oscars-bradley-terry-teams-multiyear.stan

/**
 * Bradley-Terry model for teams, where each team is made up of
 * players, and the ability of a team is the sum of the abilities of
 * its players.
 */
data {
  int<lower = 0> K;                          // players
  int<lower = 0> J;                          // players per team
  int<lower = 0> N;                          // matches per year
  int<lower = 0> Y;                          // years
  int<lower = 1, upper = K> team0[Y, N, J];  // team 0 players
  int<lower = 1, upper = K> team1[Y, N, J];  // team 1 players
  int<lower = 0, upper = 1> y[Y, N];         // winner
}
parameters {
  vector[K] alpha_std;
  real<lower = 0> sigma;
}
transformed parameters {
  vector[K] alpha = sigma * alpha_std;    // alpha ~ normal(0, sigma)
}
model {
  sigma ~ lognormal(0, 0.5);                // zero avoiding, weakly informative
  alpha_std ~ normal(0, 1);                 // hierarchical, zero centered
  for (year in 1:Y)                         // additive Bradley-Terry model
    for (n in 1:N)
      y[year, n] ~ bernoulli_logit(sum(alpha[team1[year, n]]) - sum(alpha[team0[year, n]]));
}
generated quantities {
  int<lower=1, upper=K> ranking[K];       // rank of player ability
  {
    int ranked_index[K] = sort_indices_desc(alpha);
    for (k in 1:K)
      ranking[ranked_index[k]] = k;
  }
}