Hussar
Legend
/snip
Baseball seems to allow a player to make propositions ("I propose I get to run around all the bases!"), and a mechanic for determining success, but it is not a role playing game because it lacks a fictional narrative. You can tell the story of the game, but it is non-fiction, as those events actually happened in the real world.
I would like to say that I pretty much agree with @Celebrim here. And, I'm saying that just for the novelty of it.

But, I would disagree with this quoted point. The player doensn't get to propose that he gets the opportunity to run all around the bases. He can only run the bases when the mechanics allow him to do so. In fact, he has no choice sometimes (squeeze play, runner behind him) and must run after he hits the ball.
I suppose you could argue that he could hit the ball and then stand there doing nothing, but, at that point, he's refusing to play the game. It's like saying a Monopoly player could refuse to roll the dice on his turn. It's true, but, kinda beside the point.