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An analytically solvable model for soccer: further implications of the classical Poisson model

Fry, John and Hastings, Tom and Serbera, Jean-Philippe (2017): An analytically solvable model for soccer: further implications of the classical Poisson model.

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Abstract

In this paper we discuss an exactly soluble statistical model for soccer. By taking into account key features of soccer matches (goals are rare, goal-scoring patterns are not well understood) we arrive at a version of the classical Poisson model but with constraints on the expected total number of goals in a game. Closed form expressions are derived for expected scores and match outcomes. We are also able to reconstruct an empirically observed inverse strike-back effect pertaining to teams scoring consecutive goals. We produce analytical results for perfectly competitive soccer leagues where draws are tied to the average number of goals in a game. An empirical application to the 2016 UEFA European Championships is also discussed.

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