A bivariate poisson distribution is a multivariate distribution of two variables that each follow marginal distributions that are poisson. However, the advantage of the bivariate distribution is that it allows us to model the positive covariance between the two goal counts. In this paper I fit various different bivariate poisson models in a Bayesian framework using the Stan programming language and analyzed which specification of the covariance term led to the best predictions. I compared these results to the predictions made by pairwise comparison models such as the Davidson model. The Davidson model is an extension of the Bradley-Terry model that can account for draws, which are a large occurrence in professional soccer matches. These models were fit using Maximum Likelihood Estimation. The paper definitively shows the advantages of the bivariate poisson models over the pairwise comparison models in predicting the outcomes of soccer matches, presumably because the poisson models are able to incorporate more information.