An Offensive Earned-Run Average for Baseball

This paper studies a baseball statistic that plays the role of an offensive earned-run average (OERA). The OERA of an individual i s simply the number of earned runs per game that he would score if he batted in all nine positions in the line-up. Evaluation can be performed by hand b y scoring the sequence of times at bat of a given batter. This statistic has the obvious natural interpretation and tends to evaluate strictly personal rather than team achievement. Some theoretical properties of this statistic are developed, and we give our answer to the question, "Who is the greatest hitter in baseball his-tory?" UPPOSE THAT we are following the history of a certain batter and want some index of his offensive effectiveness. We could, for example, keep track of a running average of the proportion of times he hit safely. This, of course, is the batting average. A more refined estimate ~vould be a running average of the total number of bases pcr official time a t bat (the slugging average). We might then notice that both averages omit mention of ~valks. Perhaps what is needed is a spectrum of the running average of walks, singles, doublcs, triples, and homcruns per official time a t bat. But how are we to convert this six-dimensional variable into a direct comparison of batters? Let us consider another statistic. The first time in the batter's career let us take note of the outcome. For example, a single IT-ill put him on first base with no outs. The second time in his career that he comes to bat, let us again take note of the outcome and update the outs, men on base, and number of runs scored accordingly. Continuing in this fashion, we shall generate a number of a batter's personal innings together with the scores produced by him as his career progresses. Thus, for example, a batter IT-hose career begins "single, out, double, out, walk, walk, homcrun, out," will have generated five runs in his first personal inning. The statistic so generated is another measure of batter effectiveness and the units are the ex