Release ARAM match making formula

I have about 2500 ARAM games played and I feel that the matchmaking process (specifically what champs are given) can't be completely random. I own every champion and will gladly play any champion. I am currently 70 games above a .500 winning percentage which has been a daunting climb. From my perspective, I feel that the following things occur when assigning champions for my games:

• Free champions tend to show up more in games. I actually play a mini game where I play several ARAM games and try to guess what champions are free that week.
• Following a winning streak or a high percentage of wins, I tend to get champions that I have a low win percentage with and have a lower kill participation with.
• Following a losing streak or a high percentage of losses, I tend to get champions that I have a high win rate and high kill participation with.
• Following a winning streak or high percentage of wins, I tend to face "god tier" champs more often. For example, when I got to 75 wins above .500, I lost 4 out of 5 games following the 75 win. In all four loses, the opposing team had a Sona.

I am not looking for confirmation. I understand that the tendencies that I have observed in no way prove anything. I just want to hear from other players that have played a large number of ARAM games. What do you observe about the way champions are assigned? Why is it that Riot can't release how they assign champions to players? I don't want to know how they match summoners based on their ARAM mmr. I just want to know if the champion assignments are truly random.