Regarding the faceoffs discussion in the previous thread from last week - I'm not sure if there's been any more recent studies, but this one from 2012 does a great job of putting their importance into perspective:
http://statsportsconsulting.com/main/wp-content/uploads/FaceoffAnalysis12-12.pdf
It found that on average a player needs to win 76.5 more faceoffs than they lose in order for their team to gain a goal.
So for example, taking Vermette's 2015/6 season - he took 1351 faceoffs, winning 55.8% of them. If RNH replaced him for every faceoff and won them at his 43.2% career rate, he'd win 170 less. Which on average equates to a 4 goal swing for the team over the course of the season. You'd expect the differences in other areas of their games to account for far more goals.
The study supports exactly what you'd think - that winning faceoffs in the offensive/defensive zone during the PP/PK has a more significant effect. On average, a player needs to win 35 more faceoffs than they lose in the offensive zone on the power play, in order to gain a goal. That's balanced out by needing to win 163 more at even strength in the neutral zone.
So it's as you think - you'd rather win more faceoffs than you lose, but it's not a significant enough ability to take precedence over all the other skills between puck drops that make players effective. I've felt that you'd want 1 great offensive and 1 defensive player (can be the same guy) for special teams and the end of periods - where a faceoff win can be the difference between getting a shot off or not. But even then, PP/PK effectiveness depends more on puck movement and zone entry abilities than that first faceoff win. Intuitively you'd just want the chance to immediately to set up in the offensive zone as often as you can.
I think at even strength what PhoPhan wrote most applies - losing a faceoff in the offensive zone can be more advantageous, as it allows you to pressurise the defence into a costly turnover when they don't have the luxury of just launching the puck long when icing's called.
We sit 22nd this year in team FOW%. The teams below us: Winnipeg, Tampa, San Jose, NYI, Florida, Chicago, Pittsburgh, Edmonton.