Toward enhancing beta estimates

Abstract

E arly in the 1977 major league baseball season, Manny Trillo, then second baseman for the Chicago Cubs (Yea!), was hitting like a Rod Carew. On May 9, after eighty at-bats, Trillo had thirty-one hits and a batting average of .388. At the end of the season, he had been to bat 504 times. What is your estimate of his 1977 batting average? On June 13, 1978, Pete Rose, then third baseman for the Cincinnati Reds, was hitting only .267. On July31, forty-four fantastic games later, he had 138 hits in 437 at-bats, for an average of .316. What is your estimate of his 1978 batting average? Perhaps a better question than “What is your estimate . . .?” is “How would you estimate . . .?I ’ Most statistical theory suggests that one might consider Trillo’s eighty at-bats or Rose’s 437 at-bats to be samples from the populations of their seasons’ total at-bats. This being so, one might use the sample means of .388 and .316 as the estimates. Few baseball fans would argue with the .316 estimate for Rose, but most would reject the .388 estimate for Trillo. Even an indifferent fan knows that very few ballplayers finish seasons with batting averages approaching .390.