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

Excluding Thresh whose base armor does not scale with levels, base armor ranges from 65.5 ( Gnar) to 104.5 ( Rammus) at level 18.

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 →  × 1.20 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.

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.

Optimal efficiency (theoretical)

Note: Effective burst health, commonly referred to just as 'effective health', describes the amount of raw burst damage a champion can receive before dying in such a short time span that he remains unaffected by any form of health restoration (even if the actual considered damage is of sustained form). Unless champion's resists aren't reduced below zero, 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 resistance. 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 would be to ensure that you have exactly 100 more health than armor (this is true regardless of how much health and armor you actually already have).

Example: Given a theoretical situation where you start off with 0 health and 0 armor and are given an arbitrary sufficient 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.

However, this is only theoretically true if we consider both health and armor to be equally obtainable resources with simplified mechanism of skill point investment. In reality a player buys these stats for gold instead. As gold value of armor (derived from cost of basic armor item) is currently (as of season six) 7.5 times higher than gold value of health (derived from cost of basic health item), we theoretically can maximize effective health represented by product of 0.01 × health × (armor + 100) with gold as input variable by satisfying the following equation: health = 7.5 × (armor + 100). The graph and conclusions obtained by solving it are mentioned in the subsection below.

Example: Given a theoretical situation where you start off with 0 health and 0 armor and are given an arbitrary sufficient amount of gold (x ≥ 281.25), which you can either use to increase your health or armor, the way to maximize your effective health is to add points to your health until your health = 7.5 × (armor + 100) = 7.5 × (0 + 100) = 750, and then split the remaining gold in half, spend half on your health and half on your armor (as former is 7.5 times cheaper than the latter, it would lead to buying 7.5 times more additional health than armor and thus naturally reaching equality in the equation above).

Now we just formulated a simple 'rule of preserving equilibrium (or maximum effective health)':

Once equilibrium state is reached, all we need to do to preserve it is to always distribute gold equally into all involved stats for the rest of the game.

... or in our case, always 50% gold into health and 50% gold into armor.

Again this model is highly simplified and cannot be exactly applied in cases when we are buying any other item than basic armor item, Chain Vest or basic health item (for example if our decision-making process would involve Giant's Belt instead of Ruby Crystal, the above model would need to use equilibrium constant 7.6). Even considering the purchase of different armor or health items with differing gold efficiencies (quite natural expectation under real circumstances) makes use of single constant utterly impossible. Going even further, the continuous model simplifies a discrete character of real shopping, as you cannot really buy 1.5 ×  Ruby Crystals for 600, so with that much gold you opt to buy either a single Ruby Crystal or 2 ×  Cloth Armors, drastically changing the equilibrium constant to 5.0.

However, thankfully to almost linear item stats' gold efficiency a player can use weakened base equilibrium condition in a form: health ≈ 7.5 × (armor + 100) safely enough to speed up decision-making. The important thing to remember is that there is no reason to hold to it too strictly.

Note: In case of magic resistance only the basic constant 7.5 is slightly changed to 6.75.

This information is strongly theoretical and due to game limitations from champions' base stats, innate abilities and non-linearity of gold value of item stats (gold value of stats differs for different items or is even impossible to be objectively evaluated due to interference of unique item abilities), the real equilibrium function is too complicated to be any useful.

The complexity of this problem provides space for players' intuition to develop and demonstrate their itemization skills. If given sufficient amount of time, each player could perfectly analyze situation at any given moment when he exited the shop and tell what should he buy at that moment for available gold to maximize own effective health. The sheer impossibility of doing such thing in real time creates opportunity to develop the skill. Not only that but often choosing to maximize current effective health leads to suboptimal decision branches in the future. The summary on end game screen about type of fatal damage taken is a key part of this decision process as well.

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. Furthermore, these items are among all available items the best ones to distribute their gold value equally among both health and armor, thus working perfectly for rule of preserving equilibrium.

