Are 7-game World Series more
common than expected?
UPDATE: October 20, 2003--Since our original article was published, we looked at all World Series back to 1905 with a best-of-seven format. According to our unofficial count, 35 out of 94 World Series have gone to Game 7 - a rate of 37.2 percent. That's still higher than the rate one would obtain from simple probability calculations. But it may no longer represent a significant difference. "The imbalance was really created" between 1952 and 1977, said Carl Morris of Harvard, "when 15 out of 25 series went to their maximum length." "I wonder what would be revealed if a scientific study were done on the numbers," said Ben Stein, this article's author.
College Park, MD--(October 17, 2003)--As the Florida Marlins and the New York Yankees prepare to face off in the World Series on Saturday, baseball fans may already be wondering if it will be a four-game series (in which one team sweeps the other) or if it will last the full seven games. Surprisingly, however, World Series have historically gone to Game 7 much more frequently than simple probability would suggest. But our national pastime is more than math: The mismatch between baseball history and elementary probability illustrates the game's richness and subtlety--as well as the limitless potential of statistics to provide insights into the nuances of the game.
How is World Series history at odds with basic math?
Assuming that the two teams are evenly matched, simple probability yields the following chances for the number of games in the World Series:
| # games || % chance |
|4 ||12.5 |
|5 ||25 |
|6 ||31.25 |
|7 ||31.25 |
However, in the last 50 years' worth of World Series (1952-2002), the actual percentages of World Series game lengths were:
| # games || % chance |
|4 ||16 |
|5 ||16 |
|6 ||20 |
|7 ||48 |
Strikingly, 24 of the last 50 Fall Classics have gone to Game 7--a rate of 48%--much greater than the 31.25% chance that statistics suggests. The difference is worth noting, or "statistically significant," as mathematicians would say. According to Carl Morris, a professor of statistics at Harvard University, "There is only a 1% chance that at least 24 of the last 50 World Series would reach seven games if these simple probabilities were correct."
To shed light on this apparent discrepancy between baseball history and elementary probability, it's worth exploring how statisticians arrive at the numbers. The simplest probability calculations assume that each team has a 50-50 chance of winning each game.
Under this assumption, the chances for any one team to win more than one game in a row slashes in half after every game. That means that a team has a fifty-fifty chance of winning Game 1, a one-in-four chance of winning the first two games, a one-in-eight chance of winning the first three and finally, a mere one-in-sixteen chance to win all four in a row. Taking into account that both teams have a chance to win the first four games doubles the one-in-sixteen number, giving a one-in-eight (12.5%) chance for either team to sweep the World Series in just four games.
Through a similar approach, one arrives at the chances of reaching five-, six-, and seven-game series.
In the end, the result for this simple model is that the World Series has a 31.25% chance of going to seven games. That is much lower than the actual 48% of games that have gone down to the wire.
But let's factor a little baseball reality into this analysis. It's obvious that not all teams that meet in the Fall Classic are evenly matched. Some World Series have been very lopsided. But, unfortunately, this factor doesn't help to reconcile the simple probabilities with the historical results: Lopsided World Series matchups would make it easier for the stronger team to eliminate its weaker opponent early, and make it less likely for the match to go to Game 7.
However, baseball-savvy statisticians have identified some factors that could boost the frequency of seven-game series:
- Home-field advantage: one team plays the first two games at home, and the last two games at home, if the series goes more than five games. Further compounding home-team advantage is that the 6th game is played in the stadium of the team that has been on the road 60% of the time. This means that the home team may have a better chance of winning the sixth game--and bringing the series to game 7.
- Baseball strategy: According to Harvard statistician Morris, the team that's trailing the series 3-2 may put everything--their best pitchers, for example--into reaching the 7th game and giving themselves a chance to win the Series. Even if the series reaches seven games, however, the team can lose. "My point here," says Morris, a Boston Red Sox fan, "is that teams make a mistake to overuse pitching resources in the 6th game at the expense of being overly weakened for the 7th game. A lot of fans--and even managers--don't get this." But it may help explain why more series go to the final possible game.
So can a statistical approach ever accurately yield the chances of a seven-game world series? The beauty of modeling probabilities is that refinements can be made. For example, one can assume that home teams win more often than visiting teams, and this factor can be incorporated into the model.
But maybe statisticians will have to wait for 1000 years of World Series results to fully and accurately model the probabilities of different game lengths in the Fall Classic. In the meantime, math fans and baseball fans marvel alike at the nuances of baseball--the "game of inches"--that make seven-game World Series so frequent.
Professor of Statistics, Harvard University
One Oxford Street
Cambridge, MA 02138
American Institute of Physics
American Institute of Physics
We would like to thank Mike Breen of the American Mathematical Society for suggesting the idea for this article, David Harris of the American Physical Society for performing the probability calculations and Jay Hill of the University of Illinois for his nice page that shows the probability calculations in detail. Raymond Chu of the American Institute of Physics Statistical Research Center and Chip Denman of the University of Maryland also provided helpful insights.
World Series Outcomes from 1903-present
History of the World Series format
University of Illinois site shows probability calculations in more detail