To Reduce Snowball, Rework the Snowball Runes
Dark Harvest. Ravenous Hunter. Eyeball Collection. Presence of Mind. Legend: Alacrity. Chrysalis.
These are just some of the runes that give you advantages for killing enemy champions. And this is a problem, because it means that by combining these runes you can obtain huge buffs every time you kill. The result is that, if you're good at killing other champs, you'll quickly become even better at it, leading to insane snowballing.
I understand that Riot wants to incentivise champion takedowns in order to encourage more active champion-to-champion combat. But here's the thing: champions are already hugely rewarded for scoring takedowns (gold, XP, temporarily removing an opponent from the game). To give them even more advantages on takedowns is overkill.
Imagine a racing game where the person who is ahead is rewarded with even more speed. Would that make for an interesting race? No, it wouldn't. So, Riot, I suggest that if you want to make League less snowbally, rework some of the runes so that players can't obtain so many buffs on takedowns, making the deadly even deadlier, and destroying any hope for those who lost a few early fights to ever come back.