Predicting the 2026 FIFA World Cup with Sufficient Dimension Reduction of Elo Rating Histories

Mina Rezaei; S. Yaser Samadi

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arXiv · 2606.24171

Predicting the 2026 FIFA World Cup with Sufficient Dimension Reduction of Elo Rating Histories

Mina Rezaei·S. Yaser Samadi

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Abstract

We study probabilistic forecasting of the 2026 FIFA World Cup, the first edition with 48 teams and an added Round of 32. The main idea is to describe team strength not only by the current Elo rating, but by a short history of recent Elo differences. We then reduce this history to a few informative directions using categorical sufficient dimension reduction (SDR). The reduced scores are used in a Poisson double-regression model for home and away goals, which gives full outcome probabilities. We compare eleven models, including logistic regression, standard Poisson regression, ARIMA, and neural-network forecasts of the Elo series, gradient boosting, an ensemble model, and four categorical SDR variants based on sliced inverse regression (SIR) and sliced average variance estimation (SAVE). The models are evaluated out of sample on the 2018 and 2022 World Cups using the ranked probability score (RPS). The results show that SDR-based poisson models improve the traditional approaches, suggesting that recent Elo history contains useful predictive information that is not captured by the current Elo difference alone.

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Mina Rezaei, S. Yaser Samadi. 2026-06-23. Predicting the 2026 FIFA World Cup with Sufficient Dimension Reduction of Elo Rating Histories. https://arxiv.org/abs/2606.24171

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