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

We apply the same model for the previous sample to this data, except that the DH variable is now coded zero for some observations in the AL, when the DH was not in effect. Therefore, the DH should now reflect the change in the costs of hitting batters induced by the DH rule itself. The results in Table 3 are quite similar to estimates of the more recent data. For this sample, when the DH is in effect pitchers are 11%-12% more likely to hit batters than without the DH rule, ceteris paribus. These results differ only slightly in magnitude from our previous estimates. We also observe pitchers, as well as position players, being hit in retaliation for hit batters in this sample. Most of the other factors are of similar magnitude and size, though some measures are no longer statistically significant. In the years following the DH, AL pitchers hit batters at a rate 14% higher than NL pitchers; thus, the DH rule dummy explains approximately 80% of the interleague difference in hit batsmen in this sample. Therefore, the results indicate that the removal of the threat of retaliation by the DH rule, not unobserved league-specific factors, is the likely cause.

VI. THE PROBLEM OF THE 1990s

Figure 1 shows the fluctuation in the rate of hit batsmen from 1921 to 2003. It is evident from the figure that the introduction of the DH in 1973 coincides with the AL's continued higher rate of hit batsmen as compared to the NL. From the introduction of the DH until the present, the AL's average yearly hit batsmen rate has exceeded the NL rate by 15%. From the beginning of the modern era of baseball until the 1970s, the hit batsmen rates varied closely, yet randomly, across leagues. For the next 21 years the AL rate exceeded the NL rate every year, which is consistent with both the deterrence and lineup composition hypotheses. But in the mid-1990s, just as economists began to study this issue and the public availability of play-by-play data ceased, a deviation in this pattern emerged. In 1994, the NL hit batsmen rate rose above the AL rate for the first time since the implementation of the DH, and the leagues' hit batter rates began to fluctuate more closely than in the past. Why was there such a dramatic shift and how does this shift impact the perceived relationship between the DH and hit batsmen? There are two important factors that contributed to this change: league expansion and a rule change in the punishment for pitchers hitting batters.

In response to criticism over the recent events of the 1990s, Goff, Shughart, and Tollison (1998) postulates that the NL expansion in 1993 diluted the talent pool of players increasing the number of accidental hit batsmen. We believe the evidence supports this contention. Fringe pitchers and hitters are more apt to make mistakes by hitting batters or getting hit by pitches. (17) In 1993, the NL hit batsmen rate fell to only 10% of the AL rate, while the average difference over the preceding 2 decades was 20%. Additionally, the mid-1990s corresponded with a dramatic increase in hit batsmen in both leagues, doubling over the decade. The expansion hypothesis is consistent with both the change in the difference between leagues and the rise in hit batters overall. In the two rounds of expansion, three of the four expansion teams joined the NL with one existing AL team (Milwaukee) shifting to the NL. But more importantly, the asymmetric expansion draft rules in 1993 favored expansion players coming from NL rosters. Therefore, the expansion diluted the talent pool of both leagues but affected NL rosters to a greater degree than AL rosters. (18) From 1993 to 1997, as the expansion players eased into the league, the NL rate exceeded the AL rate in 3 of the 5 years, with the AL rate being 2% lower than the NL rate, on average. But in 1998, when both leagues added a team, there was no asymmetry between leagues in drafting expansion players. Interestingly, the disruption to the previous pattern was noticeably smaller. Since the last round of expansion in 1998, only once (2000) has the NL rate exceeded the AL rate, with the AL rate exceeding the NL rate by an average of 6.5%.