Not as rare as the tripleheader, the last one being in 1920, the doubleheader is a relatively rare feature of MLB and is traditionally defined as two games played between the same teams on the same day in front of the same crowd, but which is more generally used these days to refer to two games played by a team in a single day, but in front of different crowds and not in immediate succession.
They typically occur later in the season, as they are no longer scheduled, but are the result of games being called off, most often due to bad weather.
In 1969, Michael L Goodman published an article in The American Statistician titled On the Incidence of Swept Double-Headers in which the author claimed that contrary to popular opinion, doubleheaders are more often swept than split:
1969 was a long time ago, but over the last ten seasons, including the current one, I make it pretty much 50/50, with 130 sweeps to 134 splits, but there's an interesting, and perhaps not totally unexpected, tendency for teams to sweep in the later months of the regular season.
If the public perception is that it's difficult for a team to sweep, you might ask yourself how does backing the winner of doubleheader game one in game two work out?
Turns out overall, not too well, with a negative ROI of around 3.4%.
In September and October though, when for many teams the season is effectively over, and for others, they are fighting for a post-season place, it's a different story.
Here, backing the game one winner in game two has an ROI of 25.7% (ML) and 24.8% (RL).
When the team is the underdog, the returns increase to 46.8% and 27%, and when the 'dog has fewer wins in the season than their opponent, we're up to 82.9% and 40.5%.
And when the 'dog is at home, the ROIs are a ridiculous 151.9% and 82.2% respectively, but we're also down to a very small sample size!
There have been 31 doubleheaders this season so far, with another one today (Washington Nationals v Philadelphia Phillies) and one on Friday (Chicago White Sox v Detroit Tigers).
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