One-Match-Ahead Forecasting in Two-Team Sports with Stacked Bayesian Regressions

Max W. Y. Lam 1
  • 1 Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong


There is a growing interest in applying machine learning algorithms to real-world examples by explicitly deriving models based on probabilistic reasoning. Sports analytics, being favoured mostly by the statistics community and less discussed in the machine learning community, becomes our focus in this paper. Specifically, we model two-team sports for the sake of one-match-ahead forecasting. We present a pioneering modeling approach based on stacked Bayesian regressions, in a way that winning probability can be calculated analytically. Benefiting from regression flexibility and high standard of performance, Sparse Spectrum Gaussian Process Regression (SSGPR) – an improved algorithm for the standard Gaussian Process Regression (GPR), was used to solve Bayesian regression tasks, resulting in a novel predictive model called TLGProb. For evaluation, TLGProb was applied to a popular sports event – National Basketball Association (NBA). Finally, 85.28% of the matches in NBA 2014/2015 regular season were correctly predicted by TLGProb, surpassing the existing predictive models for NBA.

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  • [1] I. Bhandari et al., Advanced Scout: Data Mining and Knowledge Discovery in NBA Data, Data Mining and Knowledge Discovery, 1(1), 121–125, 1997.

  • [2] D. B. Hausch & W. T. Ziemba, Handbook of Sports and Lottery Markets, Elsevier, 2011.

  • [3] M. Ottaviani & P. N. Sørensen, Surprised by the Parimutuel Odds?, The American Economic Review, 99(5), 2129–2134, 2009.

  • [4] M. Haghighat et al., A Review of Data Mining Techniques for Result Prediction in Sports, Advances in Computer Science: an International Journal, 2(5), 7–12, 2013.

  • [5] M. Lázaro-Gredilla et la., Sparse Spectrum Gaussian Process Regression, Journal of Machine Learning Research, 11(Jun), 1865–1881, 2010.

  • [6] C. E. Rasmussen & C. K. Williams, Gaussian Processes for Machine Learning, MIT Press, 2006.

  • [7] D. J. MacKay, Introduction to Gaussian Processes. NATO ASI Series F Computer and Systems Sciences, 168, 133–166, 1998.

  • [8] D. Duvenaud, Automatic Model Construction with Gaussian Processes, Doctoral Dissertation, University of Cambridge, 2014.

  • [9] R. M. Neal, Bayesian Learning for Neural Networks, Springer Science & Business Media, 118, 2012.

  • [10] Y. Gal & R. Turner, Improving the Gaussian Process Sparse Spectrum Approximation by Representing Uncertainty in Frequency Inputs, In: 32nd International Conference on Machine Learning, 655–664, 2015.

  • [11] N. Wiener, Generalized Harmonic Analysis, Acta mathematica, 55(1), 117–258, 1930.

  • [12] A. Khintchine, Korrelationstheorie der Stationren Stochastischen Prozesse, Mathematische Annalen, 109(1), 604–615, 1934.

  • [13] S. Bochner, Monotone Funktionen, Stieltjessche Integrale Und Harmonische Analyse, Mathematische Annalen, 108(1), 378–410, 1933.

  • [14] J. Quiñonero-Candela et la., A Unifying View of Sparse Approximate Gaussian Process Regression, Journal of Machine Learning Research, 6(Dec), 1939–1959, 2005.

  • [15] J. S. Simonoff, Smoothing Methods in Statistics, Springer Science & Business Media, 2012.

  • [16] E. S. Gardner, Exponential Smoothing: The State of the Art, Journal of Forecasting, 4(1), 1–28, 1985.

  • [17] D. Oliver, Basketball on Paper: Rules and Tools for Performance Analysis, Potomac Books, Inc., 2004.

  • [18] W. L. Winston, Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football, Princeton University Press, 2012.

  • [19] D. Kingma & J. Ba, Adam: A Method for Stochastic Optimization, In: International Conference on Learning Representations 2014, 1–13, 2014.

  • [20] C. Saunders et la., Ridge Regression Learning Algorithm in Dual Variables. In: 15th International Conference on Machine Learning, 515–521, 1998.

  • [21] S. An et la., Face Recognition Using Kernel Ridge Regression. In: Computer Vision and Pattern Recognition 2007, IEEE, 1–7, 2007.

  • [22] M. Xu et la., Decision Tree Regression for Soft Classification of Remote Sensing Data, Remote Sensing of Environment, 97(3), 322–336, 2005.

  • [23] Y. Freund, & R. E. Schapire, A Desicion-Theoretic Generalization of On-line Learning and An Application to Boosting, In: European Conference on Computational Learning Theory 1995, Springer Berlin Heidelberg, 23–37, 1995.

  • [24] J. H. Friedman, Greedy Function Approximation: a Gradient Boosting Machine, Annals of Statistics, 1189–1232, 2001.

  • [25] L. Breiman, Random Forests, Machine learning, 45(1), 5–32, 2001.

  • [26] F. Pedregosa et la., Scikit-learn: Machine Learning in Python, Journal of Machine Learning Research, 12(Oct), 2825–2830, 2011.

  • [27] J. Quinonero-Candela et la., Evaluating Predictive Uncertainty Challenge. In: Machine Learning Challenges. Evaluating Predictive Uncertainty, Visual Object Classification, and Recognising Tectual Entailment, Springer Berlin Heidelberg, 1–27, 2006.

  • [28] J. Kohonen & J. Suomela, Lessons Learned in the Challenge: Making Predictions and Scoring Them. In: Machine Learning Challenges. Evaluating Predictive Uncertainty, Visual Object Classification, and Recognising Tectual Entailment, Springer Berlin Heidelberg, 1–27, 2006.

  • [29] D. Miljković et la., The Use of Data Mining for Basketball Matches Outcomes Prediction, In: 8th International Symposium on Intelligent Systems and Informatics (SISY), IEEE, 309–312, 2010.

  • [30] C. Cao, Sports Data Mining Technology Used in Basketball Outcome Prediction, Masters Dissertation, Dublin Institute of Technology, 2012.

  • [31] M. Beckler et la., NBA Oracle, – 2009/10701report.pd f, 2013.

  • [32] E. Zdravevski, & A. Kulakov, System for Prediction of the Winner in a Sports Game, In: ICT Innovations, Springer Berlin Heidelberg, 55–63, 2009.

  • [33] B. Loeffelholz et la., Predicting NBA Games Using Neural Networks, Journal of Quantitative Analysis in Sports, 5(1), 1–15, 2009.


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