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, 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.

Damage reduction

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

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

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).

Armor Penetration, Lethality

The Armor Penetration and Lethality stats simply negate some armor of the target (see Armor penetration). The damage calculation then uses the effective armor values after the reduction; the actual damage formulae are not changed.

Armor penetration, lethality and armor reduction can be treated as negative armor in damage calculations.

Stacking armor

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

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

Example: A unit with 60 armor has 60% 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 hitpoints. Each additional point of armor increases the effective health pool (against physical damage) by 1%.  This is not changed by the amount of armor already held.

Example: A unit starts with 1000 health and 100 armor, giving it 2000 effective health. Increasing its health from 1000 to 2000 would change its effective health from 2000 to 4000 (due to the 100 armor already held). Increasing the unit's armor by another 100 units would then yield 2000 additional effective health.

However, stacking armor can be gold inefficient, depending on the HP pool: if, say, an investment of 100g into armor increased your effective HP by 30, but the same 100g would buy you 60 HP, then buying the HP would be twice as gold efficient than buying the armor. The same is true in reverse, if the armor value is relatively low; buying HP in that case would be less efficient than buying armor.

In that sense, stacking armor can have diminishing returns if gold value is taken into account. Also, from a practical point of view, increasing resistances (or HP) on a champion becomes less effective if the unit is already very hard to kill.

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

• Braum's Stand Behind Me
• Leona's Eclipse
• Malphite's Brutal Strikes and Ground Slam
• Ornn's Living Forge and Searing Charge
• Poppy's Stubborn to a Fault
• Rammus' Spiked Shell and Defensive Ball Curl
• Sejuani's Frost Armor
• Taric's Bravado, Bastion, and Dazzle
• Trundle's Subjugate

Items

• Bramble Vest
• Iceborn Gauntlet
• Thornmail

Runes

• Conditioning

Increasing armor

Items

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• Gargoyle Stoneplate
• Knight's Vow

Champion abilities

• Anivia's Rebirth
• Braum's Stand Behind Me
• Gnar's Rage Gene
• Garen's Courage
• Graves' Quickdraw
• Jax's Grandmaster's Might
• Jayce's Transform Mercury Hammer
• Kennen's Lightning Rush
• Leona's Eclipse
• Malphite's Brutal Strikes
• Nasus' Fury of the Sands
• Olaf's Ragnarok
• Orianna's Command Protect
• Ornn's Living Forge
• Poppy's Stubborn to a Fault
• Rammus' Defensive Ball Curl
• Sejuani's Frost Armor
• Shyvana's Fury of the Dragonborn
• Singed's Insanity Potion
• Taric's Bastion
• Thresh's Damnation
• Trundle's Subjugate
• Wukong's Stone Skin

Runes

• Aftershock
• Conditioning
• Shield Bash

Ways to reduce armor

Main article: Armor penetration

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 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

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

Champion Level	Top 5 champions		Bottom 5 champions
Level 1
Level 18

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

• Armor has a gold value of 20 (300 ÷ 15). This value is derived from the basic item for armor.

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Last updated: March 12, 2018 V8.5

• One of the biggest amount of armor any champion can obtain, aside from  Thresh or a Jax with Gathering Storm, is 2694.962488 (which reduces physical damage by 96.422%), being a level 18  Sejuani.
• Base stats: 82 armor
• Runes:
  • Conditioning
  • Aftershock
• Items:
  • 6 Frozen Hearts
• Buffs:
  • Sejuani's Fury of the North
  • Taric's Bastion
  • Braum's Stand Behind Me
  • Orianna's Command Protect
• Taric's armor:
  • Base stats: 97.8 armor
  • Items =  100 × 6 = 600 armor
  • Runes =  8 + 120  = 128 armor
  • Armor Amplification = 1 + 0.06 = 1.06
    • Taric's (armor = 600 + 128 + 97.8) × 1.06 = 875.84
    • Bastion's bonus = 875.84 × 0.2 = 175.169 bonus armor
• Braum's bonus armor:
  • Items = 100 × 6 = 600 armor
  • Runes = 8 + 120 = 128 armor
    • Braum's armor = 600 + 128 = 728 bonus armor
    • Stand Behind Me's bonus = 27.5 + 728 × 0.16 = 143.98 bonus armor
• Sejuani's armor:
  • Base stats: 82 armor
  • Items =  100 × 6 = 600 armor
  • Runes = 8 + 120 = 128 armor
  • Buffs =  175.169 +  143.98 + 30 = 349.1496 armor
  • Armor Amplification = 1 + 1.1053 +  0.1053  = 2.2105
    • Sejuani's armor = (82 + 600 + 128 + 349.1496) × 2.2105 + 132.6316 = 2694.962488 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

Champion statistics