Statistical modelling for predicting football outcomes: an R implementation of the Dixon-Coles model and applications to the 2021-2022 Serie A championship

This repository contains an R implementation of my BSc thesis in Statistics (University of Trieste)

Short abstract

Football is undoubtedly one of the most beloved sports globally, and statistical analysis to understand the dynamics of the game and predict its outcomes is becoming increasingly important. The main objective of my thesis project is to evaluate the effectiveness of goal-based statistical models, which aim to predict the number of goals scored by the two teams competing in a football match.

Firstly, we will seek to identify a suitable probability distribution to describe the number of goals scored. Subsequently, we will delve into the key model concepts available in the scientific literature. We will begin by examining the model introduced by Maher, analyzing its strengths and limitations to comprehend the pivotal aspects to be included in the statistical modeling of football outcomes. Among these aspects, we will explore the consideration of team-specific attacking and defensive strengths, the influence of playing at home (home effect), and the impact of teams' current form (both physical and psychological) on their performances. All this will lead to the Dixon and Coles model, one of the most renowned and widely used goal-based models in the world of sports statistics. The analyzed models were then implemented using R software, adopting a from scratch approach. Leveraging historical data from the 2021-2022 Serie A championship, the thesis will delve into specific applications of the model, even extending beyond the mere prediction of match outcomes.

In summary, this thesis project aims to provide a comprehensive overview of goal-based models and to enhance their understanding through empirical applications to the 2021-2022 Serie A championship, thereby offering empirical evidence of their effectiveness.

For more details about my thesis project, see report.

R scripts

Some brief information about the R scripts contained in this repository (more details in the scripts' headers)

Preliminary analysis

• poisson_approximation.R : analysis of Poisson as an approximation for Teams's Goals
• home_effect.R : an empirical proof of a home effect in football

Parameters estimation

• Maher_parameters_estimation.R : estimation of Maher model's optimal parameters (using all season matches as training-set)
• DC_static_parameters_estimation.R : estimation of Dixon-Coles static model's optimal parameters (using all season matches as training-set)
• DC_dinamic_parameters_estimation.R : estimation of Dixon-Coles dinamic model's optimal parameters (over the 2nd half of the season)
• xi_profile_loglike.R : estimation of the best value of $\xi$ (parameter of dinamic Dixon-Coles model) through a profile log-likelihood (PLL) approach
• estimates_precision.R : determination of standard errors and confidence intervals for models' estimates (determined using all season matches as training-set)

Applications to the 2021-2022 Serie A championship

• DC_predictions_matchday38.R : predictions of Dixon-Coles (dinamic) model for the last matchday (38th)
• abilities_over_time.R : attack and defence abilities timeseries over the 2nd half of the league
• home&rho_over_time.R : timeseries of home effect and correlation coefficients over the 2nd half of the league

Models comparison and evaluation

• brier_score.R : implementation of Brier Score metric to compare models
• pseudoR2.R : implementation of Pseudo-$R^2$ metric to compare models
• confusion_matrices.R : implementation of confusion matrices to analyze models' performances

As previously mentioned, all the analyzed models were implemented using a from scratch approach. This means that every function, from lower to higher level, was built starting from zero. For more details about these functions check the directory functions. Models' optimal parameters, instead, can be found in the directory parameters.