Are there Stats on which roles have higher win%?

There are one of each role every game. Every game has a winner and a loser. The winrate for every role is 50%, because every game has a winner in that role and a loser in that role theoretically.

I don't see how there could be.

In every single game (with the exception of non-meta compositions), each lane/role will have a winner and loser.

You mean the role that influences the game the most look at the highest average winrates of champions and see if they are disproportionately in one role take into account play rate that is the role

The most influental roles at the moment is jungle then midlane then support and adc being tied for third. If you are talking which lane you should main, then go for the one that suits your playstyle the most.