Game Theory and Baseball Relief Pitchers
http://www.economist.com/blogs/gametheory/2016/10/strategy-baseball
Baseball is a sport where teams are relying on statistical analysis more and more in order to try and get an advantage over the opponent. The sport itself is a series of game theory games where the pitcher uses a mix of strategies in order to try and get the batter out. Managers do not have as much of an impact on the game as they do in football, but the one thing they do control is what pitcher is out on the mound. This article talks about how some teams are finding success in the playoffs by going away from the traditional way of managing relief pitchers.
Typically, the best relief pitcher on the team is deemed the “closer”. In the 1960’s, in an attempt to measure the impact of relief pitchers a statistic was created called a “save”. A pitcher earns a save if they enter the game with a lead of three or fewer runs and they finish the game without losing the lead. The introduction of this statistic caused the closer role to develop, which is an example of a statistic dictating behavior instead of measuring it.
The Baltimore Orioles demonstrated the problems with this approach during this years playoffs. Their closer was one of the best pitchers in baseball this year and was 47 for 47 in save opportunities. However, with the season on the line in a one-game playoff, he was not used in an extra inning game. The manager kept him on the bench so he would be available to close out the game if they were to take the lead. Instead of using their best pitcher, the Orioles lost when Ubaldo Jiménez gave up a game ending homerun. When thinking about this using game theory, it would seem obvious that in the most important situation in the season the dominant strategy would be using one of the most dominant pitchers in baseball.
The Cleveland Indians, who are currently in the world series, use a different approach when dealing with their relief pitchers. They use their best reliever, Andrew Miller, whenever the game is on the line. They use him as early as the sixth inning and he won the ALCS MVP while only having one save. The leverage index is a measure of how important a particular situation is in a baseball game depending on the inning, score, outs, and runners on base. It would make sense to have your best pitcher on the mound during these high leverage situations even if they are not “save situations”.