This is an empirical investigation of the winning function in major league baseball. As more star players are added to a team by signing free agents, the winning percent for that team first increases at an increasing rate but eventually at a decreasing rate. In Rodney Fort's Sports Economics textbook, this theoretical production curve is shown graphically for major league baseball but is not estimated with a regression model. This is surprising because a production function is not only important on its own, but it also plays a significant role in supporting the shapes of subsequent cost and profit functions in Fort's text. In this paper I empirically estimate the winning function by identifying and summing the star hitters and pitchers by team, and then correlating these numbers to team win percents. I define a star player as one with a slugging percentage or on-base percentage one standard deviation above the league average for starting players. Star pitchers and relievers will be similarly defined. I aggregate ten years of league cross-sections (2002-11), and investigate several alternative functional forms. The key issue is whether the estimated parameters of a given functional form support the theoretical curvature shown in Sports Economics.
Thomas Bruggink. "Production Functions in Major League Baseball: A Star Input Method." Proceedings of the New York State Economics Association. vol. 7, October 2014, p. 4-12
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