West coast games tend to start at 3am here. Those are games like LA dodgers vs SF and LAA vs Oakland.
The majority of games start at 12.05am 12.10am 1.05 am 1.10am here. During the week anyway.
Anyone who hasn't already should sign up to MLB TV. You get a free game of the day that you can watch in excellent quality on a laptop or HTPC. Doesn't cost a thing. You can also subscribe for a reasonable fee and get access to all the games.