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

At level 18, base armor ranges from 28 (Thresh OriginalSquare Thresh) whose base armor does not scale with levels or 66.6 (Kassadin OriginalSquare Kassadin) to 130 (Pyke OriginalSquare Pyke).

Gold Value

  • Armor has a gold value of Gold 20 per point.

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

Items

Runes

Increasing armor

Items

Item Cost Amount Availability
Aegis of the Legion item Aegis of the Legion1100 Gold30All maps
Bramble Vest item Bramble Vest1000 Gold35All maps
Chain Vest item Chain Vest800 Gold40All maps
Circlet of the Iron Solari item Circlet of the Iron Solari2200 Gold45All maps
Cloth Armor item Cloth Armor300 Gold15All maps
Dead Man's Plate item Dead Man's Plate2900 Gold60All maps
Forgefire Cape item Forgefire Cape2750 Gold100All maps
Frozen Fist item Frozen Fist2700 Gold125All maps
Frozen Heart item Frozen Heart2700 Gold100All maps
Gargoyle Stoneplate item Gargoyle Stoneplate2500 Gold40All maps
Glacial Shroud item Glacial Shroud900 Gold20All maps
Guardian Angel item Guardian Angel2800 Gold40Summoner's Rift
Iceborn Gauntlet item Iceborn Gauntlet2700 Gold65All maps
Knight's Vow item Knight's Vow2200 Gold40All maps
Locket of the Iron Solari item Locket of the Iron Solari2200 Gold30All maps
Moonflair Spellblade item Moonflair Spellblade2400 Gold50Twisted Treeline
Ninja Tabi item Ninja Tabi1100 Gold20All maps
Ohmwrecker item Ohmwrecker2650 Gold50Summoner's Rift, Nexus Blitz
Randuin's Omen item Randuin's Omen2900 Gold70All maps
Raptor Cloak item Raptor Cloak900 Gold30All maps
Righteous Glory item Righteous Glory2650 Gold30All maps
Seeker's Armguard item Seeker's Armguard1100 Gold30All maps
Sunfire Cape item Sunfire Cape2750 Gold60All maps
Thornmail item Thornmail2900 Gold80All maps
Talisman of Ascension item Timeworn Talisman of Ascension2200 Gold45Twisted Treeline
Warden's Mail item Warden's Mail1000 Gold40All maps
Wooglet's Witchcap item Wooglet's Witchcap3400 Gold45Twisted Treeline
Wooglet's Witchcrown item Wooglet's Witchcrown3400 Gold45Twisted Treeline
Zeke's Convergence item Zeke's Convergence2250 Gold60All maps
Zhonya's Hourglass item Zhonya's Hourglass2900 Gold45Summoner's Rift, Howling Abyss, Nexus Blitz
Zhonya's Paradox item Zhonya's Paradox2900 Gold60Summoner's Rift, Howling Abyss, Nexus Blitz
Zz'Rot Portal item Zz'Rot Portal2700 Gold55Summoner's Rift, Nexus Blitz

Champion abilities

Runes

Ways to reduce armor

Note that armor penetration and armor reduction are different.

Armor vs. health

HP Armor LW VS

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 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 OriginalSquare Leona's Eclipse Eclipse or Cho'Gath OriginalSquare Cho'Gath's Feast 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

Champions with the lowest or highest armor before items, runes, or abilities
Champion Level Top 5 champions Bottom 5 champions
Level 1 1. Tahm Kench OriginalSquare Tahm Kench
1. Braum OriginalSquare Braum
1. Leona OriginalSquare Leona
47 armor 1. Orianna OriginalSquare Orianna 17.04 armor
2. Pyke OriginalSquare Pyke 45 armor 2. Malzahar OriginalSquare Malzahar 18 armor
3. Alistar OriginalSquare Alistar 44 armor 3. Lux OriginalSquare Lux 18.72 armor
4. Pantheon OriginalSquare Pantheon
4. Taric OriginalSquare Taric
4. Blitzcrank OriginalSquare Blitzcrank
40 armor 4. Kassadin OriginalSquare Kassadin
4. Aurelion Sol OriginalSquare Aurelion Sol
19 armor
5. Yorick OriginalSquare Yorick
5. Darius OriginalSquare Darius
5. Maokai OriginalSquare Maokai
5. Nautilus OriginalSquare Nautilus
39 armor 5. Azir OriginalSquare Azir
5. Heimerdinger OriginalSquare Heimerdinger
19.04 armor
Level 18 1. Pyke OriginalSquare Pyke 130 armor 1. Thresh OriginalSquare Thresh 28 armor
2. Braum OriginalSquare Braum 115 armor 2. Kassadin OriginalSquare Kassadin 66.6 armor
3. Rammus OriginalSquare Rammus 109.1 armor 3. Orianna OriginalSquare Orianna 68.04 armor
4. Urgot OriginalSquare Urgot 108.25 armor 4. Azir OriginalSquare Azir
4. Heimerdinger OriginalSquare Heimerdinger
70.04 armor
5. Leona OriginalSquare Leona 108.2 armor 5. Ryze OriginalSquare Ryze 72.552 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 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 Crystal item Ruby Crystals for Gold 600, so you either opt to buy a single Ruby Crystal item Ruby Crystal or 2 × Cloth Armor item 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


Last updated: March 12, 2018 V8.5


Thresh OriginalSquare 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

  1. Should you buy Armor or Health?
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