A birth process model for association football matches

Data from over 4000 recent association football (soccer) matches from the main English competitions show clear evidence that the rate of scoring goals changes over the course of a match. This rate tends to increase over the game but is also influenced by the current score. We develop a model for a soccer match that incorporates parameters for both the attacking and the defensive strength of a team, home advantage, the current score and the time left to play. This model treats the number of goals scored by the two teams as interacting birth processes and shows a satisfactory fit to the data. We also investigate football cliches and find evidence that contradicts the cliche that a team is more vulnerable just after it has scored a goal. Our model has applications in the football spread betting market, where prices are updated during a match, and may be useful to both bookmakers and bettors.