Chicago goalie Corey Crawford
It's become almost a 50-50 proposition.
Those two recent winners give the goaltending position even more weight when considering the award.
Voters tend to look first at goaltenders, especially with save percentages on the rise and standout saves burning brightly in their memory.
However, there's no guarantee that a goaltender will once again walk away with the trophy this year.
Here's our ranking of the top candidates for this year's Conn Smythe Award after the first round of the playoffs.
Erik Karlsson is a longshot to win the Conn Smythe Trophy. That's largely because the Ottawa Senators are playing the Pittsburgh Penguins in the second round and it doesn't seem likely that Karlsson's teammates have the firepower to hang with the Pens.
That was also the case when the Senators took on the Montreal Canadiens in the first round, and Ottawa walked away with that series in five games.
If the Senators can pull off the upset, Karlsson will almost certainly play a huge role. He is the best offensive defenseman in the NHL by a wide margin and he gives the Ottawa attack a high degree of danger.
Karlsson, who returned from a partially torn Achilles late in the season, scored one goal and five assists against the Canadiens and was plus-five in the series.
Once he gets his rhythm, he is a nearly unstoppable force.
Antti Niemi has a chance to lead the San Jose Sharks to their first Stanley Cup.
If he does, it wouldn't be the first time that his stellar play brought his team hockey's most honored treasure. Niemi, you will remember, was in goal for the Chicago Blackhawks when they won the Stanley Cup in 2010.
The Blackhawks figured they could get along without their hero/goaltender and let him sign with the San Jose Sharks. He has been stellar this season and his play has continued during the playoffs.
He backstopped the Sharks to a four-game sweep of the Vancouver Canucks. Niemi gave up eight goals in the series and he has a 1.86 goals against average and a .937 save percentage.
The Sharks have a long way to go to become serious Stanley Cup contenders. If they get there, Niemi is sure to author some very significant chapters.
Crosby scored nine points in five games and is tied for third in playoff production. However, he has not looked the way Crosby is supposed to look.
That's probably about to change. When you miss more than a month after getting your jaw shattered by a deflected slap shot, it's hard to come back with all guns blazing.
Crosby started to assert himself in the Pens' sixth and final game against the Islanders. He's not likely to slow down.
If the Penguins meet expectations and roar through the Eastern Conference, Crosby will almost certainly be the NHL's leading postseason scorer.
That will give him an excellent case for earning the Conn Smythe Trophy.
If Crosby is destined to be the NHL's leading playoff scorer this year, why does he rate as only the sixth-leading candidate for the Conn Smythe Trophy?
Because he's got formidable competition on his own team. Evgeni Malkin already has a playoff MVP award on his resume and he looked like he was ready to win a second by the time the Pens' first-round series against the Islanders ended.
Malkin not only scored 11 points in the six games, he was playing excellent defense as well. He blocked a key Islanders shot late in the third period that might have forced the Penguins to play a seventh game.
Malkin can do it all on the offensive end, but he is quite underrated as a defensive performer. He can get in the shooting lanes, bait opponents into poor passes and take the puck away with ease.
He's not quite as flashy as Crosby, but he can be just as effective.
Look at the top of the NHL scoring leaders after the first round of the playoffs and you will find David Krejci of the Boston Bruins.
Krejci is a magician with the puck who has superb instincts. He doesn't often play like a dominant competitor in the regular season, but when the postseason bell rings, he becomes a different player.
The Bruins' center is all skill, finesse and intelligence. He has 13 points and is tied for the league lead with five goals.
On a team noted for its bruising strength, Krejci brings great vision and timing. He sees openings that many other players simply miss and he knows how to exploit them.
If the Bruins build off their first-round, seventh-game miracle against the Toronto Maple Leafs and make a long run in the playoffs, Krejci has a chance to lift the Conn Smythe Trophy after the last playoff game.
He did it last year and he could do it again this year.
It's tough to repeat as Stanley Cup champions, but the Los Angeles Kings showed they are going to be a very tough out this year. Unlike the previous two Stanley Cup winners, the Kings were not bounced out in the first round the way the Chicago Blackhawks were in 2011 and the way the Boston Bruins were in 2012.
Jonathan Quick is a huge reason behind the Kings' success. Perhaps their biggest reason. He is extremely athletic in the net and he combines that characteristic with great anticipation and knowledge of the opponents' strengths and weaknesses.
After getting off to a rough start in the first two games of the playoffs against the St. Louis Blues, he was superb. Quick has a 1.58 GAA and a .944 save percentage as the second-round series with the San Jose Sharks begins.
The Kings believe that Quick can lead them to another championship and they just might be right.
The New York Rangers had the most ordinary of regular seasons. They were thought of as Eastern Conference favorites when the season got underway, but they were unimpressive for long stretches.
They could not score and the only reason they remained in contention for a playoff spot was the stellar play of Henrik Lundqvist in goal.
The Rangers have appeared to find that extra gear that was missing during the regular season. They survived a tough first-round series against the Washington Capitals and they are only getting stronger.
If they win the championship, pencil in Lundqvist's name as the likely Conn Smythe Trophy winner. He shut out the Capitals in the sixth and seventh games and has a 1.65 GAA and a .947 save percentage.
Lundqvist won the Vezina Trophy as the best goalie in the league last year and he is a finalist for the award this year. He is certainly capable of bringing home even more hardware later this spring.
The Chicago Blackhawks are the odds-on favorite to represent the Western Conference in the Stanley Cup Finals.
The Presidents' Trophy winners have a deep and talented team loaded with star power. When they won the Stanley Cup in 2010, Jonathan Toews was named MVP over teammates that included Patrick Kane and Antti Niemi. However, Toews had just two points in the first round against the Minnesota Wild and may not be able to make a run at the award this time around.
If the Blackhawks are going to win their second Stanley Cup in four years, Corey Crawford is going to give them an outstanding performance in goal. So far, he is on his way, leading the NHL with a 1.32 GAA and a .950 save percentage.
Crawford may not have the reputation of a Lundqvist or a Quick, but he is performing better than any goalie in the NHL playoffs and is the leading candidate for the Conn Smythe award.