This Year's Baseball All-Star Game Was a Mathematical Marvel

July 19, 2008

Baseball's All-Star Game has been played since 1933, but the latest edition set a new record as the longest game in the midsummer classic's history. This year's 15-inning marathon lasted nearly 5 hours, with the American League winning 4-3. The game, says mathematician Darren Glass of Gettysburg College, "was definitely a rare occurrence and one we should not expect to see again in our lifetimes."

Glass's research suggests that a 15-inning game has only a 0.2% chance of occurring (about once in 500 games). His statistics come from a study of scoring patterns in baseball games over the past 135 years.

Glass and colleague Philip J. Lowry of the City University of New York reveal the probability that a baseball game will last a given number of innings in their article "Quasigeometric Distributions and Extra Inning Baseball Games," published in the April Mathematics Magazine.

"This year," Glass says, "the American League has averaged 4.61 runs per game and the National League has averaged 4.48 runs per game." Plugging the appropriate numbers into their mathematical model, he says, shows that the probability a game would last exactly 15 innings is .0022 and the probability that it would last at least 15 innings is .0049.

"In other words," Glass noted, "if these two teams played each other 1,000 times, then we would expect the game to still be tied after 14 innings in 5 of those games and to end in the 15th inning in two of those games."

The longest Major League ballgame took place in 1920 between Brooklyn and Boston. It lasted 26 innings. In the last ten years, 155 games have gone at least 15 innings. About half of these ended at 15 innings.

Glass describes this year's All-Star Game as a mathematical marvel. Baseball fans, however, know that good pitching almost always bests good hitting—and that baseball is a game of inches, as the final play at the plate during the latest All-Star Game attested.  

Source: Gettysburg College, July 16, 2008.