The update to our RAPM model for skaters is very small (and somewhat technical), but we'll try and give a brief overview here. https://twitter.com/EvolvingHockey/status/1315879895508148224

The RAPM regressions we run are regularized linear regressions (ridge/L2) - meaning there is "shrinkage" (penalization) applied to the coefficients that pulls skaters with low TOI closer to the mean. This parameter is called lambda and it is determined through cross validation.

When the regressions are run for each season, the lambda value will be slightly different depending on the season. This is what is expected, but we have found that the slight variations in these lambda values can cause a bias, we'll call it, when comparing different seasons.

Because of this, we have chosen to use a "unified lambda" value for all RAPM regressions (respectively). To find these "unified lambda" values, we have simply averaged the lambda values for all full 82-game seasons (12-13 and 19-20 excluded) for each regression.

We feel this potentially allows for a better comparison across seasons. When comparing the new and old methods, none of the regressions ever had a Pearson R of less than 0.99 (other than SHD GA/60 which was 0.986).

So, again, this is very minimal but something we've wanted to update for a while. Our Team RAPM regressions already use a unified lambda because this effect is much larger at the team level (technically, it's an "APM" because lambda = 0 which is just linear regression)...

We will be making the same update to our xGAR sub-models as the lambda values for all regressions used in that model are not unified. This will likely result in a larger change, but we will have to test it out before we can be sure.

We will also be exploring an "inflation factor" to see if we can get the xGAR sub-models to more accurately match the magnitudes of the GAR sub-models. More to come in the future!