Dealing With Splitpushing

First of all, splitpushing is completely viable and though it's a pain in the ass, it's a perfectly acceptable tactic and I don't judge you for doing it.

I play top and mid, often teamfight champs like Ryze and Rumble. Now today I had a Rumble game against a Jax in top. He didn't really know how to fight me and their jungler was never around, so I shoved him under tower, warded, shoved some more, killed him (although he got a first blood on me :P) and fought when he went to stun and trade, usually winning. I was going to get ganked by jungle and mid (Riven and Ziggs) and managed to get some kills from that, coming out of lane 5/2/2.

I thought I won, so I TP'd bot to help out our Jhin and Lux, who were doing horribly. Got their Vayne and almost Janna, but I lost top turret. I figured "ok, good trade, get Jhin back on his feet." Jax took another tower when I went bot again and I got jumped when I was hiding in a bush. By now he had about equal gold to me and was the same level. I chased him off then went mid to fight. By the time I saw him again, he was massively fed from splitpushing, and I couldn't really shut him down with my 1 slow.

My question is, how do I stop splitpushers as a teamfight character? I prefer fighting rather than farming, as you can tell by my champ choice, but most characters I play (with the exceptions of the few Fiora and Zed games) don't have huge potential to take towers or move to stop splitpushers.

Thanks!

[slayer-pantheon-thumbs]