It's funny that you mention Hollinger, especially in a thread that has championed the Dallas Mavericks as a "moneyball team". Hollinger hated the Mavs, especially in that championship season, and his power rankings always ranked them lower than their place in the standings. Cuban uses all sorts of approaches, but let's not act like they were basketball's Oakland Athletics. They stressed defense, hardly an advanced concept.
Also, regarding the Red Sox, they didn't exactly win because of Sabremetrics either. They won largely because of their payroll, as others have said. Yes, they did integrate Sabremetrics and it largely helped, but the biggest reasons were their high profile stars. Now, people like to mention Ortiz, as Bill James was the guy who wanted him. Don't get me wrong, I can easily see why James liked him at the time, but if the Sox got the Ortiz Bill James thought they were getting, they wouldn't have won jack.
I do like looking at advanced stats, it helps a little, but they really won't play a huge factor in hockey. Scouting can tell you many things you'd learn from them, so while it's nice for us fans, I don't think it plays a huge part for teams. The biggest thing I take from them is the ability to see if someone's normal stats are inflated, due to things like quality of competition or zone starts. But if you're watching that player every game, you probably see that already.
Not to say they should be ignored, but I'm really not a fan of CORSI, which consists of very little context, and that seems to be the main advanced stat in hockey. Also doesn't help when you have a guy like Jay Feaster, who seems to be a pretty big fan of advanced stats, is also terrible at building a team and was very close to making one of the worst moves in NHL history yesterday. Overall, there really isn't much of an example of advanced stats working out much in the NHL, so I can definitely see why some are hard to get behind them.