The St. Louis Blues goalie, who lived out a childhood dream by hoisting the Cup in June, has spent three straight offseasons at BioSteel Camp competing with and against forwards like Seguin of the Dallas Stars and McDavid of the Edmonton Oilers.
He wasn't an NHL player during the first two; instead he was a feisty competitor working his way through the minor leagues and struggling to show the naysayers that he would be in the NHL one day. All the while, McDavid and Seguin could see the roots of a goalie who was on the path of doing just that.
"I'm not (surprised)," McDavid said this week when asked about Binnington's success. "I think all he needed was an opportunity.
"I've been able to play against him a couple of times here, and each and every year you've seen him progress. Now he's a Stanley Cup champ."
Video: Jordan Binnington checks in at No. 8 on the list
For Seguin, the bond with Binnington is somewhat ironic, to say the least.
The four-day BioSteel Camp, run by longtime sports and fitness trainer Matt Nichol, culminates with a four-team tournament. The teams are drafted by their captains. Seguin, who is pretty much a captain every year, used his No. 1 pick to select Binnington three consecutive times.
How did Binnington repay that trust? By helping the Blues defeat Seguin and the Stars 2-1 in the second overtime in Game 7 of the Western Conference Second Round on May 7.
"Ya, how about that?" Seguin told NHL.com on Tuesday. "I wish I knew more spots I could remember to shoot on him during that game."
Seguin won't make that mistake again.
"I've been studying him a little bit more at this year's camp," Seguin said, breaking into a wry grin. "Don't tell him I told you that.
"Seriously, he's a great goalie. He's just a guy that competes hard. He's got a great head on his shoulders. He's a good person. He doesn't fit the general shoes of being a weird person like most goalies are. But he's a heck of a goalie and he will be for many years.
"I've actually been shooting on him for, I don't know, four or five years now, and doing private skates. I've always seen something in him. I think that a lot of us shooting on him have. That's why I always picked him first."
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A year ago, Binnington left BioSteel Camp and went to Blues training camp, where he was listed as the No. 4 goalie on the depth chart.
Cue his Cinderella story.
Binnington made his first NHL start Jan. 7. By the time the regular season ended, he was 24-5-1 with a 1.89 goals-against average, a .927 save percentage and five shutouts, and would be named a finalist for the Calder Trophy as NHL rookie of the year.
The best was yet to come.
Binnington set a rookie record for wins by a goalie in a single Stanley Cup Playoffs, going 16-10 with a 2.46 GAA, a .914 save percentage and one shutout in 26 games to help the Blues win the Cup for the first time in their 51-season history. The championship earned him a parade, where he was presented a key to the city in his hometown of Richmond Hill, just north of Toronto.
The sudden fame did not cause him to forget those who had previously supported him.
"Segs, he was one of the guys who first believed in me, taking me first overall a couple of times in this camp," Binnington told NHL.com on Tuesday. "We have back-to-back titles in this camp, so we're trying to defend it in a way.
"Segs, Connor, there are some elite players in this camp. That's why it's so special. You want to surround yourself with good athletes and strong people, and that's what it's all about.
"This is a special camp. The tempo is great and it's just a bunch of athletes competing and putting the whole summer into their game. It's a lot of work, a lot of fun, and we'll finish it with a lot of fun Thursday and then go our separate ways. It's a special week for all of us."
Video: Top 10 saves of 2018-19: Binnington
It's also the stage where Binnington proved he belonged in the NHL, goalie development coach Andy Chiodo said. Chiodo began working with Binnington at BioSteel Camp three years ago and was impressed by his work ethic.
"On the ice, off the ice, in the gym, technically, emotionally, personally, when you are in an environment where you're doing that and the people around you start seeing that and responding with comments like 'You look great' and 'You should be in the NHL', naturally that's going to give you confidence," Chiodo said. "Binner has done a great job earning those things."
Not to mention a Stanley Cup ring.
"All the power to him," McDavid said.