Advanced statistics have value, but are often crude approximations, for example, just like football, you can't determine the responsibility for an interception without knowing the play, in hockey, how a player fares is both a product of the players around him and his responsibilities.
Teams have better information than outsiders, so can make better use of statistics, because they know the context in which those statistics were created.
One important factor to keep in mind, when a stat is highly variable from year to year with the same player in the same situation, that suggests it may not be measuring anything, that's it's primarily random in nature - the "eyeball test" is just not a check on statistical evaluation of players, it's a check on the statistics themselves.
Unfortunately, too many people think correlation = causation, and ignore "left out variable error," i.e., the equation is underspecified and other factors have resulted in either a spurious correlation or what you're measuring is really the impact of another factor that you haven't identified.
My simple rule is that correlations (or statistics proporting to measure performance) are insufficient, you have to show causality, not just through statistical tests but through a credible "story" that explains the mechanism (or the statistic). Example, do better CORSI numbers mean better play or does certain types of play inflate those numbers?
However, refusing to use statistics is sheer ignorance, more information is better than less information, and a smart executive uses whatever credible information she can obtain to make better decisions.
