Armor, or AR, is one of the two damage resistance subtype stats. It reduces incoming physical damage by a percentage.

• Armor stacks additively.

Every champion has a certain amount of base armor that increases through growth per level. Total armor refers to base plus bonus armor. Bonus armor can be gained from any source other than levels, for example from abilities, buffs, items, runes, and others.

Excluding the intentional outlier of Thresh (whose base armor does not increase through growth per level and is 33), base armor values at level 18 range from 87 ( Kassadin) to 149.4 ( Mega Gnar).

Gold Value

• Armor has a gold value of 20 per point.

Armor formula[]

Armor determines by how much incoming physical damage is reduced before it applies to the target's health. The incoming pre-mitigation damage is mitigated through armor into a reduced amount of post-mitigation damage. This post-mitigation damage equals the actual amount of health deducted from the unit. Also, armor reduces an amount of pre-mitigation damage by a percentage; in other words, armor can be interpreted as effectively increasing the  nominal health of a unit by a percentage, when receiving physical damage.

To calculate the post-mitigation damage (meaning health deduction) given an amount of incoming physical damage and the target's armor, the following formula is used, where:

• ${\displaystyle \rm {R}}$ is armor
• ${\displaystyle d_m}$ is post-mitigation damage
• ${\displaystyle d_r}$ is pre-mitigation, or "raw", physical damage

${\displaystyle {\rm {post\ mitigation\ damage}}={\rm {physical\ damage}}\times {\begin{cases}{100 \over 100+{\rm {R}}},&{\rm {if\ {\rm {Armor}}}}\geq 0\\2-{100 \over 100-{\rm {R}}},&{\rm {otherwise}}\end{cases}}}$

Due to the order of operations for resistance penetration and reductions, negative values almost never occur. Therefore, ignoring negative armor values, the following simpler formula may be used:

${\displaystyle d_{m}={d_{r} \over 1+{{\rm {R}} \over 100}}}$

Solving for raw physical damage instead gives:

${\displaystyle d_{r}=d_{m}\times {\Bigl (}1+{\frac {\rm {R}}{100}}{\Bigr )}}$

The second formula proves that armor increases nominal health by a percentage against physical damage; this is called effective health. Every 1 point of armor adds 1% to the effective health pool. Also see "Stacking armor" section below.

Examples using 1000 health and 1000 pre-mitigation damage, for the sake of simplicity:

• 25 Armor
  • 25% effective health increase → 1000 nominal health becomes 1000 × (1 + 25 ÷ 100) = 1000 × 1.25 = 1250 total effective health against physical damage
  • 1000 raw damage ÷ (1 + 25 ÷ 100) = 1000 ÷ 1.25 = 800 post-mitigation damage → 20% total physical damage reduction
• 100 Armor
  • 100% effective health increase → 1000 nominal health becomes 1000 × (1 + 100 ÷ 100) = 1000 × 2 = 2000 total effective health against physical damage
  • 1000 raw damage ÷ (1 + 100 ÷ 100) = 1000 ÷ 2 = 500 post-mitigation damage → 50% total physical damage reduction
• 200 Armor
  • 200% effective health increase → 1000 nominal health becomes 1000 × (1 + 200 ÷ 100) = 1000 × 3 = 3000 total effective health against physical damage
  • 1000 raw damage ÷ (1 + 200 ÷ 100) = 1000 ÷ 3 = 333.3 post-mitigation damage → 66.6% total physical damage reduction

Stacking armor[]

Following the above damage formula, each point of armor increases the effective health pool against physical damage by 1%, formally:

${\displaystyle {\rm Effective\ health} = \left(1 + \frac{{R}}{100}\right)\times{\rm Nominal\ health}}$

Example: A unit with 60 armor has 60% increased health against physical attacks. If the unit had 1000 maximum health it would take 1600 physical damage to kill it.

By definition, armor does not give diminishing returns of effective health. Each additional point of armor increases the effective health pool (against physical damage) by another 1% of maximum health. This is not influenced by how many points of armor are already held.

If a unit's armor is negative due to reduction 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. This is an exotic case with only a select few in-game applications.

For a more detailed explanation, see this video.

Armor as scaling[]

Effects may benefit from (scale off of) a percentage/ratio, of total armor, or bonus armor.

Champions[]

Self[]

Enemy[]

Items[]

Self[]

Runes[]

Self[]

Neutral buffs[]

Self[]

• Mountainous Vigor

Increasing armor[]

Items[]

This table is automatically generated based on the data from Module:ItemData/data.

