pi-football: A Bayesian network model for forecasting Association Football match outcomes

A Bayesian network is a graphical probabilistic belief network that represents the conditional dependencies among uncertain variables, which can be both objective and subjective. We present a Bayesian network model for forecasting Association Football matches in which the subjective variables represent the factors that are important for prediction but which historical data fails to capture. The model (pi-football) was used to generate forecasts about the outcomes of the English Premier League (EPL) matches during season 2010/11 (but is easily extended to any football league). Forecasts were published online at www.pi-football.com prior to the start of each match. In this paper, we demonstrate that a) using an appropriate measure of forecast accuracy, the subjective information improved the model such that posterior forecasts were on par with bookmakers ' performance; b) using a standard profitability measure with discrepancy levels at ≥ 5%, the model generates profit under maximum, mean, and common bookmakers ’ odds, even allowing for the bookmakers ' built-in profit margin. Hence, compared with other published football forecast models, pi-football not only appears to be exceptionally accurate, but it can also be used to 'beat the bookies'

Bayesian networks for prediction, risk assessment and decision making in an inefficient Association Football gambling market.

PhDResearchers have witnessed the great success in deterministic and perfect information domains. Intelligent pruning and evaluation techniques have been proven to be sufficient in providing outstanding intelligent decision making performance. However, processes that model uncertainty and risk for real-life situations have not met the same success. Association Football has been identified as an ideal and exciting application for that matter; it is the world's most popular sport and constitutes the fastest growing gambling market at international level. As a result, summarising the risk and uncertainty when it comes to the outcomes of relevant football match events has been dramatically increased both in importance as well as in challenge. A gambling market is described as being inefficient if there are one or more betting procedures that generate profit, at a consistent rate, as a consequence of exploiting market flaws. This study exhibits evidence of an (intended) inefficient football gambling market and demonstrates how a Bayesian network model can be employed against market odds for the gambler’s benefit. A Bayesian network is a graphical probabilistic model that represents the conditional dependencies among uncertain variables which can be both objective and subjective. We have proposed such a model, which we call pi-football, and used it to generate forecasts for the English Premier League matches during seasons 2010/11 and 2011/12. The proposed subjective variables represent the factors that are important for prediction but which historical data fails to capture, and forecasts were published online at www.pi-football.com prior to the start of each match.For assessing the performance of our model we have considered both profitability and accuracy measures and demonstrate that subjective information improved the forecasting capability of our model significantly. Resulting match forecasts are sufficiently more accurate relative to market odds and thus, the model demonstrates profitable returns at a consistent rateEngineering and Physical Sciences Research Council (EPSRC; Agena Ltd for software support