new version of bpl, implemented in numpyro
The statistical model behind bpl is a slight variation on the Dixon & Coles approach.
The likelihood is:
where y_h and y_a are the number of goals scored by the home team and the away team, respectively. a_i is the attacking aptitude of team i and b_i is the defending aptitude of team j. gamma_i represents the home advantage for team i, and tau is a correlation term that was introduced by Dixon and Coles to produce more realistic scorelines in low-scoring matches. The model uses the following bivariate, hierarchical prior for a and b
X_i are a set of (optional) team-level covariates (these could be, for example, the attack and defence ratings of team i on Fifa). beta are coefficient vectors, and mu_b is an offset for the defence parameter. rho encodes the correlation between a and b, since teams that are strong at attacking also tend to be strong at defending as well. The home advantage has a log-normal prior
Finally, the hyper-priors are