# Modeling outcomes of soccer matches

arXiv: https://arxiv.org/abs/1807.01623 · HTML: https://mlsanity.com/paper/1807.01623/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2018.

## Built on by (most cited first, 4 of 4)

- [Statistical inference for pairwise comparison models](https://mlsanity.com/paper/2401.08463/) (2024)
- [Machine Learning for Soccer Match Result Prediction](https://mlsanity.com/paper/2403.07669/) (2024)
- [Evaluating Soccer Match Prediction Models: A Deep Learning Approach and Feature Optimization for Gradient-Boosted Trees](https://mlsanity.com/paper/2309.14807/) (2023)
- [Pairwise Comparisons without Stochastic Transitivity: Model, Theory and Applications](https://mlsanity.com/paper/2501.07437/) (2025)

## Abstract (arXiv)

We compare various extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley-Terry extensions are estimated by maximizing the log-likelihood, or an appropriately penalized version of it, while the posterior densities of the parameters of the hierarchical Poisson log-linear model are approximated using integrated nested Laplace approximations. The prediction performance of the various modeling approaches is assessed using a novel, context-specific framework for temporal validation that is found to deliver accurate estimates of the test error. The direct modeling of outcomes via the various Bradley-Terry extensions and the modeling of match scores using the hierarchical Poisson log-linear model demonstrate similar behavior in terms of predictive performance.