In this talk I will show how to construct a better football league table than the official ranking based on accumulated points to date. The aim of this work is (only) to produce a more informative representation of how teams currently stand, based on their match results to date in the current season; it is emphatically not about prediction. A more informative league table is one that takes proper account of "schedule strength" differences, i.e., differing numbers of matches played by each team (home and away), and differing current standings of the opponents that each team has faced.
This work extends previous "retrodictive" use of Bradley-Terry models and their generalizations, specifically to handle 3 points for a win, and also to incorporate home/away effects coherently without assuming homogeneity across teams. Playing records that are 100% or 0%, which can be problematic in standard Bradley-Terry approaches, are incorporated in a simple way without the need for a regularizing penalty on the likelihood. A maximum-entropy argument shows how the method developed here is the mathematically "best" way to account for schedule strength in a football league table.
Illustrations will be from the English Premier League.
The talk was given by David Firth from the University of Warwick.