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แม่แบบ:As is a stat shared by all units, including monsters, and buildings. Increasing แม่แบบ:As reduces the physical damage the unit takes. Each champion begins with some แม่แบบ:As which increases with level ( being the only exception). You can gain additional แม่แบบ:As from abilities, items, masteries, and runes. แม่แบบ:As stacks additively.

Excluding whose แม่แบบ:As does not scale with levels, แม่แบบ:As ranges from {{#vardefine:n|65.5}}65.5 () to {{#vardefine:n|104.5}}104.5 () at level 18.

## Damage reduction Edit

Incoming แม่แบบ:As is multiplied by a factor based on the unit's แม่แบบ:As:

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

Examples:

## Stacking armor Edit

Every point of แม่แบบ:As requires a unit to take 1% more of its maximum health in แม่แบบ:As to be killed. This is called แม่แบบ:As.

Example: A unit with แม่แบบ:As has 60% more of its แม่แบบ:As in แม่แบบ:As, so if the unit has แม่แบบ:As, it will take แม่แบบ:As to kill it.

What this means: by definition, แม่แบบ:As does not have diminishing returns in regard of effective hitpoints, because each point increases the unit's แม่แบบ:As against แม่แบบ:As by 1% of its current แม่แบบ:As whether the unit has แม่แบบ:As or แม่แบบ:As. However, แม่แบบ:As and แม่แบบ:As have increasing returns with respect to each other.

Example: A unit starts with แม่แบบ:As and แม่แบบ:As giving it แม่แบบ:As. Now, it increases its แม่แบบ:As from 1000 to 2000, thereby increasing its แม่แบบ:As from 2000 to 4000. Increasing the unit's แม่แบบ:As by 100 at both แม่แบบ:As levels would yield แม่แบบ:As and แม่แบบ:As, respectively. If we were to consider two แม่แบบ:As levels and then increase both by a static amount of แม่แบบ:As, we would see a similar increased return of แม่แบบ:As for the same แม่แบบ:As.

Therefore, buying only แม่แบบ:As is แม่แบบ:As compared to buying the optimal balance of แม่แบบ:As and แม่แบบ:As. It is important to not stack too much แม่แบบ:As compared to แม่แบบ:As or else the แม่แบบ:As will not be optimal.

When a unit's แม่แบบ:As is negative because of แม่แบบ:As or debuffs, แม่แบบ:As has increasing returns with respect to itself. This is because negative แม่แบบ:As cannot reduce แม่แบบ:As to less than แม่แบบ:As. A unit with แม่แบบ:As has แม่แบบ:As (gains {{#vardefine:n|−33.33%}}−33.33%) of its แม่แบบ:As as แม่แบบ:As.

## Optimal efficiency (theoretical) Edit

Note: แม่แบบ:As, 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 แม่แบบ:As (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 แม่แบบ:As in their แม่แบบ:As bar and it can be increased by buying items with extra แม่แบบ:As, แม่แบบ:As and แม่แบบ:As. In this article, แม่แบบ:As will refer to the amount of raw 'แม่แบบ:As' a champion can take.

In almost all circumstances, champions will have a lot more แม่แบบ:As than แม่แบบ:As such that the following inequality will be true: แม่แบบ:As > แม่แบบ:Asแม่แบบ:Plus100.

If this inequality is true, a single point of แม่แบบ:As will give more 'แม่แบบ:As' to that champion than a single point of แม่แบบ:As.

If (แม่แบบ:As < แม่แบบ:Asแม่แบบ:Plus100), 1 point of แม่แบบ:As will give more แม่แบบ:As than 1 of แม่แบบ:As.

If (แม่แบบ:Asแม่แบบ:Equalsแม่แบบ:Asแม่แบบ:Plus100), 1 point of แม่แบบ:As will give exactly the same amount of แม่แบบ:As as 1 point of แม่แบบ:As.

Because of this relationship, theoretically, the way to get the maximum amount of แม่แบบ:As from a finite combination of แม่แบบ:As and แม่แบบ:As would be to ensure that you have exactly 100 more แม่แบบ:As than แม่แบบ:As (this is true regardless of how much แม่แบบ:As and แม่แบบ:As you actually already have).

