ARAM Biased Toward Free Week Champs?

Has anyone seen a statement from Riot or personal experience about ARAM appearing to be not so random?

On my first account, with over 100 champs, I'm still more likely to get one of the free week champions then to get one of the ones I own. Just being a personal observation over 100s of games, I decided to create a test trial to see if it really was random Out of 25 games, I got a free week champion 16/25 games, a champion I owned 4/25 games, and one that was both free and owned 5/25 times.

There's also an issue with getting the same champion 2 or 3 games in a row, which always tends to be a free week champion, and is extremely unlikely being on an account that owns over 100 champs. Ignoring the chances of other people getting the champ, my individual chance of getting a champ 3 games in a row would be (1/136) * (1/136) * (1/136), 0.0000003975, or 0.00003975% of happening 3 times in a row. 2 times in a row would be (1/136)*(1/136) = 0.000054, or 0.0054% chance of happening. Now this isn't some rare occurrence, I've seen many times where I'd get the same champ 2 or 3 times in a row. This could be some issue with their random number generator being based on a seed that doesn't change often enough, because the math and programming behind creating random choices is incredibly simple.

I have to assume they either just didn't put a lot of effort into making it truly random, or there is a mathematical bias toward the free week champs, because with these chances this should be an extreme rarity, not a regular occurrence.