Mlb Shrinkage

Small-sample rate leaders regress toward the group mean under empirical-Bayes shrinkage; the raw leaderboard overstates them.

confirmednull (a finding)not testabledescriptivepending

No committed chart for this module — the receipts below are the evidence.

Caveats & confounds

Method. Beta-binomial prior fit per group by method of moments: pooled mean m = sum(k)/sum(n); kappa (=alpha+beta) solved from the Beta-Binomial moment identity Var(p_i) = m*(1-m)/kappa, i.e. kappa = m*(1-m) / max(Var(p_i) - mean(m*(1-m)/n_i), tiny) - 1, floored to 1.0 if the raw rates show no more spread than binomial sampling noise alone (non-finite or <=0 estimate). alpha=m*kappa, beta=(1-m)*kappa. shrunk_i = (k_i+alpha)/(n_i+alpha+beta) is the posterior mean; regression_i = p_i - shrunk_i.