Ranking soccer teams on the basis of their current strength: A comparison of maximum likelihood approaches

Abstract

We present ten different strength-based statistical models that we use to model soccer match outcomes with the aim of producing a new ranking. The models are of four main types: Thurstone-Mosteller, Bradley-Terry, Independent Poisson and Bivariate Poisson, and their common aspect is that the parameters are estimated via weighted maximum likelihood, the weights being a match importance factor and a time depreciation factor giving less weight to matches that are played a long time ago. Since our goal is to build a ranking reflecting the teams' current strengths, we compare the 10 models on basis of their predictive performance via the Rank Probability Score at the level of both domestic leagues and national teams. We find that the best models are the Bivariate and Independent Poisson models. We then illustrate the versatility and usefulness of our new rankings by means of three examples where the existing rankings fail to provide enough information or lead to peculiar results.

Forecasting football matches by predicting match statistics

“…The RPS is often considered appropriate for eval- To provide some context regarding the performance of the forecasts, we compare the performance with that of an alternative, strongly perform-894 ing approach to forecasting football matches. The Bivariate Poisson model, described in appendix 6, has been shown to perform favourably with respect to 9 other forecast models (Ley et al, 2019). We apply the model to our data set using the optimal half life parameter of 390 days determined by Ley et al (2019).…”

“…Other examples of systems that use attacking and defensive ratings can be found in Karlis and Ntzoufras (2003), Lee (1997) and Baker and McHale (2015). Ley et al (2019) compared ten different parametric models (with the parameters estimated using maximum likelihood) and found the Bivariate Poisson model to give the most favourable results. Koopman and Lit (2015) used a Bivariate Poisson model alongside a Bayesian approach to demonstrate a profitable betting strategy.…”

“…Generally, the larger the overround, the more difficult it is for a gambler to make a profit since the return 238 from a winning bet is reduced. Ley et al (2019), who compared it with nine other models and found it to achieve the most favourable forecast performance (according to the ranked probability score).…”

“…Performing maximum likelihood estimation with a large number of parameters is, in general, difficult and there is a risk of falling into local optima. We follow the approach used by Ley et al (2019)…”

The efficacy of league formats in ranking teams

“…The main goal of this article is to study which tournament types rank teams according to their strengths best. To this end, we propose a detailed simulation methodology based on a team strength (rating) model, see also (Ley et al, 2018). As a contribution to the theory and practice of team strength modelling, we propose a Poisson model in which attacking and defensive strengths exhibit a particular correlation structure that is achieved by adjusting the model's regularization term.…”