ABSTRACT
One aspect of baseball that makes it a popular topic for statistical analysis is that the game is comprised of a series of individual batter versus pitcher matchups. These matchups are at the heart of the large data sets that are analyzed by baseball enthusiasts (e.g., Albright, 1993, James, 2006). The following anecdote indicates exactly how important information about these matchups can be in professional baseball. It was reported that Los Angeles Dodger player Kenny Lofton was rested by Dodger manager Grady Little during the team’s August 29, 2006 game against the Cincinnati Reds because of Lofton’s record against the scheduled Reds pitcher, Eric Milton. Lofton, whose season-long batting average (proportion of batting attempts resulting in base hits) was 0.308 at the time and whose career batting average was 0.299, had just one hit in 19 career attempts against Milton. This is a batting average of 0.056, considerably lower than Lofton’s usual level of performance. Baseball players oc-
casionally take a night off during the season and to the manager this seemed like the perfect night to give Lofton a rest. But is it? Lofton’s substitute that night had a batting average of 0.273 at the time, somewhat lower than Lofton’s average. This raises an important question about how a baseball manager should combine the limited information about a particular batter-pitcher matchup with the larger amount of data available about the individual players. Some managers are reputed to believe strongly in the importance of batter-pitcher matchups. In the book Three Nights in August, author Buzz Bissinger tells us that St. Louis Cardinal manager Tony LaRussa carries a card each game with the performances of his players against the pitchers of the opposing team (Bissinger, 2005). There is certainly baseball logic that supports considering such data. The way a certain pitcher releases the ball may make it easier for a particular hitter to see it, or a certain pitcher’s tendencies (to throw mainly fastballs for example) may match up well with a particular hitter’s strengths. At the same time however some basic statistics suggests that poor performance against one pitcher may just reflect bad luck. After all there is about a 1=130 0:009 chance that a hitter of Lofton’s ability would have one hit in 19 attempts just by chance. Lofton’s been around a long time and opposed many pitchers. Is he really having a tough time with Milton? Or has he just been unlucky? In what follows we look more closely at baseball pitcher-hitter matchups using a hierarchical beta-binomial model.
