Random forests and correlated trees

Why does reducing correlation among trees help a random forest, even if individual trees become slightly weaker?

The variance of an average depends on both individual variances and pairwise covariances. Averaging highly correlated errors yields limited variance reduction. Feature subsampling and bootstrap variation can reduce correlation, potentially improving the ensemble despite weaker components. The benefit is empirical and does not remove bias or distribution shift. Tune feature sampling and leaf controls using the intended evaluation procedure.