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

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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.