ARAM should be pseudo-random, not random.
We all know that every time you don't crit, you increase your chance of critting on the next autoattack. It's not totally random.
In ARAM, the same thing should happen with the champions chosen - they shouldn't be totally random. Rather, they should be separated into various tiers of power, and ensured that both teams have equal numbers of champions from each pool.
Ex. Tier 1: Sona, Kog'Maw, Varus, Ziggs Tier 2: Sivir, Azir Tier 3: Vayne, Thresh Tier 6: Eve, Rek'Sai
Just some examples. If it was pseudo-random, then each team would get 2 tier 1's, and one of each of the others I've named.
This would ensure that both teams have a roughly equal chance of winning, while still keeping the "random" nature of aram intact. This would thus also solve the issue of aram smurfs.
I don't know about you guys, but I'm sick and tired of facing a team with Sona, Ezreal, and Kog'Maw with a team of short ranged & melee champions.

every second game and
like two times a year.