Baseball: 2008 All-star Game Was Mathematical Marvel

His research suggested that there was a 0.2% chance of a 15-inning game occurring and that a game like this would happen only once out of every 500 games. Glass along with Phil Lowry, a professor at the City University of New York, researched the distribution of baseball scores to answer the question, “What is the probability that a given baseball game will last a given number of innings?” Their research recently appeared in Mathematics Magazine.

According to Glass, an All-Star game should last fewer innings because the batters are better than average. But he admits that other factors such as different game strategies used or the talent level of the pitchers changes his predictions. It should be that a game between two bad teams would last longer.

The longest major league ballgame on record was played between Brooklyn and Boston in 1920 and lasted 26 innings. The longest minor league ballgame was between Rochester and Pawtucket in 1981 and lasted 33 innings. In the last decade, there have been 155 games that have lasted 15 innings or more. 73 of those lasted exactly 15 innings. In all of major league baseball history through 2006, there have been 980 games, which have lasted 15 innings or more. 426 of those lasted exactly 15 innings.

Last night’s All-Star game ended in the bottom of the 15th inning with a walk-off sacrifice fly. The game lasted 290 minutes and used 23 pitchers. Every player on both rosters was used. In terms of length of time, it was the longest All-Star game in MLB history.

“This year the American League has averaged 4.61 runs per game and the National League has averaged 4.48 runs per game. Plugging these numbers into our model predicts that there was a .0022 probability that the game would last exactly 15 innings, and a .0049 probability that it would last at least 15 innings. In other words, 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.”

Glass stands by that what happened this year was a mathematical marvel.