arXiv:2610.32023v1 Announce Type: cross Abstract: Regression adjustment is widely used to improve the precision of average treatment effect estimates from randomized controlled trials. Interacted regression weakly dominates simple regression in terms of its first-order behavior but, in 50-50 randomized trials, the asymptotic variance of both methods is the same and so relative performance is determined by higher-order behavior. Here, we conduct a higher order analysis to compare simple vs. interacted regression adjustments in the equal-probability case. The relative performance of the methods depends on a number of factors including feature skewness, treatment-effect heterogeneity, heteroskedasticity, and nonlinear misspecification, and can favor either estimator. However, in some practically important settings, including when features are skewed and outlying feature values are associated with higher outcome noise, simple regression can outperform interacted regression by a material amount.