Armor

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 ( being the only exception). You can gain additional armor from abilities, items, masteries, and runes. Armor stacks additively.

Excluding whose base armor does not scale with levels, base armor ranges from   to   at level 18.

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

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

Examples:
 * 25 armor &rarr; &times; incoming physical damage (20% reduction, +25% effective health).
 * 100 armor &rarr; &times; incoming physical damage (50% reduction, +100% effective health).
 * &minus;25 armor &rarr; &times; incoming physical damage (20% increase, 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.
 * 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 units 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 HP and armor. It is important to not stack too much armor compared to HP or else the effective HP 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 has (gains ) of its maximum health as effective health.

Optimal Efficiency (theoretical)
''Note: 'Effective Health' describes the amount of raw damage a champion can receive before dying. It will always be more than or equal to a champion's displayed Health in their Health bar and it can be increased by buying items with extra Health, Armor and Magic Resist. In this article, Effective Health will refer to the amount of raw 'Physical Damage' a champion can take.''

In almost all circumstances, champions will have a lot more Health than Armor such that the following inequality will be true: Champion-Health > (Champion-Armor + 100).

If this inequality is true, a single point of Armor will give more 'Effective Health' to that champion than a single point of Health.

If (Health < Armor + 100), 1 point of Health will give more Effective Health than 1 of Armor.

If (Health = Armor + 100), 1 point of Health will give exactly the same amount of Effective Health as 1 point of Armor.

Because of this relationship, theoretically, the way to get the maximum amount of Effective Health from a finite combination of Health and Armor is to ensure that you have exactly 100 more Health than Armor (this is true regardless of how much Health and Armor you actually have).

Example: Given a theoretical situation where you start off with 0 Health and 0 Armor and are given an arbitrary number of stat points (x > 100) each of which you can either use to increase your Health or Armor by 1 point, the way to maximize your Effective Health is to add points to your health until your Health = (Armor + 100) = (0 + 100) = 100, and then split the remaining stat points in half, spend half on your Health and half on your Armor.

It's important to note that this information is purely theoretical and due to limitations from the game from champions' base stats and item stats it is incredibly difficult to acquire enough Armor to satisfy the conditions given above (to the point where players shouldn't attempt to if they are trying to actually win games).

Instead, broadly speaking, items which provide both Health and Armor give a very high amount of Effective Health against Physical Damage compared to items which only provide Health or only provide Armor. These items should be purchased when a player is seeking efficient ways to reduce the physical damage they take by a large amount.

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

 * grants armor equal to +  to himself and the target ally for 3 seconds.
 * grants armor to herself equal to +  for 3 seconds, deals damage after that time to units around her, and retains the defensive buff for an additional 3 seconds if any enemy is struck by the blast.
 * passively grants armor to himself equal to.
 * deals +  +  physical splash damage per basic attack in a 225-radius.
 * deals +  +  magic damage.
 * grants to himself equal to.
 * increases his armor by for 6 seconds, and deals  +  magic damage to enemies who basic attack him.
 * grants his next basic attack bonus magic damage equal to after using an ability.
 * passively grants bonus armor to himself and  to himself and nearby allied champions.
 * deals +  magic damage in a 375-radius and reduces nearby enemy armor by  +  for 4 seconds.
 * steals instantly . He continues to drain an additional over 4 second before decaying 4 seconds after the drain completes.

Items

 * , upon being hit by a basic attack, reflects magic damage back to the attacker equal to plus 15% of the incoming damage (before being reduced by defenses).
 * , After using an ability, your next basic attack (on-hit) creates an ICY ZONE around the target for 2 seconds. This zone has a radius of 190 units. (1.5 second cooldown.)

