How do I make him feel good about himself?

If he doesn't understand better to drop being sarcastic with him. The worst part in being sarcastic is that the person on the other side just forgets to understand when to take you seriously.

Guys do not want to be beat by girl (especially sports) - it totally makes them feel like masculine (I know it stupid). Obviously he doesn't seem to like your good humored teasing/sarcasm, so that would be a clue to stop it. Unless he teases/is sarcastic with you when he beats you in track (doesn't like he has) then is appropriate/ok to use sarcasm. If he can dish it out then he should be able to take it. It is the time, manner, and way that you are sarcastic. Maybe he enjoys the sarcasm & competitiveness before you run track, but does not however appreciate it when you beat him. Perhaps he isn't a very good loser. I mean, really how many guys would want a girl to beat him at a sport? - It's an ego thing.

It's obvious your sarcasm is not appreciated when you beat him at a race (so, really it's time to stop). People (yes, guys included) can be sensitive when it comes to certain things. So, the best is to use your wonderful interpersonal skills and learn when to lay-off. If it bothers you that he cannot take your sarcasm/teasing, then best use it on a guy who can. Hope you get my drift.