BATTER UP! MORAL HAZARD AND THE EFFECTS OF THE DESIGNATED HITTER RULE ON HIT BATSMEN

I. INTRODUCTION Despite its relatively recent appearance in the literature, the theory of moral hazard has proved to be rich in empirical implications. It has been applied fruitfully in a wide variety of settings, including medical insurance, property and casualty insurance, labor contracts, savings and loan failures, and credit rationing.(1) Perhaps the most frequently cited application of this idea is Sam Peltzman's [1975] study of mandatory seat belt laws. He reported evidence suggesting that drivers respond rationally to such laws, which reduce the risk of injury or death in automobile accidents, by driving more recklessly. Hence, while mandatory seat belt laws have resulted in fewer automobile fatalities, they have increased the number of non-fatal accidents and accidents involving damage to property and pedestrians. In this paper we argue that the introduction of the designated hitter (DH) rule in the American League but not the National League of Major League Baseball in 1973 created the potential for a classic moral hazard problem. Because they are not required to appear at the plate, American League pitchers can throw at opposing hitters with greater impunity (i.e., at a lower cost) than National League pitchers, who must take their turn at bat. The economic theory of moral hazard clearly predicts that more batters will be hit in the American League under such circumstances, an implication which is supported by the empirical evidence reported herein. After controlling for other relevant factors, we find that American League batters have been hit by pitches at rates 10% to 15% higher than their National League counterparts in the typical post-DH rule season. II. THE SIMPLE ECONOMICS OF HITTING BATTERS We model pitchers as the ultimate decision makers with regard to behavior that leads to hit batters. In making this assumption, we ignore the principal-agent relation between pitchers and managers as well as any externalities arising among players that may influence the number of batters hit by pitches. Managers sometimes instruct pitchers to throw at a batter, presumably to cool off opponent's bats or to retaliate for opposing pitchers throwing at his team. On occasion, a pitcher may view his own personal interests., in terms of runs and income, as diverging from the manager's interests, so that he would not carry out such instructions to the letter.(2) In any case, a batter may be hit when the pitcher makes a deliberate attempt to do so or when the pitcher has not expended much effort to avoid hitting him. While the distinction between the two causes of hit batsmen may be important in its own right, we treat them as being observationally equivalent. Both amount to the pitcher altering the probability of hitting a batter by changing the intended location and speed of his pitches. In our elementary approach, a pitcher's decision to raise or lower this probability hinges on a marginal decision-making calculus of weighing the expected benefits against the expected costs of hitting a batter. These benefits and costs would ultimately affect the pitcher's expected utility by influencing his lifetime income and consumption possibilities, his utility from the indulgence of personal preferences, or both. Increasing the probability of hitting a batter can potentially benefit the pitcher in several ways. Hit batsmen may become more reluctant now and in future games to lean over the plate, thereby reducing their effectiveness against pitches low and outside; they may become more susceptible to being fooled by curve balls that give the illusion of being inside; or they may "dig in" less and thereby reduce their power. All of these effects lower the probability of runs being scored against the pitcher in present and future appearances. Additionally, the pitcher may alter the probability of hitting batters in order to retaliate against similar tactics being used by opposing pitchers. This may be a means of neutralizing an opponent's strategy of throwing at batters, and, hence, help increase run production by the pitcher's own team. …