The sample average is a natural estimate for the mean of any random event, and in most situations no estimation rule will perform uniformly better. However, when considering k samples (k>3), shrinkage estimators provide an improvement over the observed sample averages for estimating simultaneously the k means. Consider the problem of predicting season batting averages for 18 baseball players from their performances after 45 times at bat. A related problem from health policy involves predicting the annual rates at which states perform a certain medical procedure from one month of data. For both examples, "shrinking" the observed rates towards a smoothed value results in improved accuracy.