An Empirical Estimation of a Production Function: The Case of Major League Baseball

All productive enterprises, whether they be for profit or non-profit, are similar in that they all in volve a production process and therefore a produc tion function. The production function, once identified, not only demonstrates the relationship between inputs and outputs, but may also give the producer information concerning factor shares, marginal productivity, and returns to scale. The producer is then able to choose the most efficient combination of factors, as well as be made aware of any tradeoffs that exist among the factors; for ex ample, the substitution of capital for labor. Identi fying its production function is a key element in maximizing the efficiency of any enterprise. Team sports, such as baseball, are similar to other enterprises in this respect. A team attempts to provide a product (victories)1 by employing various inputs (the skills of the team members). Like any other enterprise, it is helpful to the baseball team to be able to identify its production functioa The production function could then serve as a basis for team member salaries, as well as determin ing which team members should play. Just as a manufacturer may be concerned with a tradeoff between capital and labor, a baseball team may fac& the problem of playing an individual who is a good hitter versus one with more power. In acquir ing talent through trades and the free agent market, the team must again make decisions on such trade offs. For example, the question of whether a power hitter should be traded for a singles hitter,2 or whether the team should be willing to sacrifice hitting strength to acquire more pitching strength, must be answered. These decisions are all made in the context of a baseball production function, although most likely based on an informal notion of the production function rather than on more formal knowledge supported by empirical evidence. This paper has two purposes. The first is to identify those factors that contribute to team suc cess, and then to empirically estimate the effect of each factor. Secondly, the results of the empirical testing will be employed in constructing a measure of a league's most valuable player,