Baseball team strengths

Assign each team a nonnegative strength value. (For normalization, say, have the sum of strengths be unity or something.) If two teams of strength X and Y play each other, let the probability that X wins be X/(X+Y), and likewise for Y. Find the assignment of strengths with maximum likelihood of explaining the season. An challenging problem is to determine when a team is ``mathematically eliminated'' (under all possible results of future games) from finishing at least n-th in the strength standings.