Hey Ricardo, thanks for your response. We've actually been working on adding track-specific adjustments for the Elo scores, I kind of forgot to include it in the post itself. How to best model the track impact is something I thought about over the summer: the qualifying model currently simply treats each track as independent. However, certain tracks in F1 are similar, and you'd expect a constructor who does well in one to do well in the other (e.g. Spa and Monza). I tried using a version of matrix factorization (algorithm often used in recommender systems) to have performance in similar tracks affect predictions to a track, but this didn't improve the evaluated performance of the model so the idea was scrapped.

The Elo ratings are currently updated using exponential moving averages because it was quick to implement. The Monte Carlo simulation also uses a very simple combination of normal distribution and a constant standard deviation to add randomness to the predicted results (the qualifying model is a bit more complex). I agree that methods like Bayesian inference could give a much more "scientific" idea on the possible distribution a driver's score in a race could fit into, and how much their score should change after each race. However, I'm not 100% convinced on whether Bayesian inference itself would work since the underlying distribution of possible scores in F1 varies (as an example, Ferrari are much weaker this season than in the season before). I believe Bayesian inference assumes the underlying distribution remains the same.