Watching sports, for me anyway, is relaxing. I love when any Chicago team, except the White Sox, beat their biggest rival.
I think the joy in it is because you find you are not only rooting for the team but actually becoming a part of the team. It's very immature and not intelligent, but I believe this is the way of the fan.
The players invest themselves in preparation of being athletic and good at the sport, the fan invests their time, money, and heart into the team they choose to root for. It is primal to want to win, and I think this is what gives fans their joy when watching their favorite sports.