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

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.