Paper overview
Abstract
Football forecasting interfaces often highlight only the most likely outcome and its top probability. This paper argues that the headline probability is incomplete in a three-outcome 1X2 setting, because it does not describe how the remaining probability mass is distributed across draw and away/home alternatives.
The study uses Shannon entropy as a complementary concentration measure for calibrated football probability distributions. On a historical Foresportia case-study dataset of 14,650 completed forecasts, a low-entropy rule, H ≤ 1.15 bits, selects fewer matches than a naive pmax ≥ 0.60 filter, but produces a cleaner observed success segment. The interpretation is selective rather than universal: entropy does not remove football uncertainty, but it helps identify forecasts whose full distribution is less diffuse and can therefore be communicated more responsibly.
Key results
- Historical dataset: 14,650 completed football forecasts.
- Naive pmax ≥ 0.60 filter: 2,157 matches, 1,709 correct outcomes, 79.2% observed success.
- Low entropy H ≤ 1.15 filter: 759 matches, 671 correct outcomes, 88.4% observed success.
- Latest 100 comparison: 62/100 for pmax ≥ 0.60 vs 88/100 for H ≤ 1.15.
Interpretation
The entropy filter is intentionally selective. Its value is not higher coverage, but cleaner separation between forecasts that merely have a high leading probability and forecasts whose entire 1X2 distribution is more concentrated.
This distinction matters in football because draw probability can remain structurally important behind a favorite. A forecast can look strong by pmax while still carrying enough residual draw mass to make the confidence fragile.
Citation
Use the DOI link above for the persistent citation record. BibTeX:
@misc{barbedienne2026beyond,
title = {Beyond Top Probability: Shannon Entropy as a Confidence Signal in Football Forecasting},
author = {Barbedienne, Quentin},
year = {2026},
month = {May},
doi = {10.5281/zenodo.20162105},
url = {https://doi.org/10.5281/zenodo.20162105}
}Disclaimer
This research page and the linked PDF are provided for applied sports analytics and probabilistic forecasting discussion. They are not betting advice, financial advice, or individualized recommendations. No football forecast should be read as a guaranteed outcome.