Pushing waves to get out of bronze

The past few games I have played, I tried to just push the shit out of every lane all the fucking time. Its the only reason we won the last game I played and it seems like it makes the other team need to split up more and become disorganized. The more I pushed the easier it became to push and also win group fights. We couldn't win a straight up 5v5. I'd shoot a lazer and then everyone on my team would freak and die, mundo would usually run away or not tank. or tank at the wrong times.

Idk what to do ab my team. They suck if I try to help them teamfight. I'd go in and assassinate two people with akali (different game before i really realised how this worked) and then my entire team would be dead before I turn got finished with the adc.

The last game worked out because it was easier for my team to catch ppl out when the enemy split up to deal with one pushed lane or the other. Anyway, I was wondering what are the split pushers with the highest move speed and best team fighting? Victor worked out pretty well. Akali split pretty well, but didn't teamfight that well. Like I said, my team would die while I assassinated someone.