Sivir
Life’s Cheap, Death Pays
Lane harassment and consistent damage output.
Precision
Improved attacks and sustained damage
Fleet FootworkAttacking and moving builds Energy stacks. At 100 stacks, your next attack heals you and grants increased
MS .
Absorb LifeKilling a target heals you.
Legend: AlacrityTakedowns on enemies grant permanent Attack Speed.
Cut DownDeal more damage to high health enemy champions.
Sorcery
Empowered abilities and resource manipulation
CelerityAll
Move Speed bonuses are 7% more effective on you and gain1% Move Speed .
Gathering StormGain increasing amounts of AD or AP,
adaptive over the course of the game.
Adaptive Force
+9
Adaptive Force Adaptive Force
+9
Adaptive Force 
Health Scaling
+10-180 Health (based on level)
Why Fleet Footwork
Fleet Footwork is a great AD Carry keystone for champions who can be abused by their short range, allowing them to sustain reliably into the late game.
Why Absorb Life
Overheal **synergizes well with Fleet Footwork, Bloodline, and Taste of Blood**, keeping to topped off in lane.
Why Legend: Alacrity
Sivir's 3 item power-spike typically only includes 1 Attack Speed item so the extra bit from Alacrity lets you get in more of those hard hitting autos.
Why Cut Down
Cut Down is great for chopping down tanks, melee supports, and mid laners who might build Rylais and/or Liandries.
WhyCelerity
Sivir is the queen AD Carry of moving fast and Celerity further enhances that, synergizing well with your [R] and passive Movement Speed.
WhyGathering Storm
If there is one thing Sivir does better than any other AD Carry, that's clearing minion waves to stall out games. Gathering Storm empowers your ability to stall games into the late game and stack massive Attack Damage to take over a teamfight.