Abstract
Statistical modelling of sports data is indispensable to analyse the sports behaviour and apprehend significant inferences that are helpful to adopt decisive strategies before or during the sports events. This paper introduces a stochastic model as the distribution of difference derived from the Bivariate Affine-Linear Exponential distribution. The distribution of difference is first ever used to model the margin of victory that provides an adequate fitting on the observed data. A simulation study is carried out to observe the stability of the model parameters through their average estimated values, biases, standard errors, root mean square errors and confidence intervals. The performance of the proposed model is examined by applying it on the real data of the National Football League and comparing the results with those of the existing models. Finally, the quantile function of the proposed distribution is used to assess the possible range of point spreads for winning the bet in a particular game.