There is a recent story over at Science News On-Line about how time zones can affect baseball games (here).
Basically it says that if one team travels 3 times zones, when the other doesn't, then there is a statisical advantage to the non time zone changing team. The result seems to be less for teams traveling east than for ones going west. The article also says that these games are a small number each year (like 16). Assuming that they tend to even out, it's not clear that it will make a big difference, but with Championships determined by 1 or 2 games, it might matter. It makes those teams that "send pitchers ahead" look really smart.
So here's a case where the statistics are clear. Wanna bet that baseball ignores them? I wonder if the bookies will?
I suspect that the effect is even bigger in football, and, with fewer games in those seasons, it could really be a big deal, and if I owned a team that made the playoffs, I'd get my team there at least 3 days early to get the time zone adjustment done. But that's me...