Item	Cost	Amount	Availability
Bloodletter's Curse Bloodletter's Curse	2500	30	Arena
Bramble Vest Bramble Vest	800	30	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Chain Vest Chain Vest	800	40	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Cloth Armor Cloth Armor	300	15	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Cruelty Cruelty	0	30	Arena
Darksteel Talons Darksteel Talons	0	55	Arena
Dead Man's Plate Dead Man's Plate	2900	45	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Death's Dance Death's Dance	3200	40	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Eleisa's Miracle Eleisa's Miracle	0	65	Arena
Frozen Heart Frozen Heart	2500	65	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Gargoyle Stoneplate Gargoyle Stoneplate	0	65	Arena
Glacial Buckler Glacial Buckler	950	20	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Guardian Angel Guardian Angel	3200	45	Arena, Classic Summoner's Rift 5v5
Iceborn Gauntlet Iceborn Gauntlet	2600	50	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Jak'Sho, The Protean Jak'Sho, The Protean	3200	50	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Knight's Vow Knight's Vow	2200	40	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Locket of the Iron Solari Locket of the Iron Solari	2200	30	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Plated Steelcaps Plated Steelcaps	1000	25	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Radiant Virtue Radiant Virtue	0	35	Arena
Randuin's Omen Randuin's Omen	2700	75	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Seeker's Armguard Seeker's Armguard	1600	25	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Shattered Armguard Shattered Armguard	1600	25	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Shield of Molten Stone Shield of Molten Stone	0	100	Arena
Steel Sigil Steel Sigil	1100	30	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Sunfire Aegis Sunfire Aegis	2700	50	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Talisman of Ascension Talisman of Ascension	0	0	Arena
The Golden Spatula The Golden Spatula	0	40	Arena
Thornmail Thornmail	2700	70	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Trailblazer Trailblazer	2500	40	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Unending Despair Unending Despair	2800	55	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Vigilant Wardstone Vigilant Wardstone	2300	25	Classic Summoner's Rift 5v5
Warden's Mail Warden's Mail	1000	40	Nexus Blitz, Classic Summoner's Rift 5v5, All Random All Mid
Watchful Wardstone Watchful Wardstone	1100	10	Classic Summoner's Rift 5v5
Wooglet's Witchcap Wooglet's Witchcap	0	50	Arena
Zeke's Convergence Zeke's Convergence	2200	25	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid
Zhonya's Hourglass Zhonya's Hourglass	3250	50	Nexus Blitz, Arena, Classic Summoner's Rift 5v5, All Random All Mid

Item passives[]

Champion abilities[]

Runes[]

Neutral buffs[]

• Mountainous Vigor

Reducing Armor[]

Main article: Armor penetration

Armor can be negated by armor penetration, armor reduction, and Lethality, treated as negative values in damage calculations. The calculation then uses the effective armor values after the reduction; the actual damage formulae are not changed.

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 the line for magic resistance 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 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 damage, HP can be more efficient than resistances.
• 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 vamp 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

Champions with the lowest or highest armor before items, runes, or abilities

Champion Level	Top 5 champions		Bottom 5 champions
Level 1	1. Leona 1. Alistar 1. Pyke 1. Braum	47 armor	1. Veigar 1. Malzahar 1. Taliyah 1. Cassiopeia	18 armor
	2. Tahm Kench	42 armor	2. Kassadin 2. Annie 2. Heimerdinger	19 armor
	3. Taric 3. Rammus 3. Pantheon	40 armor	3. Orianna	20 armor
	4. Gwen 4. Nautilus 4. Darius 4. Yorick	39 armor	4. Ahri 4. Twisted Fate 4. Lux 4. Karthus 4. Zoe 4. Neeko 4. Ziggs 4. Hwei 4. Anivia	21 armor
	5. Poppy 5. Nocturne 5. Kayn 5. Aatrox 5. Cho'Gath 5. Garen 5. Gragas 5. Shyvana	38 armor	5. Xerath 5. Azir 5. Vel'Koz 5. Aurelion Sol 5. LeBlanc 5. Fizz 5. Jayce 5. Ryze 5. Lissandra 5. Lillia	22 armor
Level 18	1. Mega Gnar	149.4 armor	1. Thresh	33 armor
	2. Braum	135.4 armor	2. Kassadin	87 armor
	3. Rammus	133.5 armor	3. Aurelion Sol	90 armor
	4. Leona	128.6 armor	4. Heimerdinger	90.4 armor
	5. Darius 5. Gwen 5. Yorick	127.4 armor	5. Orianna	91.4 armor

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*. 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 can be increased by buying items with extra health, armor and magic resistance. In this section, effective health will refer to the amount of raw 'physical damage' a champion can take.

