Alright, the Data is in.
First and foremost, Overall there were definitely less streaks than gathered data before weighted dice. While documenting combat rolls Advantage and Disadvantage started to centralize very early for the player and enemies in combat. They both match what we would expect from Advantage and Disadvantage. Normal attack rolls for the player and enemy had an interesting story.
Omigod! Who are you? I'll tell you what this reminds me of. I heard this story about a statistician who got thrown into prison. And he kept track of the days by keeping a tally chart on his cell wall. If I read between the lines, it seemed like he was paranoid that if he didn't do so, that the prison would be able to convince him that he hadn't been there for as long as he knew he'd been there.