In-game win probabilities for the National Rugby League

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This paper develops new methods for providing instantaneous in-game win probabilities for the National Rugby League. Besides the score differential, betting odds, and real-time features extracted from the match event data are also used as inputs to inform the in-game win probabilities. Rugby matches evolve continuously in time, and the circumstances change over the duration of the match. Therefore, the match data are considered as functional data, and the in-game win probability is a function of the time of the match. We express the in-game win probability using a conditional probability formulation, the components of which are evaluated from the perspective of functional data analysis. Specifically, we model the score differential process and functional feature extracted from the match event data as sums of mean functions and noises. The mean functions are approximated by B-spline basis expansions with functional parameters. Since each match is conditional on a unique kickoff win probability of the home team obtained from the betting odds (i.e., the functional data are not independent and identically distributed), we propose a weighted least squares method to estimate the functional parameters by borrowing the information from matches with similar kickoff win probabilities. The variance and covariance elements are obtained by the maximum likelihood estimation method. The proposed method is applicable to other sports when suitable match event data are available.