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Conventional adjusted plus-minus does a poor job of predicting the outcome of future games, particularly when you have less than a season of data. Adding regularization greatly improves accuracy, and some player ratings change dramatically.
The enhancement with the RAPM is a Bayesian technique in which the data is combined with theoretical beliefs regarding reasonable, large data ranges for the parameters in order to produce more accurate models. That is what ridge regression does.
RAPM is about twice as accurate as an APM using standard regression and using 3 years of data, where the weighting of past years of data and the reference player minutes cutoff has also been carefully optimized.