In sports usage: A player that is always pissed off. Usually said off an outstanding player when anything short of perfection isn't good enough. If Randy Johnson gets a win, he should have struck out 15, or have thrown a shut-out, or a no hitter. Basically a red ass is never pleased with his or his teammates performance on most occasions.
Player A: What's eating him, he just went 3 for 4 and we're only a game out of first?
Player B: He's such a red ass that even if he went 5 for 5 and we were 10 games in first he still wouldn't crack a smile.