Example: Given a theoretical situation where you start off with แม่แบบ:As and แม่แบบ:As and are given an arbitrary sufficient number of stat points (x ≥ 100), each of which you can either use to increase your แม่แบบ:As or แม่แบบ:As by 1 point, the way to maximize your แม่แบบ:As is to add points to your แม่แบบ:As until your แม่แบบ:Asแม่แบบ:Equals(แม่แบบ:Asแม่แบบ:Plus100)แม่แบบ:Equals(0แม่แบบ:Plus100)แม่แบบ:Equals100, and then split the remaining stat points in half, spend half on your แม่แบบ:As and half on your แม่แบบ:As.

However, this is only theoretically true if we consider both แม่แบบ:As and แม่แบบ:As to be equally obtainable resources with simplified mechanism of skill point investment. In reality a player buys these stats for แม่แบบ:As instead. As แม่แบบ:As of แม่แบบ:As (derived from cost of basic armor item) is currently (as of season six) {{#vardefine:n|7.5}}7.5 times higher than แม่แบบ:As of แม่แบบ:As (derived from cost of basic health item), we theoretically can maximize แม่แบบ:As represented by product of {{#vardefine:n|0.01}}0.01แม่แบบ:Timesแม่แบบ:Asแม่แบบ:Times(แม่แบบ:Asแม่แบบ:Plus100) with แม่แบบ:As as input variable by satisfying the following equation: แม่แบบ:Asแม่แบบ:Equals{{#vardefine:n|7.5}}7.5แม่แบบ:Times(แม่แบบ:Asแม่แบบ:Plus100). The graph and conclusions obtained by solving it are mentioned in the subsection below.

Example: Given a theoretical situation where you start off with แม่แบบ:As and แม่แบบ:As and are given an arbitrary sufficient amount of แม่แบบ:As (x ≥ {{#vardefine:n|281.25}}281.25), which you can either use to increase your แม่แบบ:As or แม่แบบ:As, the way to maximize your แม่แบบ:As is to add points to your แม่แบบ:As until your แม่แบบ:Asแม่แบบ:Equals{{#vardefine:n|7.5}}7.5แม่แบบ:Times(แม่แบบ:Asแม่แบบ:Plus100)แม่แบบ:Equals{{#vardefine:n|7.5}}7.5แม่แบบ:Times(0แม่แบบ:Plus100)แม่แบบ:Equals750, and then split the remaining แม่แบบ:As in half, spend half on your แม่แบบ:As and half on your แม่แบบ:As (as former is {{#vardefine:n|7.5}}7.5 times cheaper than the latter, it would lead to buying {{#vardefine:n|7.5}}7.5 times more additional แม่แบบ:As than แม่แบบ:As and thus naturally reaching equality in the equation above).

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

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

... or in our case, always แม่แบบ:As into แม่แบบ:As and แม่แบบ:As into แม่แบบ:As.

Again this model is highly simplified and cannot be exactly applied in cases when we are buying any other item than , or (for example if our decision-making process would involve instead of , the above model would need to use equilibrium constant {{#vardefine:n|7.6}}7.6). Even considering the purchase of different แม่แบบ:As or แม่แบบ:As items with differing แม่แบบ:As (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 {{#vardefine:n|1.5}}1.5แม่แบบ:Times for แม่แบบ:G, so with that much แม่แบบ:As you opt to buy either a single or 2แม่แบบ:Times, drastically changing the equilibrium constant to {{#vardefine:n|5.0}}5.0.

However, thankfully to almost linear item stats' แม่แบบ:As a player can use weakened base equilibrium condition in a form: แม่แบบ:As ≈ {{#vardefine:n|7.5}}7.5แม่แบบ:Times(แม่แบบ:Asแม่แบบ:Plus100) 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 แม่แบบ:As only the basic constant {{#vardefine:n|7.5}}7.5 is slightly changed to {{#vardefine:n|6.75}}6.75.