Champion abilities
Note: Only the armor buff effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.
 * allows her to enter an egg-state for up to 6 seconds upon reaching 0 health. While in this state, she will receive an armor modifier of.
 * increases armor by +  to himself and the target ally for 3 seconds.
 * increases an allied champion's armor by for 4 seconds.
 * increases his armor by (2level) when transform into.
 * permanently gains 0. 25 bonus armor every time he kills an enemy, up to a maximum of 30.
 * increases his armor by every second he remains in combat. This bonus stacks up to 10 times. Graves is considered in combat if he has dealt or received damage in the last 3 seconds.
 * increases his armor by.
 * increases his armor by for 4 seconds.
 * increases her armor by +  for 3 seconds, deals damage after that time to units around her, and retains the defensive buff for an additional 3 seconds if any enemy is struck by the blast.
 * passively grants armor to himself equal to.
 * increases an allied unit's armor by for 6 seconds.
 * passively increases his armor by when he is not under the effects of.
 * increases an allied champion's armor by for as long as the ball is attached to them.
 * increases his armor by for 6 seconds, and deals  +  magic damage to enemies who basic attack him.
 * Rengar lets out a battle roar, damaging enemies increases his armor by for 4 seconds. Rengar gains additional 50% armor for each enemy champion or large monster hit.
 * grants her bonus armor each times she damages an enemy with an ability or attack for 2 seconds. Subsequent damage will increase the duration by 2 seconds up to a cap of 8 seconds, after where damage will refresh the duration.
 * passively increases her armor by . This bonus is doubled while she is in Dragon Form.
 * increases his armor by for 25 seconds.
 * passively grants bonus armor to himself and  to himself and nearby allied champions.
 * passively generates souls for him to collect, with each soul collected granting armor permanently.
 * steals instantly . He continues to drain an additional over 4 second before decaying 4 seconds after the drain completes.
 * passively grants him armor for each nearby enemy champion.
 * increases his armor by for each enemy champion hit for 8 seconds.

Masteries

 * increases bonus and  by %.
 * grants your champion and  for each nearby enemy champion

Ways to reduce armor
See armor penetration. Note that armor penetration and armor reduction are different.

Armor vs. Health
Note: The following information also applies to Magic Resist.

It can be helpful to understand the equilibrium between maximum HP and Armor, which is represented in the graph 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 HP 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/magical damage in the enemy team, the more effective will buying HP be.

There are many other factors which can effect whether you should buy more Armor or HP, such as these key examples:
 * Unlike health, increasing armor also makes healing more effective because it takes more effort to remove the unit's health than it does to restore it.
 * HP helps you survive both magic and physical damage. Against a team with mainly burst or just low magical damage HP can be more efficient than MR.
 * Percentage armor reduction in the enemy team tilts the optimal HP:Armor ratio slightly in the favor of HP.


 * Whether or not the enemy is capable of delivering true damage or percent health damage, thus reducing the value of armor and HP stacking respectively.
 * The presence of resist or HP steroids built into your champion's kit, such as in or.
 * Against sustained damage Life steal and healing abilities can be considered as contributing to your maximum HP (while being mostly irrelevant against burst damage).
 * The need to prioritize specific items mainly for their other qualities (regardless of whether or not they contribute towards the ideal balance between HP and resists).

Trivia
(Last updated 26/05/2016 on patch 6.10)


 * Armor has a gold value of (30015). This value is derived from the basic item for armor.
 * One of the biggest amount of armor any champion can obtain, aside from, is  (which reduces physical damage by %), being a level 18.


 * Base stats: 
 * Runes:
 * 9GMarks (1).png Marks of Armor (+9 armor)
 * 9GSeals (2).png Scaling Seals of Armor (+93 armor)
 * 9GGlyphs (1).png Glyphs of Armor (+9 armor)
 * 3GQuintessences (2).png Scaling Quintessences of Armor (+3 armor)
 * Masteries:
 * 5 points in (+)
 * 5 points in (+35 armor)
 * Items:
 * 6 (+6100 armor)
 * Buffs:
 * (+90 armor)
 * (+30 armor)
 * (+22 armor) (this mastery can not stack)
 * (+ armor)
 * (+ armor)


 * Relevant mathematics:
 * bonus armor:
 * Items
 * Runes
 * Mast. & Buffs
 * Bonus Armor Amplification
 * bonus armor(60015)


 * armor:
 * Base stats: 
 * Items
 * Runes
 * Mast. & Buffs
 * Bonus Armor Amplification
 * armor(60015)


 * armor:
 * Base stats: 
 * Items
 * Runes
 * Mast. & Buffs
 * Bonus Armor Amplification
 * Armor Amplification
 * armor(((600)))


 * Having an enemy with the same setup use  on  will yield a total of  armor. This is the highest possible finite amount of armor (without using metagame effects—see below), and reduces physical damage by %.


 * armor


 * armor:
 * Base stats: 
 * Items
 * Runes
 * Mast. & Buffs
 * Bonus Armor Amplification
 * armor(600)

It is still possible to go higher through metagame functions. If a summoner disconnects from the server and is in the fountain, his champion will gain 1000 armor. With the same setup as above, a disconnected  with a disconnected  will have approximately 2779 armor. cannot exceed this. This reduces physical damage by.

, with his effectively infinite stacking, can obtain a maximum of  armor off his passive alone. With the same set-up as above, he can obtain a total of about armor, reducing physical damage by. If he disconnects, he can obtain up to armor, reducing it by