A CHARACTERIZATION OF THE POISSON-DISTRIBUTION AND THE PROBABILITY OF WINNING A GAME

The probability P(lambda, mu) that a team with mean score lambda beats a team with mean score mu is calculated when the score of each team is Poisson distributed. It is found that partial-derivative(lambda, mu)/partial-derivativelambda is equal to the probability of a tie. When this equality holds for any distribution of the score of the team with mean mu, it is shown that the score of the team with mean lambda must be Poisson distributed. The Poisson distribution is shown to fit certain baseball data, and it is also applied to some soccer data.