Against Pythagorean Expectation Benchmarking

Abstract

Baseball analysts regularly purport to find one or another element of team composition generates deviations from teams’ predicted Pythagorean Expectation (PE) winning percentages. This paper critically assesses these findings. For this purpose, it constructs two separate but convergent empirical null baselines against which purported PE-deviation influences can be validly assessed. Using Bayesian False Discovery Rates, it finds that none of the putative elements of team composition identified as generating such deviations—including manager skill, relief-staff quality, starting-pitcher variance, bench depth, and team slugging percentage—genuinely do: in every case, seemingly “significant” effects are overwhelmingly more consistent with chance than with any systematic influence. The paper also uses the empirical nulls to identify a minimum detectable effect threshold for influences asserted to be associated with PE deviations. In order for such an effect to be attributed to a systematic, non-chance influence, it would have to account for some 45%-60% (depending on sample size) of the variance unexplained by PE, which already has an R² of 0.90. The prospect of finding team-composition impacts this large (ones essentially dispositive of variance in MLB records) is not credible. The team-composition elements in question are undoubtedly consequential. But their effect on team PE residuals does not supply a valid benchmark for demonstrating that.