I see a rivalry as not having a pretty sure bet on who's going to win when the same two players continually meet each other. If Roger and Rafael meet each other in the final of the next tournament they both play in, I don't think anyone can say beyond a reasonable doubt which one will be victorious. Rafa might have the last several matches, but would it surprise anyone if Roger won the next one? In contrast, if it's Roger/Andy, it's a pretty good bet who's going to win that match-up. So, in my opinion... Roger/Rafa = rivalry Roger/Andy = not so much.
I think this is a very good point. It's certainly a rivalry in my eyes. The outcome of their matches is simply too much up in the air. Nadal gets the best of Federer a lot these days but it doesn't change that it's up in the air. Going into the 5th set of the AO final on Sunday, who did y'all think was gonna win? Part of what made Andy-Roger seem like a non-rivalry is that Andy was having a very difficult time even taking sets from Roger. Roger and Rafa play each other very close.