The James Function
نویسندگان
چکیده
In his 1981 Baseball Abstract [8], Bill James posed the following problem: suppose two teams A and B have winning percentages a and b, respectively, having played equally strong schedules in a game such as baseball where there are no ties. If A and B play each other, what is the probability p(a, b) that A wins? This question is perhaps more relevant to other sports, because in baseball the outcome is particularly sensitive to the pitching matchup. (In 1972, the Philadelphia Phillies won 29 of the 41 games started by Steve Carlton, and 30 of the 115 games started by their other pitchers.) The answer is quite interesting, even if its applicability is somewhat limited by the tacit assumption of uniformity. For 0 < a < 1 and c > 0, define qc(a) by
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