Heavy tails and negative correlation in a binomial model for sports matches: applications to curling

A binomial model for sports matches is developed making use of the maximum possible score $n$ in a game. In contrast to previous approaches the scores of the two teams are negatively correlated, abstracting from a scenario whereby teams cancel each other out. When $n$ is known, analytical results are possible via a Gaussian approximation. Model calibration is obtained via generalized linear modelling, enabling elementary econometric and strategic analysis to be performed. Inter alia this includes quantifying the Last Stone First End effect, analogous to the home-field advantage found in conventional sports. When $n$ is unknown the model behaviour is richer and leads to heavy-tailed non-Gaussian behaviour. We present an approximate analysis of this case based on the Variance Gamma distribution.