a similar increased return of effective health for the same nominal health.

Therefore, buying only armor is gold inefficient compared to buying the optimal balance of health and armor. It is important to not stack too much armor compared to health or else the effective health will not be optimal.

When a unit's armor is negative because of armor reduction or debuffs, armor has increasing returns with respect to itself. This is because negative armor cannot reduce effective health to less than 50% of actual health. A unit with -100 armor has 66.67% of nominal health (gains −33. 33 %) of its maximum health as effective health.

Armor as scaling

These use the champion's armor to increase the magnitude of the ability. It could involve total or bonus armor. By building armor items, you can receive more benefit and power from these abilities.

Champions

Items

Runes

Increasing armor

Items

Champion abilities

Runes

Ways to reduce armor

Note that armor penetration and armor reduction are different.

Armor vs. health

Note: The following information similarly applies to magic resistance. As of season six, the base equilibrium line for armor is a function:

health = 7. 5 × (armor + 100)

while for magic resistance the line is a bit shifted down and less steep:

health = 6. 75 × (magic resistance + 100)

It can be helpful to understand the equilibrium between maximum health and armor, which is represented in the graph[1] on the right. The equilibrium line represents the point at which your champion will have the highest effective health against that damage type, while the smaller lines represent the baseline progression for each kind of champion from level 1-18 without items. You can also see that for a somewhat brief period in the early game health is the most gold efficient purchase, however this assumes the enemy team will only have one type of damage. The more equal the distribution of physical damage/magic damage in the enemy team, the more effective will buying health be.

There are many other factors which can effect whether you