Sorry, but just because we have played that many times and no one has the edge over the other means we have played each other for a long time and it has been a coin flip.
When I was in school Baylor was a game just like Rice. The rivalry was SMU, Tech was always a wild game, and then we were excited about playing Texas.
The only time I can recall the Baylor game getting much attention was the year after that asshat Teaff ran up the score because he thought FA did the same to him the year before in one of FA's rare blow-out victories.