The 70-200 F2.8 is a popular lens for indoor sports like hockey and basketball but doesn't quite have the reach for football, baseball or soccer.
There is still a reason to take it to the ball game though. It gives you a chance at that once a game photo where the receiver is diving for the ball right in front of you, or crossing the goal line near the corner where you're standing.
In most cases your long lens is a 300mm or 400mm, so the short zoom gives you a second chance when the action comes close.
At the game on Saturday I was using the 70-400mm Sony lens as my main lens, and when the light dropped after the second half I was glad I had the 70-200 with me because of it's F2.8 speed. It wouldn't have been an issue if I had the 300mm F2.8 lens with me, but in this case I didn't and turned to the fast zoom when the sun went down.
It's not ideal but if you shoot a loose image with the 70-200 you can always crop if you have to.