Abstract
It is well known that the number of goals in a football game follows a Poisson distribution very well. Therefore, the intensity parameters of Poisson distributions, followed by the number of goals gained/lost by a team, can be regarded as the indices of the offensive/defensive performance of the team. Teams belonging to a professional football league have many games throughout the season. The performances of such teams should be considered not to be constant throughout the season. A Poisson regression model with varying coefficients is proposed to analyze and visualize the time-varying performance indices of football teams. It is also applicable to estimating the performances up to the middle of a season, and estimated performances can be used to predict the future game’s outcome probabilities. These methods are demonstrated with the data of the Japanese professional football league.
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