Prior, of course, was doing it on purpose.
"I'm honored to have the opportunity to coach him," said Prior, the Golden Knights goaltending coach. "But I'm different in that I don't care what he thinks.
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"As a coach, I believe you need to have the answers. It's wrong to expect the athlete to have the answers. They don't have your experience. So I made that clear to him that you have to trust my judgment on things."
Under Prior's tutelage, Fleury, a three-time Cup winner with the Pittsburgh Penguins, is playing some of the best hockey of his career: He is 13-4 in the Stanley Cup Playoffs with a 1.88 goals-against average, .939 save percentage and four shutouts entering Game 3 of the Stanley Cup Final at the Washington Capitals on Saturday (8 p.m. ET; NBCSN, CBC, SN, TVAS). The series is tied 1-1, and the goalie is a big reason Vegas is three wins from a championship in its inaugural season.
Prior, 61, helped an elite athlete become an even better goaltender.
Video: WSH@VGK, Gm2: Fleury makes acrobatic save on Oshie
"He likes to think stuff over," said Fleury, 33. "He has his own point of view on things, [is] a great guy and fun to be around. It was an easy transition for me to come here and have with me, help me on the ice and off the ice."
Prior's influence is evident not just in Fleury's play, but everywhere you look in the Cup Final. He was the Capitals goaltending coach for 16 seasons until August 2013, the key figure in the development of Washington's current goalies, starter Braden Holtby and backup Philipp Grubauer.
"He's obviously one of the best," Holtby said. "He helped me a ton. He taught me how to practice correctly, how to really analyze my game honestly and grow in different ways."
For Prior and Fleury, the path to the Final had plenty of twists and turns. Fleury sustained a concussion Oct. 13 against the Detroit Red Wings and missed almost two months, returning to the lineup Dec. 12 against the Carolina Hurricanes. He went 29-13-4 with a 2.24 GAA and .927 save percentage in 46 games (all starts). The GAA and save percentage were NHL career highs for Fleury, in his 14th season in the League.
Prior had a heart attack Jan. 4 in St. Louis and was rushed to the hospital, Sports Illustrated reported Thursday. The report said that two of his arteries were 99 percent blocked. Prior returned Jan. 7, watching a game from the press box at T-Mobile Arena, and was back on the ice a few days later.
In addition to Fleury, backup Malcolm Subban and third-string goalie Oscar Dansk were injured in October (both lower body). The injuries resulted in the Golden Knights using five goalies this season, all by Nov. 14 (Maxime Lagace and Dylan Ferguson were the others).
Subban played 22 games this season, Lagace 16, Dansk four and Ferguson one. The previous combined NHL experience of those four players consisted of two games, both by Subban when he was with the Boston Bruins.
It mattered little; the four combined to go 22-11-3 with a 3.10 GAA and .896 save percentage, and Vegas won the Pacific Division.
"I don't want to sound too cocky, but I believed in these guys," Prior said. "I had a hand in us identifying them and offering them the opportunity. I would say people around me were more nervous about the situation. I asked (Vegas general manager) George (McPhee) if he'd let me try with these guys because we weren't, at that point, bound for the playoffs. We didn't know it was going to be in our future.
Video: WSH@VGK, Gm2: Fleury seals post to stop wraparound
"Once we got into it, it was apparent to me they were holding their own. They were all good young prospects and they kept us afloat."
The Vegas goalies would prefer not to get specific about Prior's magic touch.
"We keep it in the goalie circle exactly what he does," Lagace said, smiling.
He did speak in general terms about Prior's methods.
"He's got a different approach but it does help your game, makes you more aggressive and improves your confidence," Lagace said. "It's different the way he teaches it. He's a very honest coach. If there's something wrong he's going to tell [you]. But the same point, if you do something right he's going to tell you. He works you hard."
Prior said he wanted them to experience failure in practice.
"I set all of our goalies up in drills that they fail in," he said. "That's frustrating for a goalie getting scored on. Marc and I've had this conversation because he's not used to getting scored on. I make him play the situation honest, not cheat to get some kind of advantage.
"I said if we don't train in an area where you're going to fail, we're not making you better. It makes no sense for me to put you in a situation, in a drill where you're just going to stop the puck. So those were the things initially that rubbed him the wrong way."
Lagace said he loves working with Prior and that those methods helped him prepare better for games. Not that it was easy for the 25-year-old.
"If it's a bad day and you're on the edge and you keep getting scored on because it's a hard situation, it gets on you," said Lagace, the backup for the past five games (Subban has an undisclosed injury). "If you just succeed in practice, you get lazy and the way he approaches things he makes you work hard in pretty much impossible situations sometimes."
Holtby, selected by the Capitals in the fourth round (No. 93) of the 2008 NHL Draft, won the Vezina Trophy in 2015-16, his sixth NHL season. He continues to apply Prior's teachings.
Video: Ryan Whitney breaks down the play of Braden Holtby
"Before, as a young kid, I just thought if you could just work as hard as you can, that's how you get better," said Holtby, 28. "But there's strategic ways and he was awesome, very calm, very unbiased watching games.
"The result didn't affect him at all. He was about the process, and that taught me a lot at that stage of my career. I still use a lot of his methods, just focusing on process to get better, get more consistent."
Speaking before the Capitals advanced to the Final, Prior was unfazed by the notion that he might face his former pupils for the championship.
"It's a strange situation for me, but I've been there before," Prior said. "Last time I was in the Final 20 years ago was with Washington (against the Red Wings) and I had to face Chris Osgood, who I also coached in Detroit."
Then, as now, Prior's boss was McPhee, Washington's GM from 1997-2014. The Capitals were swept by the Red Wings.
"Lot of water under the bridge since that series," Prior said.
NHL.com staff writer Tom Gulitti contributed to this report.
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