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

• Braum's Stand Behind Me grants armor equal to 15 / 17.5 / 20 / 22.5 / 25 (+ 10 / 11.5 / 13 / 14.5 / 16% bonus armor) to himself and the target ally for 3 seconds.
• Leona's Eclipse grants armor to herself equal to 20 / 30 / 40 / 50 / 60 (+ 20% bonus armor) 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.
• Malphite's Brutal Strikes passively grants armor to himself equal to 15 / 20 / 25 / 30 / 35% of his total armor.
  • Malphite's Brutal Strikes deals 15 / 30 / 45 / 60 / 75 (+ 15% armor) (+ 10% AP) splash physical damage per basic attack in a 225-radius.
  • Malphite's Ground Slam deals 60 / 100 / 140 / 180 / 200 (+ 30% armor) (+ 20% AP) magic damage.
• Poppy's Steadfast Presence passively grants armor to herself equal to 15% of her total armor, increased to 30% of her total armor while below 40% maximum health.
• Rammus' Spiked Shell grants attack damage to himself equal to 25% of his total armor.
  • Rammus' Defensive Ball Curl increases his armor by 40 / 60 / 80 / 100 / 120 for 6 seconds, and deals 15 / 25 / 35 / 45 / 55 (+ 10% armor) magic damage to enemies who basic attack him.
• Taric's Bravado grants his next two basic attack bonus magic damage equal to Template:Pp18 (+ 15% bonus armor) after using an ability.
  • Taric's Bastion passively grants himself and his Bastion-marked 10 / 12.5 / 15 / 17.5 / 20% of Taric's armor as bonus armor.
  • Taric's Dazzle deals 60 / 105 / 150 / 195 / 240 (+ 50% AP) (+ 30% bonus armor) magic damage.
• Trundle's Subjugate steals instantly 20% of the target's armor. He continues to drain an additional 20% the target's armor over 4 second before decaying 4 seconds after the drain completes.

Items

• Thornmail, upon being hit by a basic attack, reflects magic damage back to the attacker equal to 25% of your bonus armor plus 15% of the incoming damage (before being reduced by defenses).
• Iceborn Gauntlet, 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 (+ 55% bonus armor) units (1.5 second cooldown).

Increasing armor

Items

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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.

• Anivia's Rebirth 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 .
• Braum's Stand Behind Me increases armor by 15 / 17.5 / 20 / 22.5 / 25 (+ 10 / 11.5 / 13 / 14.5 / 16% bonus armor) to himself and the target ally for 3 seconds.
• Galio's Bulwark increases an allied champion's armor by 30 / 45 / 60 / 75 / 90 for 4 seconds.
• Gnar's Rage Gene increases his armor by (2 × level) when transform into Mega Gnar.
• Garen's Courage permanently gains 0.25 bonus armor every time he kills an enemy, up to a maximum of 30.
• Graves' Quickdraw increases his armor by 10 / 15 / 20 / 25 / 30 for 4 seconds. This bonus stacks up to 4 times with each consecutive use of Quickdraw.
• Jayce's Transform: Mercury Hammer increases his armor by 5 / 15 / 25 / 35.
• Kennen's Lightning Rush increases his armor by 10 / 20 / 30 / 40 / 50 for 4 seconds.
• Leona's Eclipse increases her armor by 20 / 30 / 40 / 50 / 60 (+ 20% bonus armor) 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.
• Malphite's Brutal Strikes passively grants armor to himself equal to 15 / 20 / 25 / 30 / 35% of his total armor.
• Olaf's Ragnarok passively increases his armor by 10 / 20 / 30 when he is not under the effects of Ragnarok.
• Orianna's Command: Protect increases an allied champion's armor by 10 / 15 / 20 / 25 / 30 for as long as the ball is attached to them.
• Rammus' Defensive Ball Curl increases his armor by 40 / 60 / 80 / 100 / 120 for 6 seconds, and deals 15 / 25 / 35 / 45 / 55 (+ 10% armor) magic damage to enemies who basic attack him.
• Rengar's Battle Roar Rengar lets out a battle roar, damaging enemies increases his armor by 10 / 15 / 20 / 25 / 30 for 4 seconds. Rengar gains additional 50% armor for each enemy champion or large monster hit.
• Sejuani's Frost Armor 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.
• Shyvana's Dragonborn passively increases her armor by . This bonus is doubled while she is in Dragon Form ().
• Singed's Insanity Potion increases his armor by 35 / 50 / 80 for 25 seconds.
• Taric's Bastion passively grants 10 / 12.5 / 15 / 17.5 / 20% of his total armor to himself and a linked ally.
• Thresh's Damnation passively generates souls for him to collect, with each soul collected granting 0.75 armor permanently.
• Trundle's Subjugate steals instantly 20% of the target's armor. He continues to drain an additional 20% the target's armor over 4 second before decaying 4 seconds after the drain completes.
• Wukong's Stone Skin passively grants him armor for each nearby enemy champion.
• Xin Zhao's Crescent Sweep increases his armor by 15 / 20 / 25 for each enemy champion hit for 8 seconds.

