Suppose a number of pairs of teams or products are compared on the basis ofnbinomial trials. Although we cannot know from the outcomes which teams or products were actually better, we wish to estimate the average probability that the better team or product wins a given trial, and thus to measure the discrimination provided by our test. World Series data provide an example of such comparisons. The National League has been outclassed by the American League teams in a half-century of World Series competition. The American League has won about 58 per cent of the games and 65 per cent of the Series. The probability that the better team wins the World Series is estimated as 0.80, and the American League is estimated to have had the better team in about 75 per cent of the Series.