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Nested Zero Inflated Generalized Poisson Regression for FIFA World Cup 2022

Lorenz A. Gilch

TL;DR

This work tackles the problem of forecasting a complex, low-scoring international tournament by introducing a nested zero-inflated generalized Poisson regression (ZIGP) that integrates team Elo rankings, match location, and attack/defense covariates. The model treats each match score as a ZIGP random variable with parameters estimated via regression, and combines two dependent score processes to produce joint match outcomes, subsequently using Monte Carlo simulation to forecast the entire World Cup 2022 with 100,000 tournament runs. Validation against historical events (2010–2018 World Cups and EURO 2016/2020) shows mixed but generally favorable improvements over standard Poisson models, particularly in 2010 and 2014, while still offering competitive performance in other cases. The forecast for World Cup 2022 identifies Brazil and Argentina as top contenders, provides detailed group-stage probabilities, and delivers probabilistic insights into playoff progression, demonstrating the practical utility of the ZIGP approach for sports forecasting.

Abstract

This article is devoted to the forecast of the FIFA World Cup 2022 via nested zero-inflated generalized Poisson regression. Our regression model incorporates the Elo points of the participating teams, the location of the matches and the of team-specific skills in attack and defense as covariates. The proposed model allows predictions in terms of probabilities in order to quantify the chances for each team to reach a certain stage of the tournament. We use Monte Carlo simulations for estimating the outcome of each single match of the tournament, from which we are able to simulate the whole tournament itself. The model is fitted on all football games of the participating teams since 2016 weighted by date and importance. Validation with previous tournaments and comparison with other Poisson models are given.

Nested Zero Inflated Generalized Poisson Regression for FIFA World Cup 2022

TL;DR

This work tackles the problem of forecasting a complex, low-scoring international tournament by introducing a nested zero-inflated generalized Poisson regression (ZIGP) that integrates team Elo rankings, match location, and attack/defense covariates. The model treats each match score as a ZIGP random variable with parameters estimated via regression, and combines two dependent score processes to produce joint match outcomes, subsequently using Monte Carlo simulation to forecast the entire World Cup 2022 with 100,000 tournament runs. Validation against historical events (2010–2018 World Cups and EURO 2016/2020) shows mixed but generally favorable improvements over standard Poisson models, particularly in 2010 and 2014, while still offering competitive performance in other cases. The forecast for World Cup 2022 identifies Brazil and Argentina as top contenders, provides detailed group-stage probabilities, and delivers probabilistic insights into playoff progression, demonstrating the practical utility of the ZIGP approach for sports forecasting.

Abstract

This article is devoted to the forecast of the FIFA World Cup 2022 via nested zero-inflated generalized Poisson regression. Our regression model incorporates the Elo points of the participating teams, the location of the matches and the of team-specific skills in attack and defense as covariates. The proposed model allows predictions in terms of probabilities in order to quantify the chances for each team to reach a certain stage of the tournament. We use Monte Carlo simulations for estimating the outcome of each single match of the tournament, from which we are able to simulate the whole tournament itself. The model is fitted on all football games of the participating teams since 2016 weighted by date and importance. Validation with previous tournaments and comparison with other Poisson models are given.
Paper Structure (21 sections, 23 equations, 4 figures, 14 tables)

This paper contains 21 sections, 23 equations, 4 figures, 14 tables.

Table of Contents

  1. Introduction
  2. The Nested ZIGP Model
  3. Preliminaries
  4. Involved data
  5. Nested Zero-Inflated Generalized Poisson Regression
  6. Goodness of Fit Tests
  7. ZIGP Regression for $\hat{G}_A$
  8. ZIGP Regression for $\check G_A$
  9. ZIGP Regression for $G_B$
  10. Further Poisson Models
  11. Independent Poisson Regression
  12. Bivariate Poisson Regression
  13. Validation of the ZIGP Model
  14. Scoring Functions
  15. Comparison of Different Models
  16. ...and 6 more sections

Figures (4)

  • Figure 1: ZIGP regression (\ref{['equ:ZIGP-regression1']}) for Spain.
  • Figure 2: ZIGP regression (\ref{['equ:ZIGP-regression2']}) for Brazil.
  • Figure 3: ZIGP regression (\ref{['equ:ZIGP-regression3']}) for Wales' away matches against stronger opponents, who score exactly $2$ goals.
  • Figure 4: Probabilities for the score of the preliminary round match Spain vs. Germany (group E) in Qatar.