I always find sports streaming through the Apple TV app just plain sucks. I have MLB TV and NHL Gamecenter and when I launch the apps for a baseball or hockey game it is constantly messing up, even if I have an amazing internet connection. I have tried it as well for NBA with the same results. I mostly launch the app from my phone or iPad, then use Air Play. It is much better that way.
Sports streaming really needs a boost in some ways. Especially going live. There are times when my stream for a hockey game gets almost 2-3 minutes of "on the clock" game time down from the real event, and I end up getting a notice on my phone of a score before I see it. It is mostly with Apple TV, and can be incredibly frustrating. But then again, my Apple TV and most of my friend's Apple TV's have the same issue.