how unusual was it that the visiting team won all 7 games of the World Series?

Last night the Washington Nationals beat the Houston Astros in the seventh game of the World Series. The visiting team won all seven games of the series. This has never happened before.

Two evenly matched teams should each win about half of the time. Home field advantage indicates that the home team has a slight advantage, with the home team in Major League Baseball winning approximately 55% of their games and the visiting team winning 45% of their games.

The probability that the visiting team wins all seven games in a seven game series is:

(0.45)^7 = 0.0037

This is less than 1% and while it is rare, we would expect the visiting team to win all seven games every 268 World Series or so. There have been 114 World Series so far.

For comparison, the probability that the home team wins all seven games in a seven game series is:

(0.55)^7 = 0.0152

To put this in context, the home team is four times as likely to win all seven games in a seven game series than the visiting team. The home team won all seven games of the World Series three times, which is about what we would expect based on the math above.

So far, either the home team or the visiting team winning all games in a seven game series would account for about 2% of all possible outcomes for a seven game series. The other 98% captures a mix of home and visiting team victories as well as the series ending in fewer than seven games.