Crow wrote: ↑Wed Oct 10, 2018 1:29 am

Could you walk thru one player estimate step by step? I don't understand how the Bayesian RAPM table and your words sync up. What exactly is the 3rd column and how is calculated? Same for 5th and final columns. The table itself is not sufficient to do the calculation of the final column by simple mathematical operators is it?

You have 10 players on the court. Team A outscores Team B by +20 per 100 possessions played (the stint was much shorter than 100 possessions, of course).

However, Team A had their starters in and Team B was playing scrubs. Each player has their own Bayesian Prior based on how many MPG they are playing that season and how good the team as a whole is. Suppose Team A has an average Bayesian Prior of +1 for each player. Conversely, Team B has an average Bayesian Prior of -1 for those 5 players.

In the pre-processing step, the observed production is adjusted by subtracting out the priors. The adjusted observation would be +20 -(+5) + (-5) = +10.

Then, the full RAPM would be run on the season or group of seasons as a whole, using these adjusted observations.

The RAPM results for each player are then added to the average prior for that player over the duration of the RAPM--this is the post-processing step.

For example: in the 20 year RAPM, Kobe Bryant had a wide range of Bayesian Priors, with an average prior over the duration of +3.5 (as seen above). Each observation was adjusted based on the specific Bayesian Prior for the given season. The RAPM was then run on the adjusted observations, yielding a rating for Kobe of -0.1. Then, his average prior was added back in (the +3.5). Thus his total Bayesian RAPM was +3.4.

For most players that have a very large number of observations, like Kobe, the addition of the Bayesian Prior only has a minor impact. For players with fewer minutes, it can be very significant. It also makes a significant difference if there is a lot of collinearity with a few players and RAPM has trouble disentangling them. (Jimmy Butler, for instance, jumped from +1.2 to +3.7 with the addition of his the prior.)