Masteries

•  Unyielding increases bonus armor and magic resistance by 1 / 2 / 3 / 4 / 5%.
•  Legendary Guardian grants your champion 0.6 / 1.2 / 1.8 / 2.4 / 3 armor and 0.6 / 1.2 / 1.8 / 2.4 / 3 magic resistance for each nearby enemy champion

Runes

Name	Type	Tier 1 (Lesser)	Tier 2 (Normal)	Tier 3 (Greater)
Armor	Mark	X	X	0.91 205 Influence Point
	Seal	0.56 N/A	0.78 1 Influence Point	1 205 Influence Point
	Glyph	X	X	0.7 205 Influence Point
	Quintessence	2.37 N/A	3.32 1 Influence Point	4.26 1025 Influence Point
Armor, scaling (Armor per level)	Mark	X	X	X
	Seal	X	X	0.16 per level (3) 410 Influence Point
	Glyph	X	X	X
	Quintessence	X	X	0.38 per level (6.84) 1025 Influence Point

Ways to reduce armor

See armor penetration. Note that armor penetration and armor reduction are different.

Armor vs. health

Note: The following information similarly applies to Magic Resist. 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 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 should buy more armor or health, such as these key examples:

• Unlike HP, increasing armor also makes healing more effective because it takes more effort to remove the unit's HP than it does to restore it.
• HP helps you survive both magic damage and physical damage. Against a team with mainly burst or just low magic damage, HP can be more efficient than MR.
• Percentage armor reduction in the enemy team tilts the optimal health: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 health stacking respectively.
• The presence of resist or HP steroids built into your champion's kit, such as in Leona's Eclipse or Cho'Gath's Feast.
• 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).

List of champions' armor

Main article: List of champions' armor

The highest and lowest base armor champions

Champion Level	Top 5 champions		Bottom 5 champions
Level 1	1. Rammus	36.2325 armor	1. Thresh	33 armor
	2. Darius	35.438 armor	2. Orianna	17.123 armor
	3. Sejuani	30.26675 armor	3. Lux	17.438 armor
	4. Skarner	29.712 armor	4. Kalista	20.438 armor
			4. Vayne
	5. Cho'Gath	34.575 armor	5. Azir	18.575 armor
			5. Heimerdinger
Level 18	1. Rammus	126.46 armor	1. Thresh	33 armor
	2. Braum	128.744 armor	2. Gnar	90.164 armor
	3. Darius	120.744 armor	3. Orianna	86.024 armor
	4. Maokai	116.744 armor	4. Azir	100.6 armor
			4. Heimerdinger
	5. Hecarim	117.674 armor	5. Zyra	95.024 armor

Trivia

(Last updated September 5th, 2016 on patch 6.17)

• Armor has a gold value of 20 (300 ÷ 15). This value is derived from the basic item for armor.
• One of the biggest amount of armor any champion can obtain, aside from Thresh, is 1706.9450882 (which reduces physical damage by 94.466%), being a level 18 Malphite.

