Kai'Sa

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You Can’t Outrun the Void

Massive dueling potential and scaling damage.

Precision

Improved attacks and sustained damage

Fleet Footwork

Attacking and moving builds energy stacks. At 100 stacks, your next attack heals you and grants increased MS.
Overheal

Excess healing on you becomes a shield.
Legend: Bloodline

Takedowns on enemies grant permanent Lifesteal.
Cut Down

Deal more damage to champion with more maximum health than you.

Sorcery

9% attack speed, 10 ability power or 6 attack damage

Absolute Focus

While above 70% health, gain up to +40 Ability Power or +28 Attack Damage (based on level), Adaptive.
Gathering Storm

Gain increasing amounts of AD or AP, Adaptive over the course of the game.

WhyFleet Footwork

Fleet Footwork grants you fantastic lane sustain allows you to bandage bad matchups and stay in the game until you can get a few items and start scaling.

WhyOverheal

Overheal's extra bit of health buffer is great for all-in duels if you're able to build the shield before diving in with [R]. Items like Deaths Dance and Legend: Bloodline will help you build and shield and sustain in lane.

WhyLegend: Bloodline

Kai'Sa has a short attack range and because of that she is susceptible to a lot of incoming lane harass. Bloodline helps keep you safe and continue CSing for you item power-spikes.

WhyCut Down

Cut Down allows you to massively AoE shred any enemy champion in teamfights when you've completed your Hurricane.

Coup De Grace's execution damage help you to shred the enemy backline target's quickly and seamlessly so that you're able to get out and move on for more damage.

WhyAbsolute Focus

Absolute Focus's extra bit of Attack Damage is incredibly value and key to your dueling power. Death's Dance and Legend: Bloodline help keep you above the health threshold.

WhyGathering Storm

Gathering Storm is your late game damage insurance policy, allowing you to scale and take over fights/duel any in a 30min+ game.