Ability power

Ability Power (AP) is a champion statistic that increases the effectiveness of most abilities. It stacks additively.

Effects that benefit from ability power receive a bonus based on a certain percentage of a champion's current ability power. For example, if a spell deals 100 (+20% AP) damage and a champion has 50 ability power, the spell's damage will increase by 10. In-game, spell descriptions do not display the percentage, but do display the resulting bonus; the previous example would display as 100 (+10).

Ability power has a theoretical gold value of 21.75 per unit. This means that Needlessly Large Rod is the most efficient AP core item, with a gold/AP ratio of 20.833∞.The costs of these stats are always offset by increased final costs of their upgraded items.

Increasing Ability Power

Items

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Specific to Viktor

Prototype Hex Core: Passive: Grants 1 − 18 (based on level) ability power and 10 − 180 (based on level) mana.
The Hex Core mk-1: Passive: Grants 3 − 54 (based on level) ability power and 15 − 270 (based on level) mana.
The Hex Core mk-2: Passive: Grants 6 − 108 (based on level) ability power and 20 − 360 (based on level) mana.
Perfect Hex Core: Passive: Grants 10 − 180 (based on level) ability power and 25 − 450 (based on level) mana.

Champion Abilities

Note: Only the ability power buffs of these abilities are shown here. To read more information on each of these abilities, follow the links to their champions' pages.

Galio's Runic Skin adds 50% of his total magic resistance to his ability power.
Singed's Insanity Potion grants him 35 / 50 / 80 ability power for 25 seconds.
Thresh's Damnation passively generates souls for him to collect, with each soul collected permanently granting 0.75 ability power.
Veigar's Phenomenal Evil Power permanently grants him 1 ability power whenever he hits an enemy champion with an ability, and 5 ability power whenever he scores a champion takedown.
Vladimir's Crimson Pact grants ability power equal to 4% of his bonus health.

Masteries

Natural Talent: Grants 0.4 / 0.8 / 1.2 / 1.6 / 2 + (0.089 / 0.178 / 0.267 / 0.356 / 0.444 × level) attack damage (2 / 4 / 6 / 8 / 10 at level 18) and 0.6 / 1.2 / 1.8 / 2.4 / 3 + (0.133 / 0.267 / 0.4 / 0.533 / 0.667 × level) ability power (3 / 6 / 9 / 12 / 15 at level 18).

Neutral buffs

The Dragon Slayer buff grants +8 / 16 / 24% ability power.
The Hand of Baron buff grants up to +40 ability power (among other bonuses) for 3 minutes.

Runes

	Type	Tier 3	% of Highest	Price
Ability Power
	Mark	0.59	36%	410 Influence Point
	Seal	0.59	36%	410 Influence Point
	Glyph	1.19	72%	410 Influence Point
	Quintessence	4.95	100%	512 Influence Point
Scaling Ability Power
	Mark	0.1 per level (1.8)	59%	410 Influence Point
	Seal	0.1 per level (1.8)	59%	410 Influence Point
	Glyph	0.17 per level (3.06)	100%	410 Influence Point
	Quintessence	0.43 per level (7.74)	84%	1025 Influence Point

Trivia

The ability with the largest AP ratio is Annie's Summon: Tibbers, with a maximum AP ratio of (+ 515% AP) counting initial cast of (+ 65% AP) and the target taking damage from all 45 ticks of tibbers aura damage ((+ 10% AP) per tick).
The second and third bounces of Nami's Ebb and Flow scale exponentially, however the low base ratio means it will not beat other spells at normal levels of AP.
Darius, Draven, Garen, Illaoi, Kalista, Kindred, Olaf, Riven, Talon, Vayne, and Zed have no abilities or innate effects that scale with ability power.

(Last updated December 9th, 2016, patch 6.24)

Aside from Veigar and Thresh, who may obtain theoretically infinite ability power due to their respective passive effects, Ryze with Arcane Mastery and Seraph's Embrace , could have the highest ability power.
To reach this amount, Ryze must:

Be level 18 while having a full rune page of Template:Rune runes.

Have maximum ranks in the Natural Talent.
Possess the Hand of Baron buff (after 35 minutes) and three Infernal stacks of the Dragon Slayer buff, empowered by the buff of the Template:Moi.
Have a fully stacked Mejai's Soulstealer, a Rabadon's Deathcap, and 4 Seraph's Embraces.
Have consumed an Elixir of Sorcery.
Be a Conduit for Zeke's Harbinger at 100 charges (connected to Janna)

Janna must:

Be a Conduit for Zeke's Harbinger at 100 charges (connected to Ryze).

This combination will result in

Ryze having about 2120 ability power.

Ryze's ability power: X = ( Y × 0.03 + 145 + 120 + 80 × 4 ) × ( 1 + 0.35 + 0.36 + 0.2 )
Ryze's mana: Y = ( 1250 + 1000 × 4 + 200 ) × 0.0005 × X + 5450
=> X = 2120.05; Y = 11227.13.

[Last updated 13/8/2015 on patch 5.15]

The highest attainable ability power by a playable champion at level 1 (without disconnecting) is 129.2032153 on Galio thanks to his passive, Runic Skin. To reach this amount, he must:
- Have maximum ranks in the Mental Force, Arcane Mastery, Archmage, and Resistance masteries.
- Have 3 last points in Enchanted Armor.
- Have a full rune page of Template:Rune runes.
- Have bought a Amplifying Tome.
- Use Galio's Bulwark.
- Be under the effect of Braum's Stand Behind Me with five enemies nearby.
- Be under the effects of Mordekaiser's Creeping Death and Orianna's Command: Protect.

This combination will result in

Galio having 129.2032153 ability power.

Relevant mathematics:

Braum's bonus magic resist = ( + + + + + + ) × = 117.315

Galio's magic resist = (( + + () + + ) × ) + = 119.9613625

Galio's ability power = ( + + + + + + + ()) × = 129.2032153

Champion statistics

Offensive	Ability power · Attack damage · Attack speed · Critical strike chance · Critical strike damage · Armor penetration · Magic penetration · Life steal · Omnivamp · Physical vamp · True damage
Defensive	Heal and shield power · Health · Health regeneration · Armor · Magic resistance · Tenacity · Slow resist
Utility	Ability haste · Energy · Energy regeneration · Mana · Mana regeneration Movement speed · Range
Other	Experience · Gold generation

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