• Base stats: +92.1 armor
• Runes:
  • 9 ×  Marks of Armor (+9 × 0.91 armor)
  • 9 ×  Scaling Seals of Armor (+9 × 3 armor)
  • 9 ×  Glyphs of Armor (+9 × 0.7 armor)
  • 3 ×  Scaling Quintessences of Armor (+3 × 6.84 armor)
• Masteries:
  • 5 points in  Unyielding (+5% bonus armor)
  • 5 points in  Legendary Guardian (+3 × 5 armor)
• Items:
  • 6 ×  Thornmail (+6 × 100 armor)
• Buffs:
  • Taric's Bastion (+158.7321 armor)
  • Braum's Stand Behind Me (+138.73768 armor)
  • Galio's Bulwark (+90 armor)
  • Orianna's Command: Protect (+30 armor)
    •  Windspeaker's Blessing (+22 armor) (this mastery can not stack)
  • Malphite's Brutal Strikes (+35% total armor)
• Taric's armor:
• Base stats: +82.8 armor
  • Items =  100 × 6 = 600 armor
  • Runes =  0.91 × 9 +  3 × 9 +  0.7 × 9 +  6.84 × 3 = 62.01 armor
  • Mast. & Buffs =  15 = 15 armor
  • Bonus Armor Amplification =  1.05 = 1.05 = 5% bonus armor
    • Taric's armor = 82.8 + (600 + 62.01 + 15) × 1.05 = 793.6605 armor
    • Bastion's bonus = 20% armor
    • Bastion's bonus = 158.7321
• Relevant mathematics:
• Braum's bonus armor:
  • Items =  100 × 6 = 600 armor
  • Runes =  0.91 × 9 +  3 × 9 +  0.7 × 9 +  6.84 × 3 = 62.01 armor
  • Mast. & Buffs =  15 = 15 armor
  • Bonus Armor Amplification =  1.05 = 1.05 = 5% bonus armor
    • Braum's bonus armor = (600 + 62.01 + 15) × 1.05 = 710.8605 bonus armor
    • Stand Behind Me's bonus = 25 + (16% bonus armor)
    • Stand Behind Me's bonus = 25 + 113.73768
    • Stand Behind Me's bonus = 138.73768
• Malphite's armor:
• Base stats: +92.1 armor
  • Items =  100 × 6 = 600 armor
  • Runes =  0.91 × 9 +  3 × 9 +  0.7 × 9 +  6.84 × 3 = 62.01 armor
  • Mast. & Buffs =  15 +  90 +  30 +  22 +  138.73768 +  158.7321 = 454.46978 armor
  • Bonus Armor Amplification =  1.05 = 1.05 = 5% bonus armor
  • Armor Amplification =  1.35 = 1.35 = 35% armor
    • Malphite's armor = (((600 + 62.01 + 454.46978) × 1.05) + 92.1) × 1.35 = 1706.9450882 armor

• Having an enemy Trundle with the same setup use Subjugate on Malphite will yield a total of 1962.620706 armor. This is the highest possible finite amount of armor and reduces physical damage by 95.512%.

• Malphite's armor = 1706.9450882 armor
  • Subjugate's bonus = 40% of enemy's armor
  • Subjugate's bonus = 682.77803528

• Trundle's armor:
• Base stats: +73.4 armor
  • Items =  100 × 6 = 600 armor
  • Runes =  0.91 × 9 +  3 × 9 +  0.7 × 9 +  6.84 × 3 = 62.01 armor
  • Mast. & Buffs =  15 +  90 +  30 +  22 +  138.73768 +  158.7321 +  682.77803528 = 1137.24781528 armor
  • Bonus armor amplification =  1.05 = 1.05 = 5% bonus armor
    • Trundle's armor = 73.4 + (600 + 62.01 + 1137.24781528) × 1.05 = 1962.620706 armor

Thresh, with his effectively infinite stacking, can obtain a maximum of 749999.25 armor off his passive alone. With the same set-up as above, he can obtain a total of about 788575 armor, reducing physical damage by 99.9873205%.

References

Champion statistics