This information is strongly theoretical and due to game limitations from champions' base stats, innate abilities and non-linearity of แม่แบบ:As of item stats (แม่แบบ:As 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 แม่แบบ:As. 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 แม่แบบ:As 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 แม่แบบ:As and แม่แบบ:As give a very high amount of แม่แบบ:As against แม่แบบ:As compared to items which only provide แม่แบบ:As or only provide แม่แบบ:As. These items should be purchased when a player is seeking efficient ways to reduce the แม่แบบ:As they take by a large amount. Furthermore, these items are among all available items the best ones to distribute their แม่แบบ:As equally among both แม่แบบ:As and แม่แบบ:As, thus working perfectly for rule of preserving equilibrium.

## Armor as scaling Edit

These use the champion's แม่แบบ:As to increase the magnitude of the ability. It could involve total or bonus แม่แบบ:As. By building แม่แบบ:As items, you can receive more benefit and power from these abilities.

### Items Edit

• , upon being hit by a basic attack, reflects แม่แบบ:As back to the attacker equal to แม่แบบ:As 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 แม่แบบ:As units ({{#vardefine:n|1.5}}1.5 second cooldown).

## Increasing armor Edit

### Champion abilities Edit

Note: Only the แม่แบบ:As buff effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.

### Runes Edit

Name Type Tier 1 (Lesser) Tier 2 (Normal) Tier 3 (Greater)
Armor Mark X X 0.91}}0.91

205 IP

Seal {{#vardefine:n|0.56}}0.56

N/A

{{#vardefine:n|0.78}}0.78

1 IP

1

205 IP

Glyph X X 0.7}}0.7

205 IP

Quintessence {{#vardefine:n|2.37}}2.37

N/A

{{#vardefine:n|3.32}}3.32

1 IP

{{#vardefine:n|4.26}}4.26

1025 IP

Armor, scaling

(Armor per level)

Mark X X X
Seal X X {{#vardefine:n|0.16}}0.16 per level (3)

410 IP

Glyph X X X
Quintessence X X {{#vardefine:n|0.38}}0.38 per level ({{#vardefine:n|6.84}}6.84)

1025 IP

## Ways to reduce armor Edit

See armor penetration. Note that แม่แบบ:As and แม่แบบ:As are different.

## Armor vs. health Edit

Note: The following information similarly applies to Magic Resist. As of season six, the base equilibrium line for แม่แบบ:As is a function:

แม่แบบ:Asแม่แบบ:Equals{{#vardefine:n|7.5}}7.5แม่แบบ:Times(แม่แบบ:Asแม่แบบ:Plus100)

while for แม่แบบ:As the line is a bit shifted down and less steep:

แม่แบบ:Asแม่แบบ:Equals{{#vardefine:n|6.75}}6.75แม่แบบ:Times(แม่แบบ:Asแม่แบบ:Plus100)

It can be helpful to understand the equilibrium between แม่แบบ:As and แม่แบบ:As, 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 แม่แบบ:As is the most แม่แบบ:As purchase, however this assumes the enemy team will only have one type of damage. The more equal the distribution of แม่แบบ:As/แม่แบบ:As in the enemy team, the more effective will buying แม่แบบ:As be.

There are many other factors which can effect whether you should buy more แม่แบบ:As or แม่แบบ:As, such as these key examples:

## List of champions' armor Edit

The highest and lowest base armor champions
Champion Level Top 5 champions Bottom 5 champions
Level 1 1. แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor 1. แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor
2. แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor 2. แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor
3. แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor 3. แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor
4. {{#vardefine:n|แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor 4. {{#vardefine:n|แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor
4.
5. {{#vardefine:n|แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor 5. {{#vardefine:n|แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor
5.
Level 18 1. แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor 1. แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor
2. แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor 2. แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor
3. แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor 3. แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor
4. {{#vardefine:n|แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor 4. {{#vardefine:n|แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor
4.
5. แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor 5. แม่แบบ:Leveled Stat}}แม่แบบ:Leveled Stat armor

## Trivia Edit

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

, with his effectively infinite stacking, can obtain a maximum of แม่แบบ:As off his passive alone. With the same set-up as above, he can obtain a total of about แม่แบบ:As, reducing แม่แบบ:As by {{#vardefine:n|99.9873205%}}99.9873205%.

## References Edit

1. Should you buy Armor or Health?
แม่แบบ:Stats
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