A linear model for ranking the soccer championship

In the literature some interesting analysis on possible ranking methods, mainly concentrated on American football teams ranking, may be found. Under certain assumptions the ranking problem may be easily formulated as a linear eigenvalue problem. In this paper we present the application of the linear model to the last edition of the Italian national soccer championship, showing that the results from the model give some significant differences with respect to the final official ordering. After recalling the concepts of eigenvalues and eigenvectors of a square matrix and the Perron–Frobenius theorem, we use the model to get the final ordering for the teams and we compare it with the official final ordering. At the end we try to interpret the results and propose some explanations of the differences, in terms of what actually the model considers and the official scores do not.