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

V. RESULTS AND DISCUSSION

Retrosheet provides play-by-play data for both leagues from 1972 to 1992 and for the 1969 season. From this data, we extract two four-season data sets--the earliest and most recent available years--to estimate the empirical model. For each plate appearance, we extract data on the specific game situation and the seasonal performance of the players participating in the event. Initially, we focus on the four most recent years of available data, 1989-1992.

Table 2 lists the results of the logit and probit estimations of coefficients and z statistics. For ease of interpretation, we also include the odds ratio (logit) and marginal probability (probit) calculations for each variable. Most of the variables are significant and of the expected sign. Of particular interest, the DH variable is positive and significant when controlling for all other factors, including the lineup composition batter quality variables. When the DH is in effect pitchers are 15%-17% more likely to hit batters than when the DH is not in effect. Consistent with the lineup composition hypothesis, batter quality is positively related with hit batsmen, and pitchers are about 55% less likely to be hit than other batters. Also, pitcher quality is negatively related to hit batsmen. Both proxies for lack of pitch control are positively associated with a greater likelihood of hitting a batter; however, pitcher OPS is not statistically significant.

The retaliation variables tell an interesting story. Preceding events likely to provoke retaliation all tend to increase the likelihood that a pitcher hits a batter. A batter who appears at the plate following a home run is 32% more likely to be hit than when the preceding batter did not hit a home run. In response to hit batters, pitchers are more likely to hit batters the half-inning after the opposing pitcher hits a current pitcher's teammate. Though the results are not significant for players in general, a pitcher is four times more likely to be hit when an opposing player was hit in the previous half-inning. This variable, which is significant, is very important for the deterrence hypothesis. We now observe retaliation against pitchers who hit batters. This is a phenomenon previously unidentified in the aggregate data. Though pitchers are hit less frequently than other players on average, pitchers are more likely to be hit after plunking an opposing player. Therefore, pitchers do bear a very real cost to hitting batters, which is necessary to provide a deterrent to pitchers.

For the game situation variables, outs and innings seem to be relatively unimportant. Though the absolute score differential is unimportant, the relative score differential from the offense to the defense has a small but significant effect on the incidence of hit batsmen. The base runner composition variables appear to be important and consistent with our predictions.

Over this sample, the AL hit batsmen rate is 26% higher than the NL. Controlling for all of the above factors, including batter quality, the DH rule dummy explains approximately 60% of this difference. It is now clear that something other than the lineup composition created by the DH is responsible for the increase in hit batsmen differential between leagues. The most plausible explanation for this difference is the removal of a credible threat of ex post punishment of pitchers in the AL. However, it is possible that some yet unidentified factors unique to the AL may explain the sign and significance of the DH dummy since the DH occurs only in this league. For example, differences in strike zones, stadium configurations, league traditions, etc. between leagues are competing but less satisfying explanations. To be thorough, we examine a different data set that includes the 1969 and 1972-1974 seasons. (16) This is the earliest available data in the Retrosheet archives, plus this period includes some observations of the AL without the DH rule. We are slightly less confident in this data than our more recent data for a few reasons. First, the only two seasons available prior to the introduction of the DH are the noncontiguous years 1969 and 1972. Second, the late 1960s and early 1970s were low offense years for baseball. The DH was the last of several rules instituted to "fix" baseball, which was losing fans. The league responded in 1969 by lowering the pitchers mound, shrinking the strike zone to make it more hitter friendly, and adding two new teams to each league. Luckily, the exogenous events other than the DH apply to both leagues; therefore, we feel the data are useful in isolating the effect of the DH rule on hit batsmen, given that we acknowledge the deficiencies.