Covariate adjustment can increase the precision of estimates by removing unexplained variance from the error in randomized experiments, although chance covariate imbalance tends to counteract the improvement in precision. The author develops an easy measure to examine chance covariate imbalance in randomization by standardizing the average covariate difference between the treatment and control condition. The standardized covariate difference must not exceed an upper bound in order to gain precision in covariate adjusted analysis. The author then shows how to select an adequate sample size to mitigate chance covariate imbalance and improve precision in small pilot studies. (Contains 1 note and 2 tables.)