Avoiding Bias Due to Nonrandom Scheduling When Modeling Trends in Home-Field Advantage

TL;DR

This paper identifies and explains bias in mixed model estimates of home-field advantage caused by nonrandom scheduling, proposing more accurate modeling approaches for sports data analysis.

Contribution

It uncovers bias in mixed models for HFA estimation due to schedule structure and compares fixed and random effects models to improve accuracy.

Findings

Mixed models show upward bias in HFA estimates due to schedule nonrandomness.

Fixed effects models are not affected by this bias.

Conference-specific HFA trends are quantified across multiple sports and seasons.

Abstract

Existing approaches for estimating home-field advantage (HFA) include modeling the difference between home and away scores as a function of the difference between home and away team ratings that are treated either as fixed or random effects. We uncover an upward bias in the mixed model HFA estimates that is due to the nonrandom structure of the schedule -- and thus the random effect design matrix -- and explore why the fixed effects model is not subject to the same bias. Intraconference HFAs and standard errors are calculated for each of 3 college sports and 3 professional sports over 18 seasons and then fitted with conference-specific slopes and intercepts to measure the potential linear population trend in HFA.