Newswise — It's not surprising that fear is a major factor in whether a Major League Baseball pitcher decides to hit a batter. But according to a pair of researchers from Sewanee: The University of the South in Sewanee, Tenn., that's the fear on behalf of the pitcher, not the hitter " mathematically speaking.
Doug Drinen, assistant professor of mathematics, joined with Assistant Professor of Economics John-Charles Bradbury to analyze the factors that influence hit batsmen rates in a paper titled "Moral Hazard on the Mound: The Economics of Plunking," presented at last month's joint annual meeting of the American Mathematical Society and the Mathematical Association of America. Previous studies on hit batters only assessed aggregate data. But, using play-by-play data from http://www.retrosheet.org, Drinen and Bradbury analyzed situation-specific costs and benefits to pitchers.
Previous research papers agree that the Designated Hitter rule is the cause of the American League's higher rate of hit batsmen relative to the National League. Exactly why the DH rule leads to an increase in hit batsmen, however, has been the subject of some debate among economists.
One theory, called the moral hazard theory, states that the difference is due to a fear of retaliation that exists in non-DH leagues but not in DH leagues. In economic terms, the cost of pitching inside is lower in the AL. The competing theory, the lineup composition theory states that the increase is due not to lower cost, but to the higher benefit of pitching inside in the AL. Because of the DH, the AL consists of better hitters, and it makes more sense to risk hitting a good hitter than a bad one.
"The goal of our study was to sort out how much of the difference in hit batsmen rates was due to lineup composition and how much was due to moral hazard," says Bradbury. "This was just not possible without the Retrosheet data, which allowed us to examine situation-specific costs and benefits."
The study found strong evidence for the moral hazard theory. Drinen and Bradbury concluded that " during the time periods studied " fear of retaliation was responsible for 60-80 percent of the difference in HBP rates between the two leagues. In addition, the fear on the part of the pitchers is justified " since pitchers are much more likely to be plunked after having plunked an opposing hitter.
"We were not necessarily expecting fear of retaliation to play such a large role," said Drinen, who was a college pitcher as an undergraduate at Trinity University in San Antonio, Tex.
Bradbury and Drinen plan to continue studying one particular issue. Since the time period covered by the study, hit batsmen rates between the two leagues have begun to converge. The authors are searching for explanations.
"We're not sure, but it may be a product of both the recent 'double warning' rule " where both benches get warned the first time a pitcher hits a batter " and a dramatic increase in the use of relief pitchers since 1992," says Bradbury. "Since umpires warn both pitchers after someone is hit, teams essentially get a 'free pass' to hit someone first. Relief pitchers are also usually lifted for a pinch hitter and don't often bat, meaning there would be no fear of retaliation from hitting someone."
And ultimately, it's the amount of fear on the mound that may or may not stimulate a pitcher's "bean ball."