Some of the most interesting new statistics introduced by stats guys in the blogosphere have been numbers that track how many defensive and offensive zone faceoffs players are put on the ice for. For skaters, this helps adjust for the way they are being used by their coach, since for example it is an advantage for an offensive player to start their shift in the other team's end rather than having to move the puck 180 feet down the ice to get it into a scoring position. Faceoff numbers can also be used to measure which players are driving possession, by seeing whether a player ends their shift more often in the offensive or defensive zone.
I haven't seen anyone apply these numbers yet to goalies. Since goalies don't change lines, the starting and ending shift numbers are of course meaningless. However, on many shots goalies have the opportunity to either freeze or play the puck, and that choice affects the number of defensive zone draws their teams face. Also, if certain goalies are able to contribute to their teams in other ways, such as for example through their puckhandling skills, then it might show up by their team taking more draws at the other end of the rink.
Vic Ferrari at timeonice has the faceoff zone start numbers for every player in the league last year, including goalies. I'll stick to the convention used by Gabe Desjardins at Behind the Net where he has the offensive faceoff percentage for all players, a number calculated by ignoring the neutral zone faceoffs and dividing the number of offensive zone faceoffs by the total number of draws in offensive and defensive zone combined.
The correlation between the offensive faceoff percentage for starters and their backups was 0.51, which suggests that the rest of the team has a big impact on puck possession and faceoffs. That should be fairly uncontroversial. I'd expect with a bigger sample size for most of the backup goalies that number would be higher.
The correlation between offensive faceoff percentage and shots faced per 60 minutes was -0.57. I was expecting that relationship to be stronger, since all the Corsi evidence shows a big advantage to starting in the other team's zone, but again EV only for one season is a fairly small sample so there is likely a reasonable degree of luck in the numbers.
There were 9 teams that had a offensive faceoff percentage difference of 5% or more between their starting goalie and his backups. Here are the faceoff numbers for each of those teams, along with the offensive faceoff percentages and shots faced per 60 minutes:
Ryan Miller: 480 def, 433 off, 47%, 30.9 SA/60
Backups: 254 def, 282 off, 53%, 31.2 SA/60
Dwayne Roloson: 553 def, 513 off, 48%, 32.6 SA/60
Backups: 210 def, 240 off, 53%, 31.4 SA/60
Carey Price: 423 def, 409 off, 49%, 29.9 SA/60
Jaroslav Halak: 383 def, 269 off, 41%, 33.5 SA/60
Martin Brodeur: 194 def, 268 off, 58%, 28.8 SA/60
Scott Clemmensen: 434 def, 353 off, 45%, 29.0 SA/60
Kevin Weekes: 154 def, 136 off, 47%, 30.1 SA/60
New York Rangers:
Henrik Lundqvist: 459 def, 665 off, 59%, 29.0 SA/60
Steve Valiquette: 90 def, 102 off, 53%, 30.7 SA/60
Alex Auld: 322 def, 373 off, 54%, 28.0 SA/60
Backups: 390 def, 332 off, 46%, 28.3 SA/60
Martin Biron: 584 def, 484 off, 45%, 32.4 SA/60
Antero Niittymaki: 226 def, 230 off, 50%, 31.5 SA/60
Evgeni Nabokov: 510 def, 521 off, 51%, 27.1 SA/60
Brian Boucher: 150 def, 202 off, 57%, 26.2 SA/60
Vesa Toskala: 342 def, 366 off, 52%, 29.8 SA/60
Backups: 278 def, 370 off, 57%, 30.0 SA/60
The Price/Halak gap is interesting and appears to account for some of the shot differential between them, but I'm not sure how much it had to do with the goalies. I'd bet the split would be in the other direction if we were looking at this season's numbers, based on how Montreal has played in front of each of them in 2009-10. Most of the others either involve backups who didn't play very much or goalies who I wouldn't expect to have much of an effect on faceoffs, although there is one notable exception.
The biggest gap between any starter and backup, by far, is in New Jersey. Knowing what we know about those goalies, I'd say that these numbers suggest a real effect. In most starter/backup scenarios, we have to at least consider the possibility of strength of schedule being a factor, but that wasn't the case here as Clemmensen was an injury replacement for Brodeur. The Devils weren't performing exactly the same all the way through the season, but all three of their goalies had similar GAAs so it is likely that they played in fairly similar environments.
The numbers indicate that Brodeur is either helping shift the play to the other end of the ice or freezing the puck less often than the other goalies. Here are the faceoff numbers for New Jersey's goalies broken down per 60 minutes of EV play:
Brodeur: 8.6 def zone, 11.9 off zone
Clemmensen: 14.2 def zone, 11.6 off zone
Weekes: 15.4 def zone, 13.6 off zone
Brodeur keeps the puck moving a lot more than the other two (and indeed, he probably keeps it moving more than any other goalie in the league). However, the team did not take substantially more faceoffs at the other end of the rink, which makes it uncertain whether Brodeur's impact translates to the offensive side of the rink (although I would certainly like to see more data on this one).
Consistently giving the puck to teammates instead of allowing the opposing team to win control of it through a faceoff should help a team, and this may account for some of the observed shot differentials between Brodeur and his backup goalies. There are other possible benefits, such as creating more changes on the fly, which could be to the benefit of a smart bench coach who wants to get his matchups. I'd expect some tradeoff in terms of increased turnovers, but Brodeur is likely pretty efficient.
I think these results also shed a bit more light on the rebound numbers discussed earlier here that showed Clemmensen allowing a lower rate of rebound shots against than Brodeur. Given that Brodeur would have been playing the puck much more often and attempting to direct his rebounds rather than simply freezing the puck, that means he would have been facing many more opportunities to turn over the puck or for the other team to steal it and get a quick shot on goal. If Brodeur was aggressive in terms of directing rebounds and playing the puck while Clemmensen was conservative (and probably helped by a defence that gave extra attention to clearing the crease), then that would explain why Brodeur's numbers don't seem as good despite his superior skill. More opportunities usually mean more errors, no matter how good you are.
This is just a cursory look from one year's worth of data, but looking at a few more seasons' worth of data could help us better identify Brodeur's effect here and see whether any other goalies seem to have a tendency towards freezing or moving the puck.