# Ranking soccer teams on basis of their current strength: a comparison of maximum likelihood approaches

## TL;DR

This paper compares ten statistical models for ranking soccer teams based on their current strength, emphasizing predictive accuracy and practical usefulness, and identifies the Bivariate and Independent Poisson models as the most effective.

## Contribution

It introduces and evaluates ten different maximum likelihood-based models for current soccer team ranking, highlighting the most accurate approaches.

## Key findings

- Bivariate and Independent Poisson models perform best in predictive tests.
- The new rankings provide better insights than existing methods in specific examples.
- Weighted maximum likelihood estimation effectively incorporates match importance and recency.

## 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.