## October Game Theory: Intentional Walks in Playoff Baseball

Game theory, when it is first introduced, can be a confusing topic. Telling a student you are going to study “the mathematical study of optimizing agents” is one way to introduce game theory. A better way is through a relatable example. While examples exist in every business or organization, from the corporate level to individual decision making, one of the most relatable examples comes from sports, or specifically, baseball.

Baseball consists of many different situations where the application of game theory is appropriate. From the pitcher’s decisions on what pitches to throw, to the base-runner’s decision to steal, to the manager’s choice to put in a pinch-hitter, game theory can be applied in many ways. The easiest to discuss however, is a little tactical maneuver called the “intentional walk.” For those unfamiliar with the tactic, an intentional walk is performed when the pitcher from one team, with instruction from his manager, deliberately throws a series of four balls to the opposing batter –usually in an unhittable manner—giving that batter a free pass to first base. The decision to give someone a free base, and potentially give the other team another run, is not one made lightly. Despite this, it is one made quite frequently, even in big, high-pressure situations such as Tuesday’s division series game between the St. Louis Cardinals and Philadelphia Phillies. To properly examine the game theory decision-making, let us imagine ourselves in the shoes of Tony La Russa.

The game is scoreless in the seventh inning, with two walks, and a man on second base. Carlos Ruiz, one of the better hitters on the Phillies is up to bat. Set to follow him is pinch hitter Ben Francisco, a slightly less dangerous hitter. If we intentionally walk Ruiz, we place two runners on base, increasing the number of runs possible on this hit from 2 to 3, but slightly decreasing the likelihood of those runs being scored.

What should we do? The statistics of intentional walks say that on average, issuing an intentional walk is a bad strategy the majority of the time. That is to say, more often than not, one should not choose to issue an intentional walk. Baseball’s many statisticians have made that point clear. That being said, there is a reason that intentional walks are sometimes issued: they often serve their purpose. In a sport, with its varying intangibles, statistics are not all that matters. As poster David Schoenfield says, “When are you a slave to the numbers, and when do you go with your gut?” On this night, La Russa went with his gut. He made the wrong call, and the Cardinals lost.

http://espn.go.com/blog/sweetspot/post/_/id/17169/rip-la-russa-but-give-credit-to-francisco