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A Characterization of the Poisson Distribution and the Probability of Winning a Game

Joseph B. Keller
The American Statistician
Vol. 48, No. 4 (Nov., 1994), pp. 294-298
DOI: 10.2307/2684837
Stable URL: http://www.jstor.org/stable/2684837
Page Count: 5
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A Characterization of the Poisson Distribution and the Probability of Winning a Game
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Abstract

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

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