And secondly, nobody is saying that possession stats perfectly correlate with success. There will always be teams that are good at possession who don't qualify for the playoffs, as happened to the Devils this year and last, and teams that get into the playoffs despite being poor possession teams. Possession isn't everything.

Thanks for the comment. Your comments about the importance of goaltending and shooting are well taken, but they are important for answering a different question than the one I was looking at. Possession metrics within a series as well as PDO help explain why teams win series from a retrospective viewpoint. That is, it helps us understand the relative importance of these things in determining the winner of a series. The question I was more interested in was more predictive in nature. That is, before the series starts, which team should we view as the favourite and which is the underdog? And by how much? As it turns out, teams with fewer points in the standings may be more likely to win a series than the team ahead of them - if they were a better possession team. This is not at all obvious, as there already is a strong correlation between a team's possession stats and its regular season points. But it turns out that, even after a full season of play, possession stats matter above and beyond how they affect a team's points. One possible (and in my opinion, likely) explanation for this is what you've pointed out - teams play differently in the playoffs, and possession matters even more then.

Take a look at the head to head playoff C% and you'll see that quite a few series were won by the teams with the better PDO (goaltending and shooting %) rather than the ones with the better C%.

Teams play different in the playoffs - you can't ignore that in your analysis.