You're playing Sivir wrong. Try Graff's Guide 2 Elo Zoo

I'm rank 7 Sivir, if that means anything.

Some quick pre-requisites before you follow these 8 simple steps to acquire elo.

1. Pick . Equip your Victorious skin. If that's not an option, Warden will do.
2. Build and a upgrade. If you're not running 10% scaling cdr runes, finish your 40%.
3. Get into the right mindset. Imagine the post-game screen.

• Next to your name, there are three numbers with slashes between them. They're small and meaningless. They don't matter.
• Next comes a purple icon, followed by a much more important number: cs.
• Finally, there's a yellow icon, and another, much larger, number. This number is high because your cs was high, but you know that it, too, does not matter. CS doesn't matter because of the gold you get, it matters because of the map pressure you create.

Now that you've got your priorities straight, you're ready to follow the guide:

1. Pick a lane to create pressure.

• If you walk past camps on your way to that lane, don't forget to clear them, too. This will help you get more items, to waveclear more quickly.

2. Instaclear the wave in that lane.

• Your goal is to do this as quickly as possible so the enemy team has no vision of you and no chance to collapse on you.

3. Do you have vision of the enemy team? If not, go to step 1.
4. Is the enemy team in your lane? If so, go to step 1.
5. Press R to run your minions down the lane super fast.
6. Did the enemy team respond to your push? If yes, go to step 1.
7. Take the next structure.
8. Was the structure the nexus? If so, collect 50g. Otherwise, return to step 1.

Okay, so realistically you should occasionally be there for teamfights and objectives (spell shield can block a dragon attack!). Once you get 2-3 inhibs you should probably group. And if your team gets really behind they might need your help with waveclear.

Don't let that distract you from the only stat that matters. Enjoy your elo.