The biggest problem with using relative corsi (measuring how much a team's possession rates improve when player x is on the ice) is that it favors the best players on bad teams. It's much easier to look good compared to a bad team like Calgary or Edmonton than it is a great team like LA or Boston. Hence guys like Gio, Brodie, Marincin, etc are near the top.
At the same time, pure corsi (a team's possession rate when player x is on the ice) favors players on good teams. It's much easier to maintain possession when playing with other great players than mediocre players. This is where Gio and Brodie separate from Marincin, who may have be the Oilers' best possession-wise, but was still below the break-even point.
The problem with throwing out random bits of advanced statistics is that there is no context. Aarongavey's list, for example, had a bunch of guys who played less than half the season. Small sample sizes can produce strange results. It's also very important to look at the context. Sure, Erik Karlsson dominates possession every time he is out there, but he starts in the offensive zone much more than the defensive zone. Shea Weber's possession numbers look awful until you consider he was playing against the best players consistently from his own zone.
The problem with advance stats in general (or at least the way many people use them currently) is that most people seem to think possession rates are the be-all-end-all, or mean absolutely nothing. I like to think of these numbers just as part of a certain player's or a certain team's game. For a team, maybe equate the importance of possession numbers to the importance of special teams. Having a bad powerplay doesn't mean you won't have a good team, but it's certainly a factor. The extreme opinions on advanced statistics really tend to take away from the information we can actually gain from them.
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