In almost all circumstances, champions will have more maximum health than armor, thus a single point of armor will give more 'effective health' to a champion than a single point of health. However, if there is a case where max health is below the value of 'armor + 100', the opposite becomes true.

Because of this relationship, theoretically, maximum effective health is attained by ensure that you have exactly 100 more max health than armor, regardless of how much health or armor you actually already have.

Example: Given a theoretical situation where you start off with 1 health and 1 armor and are given an arbitrary sufficient number of stat points (x ≥ 100), each of which you can use to increase either your health or armor by 1 point, the way to maximize your effective health is to add points to your health until your health has 100 more points than armor, then split the remaining stat points in half and share them between your health and 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. So when attempting to ensure the balance of 'health = armor + 100', consider it through gold value distributed to the stats. Because the gold value of 1 health is roughly 7.7 times smaller than 1 point of armor (as of V8.7), distribution per point of health or armor should be 11.5% gold into health and 88.5% gold into armor once the 'health = armor + 100' equilibrium is reached.

This model is highly simplified and cannot be exactly applied when buying any other item that aren't purely armor or health oriented as they deviate the equilibrium. 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 you either opt to buy a single Ruby Crystal or 2 ×  Cloth Armors, drastically unbalancing the equilibrium.

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.

Conclusion[]

This information is strongly theoretical. Due to how there are many variables aside from health, armor and gold value, "true equilibrium" is too complicated and unrealistic to achieve. However, a player can develop their intuition to itemize towards this equilibrium in a timely manner through the experience gained from the multitude of plays they perform.

The important thing to remember is that there is no reason to hold to the equilibrium too strictly, or else you might just lose the fun out of the game.

Trivia[]

• The old stat icon for armor seems to based on the old icon of Aegis of the Legion.

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Last updated: July 29, 2020, patch V10.15

Without using Thresh's Damnation, Shyvana's Fury of the Dragonborn or Jax's Grandmaster's Might with Gathering Storm which potentially allow for infinite amounts of armor, the largest amount of armor is reached with a level 18 Rammus at 3104 armor (which reduces physical damage by 96.88%).

• Runes:
  • Aftershock
  • Conditioning
  • Shield Bash
  • 2 ×  Armor rune shard
• Items:
  • 5 ×  Frozen Heart
  • 1 ×  Frozen Fist
• Buffs:
  • Rammus' Defensive Ball Curl
  • Taric's Bastion
  • Braum's Stand Behind Me
  • Orianna's Command Protect
    • Orianna has a Locket of the Iron Solari to shield to whole team, triggering Shield Bash.
  • 4 ×  Mountainous Vigor

• Taric:
  • Base armor = 97.8 armor
  • Items = 110 × 5 + 125 = 675 armor
  • Runes = 150 + 9 + 10 + 6 × 2 = 181 armor
  • Armor Multiplier = 1 + 0.24 + 0.05 = 1.29
    • Taric's armor = (97.8 + 675 + 181) × 1.29 = 1230.402 armor
    • Bastion's bonus = 1230.402 × 0.14 = 172.25628 bonus armor

• Braum:
  • Items = 110 × 5 + 125 = 675 armor
  • Runes = 150 + 9 + 10 + 6 × 2 = 181 armor
  • Armor Multiplier = 1 + 0.24 + 0.05 = 1.29
    • Braum's armor = (675 + 181) × 1.29 = 1104.24 bonus armor
    • Stand Behind Me's bonus = 26 + 1104.24 × 0.12 = 158.5088 bonus armor

• Rammus:
  • Base armor = 109.1 armor
  • Items = 110 × 5 + 125 = 675 armor
  • Runes = 150 + 9 + 10 + 6 × 2 = 181 armor
  • Buffs = 172.25628 + 158.5088 + 30 + 30 = 390.76508 armor
  • Armor Multiplier = 1 + 1 + 0.24 + 0.05 = 2.29
    • Rammus' armor = (109.1 + 675 + 181 + 390.76508) × 2.29 = 3104.9310332 armor

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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 910296.7564 armor, reducing physical damage by 99.99989016%.

References[]