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Designated hitter as moral hazard

JC Bradbury's work on hit batsmen gets a nice mention in "The Year in Ideas" section of the New York Times Magazine. JC's paper, joint with Doug Drinen, is a compelling analysis of the factors that influence a batter getting plunked in baseball, and deserves the attention.

JC gave the paper at Clemson this fall, and the seminar discussion was a lively one. One of the originators of the "moral hazard" hypothesis in this application, Bob Tollison, was in the audience. The moral hazard idea is that, since pitchers don't hit in the American League, they do not fear retaliation like their counterparts in the NL. Batters get plunked more in the AL, and Tollison and his coauthors argued in a recent paper that moral hazard was the cause of it. Other economists, including Steve Levitt, took issue with the claim, noting that the DH was less costly to hit than a pitcher. They argued that this differential cost could account for the differential rate of hit batsmen between leagues, and argued on the basis of weak correlations that the threat of retaliation was negligible.

JC's paper provides a proper burial for this latter notion. He and Drinen use several years of play by play data and detailed information about the state of the game for every at bat. The data are unequivocal: retaliation exists. Batters get hit in clusters, not at random. And if you are the pitcher who hit an opponent in the prior half inning, watch out. Furthermore, the state of the game matters a great deal. Retaliation is more likely when it's cheap - when the run differential is high, when there is an open base, etc.

The paper is a great example of the value of detailed information allowing one to uncover strong relations which are obscured by aggregate statistics. Although JC came to Clemson waving Bob Tollison's banner, Bob and the rest of us left the seminar with the conclusion that Bradbury and Drinen had created their own. Whether moral hazard is the root cause of the differences they document between leagues is a second order question. What their work does beyond a shadow of a doubt is show that hitting batters is strategic - the probability of a batter being plunked varies according to the costs and benefits of doing so. As Pink states in the New York Times, Bradbury and Drinen have shown that "the laws of economics govern the diamond as well as the front office," and that's plenty good enough.