Critical strike
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A critical strike is a basic attack that deals twice its normal damage. In the real world, it's an attack striking a vulnerable area, while in other MMO and/or RPG settings, it ties into the very common "critical hit" mechanic.
It only applies to basic attacks or certain abilities like Gangplank's Parrrley and Yasuo's Steel Tempest that act like a basic attack or Garen's Judgment and Master Yi's Alpha Strike, which are specially stated. It's important to note that you cannot score a critical strike against a building such as a turret or inhibitor (Except Jhin, whose fourth shot receives minicrits against all structures).
Most champions have different attack animations for a critical strike, though some do not; this includes mages and other champions not meant to be built using basic attacks for damage. Some of these champions performing a critical strike (if built being able to perform them) may instead have a soundbite that plays in place of an animation, typically a grunt of effort.
Critical strike is valuable for all champions who primarily deal damage with basic attacks, rather than through abilities. Some champions, such as Ashe, have an affinity for critical hits and benefit more from items that improve them. Players can increase the Chance and the Damage of critical strikes with items, abilities, and runes.
Chance
Critical strike chance, as the name states, is the chance of a champion's physical attacks dealing a critical strike. Critical strike chance stacks additively. Runes, items, and all abilities can increase critical strike chance.
When averaged over a large number of autoattacks and at Base critical damage (100% bonus damage), critical strike chance is essentially a damage multiplier where each 1% of critical chance adds 1% bonus damage. Thus at 50% critical strike chance a champion will be doing (on average) 150% damage with autoattacks, not counting Bonus critical strike damage. Because of this, critical strike chance scales well with both attack damage and attack speed. The formula for this damage multiplier is given by:
Damage multiplier = 1 + (Critical chance × (1 + Bonus critical damage))
The maximum critical strike chance you can reach at level 1 through masteries is 20.25%, excluding abilities and items, and is hard capped at 100%.
Critical strike chance has a theoretical gold value of 40 per 1% critical strike chance. This makes the most efficient core item for critical strike chance, as it grants +10% critical chance for the cost of 400 with a 40 per 1% critical chance efficiency. Note that has the same efficiency.
Increasing critical strike chance
Items
Item  Cost  Amount  Availability 

