The talk is already starting, even though he's only 25 years old, as he struggles through a difficult, goalless first round.
"Steve Stamkos. Great player. Amazing talent. But he needs a Cup."
This is the Tampa Bay Lightning captain's seventh NHL season, and so far he has averaged only four playoff games a year. That could jump if the Lightning get past the Detroit Red Wings in Wednesday's Game 7, but for the most part his young career has seen few playoff games, with a trip to the conference finals four years ago serving as the peak.
That's not exactly his fault. He was drafted first overall to Tampa Bay because it was an organization in the basement. That happens to many young stars – the worst teams get the bulk of the best picks. Stamkos has actually been lucky, as general manager Steve Yzerman has returned the Lightning to respectability in short order, building a championship-calibre team around his star while he's still young. That doesn't always happen. And with parity as pronounced as it is in the NHL, there are 10 to 14 other teams considered contenders every year.
Those are tough odds.
Winning a Stanley Cup is considered the pinnacle achievement – with good reason – but a lot of very good players never do. Marcel Dionne, Peter Stastny, Dale Hawerchuk, Adam Oates and Mike Gartner are names everyone knows, but this generation of players has many more future Hall of Famers who will never win it all.
Of the 50 highest-scoring NHL players in the past 15 years, only half have won a championship. Joe Thornton hasn't. Jarome Iginla hasn't – and his teams have made the playoffs in just eight of his 18 seasons. Daniel Alfredsson never did – and now he's retired. Add in Henrik and Daniel Sedin and Patrick Marleau and that's a talented group that's likely headed to the Hall without a ring.
Rather than rip them – and those who may ultimately join them, such as Alex Ovechkin – for being poor playoff performers, this should probably be regarded as the reality of the situation.
In 2000, the NHL expanded to 30 teams, meaning only 53 per cent of players would make the postseason and just 3 per cent would win the title each year.
Then, in 2005, the league brought in a salary cap that saw many star players signing long-term deals with the clubs that drafted them.
Even with the death of the dynasty, those two factors alone will conspire to keep many great players Cup-less.
If you were an NHL player born in 1930, you would have played in the final days of the Original Six and your chances of winning a Stanley Cup were better than 25 per cent. With six teams and smaller rosters, there were only about 150 players vying to win it.
This season, there were 974 players in the NHL, and fewer than 350 made the playoffs.
In this NHL, less than 10 per cent of those players will win a Cup. That percentage is higher for stars – especially those like Marian Hossa, who are willing to move around from contender to contender – but a huge share of the very best players simply won't win.
"When you're young, you don't really think about how tough it is," Jaromir Jagr said in 2013 when he made the finals for the first time in more than two decades, with Boston, a lifetime after winning the Cup as a big-haired 20-year-old in Pittsburgh. "Obviously you have to be on a good team, but you can be on a great team and it is no guarantee you're going to get into the final. You've got to be injury-free and your top players have to play the best hockey in those two months."
Sometimes even that's not enough.
Stamkos has a long career in front of him and is already on a very good and very young team, so his odds are good. But for someone like Ovechkin, who turns 30 in the fall, this could be his last chance to win, as the Capitals attempt to make the third round for the first time in his 10 seasons in Washington.
At best, they have about a 12-per-cent shot – one in eight – at winning it all. If it goes the other way, Ovechkin will surely get his share of blame for the drought, even though he's one of only eight NHLers to play 50 playoff games in the past 20 years and post better than a point a game.
It doesn't make a lot of sense, not when you consider how hard it is to win and how many won't.
Because not everyone can.