Well, I don't work in a sports bar, but the (silent) TVs generally DO attract some attention during playoff seasons. The masses determine the mood of the room whether it's diners or bar patrons. That's just the nature of a room that features both areas.
I would never fault some patrons that cheer for their team in a good natured way, especially because it puts them in a better mood for the rest of the night as they continue to listen to MY addition to the evening.
If the Philly teams are out of contention, I don't care about the damn game either, but our patrons are from all over and you never know who's going to come in.

If there's a bar, there is almost always a TV. If it's only a restaurant, then you get lucky and you just have to deal with the volume requests. I generally work rooms that have both.