I think that MR and TR should not be used to determine why you win or lose a game. They are average reflections of the skills involved in each game. They should be taken only as a basic performance evaluation. Why should this then not be taken as a determiner of a win or a loss? For example, let's say two teams are absolutely equal for an entire game except for a two minute stretch to start the 3rd quarter, where team A makes 4 straight three pointers. Team A outscores team B by 12 points in those two minutes. The final is a 12 point victory for team A. The TR and MR will still be basically equal.
I think that the overall box score and watching the game are the two best ways to tell why you wion or lose a game. Often times free throws, foul trouble, offensive rebounds, and/or turnovers are the factors in a win or loss, especially between teams of similar quality.
Once I scored a basket that still makes me laugh.