bpl-next 0.4.0

Bayesian models for football match prediction, based on Dixon and Coles (1997).

bpl-next

new version of bpl, implemented in numpyro

Statistical model

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