How often do NHL playoff series go the distance?

May 10, 2010

A friend of mine is visiting Chicago this week, and we got together with a group of friends for a beer. History reveals that this activity with this group results in one of two potential outcomes: a discussion that prompts several Wikipedia searches to resolve a debate about an esoteric topic, or a bet that involves sports data and statistical tests. This time, it was the latter.

The topic in question was whether or not best-of-seven series in the NHL playoffs go to seven games more or less than one would expect under a very simplistic model: individual game results are determined by coin flips. One person (“person-whose-side-I-wish-I'd-taken”) argued that NHL playoff series go the distance less than you would expect under the coin-flip model, because a matchup is typically not balanced and the probability of one team winning is greater than half. The other person (“the fool”) argued that teams that are behind in a series dig in and try harder, and thus series would go to seven as much or more than one would expect under the coin-flip model.

Being an unbiased third party, I took it upon myself to settle the bet. I was able to obtain the playoff game score data from the official NHL web page and quickly parse out only the best-of-seven series. As of the end of the 2009 season, 129 of 547 (24 percent) of the best-of-seven series actually went to seven games. By simulating the coin-flip model for 547 best-of-seven series a million times, it is clear that person-whose-side-I-wish-I'd-taken was correct, and the actual number of series that go the distance is significantly (p = 0.00003) less than one would expect under the coin-flipping model , where the 95 percent confidence interval is 150 to 193 games, or 27 to 35 percent.

distribution under simplistic coin-flip model for playoff series
The black line is the distribution of the fraction of series that go to seven games under the simplistic coin-flip model. The red line is the fraction of NHL best-of-seven playoff series that have actually gone to seven games.

For the fool who lost the bet or anyone else that wants to double check or just play around, here is the historical playoff series game scores, here is the python script to simulate the coin-flip model, and here is the cumulative distribution function of the number of series that go to seven games (out of 547) under the coin-flip model.

contributors to this post

headshot of Mike Stringer
Mike
headshot of Dean Malmgren
Dean