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

I. INTRODUCTION

Are you seriously going to throw at somebody when you're facing Randy Johnson?

--Curt Schilling (1)

In 1973, amid waning fan interest in baseball, the American League (AL) of Major League Baseball (MLB) instituted the designated hitter rule as an experiment. The stated goal of this rule change was to boost offensive output by increasing the talent pool of batters in the lineup. Traditionally, the competing teams field nine players who must play defense in the field and bat. Because of the importance of the pitcher, who is responsible for putting every ball in play, teams rely on pitching ability and ignore the hitting ability when choosing the pitcher in the lineup. Therefore, pitchers tend to be very poor hitters. By allowing teams to substitute a player of greater hitting ability known as the designated hitter (DH)--to bat for the pitcher the total offensive output increases. The experiment has since grown into an institution in the AL that differentiates it from the National League (NL), where all players must bat and play in the field.

The DH succeeded in turning the AL into the "power league" as intended, but an unintended consequence of the rule change is that the AL now has more batters hit by pitches than the NL. Traditional baseball lore holds that the lack of retaliatory punishment in the AL for hitting batters is the cause of this phenomenon. Veteran NL manager Dusty Baker describes the deterrent impact from a pitcher's point of view, "You can be bold in (the American) League and get away with [hitting batters]. It's different in our league where you have to hit." (2) Pitchers who do not have to bat (where they might face retaliation) are more willing to risk hitting batters than pitchers who do bat.

Given that the rules of the game in both leagues are identical except for the use of the DH, MLB created ideal conditions for a natural experiment to examine the impact of the DH on hit batters in a controlled setting. (3) Several economists have looked at the issue and found that there is a statistically significant relationship between the DH and hit batters. However, the reason for this difference is subject to much debate. It is possible for the hit batter differential to exist without the deterrent effect of retaliation. The rulebook punishment for hitting a batter--awarding the hit batter first base makes retaliatory enforcement costly for teams to employ. Pitchers are typically poor hitters who rarely reach base via hitting, while batters who are DHs are typically good hitters. The fewer hit batters in the NL may reflect the lineup composition, in which the pitcher must bat. NL teams will try to avoid plunking pitchers because they are relatively less likely to reach base than non-pitchers, while AL teams do not have this easy out in their batting lineups.

A problem with previous studies of the subject is their reliance on yearly aggregate data. Hit batters are rare events--approximately 1% of all plate appearances result in a hit batter--that occur in the course of game where other incentives are quite relevant. This means that identifying small changes in pitcher behavior from specific factors will be difficult to identify with aggregate data. Differentiating between the two competing explanations for the hit batter differential between leagues deterrence and lineup composition--requires micro-level data where we can control for in-game strategic incentives for hitting batters.

Using a unique play-by-play data set that allows us to control for specific factors that affect hit batters, we find that pitchers are still more likely to hit batters with a DH in the lineup than without. And though pitchers are hit more rarely than other players, pitchers do experience retaliation for hitting batters. Retaliation against pitchers who plunk batters, which was not found in earlier studies, is needed to generate an effective deterrent for pitchers in the NL. These findings provide support for the deterrence hypothesis that the threat of retaliation against pitchers who hit batters does impact the probability that a pitcher will hit a batter and demonstrate the importance of informal enforcement mechanisms in deterring criminal behavior. Furthermore, we show that it is likely that the addition of formal administrative punishments for hitting batters by MLB may, in fact, have increased the incidence of hit batters in both leagues. The remainder of the paper is organized as follows. Section II reviews the previous literature, concentrating on the empirical problems with these studies. Section III discusses the strategic incentives for hitting batters. Section IV presents the empirical model with section V discussing the findings. Section VI discusses a peculiar deviation in the pattern of hit batters in the 1990s. Section VII concludes the paper.

II. A REVIEW OF PREVIOUS STUDIES

Goff, Shughart, and Tollison (1997, hereafter, GST) first examined the hypothesis that the cost differential to pitchers for hitting batters induced by the DH is the cause of the interleague difference in hit batsmen. Using annual league time series data from 1901 to 1990, GST analyzes changes in the difference in hit batsmen between leagues before and after the implementation of the DH. The results indicate that, controlling for several factors, the introduction of the DH raised the level of hit batsmen in the AL 15% higher than the NL, consistent with the hypothesis that the DH removes an effective criminal deterrent. However, though the evidence is clear that the DH is associated with an increase in hit batsmen, it is not necessarily a consequence of the lesser deterrent to hitting batters in the AL. Trandel, White, and Klein (1998, hereafter, TWK) and Levitt (1998) are skeptical of the interpretation of GST on two grounds. First, adding the DH raises the marginal benefit of hitting batters due to the existence of an additional good batter in the lineup. Because pitchers are poor hitters, few teams want to risk hitting the other pitcher. Replacing the pitcher with the DH places a batter more worthy of plunking in the lineup. As TWK state, "the difference [in hit batsmen] is largely because the AL batters are (on average) better hitters, and are thus less costly and more beneficial to hit." Therefore, the aggregate increase in hit batsmen in the AL over the NL may be attributed to increased rewards rather than the lowered punishment for hitting batters. (4) Second, the deterrence story seems implausible because pitchers are rarely hit, and therefore, the probabilistic penalty of retaliation for hitting batters is too small to have any real effect in a pitcher's decision calculus. Hitting the pitcher in retaliation may actually reward the instigator by putting the weak-hitting pitcher on base. Given that pitchers know this, it is unlikely that pitchers consider reciprocal retaliation to be a cost. As evidence, Levitt (1998) finds that there is no correlation between pitchers hitting batters and pitchers being hit themselves, and pitchers are hit so rarely that they would have to be hypersensitive to the relative price change induced by the DH. (5) Trandel (2004) finds similar results for the 1974-1977 seasons using the same test and finds little evidence of retaliation against any pitcher. All of these studies conclude that the increase in the frequency of hit batsmen in the AL likely reflects changes in the batting lineup composition and not a deterrent response by pitchers. (6)