Crime and punishment in Major League Baseball: the case of the designated hitter and hit batters

Economic Inquiry, Jan, 2007 by John Charles Bradbury, Douglas J. Drinen

It is this last cost which is the main subject of discussion. AL and NL pitchers bear identical costs and benefits when facing batters except for the reciprocal retribution. AL pitchers do not bat and therefore bear a lower cost for hitting a batter than NL pitchers. GST hypothesizes that this relative price difference induces AL pitchers to hit more batters than NL pitchers hit. (8) This is not to say that any pitcher actively seeks to consume hit batsmen purposely (at least not most of the time). Instead pitchers engage in riskier behavior (e.g., throwing inside, faster) when DHs bat in their place, which results in a greater number of hit batsmen. Cy Young award--winning pitcher Randy Johnson, who has played in both leagues, explains, "If you're the pitcher and you're playing in the American League, then you may have a tendency to throw inside a little bit more knowing when that ninth hole comes up, you won't be hitting. You're protected in that regard." (9) This is a behavioral response similar to automobile drivers in Peltzman (1975), which documents seat belt laws inducing motorists to engage in riskier behavior that leads to car accidents. Lowering the negative consequences of an action leads people to take more risks that result in the negative outcome.

However, the critics of the deterrent hypothesis propose that the expected punishment for plunking is too minor to have much, if any, effect on an NL pitcher's decision when he pitches to batters. On average, hitting the pitcher is not a good idea. If retaliation does provide a deterrent, pitchers would have to be extremely sensitive to that threat. However, circumstances arise where the benefits of hitting a pitcher exceed the costs. This may occur in the course of the same game in which a pitcher hits a batter, or it may occur in some future game. (10) Though pitchers are hit less than other position players, it is possible that pitchers may be hit more than they ought to be, given their hitting abilities. Ultimately, this is an empirical question. Using the data we describe in the following section, we can answer the questions central to the analysis.

IV. EMPIRICAL MODEL

A data-gathering project known as Retrosheet has carefully reconstructed baseball play-by-play data for many seasons. (11) Using a computer program, we extracted data by plate appearance from the Retrosheet data. From this we can observe the exact game situation when a player is hit or not hit; thereby, we can control for the costs and benefits of hitting any particular player during a plate appearance. (12) We use a predictive model to estimate the likelihood that a batter is hit given five categories of influences on hitting batters: deterrence (DH), batter quality (BQ), pitcher quality (PQ), retaliation (R), and game situation (GS). Thus,

[HBP.sub.j] = [[alpha].sub.j] [beta][DH.sub.j] [lambda][BQ.sub.j] [gamma][PQ.sub.j] [phi][R.sub.j] [psi][GS.sub.j] [eta][YR.sub.j] [[epsilon].sub.j],

where HBP is a dummy variable equal to one when a pitcher hits a batter and zero otherwise. Subscript j represents a plate appearance, [alpha] is the constant, [epsilon] is the error term, and YR is the year. We estimate the equation using both logit and probit estimation techniques.