Sivir is a pretty strong AD carry. However, she has a health bar that is on the small side. Sivir is strong early-game and late-game, but until she has her item bar filled out she isn't a major power player, but more of a supporter. She is strong in bottom or top early on. Later on, she does good in 1v1 fights. I love using Sivir to wear down at the enemies. With this build she is constantly underestimated, and with her passive, she can run away from an enemy champion and slowly wear down their health with basic attacks every 2 seconds. She can chase after people just as well.
This build focuses on three major stats that boost Sivir:
The high attack speed paired with a high critical strike chance is very deadly. Combine those with a high movement speed and Sivir's ultimate you can chase after anybody.
NOTE: Summoner spells are not included. You should know how and when to use ignite and teleport.
EXTRA NOTE: This is my first guide. I don't have all those fancy link things. Take the 2 freaking seconds to look it up yourself!
Passive - Fleet of Foot: Every single time you attack a champion, you run faster. Doesn't that sound a little overpowered to you? This ability makes it easy to chase after and run away from enemy champs.
Q - Boomerang Blade: This attack is very powerful against a champ especially if they are all you hit, and you hit them twice. The rebound on this can surprise people. This is also good for just finishing off minions hordes at a time. Always max this out first!
W - Ricohchet: Very useful in team fights and when jungling/finishing off minions. After your Q, max this out. The damage increase you get is very helpful to just wear enemy champions down in team fights.
E - Spell Shield: Important to have early, but maxing it out doesn't give you enough of a bonus to max it out early. Using this ability can block an ultimate like Nunu's or Lux's or Ashe's. Any that are one-hit. However, ultimate's like Miss Fortune's are more than one shot, and this ability will only block one hit. This can also block things like Leona's 'E' which immobilizes and does damage. (NOTE: Leona will still dash to you)
R/Ultimate - On The Hunt: Sivir's ultimate does no damage, but it gives her an INSANE movement bonus to her AND her nearby teammates, as well as a rather large attack speed bonus, of which only half is applied to teammates. Use this to completely destroy champions trying to run away, or to help kill dragon/baron. UPGRADE THIS EVERY TIME IT'S UP!!!
Sivir doesn't need many items.
Doran's Blade: Starting off with this just gives you a boost when it comes to slowly wearing down enemies in the beginning. The health also makes you less squishy.
Boots of Speed: Help build toward the Berserker's Greaves.
Phantom Dancer: Getting this item early in the game is a huge boost for attack speed and critical strike chance, which, when paired together, is very very deadly. Even more so with Sivir's passive making it that the more hits you land the better.
Berserker's Greaves: Gives a big speed boost and also increases the attack speed, which makes Sivir a speedy ninja early in the game.
B.F. Sword: Gives a huge attack damage bonus and helps build toward the Infinity Edge.
Zeal: A perfect item because it gives all three aspects that make a deadly Sivir. Attack speed, critical strike, and movement. It also builds towards the Trinity Force.
Infinity Edge: A very powerful item that increases damage and critical strike by HUGE amounts.
Trinity Force: A great item to boost everything late-game. It also boosts Sivir's health greatly, which makes her much less squishy.
Black Cleaver: Just an item that rounds out your item bar and gives you a pretty generous boost of damage and critical strike.
These runes are to help doing what I believe Sivir does best. Hit a lot, and hit hard. The movement speed is for pushing a lane and chasing those running champs. The attack speed is so that when you catch up to those running champs, you can get a quick hit on them and keep moving, which also preys on Sivir's overpowered passive. The critical strike is surprisingly helpful. When you are landing attacks with a chance to do 2.5x damage for each attack you want to have it happen as much as possible and have a lot of attacks in that time. Those are what the attack speed and critical strike runes are for.
Offensive mastery explanations:
+3 AD : You are an AD carry, every AD is very much wanted to fulfill your role.
+2 AD on minions : Does it need more explanation? More damage to minions = easier last hit ratio = more money = FED
+4% AS : More attack speed means better use of Sivir's passive, plus it speeds up her attack animation.
+2 AD per Level : More AD each level, good to increase that dmg per hit before any mayor items are purchased. This also unlocks Lethality
+10% ArPen : Her attacks ignores 10% of the enemies armor, thus more damage per hit. Specially when things gets tanky.
+10% CrD : Not that you going to crit that often, but those critical hits will damage 10% more. For harassing hits will sometimes be painful and force them to go back to base.
+3% LS : Good for early game lane sustain. After a few levels this skill alone gives you 3 HP back per hit.
+6 ArPen : Ignoring armor and deal more damage. Works well early on when armor isn't a big role yet. This also means minions dying faster making last hitting less of a pain.
+6% DMG on targets <40% HP : More damage to those ballsy enough to stick around sub 40% hp. Very nice early game
Defensive Mastery Explanations
+4 MR : Some extra magic resistance for those harassing spells.
+4 Armor : HP going down just a bit slower to make a difference when invading at level 1 and early lane sustain.
+6 HP per Level : Leveling up now gives you 6 more HP then normal. That is 108 extra HP by the time you reach level 18.
+30 HP : Instantly having 30 more HP at level 1 is significantly for those DMG trades.