This is to all math/stat oriented people on NSBB. With the recent discussion of the Cubs Pythagorean Win Percentage here, I want to pose the question of how to prove this a more robust statistic: the expected number of wins given the number of games played. The formal problem description is this: Suppose the Cubs have scored X number of runs, while giving up Y number of runs over G number of games. Assume each "run distribution" is equally likely. For example, if G = 3, X = 10, and Y=9, then the Cubs run distribution could be (0,10,0), or (1,9,0), or (4,3,1), etc, each all equally likely. Likewise, the opponent run distribution could be (1,4,4), (0,9,0), (2,5,2), etc, again each all equally likely. What is the expected number of wins of the Cubs, in terms of G? Can anybody think of a analytical way to solve this problem, or would I need to bust out Matlab?