  In randomized controlled trials (RCTs), treatment is often assigned by
stratified randomization. I show that among all stratified randomization
schemes which treat all units with probability one half, a certain matched-pair
design achieves the maximum statistical precision for estimating the average
treatment effect (ATE). In an important special case, the optimal design pairs
units according to the baseline outcome. In a simulation study based on
datasets from 10 RCTs, this design lowers the standard error for the estimator
of the ATE by 10% on average, and by up to 34%, relative to the original
designs.
