Abstract: The probability of winning a game in major league baseball depends on various factors relating to team strength including the past per formance of the two teams, the batting ability of the two teams and the starting pitchers. These three factors change over time. We combine these factors by adopting contribution parameters, and include a home field ad vantage variable in forming a two-stage Bayesian model. A Markov chain Monte Carlo algorithm is used to carry out Bayesian inference and to sim ulate outcomes of future games. We apply the approach to data obtained from the 2001 regular season in major league baseball.