I have tried anchoring as well as tried a different way of parameterizing the prior; neither helped the situation. I am still a bit dumbfounded how I can fix the multi-modality situation.
I anchored the first player such that it has to be extremely close to 0:
anchor = pm.Normal('anchor', skill[0], sd=0.001, observed=0)
I have searched with your ‘rating model’. If you search “rating model” the only one popping up is this thread. Separately, model runs all kinds of model comparisons which isn’t the same as a rating model; and on rating it is simply estimating rates. Nothing that actually has to do with comparisons between rates. The only thing I found was:
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Thurstone Comparative rankings and 2D shape-parameters
which has some similarities in topic but approaches it differently that unfortunately isnt applicable to my situation. -
https://docs.pymc.io/notebooks/rugby_analytics.html although very interesting and closely related, they approach the scoring from a total points rather than the difference. In my situation I argue that modelling the total points isn’t very plausible as games have varying length unlike Rugby.
Hence, I am not sure which posts you are referring to.