A discrete-time and finite-state Markov Chain model for association football matches

ABSTRACT

A birth process model proposed by Dixon and Robinson has been widely used in football spread betting market. However, multiple goals in a minute are permitted in the model, which does not conform to historical record. Moreover, it is difficult to calculate the outcome probability of the process accurately. The article presents a discrete-time and finite-state Markov chain model for real-time forecast of football matches and a recursive algorithm is derived to calculate the outcome probability accurately. The empirical study shows that the proposed model outperforms the models of Dixon and Robinson and Dixon and Coles.

KEYWORDS:

• Association football
• Discrete-time and finite-state Markov chain
• Football outcome forecast
• Maximum likelihood
• Recursive algorithm

MATHEMATICS SUBJECT CLASSIFICATION:

• 65C20
• 62M20
• 60J10
• 62P25

Acknowledgments

The authors would like to thank the editor and the two anonymous referees for their constructive comments and suggestions. We thank Beijing StausWin Lottery Operations Technology Ltd. for providing us the EPL data and the GSL data.