Well im a off and on sivir player and ive found a good item and idea set for sivir so have fun vote the build and feel free to give constuive criticism

At this point ur prolly calling me crazy for 28-0-2 But trust me it hands the dmg and the speed u need so trust me if u would like to give suggestion on it go for it

Dorans Blade is improtant for early game Dmg and the good lane lead. Then I go for the Greaves for attack speed and travel. After that I suggest picking up the Sword of Occult because if u can get a bit fed it gives u the extra attack dmg need to fight off and carry. Then head for the Bloodthirster one of the more improtant items for this build it give you the dmg the lifesteal and what this build is all about a easier carry.After that item i would pick up the phatom dancer for the Attack speed run speed and critcal srike and a dash of lifesteal. the Phatom Dancer gives a nice touch with bloodthirster and occult because the lifesteal helps u stay conistnt in big fights which complamints the Bloodthirster and the dmg speed and critcal gives the occult a sortave boost because it gives attack damage and it mixes well with that just those items in genreal mix well
then i would DEFITANLY if u have the time pick up the lich bane for attack speed and the Abily boost effect from the shen which mixed together into one slot improves alot of other items plus your carry.At this point i sell my dorans blade and pick up the Guardin angel to give u the durabilty in fights which i find VERY important espeically in a carry situation.

Depending on which items your at in the build depends upon teamwork for dorans blade (EARLY GAME SUPER EARLY) at this point im guessing u have a jungler for going to do teamwork this early u want to let ur jungler lead then run in and boomerang blade and if u can richoet.
by bersker greaves basically same stargey as before with dorans blade. At sword of occult if your team agrees to help u tell them u want the kills for occult stacks and so you can carry.
At bloodthirster u should be set for a while mainly fight in a group to get stacks for occult and if kills stacks for bloodthirster.Phatom dancer at this point u should be poking
when your tank leads the fight u should be boomerang blade richtoect auto a few times richote boomerang rinse and repeat and uve more than likely won the fight. Lich bane by now uve achived alot of dmg meaning u should use the phatoms strgey but it will be better.then guardin angel nothing truly changes.

So with teamwork items mastires and the godess known as Sivir u can pull off an easy carry with pratice ,skill, and teamwork

Really the only thing there u should question is the surge reason i say surge is mixes well with items and ulti it basically doubles ulti and with the items its unstopable in a big fight