Winning Streaks, Shutouts, and the Length of the World Series

In a recent article in this Journal [Brunner 19871, the theory of absorbing Markov chains was applied to the expected number of games in the World Series, using techniques similar to those described inolinick [ 1978, Chapter 10, Section IV] and Kemeny and Snell [1967]. Other authors have discussed the waiting time for the first occurrence of a run of M wins by either player when two players engage in a series of independent games in which each has probability 1/2 of winning a game. The results were applied to the annual Oxford-Cambridge boat race [Forfar and Keogh 1986; Boyd 19871. In fact Feller [I9701 much earlier had applied renewal theory to the theory of success runs. Keller [I9841 computed the probability of a shutout in racquetball, assuming each player has a fixed probability of winning any particular rally; and Marcus [I9851 calculated the probability of winning a game of racquetball as a function of the probabilities of winning a rally when serving and when receiving.