AR URF isn't random?

Unlucky for getting Soraka you say?

laughs in 4 out of 5 wins as URF Soraka

If you go AP tank Soraka you'll be doing good amounts of damage, your self healing will give you a surprising edge in 1v1s (against non-broken 1v1 champs), your heals will be hugely oppressive late game, and with the Ardent Censer you're giving your entire team 8 seconds of 70% bonus attack speed every 23 seconds with your ult.

My first game as URF Soraka I ended up dealing more damage to enemy champions than the Riven and Draven on my team (separately) and had ~40k healing done. URF Soraka is definitely one of my favorites. She's extremely reliable.

If it wasn't random you'd get a more even distribution on champions.

Try this out: Take a dice (preferably a 20-sided, but a 6-sided will do) and role it the number of times you have sides. Odds are you'll get at least one side that wasn't ever rolled and one side that was rolled multiple times. This can be seen on the 6-sided dice, and even more consistently on the 20-sided dice. Now imagine you had a dice with 135 sides (assuming you owned all champions), and it's not hard to see how an actually random system would randomly give you the same results as you see.

do me a favor, go to random.org and generate a number between 1 and however many champions you have. Do it however many times you've played aram, and let me know how often you get 1 specific number.