Construction of a semi-Markov model for the performance of a football team in the presence of missing data

ABSTRACT

Using play-by-play data from the very beginning of the professional football league in Turkey, a semi-Markov model is presented for describing the performance of football teams. The official match results of the selected teams during 55 football seasons are used and winning, drawing and losing are considered as Markov states. The semi-Markov model is constructed with transition rates inferred from the official match results. The duration between the last match of a season and the very first match of the following season is much longer than any other duration during the season. Therefore these values are considered as missing values and estimated by using expectation–maximization algorithm. The effect of the sojourn time in a state to the performance of a team is discussed as well as mean sojourn times after losing/winning are estimated. The limiting probabilities of winning, drawing and losing are calculated. Some insights about the performance of the selected teams are presented.

KEYWORDS:

• EM-algorithm
• estimation
• football
• log-normal distribution
• semi-Markov process
• sojourn time

Acknowledgement

The authors would like to thank the anonymous referees for their invaluable and helpful comments for the improvement of the study.

Disclosure statement

No potential conflict of interest was reported by the author(s).