Interestingly, since the original post of this thread almost a year ago, Bergevin seems to have made a 180-degree turn on analytics, or rather on the attributes and processes favored by analytics) -- he ditched the guys he acquired last offseason, made moves like swapping Gorges for a cheaper-and-better Gilbert. He's set up his D so that the top-4 is now all skill, he's arranging for an all-skill fourth-line, and he's been working on eliminating the remaining dead weight.
His team still has some serious systemic issues, but he's definitely headed in a better direction roster-wise, and his cap management moves have been pretty amazing. Heck, the team's possession is still mediocre, but it still improved by over three percentage points purely on the strength of the roster changes, and that's rather a lot.
His 2013 offseason was a complete disaster, but to his credit none of those mistakes were long-term and I think he learned quite a few lessons from that. I think we're still at least one year away from the crucial changes that will give the Habs a shot at being a genuine contender though.