"With a goaltender like Brodeur that can single-handedly stymie opponents and win games by himself, the Sabres know the goals won't come easy." (Game preview from Sabresfans)
It is generally assumed that when a goalie is good, they will steal games for their team. What constitutes "stealing" a game is pretty vague, and can range from being totally outshot yet winning anyway, to simply ending up on the winning team. Without detailed shot quality information, it is difficult to state with certainty that a game was stolen or not, because we don't know exactly how much each goalie was tested in terms of good scoring chances. Shot totals for and against will have to suffice to estimate the relative play of each team.
I do not believe in crediting a goalie with "stealing" a game if the shots are close. If two goalies face shots of similar quantity and quality, the winning goalie has outplayed the losing one, but he did not really "steal" the game. Stealing the game implies that the goalie's contribution overwhelmed all other contributions in the game, and defeated an opponent that would ordinarily be deserving of victory. This implies that the goalie's team must have been decisively outplayed, or the victory is merely claimed or earned, but not stolen.
Goalie's World magazine tracks a stat called "stolen wins". Their definition of a stolen win is a win in which the goalie's team was outshot by 10 shots or more. This is a reasonable definition, since there would have to be a huge gulf in shot quality for a goalie facing 25 shots to have had as difficult a task as one facing 35. Stolen wins alone, however, do not take into account the fact that some teams are outshot with much greater regularity. Getting outshot badly does not mean that a team has no chance to win - teams that are behind tend to take more shots, so teams are often outshot despite having the lead. In fact, stolen wins are relatively common; 47% of the time the team outshot by 10 shots or more ends up winning the game. We would expect, therefore, the top goalies in the league to have a winning record even when outshot by a large margin.
This season, Brodeur's Devils have been outshot by 10+ shots 8 times with him in net, which as a rate is slightly below league average. Of those 8 games, Brodeur won 3 of them, for a .375 winning percentage. Brodeur ranks in the bottom half of goalies, although there are some other big names also under .400 based on this measure, including Kiprusoff and Lundqvist. The best in the league are Cam Ward (4-0), Manny Legace (5-0-1), J.S. Giguere (3-0-1), Robert Esche (4-1-0), Chris Mason (7-2-0), and Fredrik Norrena (5-2-0).
For all goalies the sample sizes are naturally quite small. Tim Thomas has faced the most stolen win opportunities with 17, winning 6 of them. Roberto Luongo is second with 15, of which he won 10. Third is Rick DiPietro (13 chances, 6 wins), and fourth is the aforementioned Kiprusoff (12 chances, 3 wins and 3 OTL), which is somewhat surprising given the defensive reputation of the Calgary Flames.
To make any solid conclusions, we need more information. I looked at this stat for Martin Brodeur for the last three regular seasons, as well as his playoff career. For comparison's sake, I included Roberto Luongo in the regular season sample.
The results were decisive: Martin Brodeur has faced much fewer stolen win opportunities than average, but he has also been much less successful than average in winning them. Over the last four seasons (including this one), his team has been badly outshot 20 times in 282 games started, or less than half the league average. In those games his record was 8-10-2.
Luongo has been outshot by 10+ shots in 68 of 271 starts over the same time period, or one quarter of the time. In 31 games over the last four seasons, and 17 games over this season and last, his team won despite the severe shot advantage. In total, 31 of Luongo's 119 wins (26%) were stolen wins, while just 8 of Brodeur's 163 wins were (5%).
In the playoffs, the difference between Brodeur and his peers is equally pronounced. He has only been badly outshot 9 times in 153 playoff games, less than 6% of the time. Of those 9 games, New Jersey won only 3 of them. That means only 3% of Brodeur's career playoff wins were in games that he stole for his team, based on the definition being applied.
Here are some playoff stats for Brodeur's contemporaries:
P. Roy: 18 stolen wins in 33 chances, 54.5 % success, 12% of total wins
E. Belfour: 10 stolen wins in 28 chances, 35.7 % success, 11% of total wins
C. Joseph: 14 stolen wins in 28 chances, 50.0 % success, 23% of total wins
T. Barrasso: 16 stolen wins in 24 chances, 66.7 % success, 27% of total wins
D. Hasek: 11 stolen wins in 17 chances, 64.7 % success, 21% of total wins
O. Kolzig: 8 stolen wins in 13 chances, 61.5 % success, 40% of total wins
N. Khabibulin: 5 stolen wins in 14 chances, 35.7 % success, 16% of total wins
If one accepts this definition of stolen wins, then Martin Brodeur is very rarely called upon to steal a game, and is not particularly good at doing so, neither in the regular season nor in the playoffs. In the last four seasons, just 5% of his wins were stolen, and in his playoff career a mere 3% can be classified as "stolen". Compared to peers like Roy, Hasek, and Luongo, those numbers are very low.
This evidence indicates that Brodeur is a solid but not spectacular goalie. He has tended to end up on the winning side, both in the regular season and the playoffs, but this is only partly due to his excellent performance, and partly due to New Jersey's ability to consistently outshoot and outchance their opponents. He has had three Cup runs where he has played well, but has not really accomplished anything "singlehandedly," an opinion apparently shared by the voters for the Conn Smythe Trophy. His supposed game-stealing ability is just another example of media myth-making around the person of Martin Brodeur.