There has been an ongoing debate at this blog over how much goalies can influence the number of shots they face in the course of a hockey game. To clarify my position, I always thought it was reasonable that someone like Martin Brodeur would face fewer shots than an overmatched ECHL-level goalie with no puckhandling skills, terrible rebound control and poor positioning who just stood deep in his net quaking and looking small and leaving his teammates to take care of the defensive zone. But even in that best-possible vs. worst-possible scenario, I'd estimate a maximum difference of a few shots per game. From anywhere near the net, NHLers will likely decide to shoot no matter who is in net, and from a long distance they probably will elect to pass or stickhandle even with a weaker goalie between the pipes. Missed shots don't seem to have much of an effect, and rebound shots make up only a couple of shots against per game on average, so those things are unlikely to have a huge contribution to shots against. A top goalie might be able to intercept a pass or two that could lead to a shot, might be able to help his team exit the zone a few times with his stickhandling to avoid subsequent scoring chances against, might be able to hold onto an extra puck or two rather than allow a dangerous rebound chance, and might dissuade a few opposing shooters from shooting from moderate-level scoring positions, at least compared to our replacement level example.
When looking at NHL goalies only, however, it seems to me unlikely that anyone with very poorly developed "soft skills" would make it all the way to the best league in the world. Any differences between them would likely be substantially smaller than compared to the Brodeur/ECHL goalie example.
Can we test this hypothesis? I have repeatedly used comparisons to backup goalies on this blog, and that seems like a good tactic to address the shot prevention issue. Most of Martin Brodeur's backups were with the team only briefly and did not play many games in New Jersey, but there are a couple of backup goalies, Mike Dunham and Chris Terreri, that played a fair number of minutes with Brodeur and should provide an approximate context. I will also use results for Dunham and Terreri outside of New Jersey to estimate their own shot prevention skills for comparison.
First off, Mike Dunham. Dunham broke in with the Devils, and in two seasons in New Jersey faced 26.5 SA/60, compared to Brodeur's 24.1. Looks like Brodeur was doing well, until we realize that Dunham apparently always gives up a lot of shots. In his next six seasons, Dunham went +1.8, +1.9, +2.6, -0.9, +2.4, +1.3 compared to his backups. So he looks to be a guy who faces about 1.5 shots per game more than average. Brodeur beat him by 2.5, so that gives us an estimate of Brodeur being about a shot per game better than average.
Chris Terreri has a few years as a starter before Brodeur broke in. During those years, he was +1.3 and -0.8 playing with Sean Burke, and +0.4 and +0.1 playing with Craig Billington. Both Burke and Billington were very similar to their teammates in terms of shots against, with an average of about a half-shot per game difference between them and their teammates over their careers. Since Terreri was virtually equal with them, it implies that Terreri was about average in terms of shots against.
With Brodeur, Terreri went +1.0 in 1993-94 while sharing time, and +0.4 in 1994-95 in a backup role which may have had some effect on reducing his shots. That supports the estimate from Dunham's stats of Brodeur having a potential effect of something near a shot per game.
Interestingly, as his career went on Terreri seemed to get better at shot prevention. In 1995-96, 1996-97 and 1997-98, he played on a few bad teams and significantly outperformed his teammates in shots against (-2.8, -1.7, -1.2). When we went back to New Jersey for the 1999-2001 seasons, he was basically Brodeur's equal (24.9 SA/60 for Terreri over those 3 seasons, 24.7 SA/60 for Brodeur). Terreri may have again benefitted from weak opponents, but if he was outperforming by 1 - 1.5 shots per game in other places and then was equal with Brodeur in New Jersey, that is more evidence for a "Brodeur effect" of about a shot per game compared to the average guy.
In conclusion, there appears to be some evidence that Brodeur may prevent about a shot per game compared to average, based on comparing the results of the two backup goalies with the most games played, although the sample sizes are pretty small. Since many observers would consider Brodeur to be the best in the league at the skills that may contribute to preventing shots, I'd guess if we isolate his effect that could be considered pretty close to the maximum possible positive effect. From looking at the results of Dunham and others like him, it might be possible that the gap could be a little bigger on the other end (i.e. some goalies are substantially below average), but I think in general it is probably reasonable that goalie shots against results may vary within the range of about +/- 1 shot per game on average.
If this is the case, it raises a number of subsequent questions, such as: Are the shots being prevented/created more or less dangerous than average? Do goalies who are good at preventing shots tend to have higher save percentages? Can we isolate the specific skill that most contributes to this shot gap? Does shooter choice come into the picture at all, e.g. do shooters choose to shoot more or less often against certain goalies? Does the shot differential result primarily from even-strength play or on special teams? Is shot prevention consistent year to year? Can goalies substantially improve the number of shots they face per game? More research is certainly required in this area.