The math of an ARAM-only account

I was curious how effective they are, and what winrates look like with different amounts if champions. So I did some math.

If you bought the top 16 winrate champions for ARAM, statistically you'd have a 55.67% chance of winning every game. Which statistically makes you challenger tier if ARAM were ranked.

This is factoring in the 14 free rotation champions, of which 1.64 will statistically be copies of what you have already bought. Rerolling gives you a 11.68% chance of getting one of your champions, which bumps up your winrate a bit.

Buying the top 36 winrate champions (those over 53%), you will about the same winrate at 55.68%. Factoring in you have a higher chance of your champions being in the free rotation. The higher amount of rerolls offsets the lower winrate champions you own, plus they are still high winrate champions. You have a 25.53% chance of getting one of your champions on a reroll.

Buying all champions will give you a 51.86% winrate statistically if you reroll everytime you get one of the 87 champions that have 50% winrate or lower. And you will be getting a reroll in 2 out of 3 of your games because you own all the champions. Only 54 of the champions have a positive winrate.