机器学习预测2018世界杯冠军（英文）-2018.6.8-28页

Summary of "Prediction of the FIFA World Cup 2018 – A random forest approach with an emphasis on estimated team ability parameters"

Core Content

This paper presents a comprehensive study on predicting the outcome of the FIFA World Cup 2018 using a combination of modeling approaches. The focus is on comparing and combining random forests, Poisson regression models, and ranking methods to improve prediction accuracy.

Main Methods and Approaches

1. Random Forests

• A machine learning method that aggregates multiple decision trees.
• Used for predicting the number of goals scored by teams in matches.
• Two variants are considered:
  • Classical random forest from the ranger package.
  • Conditional inference forest from the party package, which avoids biased variable selection due to different scales of covariates.
• The ctree function from the party package is used to visualize the regression trees.
• Variable importance is used to assess the contribution of each covariate to the model.
• The most important predictors identified are: FIFA rank, Oddset probability, number of Champions League players, and Confederation of the opponent.

2. Poisson Regression Models

• Model the number of goals scored by each team in a match using Poisson distributions.
• A simple model assumes independence of the two Poisson distributions (conditional on team abilities).
• More complex models, such as the bivariate Poisson or copula-based models, allow for dependencies between the scores.
• The Lasso regularization technique is used to handle high-dimensional data and perform variable selection.
• The model is calibrated using data from the previous five FIFA World Cups and 10,000 Monte Carlo simulations.

3. Ranking Methods

• Estimate team ability parameters based on historical performance.
• These parameters are used as inputs for match simulations.
• The method is similar to the FIFA ranking system but is based on a Poisson model.
• Ranking methods are shown to perform well in predicting outcomes of both domestic and international matches.

Key Findings

• Ranking methods and random forests perform best on the training data.
• Combining random forests with team ability parameters from ranking methods significantly improves predictive power.
• The final model uses a combination of:
  • Random forest predictions for the number of goals.
  • Estimated team ability parameters from ranking methods.
• The model is used to simulate the FIFA World Cup 2018 tournament multiple times.
• Winning probabilities are calculated for all teams, with Spain slightly favored over Germany, which is the defending champion.
• Survival probabilities for all teams and tournament stages are also provided.
• The most probable tournament outcome is predicted based on the model's simulations.

Data Description

• The study uses data from the FIFA World Cups 2002–2014, including all matches.
• 16 covariates are collected for each team:
  • Economic factors: GDP per capita, population.
  • Sportive factors: FIFA rank, bookmaker odds (Oddset), performance in qualifications.
  • Home advantage: Host country, same continent as host, confederation.
  • Team structure: Average age, number of club players (Champions League/UEFA Europa League), number of players abroad.
  • Coach factors: Age, tenure, nationality.
• All metric covariates are used as differences between teams.
• Categorical covariates are included as separate variables for each team.
• The final data structure includes:
  • Goals (response variable).
  • Team and opponent.
  • Age, Rank, Oddset, etc. (predictors).
• The model treats predicted expected goals as intensity parameters of a Poisson distribution to simulate match outcomes.

Conclusion

• The final model combines random forests with team ability parameters from ranking methods.
• This combination yields better predictive performance than using either method alone.
• The model is used to simulate the FIFA World Cup 2018, resulting in:
  • Winning probabilities for all teams.
  • Survival probabilities at all tournament stages.
  • A most probable tournament outcome.
• The model slightly favors Spain over Germany, the defending champion, but overall, the results are consistent with expert predictions and bookmaker odds.

Key Variables

• GDP per capita (normalized).
• Population (normalized).
• FIFA rank (difference between teams).
• Oddset probability (converted from bookmaker odds).
• Host, Continent, Confederation, and Nationality (categorical, separate for each team).
• Average age, maximum number of teammates, number of Champions League players, number of players abroad (structure-related).
• Coach age, tenure, and nationality (coach-related).

Model Implementation

• The model is implemented in R.
• Lasso regularization is used for variable selection.
• 10-fold cross-validation is used to select the optimal tuning parameter.
• The model is fitted using the cv.glmnet function from the glmnet package.
• The final predictions are based on repeated simulations of the tournament using the model's estimated parameters.

Final Predictions

• Winning probabilities for all teams are estimated.
• Spain is predicted to have a 12.5% chance of winning.
• Germany is predicted to have a 15.8% chance.
• Brazil is predicted to have a 16.6% chance.
• Survival probabilities are also calculated for all teams at each stage of the tournament.
• The most probable outcome is determined based on the simulation results.

References

• Breiman, L. (2001): Random forests.
• Dixon, J. F., & Coles, M. G. (1997): Modeling association football scores.
• Karlis, D., & Ntzoufras, I. (2003): Analysis of sports data with bivariate Poisson models.
• Leitner, J., Zeileis, A., & Hornik, K. (2010a): Inverse tournament simulation.
• Ley, C., Van de Wiele, C., & Van Eetvelde, H. (2018): Poisson-based ranking methods.
• Schauberger, G., & Groll, A. (2018): Random forests for soccer match prediction.
• Groll, A., et al. (2015): Lasso estimation for FIFA World Cup prediction.
• Groll, A., et al. (2018): Bivariate Poisson models for soccer match outcomes.
• Zeileis, A., et al. (2018): Forecasting the FIFA World Cup 2018.

Method Comparison

• Random forests outperform traditional regression methods in predicting match outcomes.
• Ranking methods provide estimates of team strength that are used as additional covariates in the random forest model.
• Poisson regression models are useful but limited in their ability to capture dependencies between scores.
• The combination of random forests and ranking methods is shown to be the most effective approach for the FIFA World Cup 2018 prediction.