Depending on exactly what you mean by “the posterior distribution of residuals”, you may be able to get away with just grabbing samples from posterior. The posterior predictive sampling you are doing just plugs in each player’s ~ mu_a and sigma_a into a normal distribution and takes N draws (where N is the number of observations for that player). If this is what you need, then great. But if you just want that normal distribution each player, you can just iterate over players, grab their mean/SD, use them to parameterize a normal distribution and stop.
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