The value of flexibility in baseball roster construction

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Timothy C. Y. Chan

Douglas S. Fearing


Abstract: Drawing inspiration from the theory of production flexibility in manufacturing networks, we provide the first optimization-based analysis of the value of positional flexibility (the ability of a player to play multiple positions) for a major league baseball team in the presence of injury risk. First, we develop novel statistical models to estimate (1) the likelihood and duration of player injuries during the regular season, and (2) fielding abilities at secondary fielding positions. Next, we develop a robust optimization model to calculate the degradation in team performance due to injuries. Finally, we apply this model to measure the difference in performance between a team with players who have positional flexibility and a team that does not. We find that using 2012 rosters, flexibility was expected to create from 3% (White Sox) to 15% (Cubs) in value for each team, measured in runs above replacement. In analyzing the results, we find that platoon advantages (e.g., having left-handed batters face right-handed pitchers) form an important component of flexibility. As a secondary finding, based on our statistical analysis of injuries, we find that the likelihood of injury increases with age, but the duration of injury does not.