Doubleheader effect?

If anyone has a bunch of free time or an easily sortable database of MLB teams game-by-game results over a whole bunch of years, you could really help me out. I'd like to test a principle which the Yankees' television announcers repeatedly asserted on Monday, and which was true for the instantiation which they were applying it to. The principle was that "You usually split a doubleheader," and the instance of it was the Red Sox splitting their doubleheader with the Blue Jays today. While the word used was "usually", taking that to mean that doubleheaders are split more than half the time is a really boring claim, not one that's useful for predictions, and not the one the Yankees announcers were making. Their claim was that the Yankees were gaining something by the Red Sox game being rained-out on Monday, forcing the Red Sox into a doubleheader today.

They are therefore making the interesting claim that a game being doubleheader changes a teams likely performance compared to its likelihood of winning two games on consecutive days against the same opponent. While there are really quick and dirty tests of this principle I can do, like counting the number of splits
this year (11), and the number of non-splits (7), this doesn't really tell me much. Plus in 2004 it was 17 splits and 22 non-splits.

Rather, the test I'd like to do is:
1) go back to seasons where doubleheaders were far more prevalent
2) pick a somewhat random sample of teams
3) compare the samples of teams' winning percentage in non-doubleheader games on consecutive days against the same opponent with their doubleheader winning percentage, and see if the doubleheader winning percentage is closer to .500 then their end of season percentage.

This test really needs to be done during seasons when doubleheaders were far more prevalent than today to be meaningful. For instance, in this season, most teams' winning percentage for doubleheaders is going to be .000, .500, 1.000, or indeterminate, because most teams played one or no doubleheaders. In bygone days however, that was not the case. Also, the proper comparison might be end-of-season winning percentage to double-header winning percentage instead, or some other test that hasn't occurred to me. Thoughts?