mWAR: a Bayesian Estimator of Manager Value

Abstract

For a sport that is approaching a state of analytic saturation, major league baseball is devoid of one seemingly critical metric: a manager value estimator. Whether managers have ever meaningfully influenced their teams’ performances and still do today are matters of significant dissensus. Without a manager-value estimator, that debate (critical, at a minimum, to informed front-office decisionmaking) cannot be convincingly resolved. Using a sample of over 500 managers spanning the history of AL/NL seasons since 1900, this paper develops a manager-value estimator based on manager performance in relation to team records predicted by aggregate player WARs. Simulation and Bayesian methods are used to test for False Discovery Rates and to form posterior estimates in relation to Regions of Practical Equivalence. Results suggest that a substantial fraction of managers (including current and recently active ones) have over their careers influenced team “winning percentages” ≥ ± 0.012, the equivalent of ± 2 wins per 162 games. In addition to enabling historical and contemporary comparisons, the mWAR Estimator can also be calibrated to reflect the asymmetric-error costs and risk preferences that characterize the tournament structure of MLB economics.

Keywords: Statistics, Sports Analytics, Data Science, Baseball