400  10 %  Common  
800  20 %  Common  
3600  20 %  Common  
3600  20 %  Common  
2550  30 %  Common  
2600  30 %  Common  
2600  30 %  Common  
2600  30 %  Common  
1300  20 %  Common 
Temporary Effects
 Unique: When within 1000units of each other, you and your Conduit will generate 1 charge every second, up to 100, with a bonus 4 / 2 charges whenever you or your ally attack, and 8 / 4 on spell cast.
At 100 charge, dealing damage grants you and your Conduit 20% increased AP and +50% flat critical strike chance for 8 seconds.
All current charge is lost if you move further than 1000units apart or hold onto 100 charge for longer than 5 seconds. : Passive:
Champion abilities
Note: Any ability boosting attack speed has an indirect impact on the number of crits.
 Fiora's Bladework grants her 100% critical chance on her next second attack.
 Jhin's Whisper passively grants him 100% critical chance every fourth basic attack.
 Curtain Call has a guaranteed 100% critical chance on its fourth and final shot.
 Pantheon's Certain Death grants him 100% critical chance against targets below 15% of their maximum health.
 Shaco's Backstab passively grants him 100% critical chance for every basic attack striking an enemy unit from behind. This cannot happen on the same target more than once every 3 seconds.
 Talon's Noxian Diplomacy grants him 100% critical chance if he hits its target within a 170 range.
 Tryndamere's Battle Fury grants him 0.35% critical chance per point of Fury he currently has.
 Xin Zhao's Battle Cry passively grants him 100% critical chance on every third basic attack.
 Yasuo's Way of the Wanderer grants him twice the amount of critical chance.
Runes
Damage
Critical strike damage refers to the amount of damage that a champion's critical strike will deal. All champions have 200% critical strike damage by default, except Ashe with 110% damage, Jhin with 150% (reduced to 112% vs structures) and Yasuo with 180%. In most cases, critical strike damage stacks additively. Damage modifiers apply to critical strike damage normally.
Modifying Critical Strike Damage
 Champion Abilities
 Ashe's Frost Shot modifies her base critical damage to 110% + (Critical Chance × (1 + Bonus Critical Damage))
 Fiora's Bladework modifies her base critical damage to 140 / 155 / 170 / 185 / 200% from the default of 200%.
 Jhin's Whisper multiplicatively reduces his total critical damage by 25% for basic attacks.
 Shaco's Backstab modifies his base critical damage to 120%  145% (based on level) from the default of 200%.
 Xin Zhao's Battle Cry modifies his base critical damage to 125 / 137.5 / 150 / 162.5 / 175% from the default of 200%.
 Yasuo's Intent multiplicatively reduces his total critical damage by 10% for basic attacks and 25% for Steel Tempest (e.g. 200% to 190% / 175%).
Items
 Unique: Critical strike bonus damage is increased by 50%. : Passive:
Runes
Notes
 The maximum bonus critical strike damage obtainable is 95.51%, as follows:
 For most champions, the maximum critical strike damage available is 200% for a total of amount of 295.51% AD on their critical strikes.
 Ashe with 100% critical strike chance will deal 328.265% AD on her critical strikes thanks to her innate passive Frost Shot.
Skills affected by Critical Chance
Certain skills are capable of critical strikes and/or are affected by critical chance.
 Most of them only do bonus 100% AD × (Total critical damage − 100%) if they critically strike.
 Blitzcrank's Power Fist
 Caitlyn's Headshot: Against champions.
 Darius' Crippling Strike
 Draven's Spinning Axe
 Gangplank's Parrrley
 Garen's Decisive Strike
 Jinx's Switcheroo!
 Nautilus' Staggering Blow
 Nidalee's Takedown: Magic damage, benifiting from Life steal.
 Nocturne's Umbra Blades
 Quinn's Harrier
 Renekton's Ruthless Predator: Only applicable to first hit.
 Riven's Runic Blade
 Shyvana's Twin Bite: Only applicable to first hit.
 Trundle's Chomp
 Vayne's Tumble
 Viktor's Discharge: Magic damage, benifiting from Life steal.
 Volibear's Rolling Thunder
 Wukong's Crushing Blow
 Xin Zhao's Three Talon Strike
 Others
 Caitlyn's Headshot: Critical strikes do bonus 250% AD × (Total critical damage − 100%) against minions and monsters.
 Garen's Judgment: Critical strikes do bonus entire damage portion × (Total critical damage − 100%).
 Jayce's Hyper Charge: Critical strikes do bonus entire damage × (Total critical damage − 100%).
 Jhin's Curtain Call: The final shot is a critical strike, doing bonus entire damage × (Total critical damage − 100%).
 Lucian's Lightslinger: The additional shot does bonus entire damage × (Total critical damage − 100%) if it is a critical strike.
 Master Yi's Double Strike: The additional strike does bonus 50% AD × (Total critical damage − 100%) if it is a critical strike.
 Alpha Strike: Critical strikes do bonus 60% AD × (Total critical damage − 100%).
 Miss Fortune's Bullet Time: Each wave can critically strike, dealing 20% × (Total critical damage − 100%) bonus damage.
 Nasus' Siphoning Strike: Critical strikes do bonus base damage × (Total critical damage − 100%).
 Yasuo's Steel Tempest: Critical strikes do bonus 75% AD × (Total critical damage − 100%).
 Additions
 Shaco's Backstab: Critical strikes do increased damage after critical modifier.
 Tryndamere's Spinning Slash: Cooldown is reduced by 1 second for every critical strike. This effect is doubled against champions.
Miscellaneous
Other skills that are not being affected by critical strikes and chances are displayed as a critical strike due to other reasons.
 Affected by Critical strike damage
 Unaffected by Critical strike damage
 Anivia's Frostbite: The 2 × damage modifier applied by being chilled by Flash Frost is given out as critical strike.
 Fizz's Seastone Trident: The triple damage dealt to a target that has been bleeding for more than 2 seconds is given out as a critical strike.
 Gangplank's Powder Keg: The damage is always given out as a critical strike.
 Gnar's GNAR!: The damage is given out as a critical strike when enemy hits terrain.
 Gragas' Barrel Roll: The damage is given out as a critical strike when the cask ferments after 2 seconds.
 Karthus' Lay Waste: Appears like a critical strike when acting like a single target spell (hitting only one enemy).
 Kog'Maw's Living Artillery: The double damage dealt to enemies under 40% of their maximum health is given out as a critical strike.
 LeBlanc's Sigil of Malice: When the sigil is shattered by Leblanc's next ability against the target, the combined damage of the sigil and the ability is given out as a critical strike.
 Miss Fortune's Double Up: The second damage is given out as critical strike when the first target is killed.
 Nidalee's Takedown: The 40% increased damage dealt to Hunted targets is given out as a critical strike.
 Pantheon's Spear Shot: Will critical strike for a +50% damage bonus due to the passive from Certain Death if the target is under 15% health.
 Ryze's Overload: The extra damage applied to a target marked with Flux is given out as a critical strike.
 Vayne's Condemn: The doubledamage applied by being knocked into a wall is given out as critical strike.
 Vladimir's Transfusion: The extra damage applied when under the effect of Crimson Rush is given out as a critical strike.
 Ziggs' Satchel Charge: The damage is given out as a critical strike when used to hexplode a tower.
Trivia
 Similarly in many MMO settings, a number of attack damagebased assassins or secondary assassinbased champions also benefit from high critical strike chance in varying form, as a means to help finish off targets faster as well as to deal more damage in bursts overall.
 The fastest way to obtain 100% critical strike chance is with Yasuo, requiring only 1200 :
 Runes: +20.25% Critical Strike Chance
 9 × Marks of Critical Strike Chance (+0.93% × 9 Critical Strike Chance)
 9 × Seals of Critical Strike Chance (+0.42% × 9 Critical Strike Chance)
 9 × Glyphs of Critical Strike Chance (+0.28% × 9 Critical Strike Chance)
 3 × Quintessences of Critical Strike Chance (+1.86% × 3 Critical Strike Chance)
 Items: +30% Critical Strike Chance
 (+10% Critical Strike Chance)
 (+20% Critical Strike Chance)
 Critical Strike Chance Amplification: 100% Critical Strike Chance
 Way of the Wanderer (+ 100% Critical Strike Chance)
 Relevant mathematics:
 Yasuo Critical Strike Chance = (20.25% + 30%) × 2 = 100.5% critical chance
Champion statistics  

Offensive 

Defensive  
Magical  
Movement 