this ban thing.....
i dont know if banning is the greatest idea.
no one quits when they get banned. they just do what tyler1 is doing. they make a new account and they beat the shit out of noobs.
maybe they lose some champions they like and a couple of skins if they are spending money on it, but really its the exact same game at level 3 as it is at level 30. with the free champion rotations there are always a couple of champs you like to play, and its arguably more fun at low level. stomping the players who are legit new.
i dont know what would be a better punishment, but there must be one. all you are really doing with bans is a mild inconvenience and giving them a new project to work on.