My feelings on advanced stats is that they are probably being overemphasized as predictors of performance--there are too many intangibles in hockey team success to by able to model performance based on something like possession stats.
But, the question of whether advanced stats do model performance can, ironically, be tested statistically. The question is do we have a statistically significant sample yet to do this (enough years of advanced stats and team performance data to determine if the former predicts the later)?
Please, someone who likes stats, take this on.
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