Variance Has a Position: A League-Wide Signal in Box-Score Projection Error

Every projection system is evaluated on how close its forecasts land– the mean error. We show that the variance of that error carries a structured, position-specific signal that the mean does not, and that the signal replicates across leagues and methods in a way that rules out the usual artifact explanations. After conditioning on prior-season production, position, age, and team context, the projection-error variance of blocks for centers is elevated by a factor of 1.26 to 2.03 relative to the rest of the league, and it couples in all 11 testable cells across four leagues (NBA, WNBA, NCAA Division I men’s and women’s) under two projection methods that share no machinery. The signal is selective: center scoring runs the opposite way (centers are more predictable scorers, in all 11 cells), veteran assists show no structure, and a center rebounding effect that appeared under the simple method dissolves under the hierarchical one– a retraction we report at equal prominence. We argue the block result is the measurable fingerprint of a mechanism the analytics literature has understood qualitatively since the Dwight effect (Goldsberry and Weiss, 2013): a block is a noisy proxy for rim deterrence, and a proxy inherits both the variance of the skill it tracks and the variance of its own noise. We pre-register a forward test on the 2026-27 season.