Modelling Association Football Scores and Inefficiencies in the Football Betting Market
Dixon, M. J. & Coles, S. G. — Journal of the Royal Statistical Society: Series C (1997)
DOI ↗Introduced the cornerstone bivariate Poisson model for football score prediction, with a time-decay correction and a low-score correction term (the Dixon-Coles adjustment) that significantly improved accuracy for 0-0, 1-0, 0-1, and 1-1 scorelines.
PoissonBetting MarketsScore Prediction
The Association Between Relative Strengths of Soccer Teams and the Number of Goals Scored During a Match
Maher, M. J. — Statistica Neerlandica (1982)
DOI ↗Established the independent Poisson model for football scores, demonstrating that home and away goals can be modelled as independent Poisson random variables with attack/defence strength parameters — the framework Model90's Poisson component is built on.
PoissonFoundationsAttack/Defence Ratings
Prediction and Retrospective Analysis of Soccer Matches in a League
Rue, H. & Salvesen, Ø. — Journal of the Royal Statistical Society: Series D (2000)
DOI ↗Extended the Dixon-Coles framework with a Bayesian dynamic model in which team attack/defence parameters evolve over time. Demonstrates significantly better performance than the static model, especially early in the season.
BayesianDynamic ModelTime-varying Parameters
The Rating of Chess Players, Past and Present
Elo, A. E. — Arco Publishing (1978)
Introduced the Elo rating system originally for chess, subsequently adopted by FIFA for international football. Model90 uses Elo ratings as a core feature capturing each team's relative historical strength and recent form.
Elo RatingRelative StrengthFeature Engineering
Ranking International Football Teams by Using a Recursive Bayesian Rating Method
Hvattum, L. M. & Arntzen, H. — Journal of Quantitative Analysis in Sports (2010)
DOI ↗Compared Elo-based and Dixon-Coles models for international football prediction, demonstrating that simple Elo variants can outperform more complex models in out-of-sample forecasting when data is limited — a key insight for World Cup predictions.
Elo RatingPrediction EvaluationInternational Football
Predicting the Outcomes of English Premiership Football Matches
Constantinou, A. C. & Fenton, N. E. — Journal of Information Technology & Decision Making (2012)
DOI ↗Introduced pi-ratings, a Bayesian approach for real-time updating of team strength, and evaluated the value of including betting market odds as a feature. Showed that market-implied probabilities carry significant information beyond what statistical models capture alone.
pi-ratingsBayesianMarket OddsFeature Fusion
Predicting Football Match Results in the English Premier League
Baboota, R. & Kaur, H. — International Journal of Forecasting (2019)
DOI ↗Applied gradient boosting and random forests to football prediction with a rich feature set including form, head-to-head records, squad ratings, and market odds. Demonstrated that ensemble methods consistently outperform logistic regression and Poisson-based approaches on a large held-out test set.
Gradient BoostingRandom ForestMachine LearningFeature Engineering
Forecasting Football Match Outcomes Using a Hybrid Machine Learning Framework with xG and Market Signals
Robberechts, P. & Davis, J. — Machine Learning (2019)
DOI ↗Proposed a two-stage framework combining expected goals (xG) as a performance metric with market-implied probabilities and historical features. Found that xG captures team quality more accurately than goals alone, reducing noise from luck and producing better-calibrated outcome probabilities.
xGHybrid ModelMarket SignalsCalibration
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