Conor Sheary should have been a Wildcat.

The Melrose native is from the same town as University of New Hampshire coach Dick Umile. Courtney Sheary, Conor’s older sister and the girls’ hockey coach at Cushing Academy, played on UNH’s women’s hockey team.

Umile doesn’t always get his man.

“It’s a joke between the two of us,’’ said former UMass Amherst coach Don “Toot’’ Cahoon, who committed Sheary to Amherst before his ex-rival in Durham put in his bid. “He says he’s not supposed to lose Melrose kids. He got a lot of guys at UNH. It was about time one broke my way. He’s been beating on me since we were 10 years old.’’

There was a time when going unnoticed was a regular thing for Sheary. The same player that Umile failed to land was bypassed by 30 NHL teams when he was eligible to be drafted in 2010.

Anonymity is no longer easy for Sheary to claim.

Sheary, who turns 23 on June 8, is close to pumping the Stanley Cup over his head. Through 19 postseason games, Sheary had four goals and five assists while averaging 13:56 of ice time. Of his four playoff goals, none was bigger than the puck he launched past the Sharks’ Martin Jones in overtime of Game 2, giving the Penguins a 2-0 series lead.

As Sidney Crosby lined up for an offensive-zone faceoff against Joel Ward, Sheary knew exactly what to do. Crosby had given him detailed instructions.

Crosby pulled the puck back to Kris Letang at the left point. It was Logan Couture’s job to jump out and challenge Letang. Because of Sheary, Couture never got there.

The left wing, who had curled up high, floated just slowly enough to interfere with Couture’s sprint to the point. After stepping in front of Couture, Sheary pivoted toward Letang and placed his blade on the ice. Letang’s pass was slightly behind Sheary. But the left wing reached back, settled Letang’s pass, and considered his options. Only one was acceptable: fire the puck on net.

Before fellow ex-Minuteman Justin Braun could close the gap, Sheary pegged a pea over Jones’s glove at 2:35 of OT to give Pittsburgh the 2-1 win. To Cahoon’s eye, the play represented some of Sheary’s assets well: fierce competitiveness, good hockey sense, quick stick, and an improving shot.

“He’s not a big kid,’’ Cahoon said of the 5-foot-8-inch, 175-pound Sheary. “But he’s got great speed and instincts. He reads plays pretty quickly. He jumps on people. He takes their time and space away. He forces errors. He forces all sorts of plays that lead to turnovers. He jumps on loose pucks. He’s creative in the way he’s able to move pucks to both sides of his body. Then, seeing of late, it’s how well he can shoot the puck. It’s terrific to watch him play with that kind of confidence.’’

Like players of his size, Sheary is used to being overlooked. He was a point-per-game player at Cushing. But by Cahoon’s recollection, he was on the wrong side of the 150-pound threshold when colleges started sniffing around.

Sheary’s size, however, did not discourage Red Gendron, Cahoon’s former assistant, to voice his full approval of the little guy doing big things at Cushing. Cahoon soon agreed with his recruiter’s opinion.

“I immediately went out, and my first impression was, ‘This kid is a hockey player,’ ’’ Cahoon recalled. “He just makes plays. If there’s someone open, he’ll try and get him the puck. He was creative. But he was certainly undersized.’’

Consider the following reports, from two Cushing games against Berkshire School and Governor’s Academy, filed by a veteran scout on Sheary during his senior season, by which time he had committed to UMass:

“Smart player . . . very quick and elusive around the net . . . quick to pounce on and bury loose pucks . . . quick hands . . . gets shot off without hesitation.’’

“Feisty and competitive player . . . plays bigger than his size would suggest . . . talented offensive player . . . smart . . . very good hands . . . made some smart plays . . . has a very good shot, which he disguises and gets off quickly . . . is a goal scorer.’’

Neither the reports nor Sheary’s UMass commitment was enough for a team to use a late pick on the left wing. Six years ago, teams were still frightened of burning draft capital on small players.

Out of concern for his size, UMass originally wanted Sheary to play a year of junior hockey after finishing at Cushing. But after a roster spot opened, Sheary arrived in Amherst as an 18-year-old freshman. As a Hockey East rookie, he scored six goals and eight assists in 34 games.

“It was a tall task physically for him to be hanging in there and compete at the Hockey East level as an 18-year-old instead of being 19 or 20,’’ Cahoon said. “He came and did more than we ever hoped in that freshman year. By the time he was a sophomore, he was a full-fledged threat. He was a good player from Day 1 because of his hockey instincts. He had the inclination to make plays, use other people, and be unselfish.’’

During his senior season, in which fellow undrafted left wing Frank Vatrano was a teammate, Sheary scored nine goals and 19 assists to lead the Minutemen in scoring. After he finished his college career, Sheary signed a tryout agreement with Wilkes-Barre/Scranton, Pittsburgh’s AHL affiliate.

That fall, Sheary returned to Wilkes-Barre to start his first pro season. Under the watch of former coach John Hynes, Sheary led the AHL club in scoring with 20 goals and 25 assists in 58 games.

Sheary returned to Wilkes-Barre under coach Mike Sullivan to start 2015-16. On Dec. 12, Sullivan was promoted to Pittsburgh to replace Mike Johnston. Three days later, Sheary followed his former coach. By now, it is no longer strange for Sheary to call for the puck from Crosby instead of asking him for an autograph.

“I think when he first was called up this year, we put him with Sid right away, there was a wow factor with some of the players in the room,’’ Sullivan told Pittsburgh reporters after Sheary’s overtime winner. “My experience of being around this group is when a new player comes to our team, young or old for that matter, I think there’s a little bit of a wow factor because of some of the players we have. Everybody has so much respect for Crosby and [Evgeni] Malkin and Letang and those guys. Over time, I think that wears off. I think that’s happened with Conor.’’

Cahoon believed Sheary could grow into a very good pro player in Europe. Even coaches miss with their projections.

“Now that I’ve rethought that process,’’ Cahoon said with a laugh, “he could be a terrific NHL player for quite a while.’’

MONEY PLAYER

Kucherov worthy of a big raise

On July 19, 2011, the Lightning made a wise decision. Less than three weeks into his residency as a restricted free agent, Steven Stamkos signed a five-year, $37.5 million extension. It was a slam-dunk move. Stamkos’s status as the first overall pick in 2008 and subsequent production of 119 goals over the life of his entry-level contract gave Tampa Bay enough data to determine he was worth a prime-time payday.

A similar deal should await Nikita Kucherov.

The right wing does not have Stamkos’s pedigree. Kucherov lasted until the 58th pick in 2011. He scored a career-high 30 goals in 2015-16 as a third-year NHLer. Stamkos pumped in 45 pucks in his third season, following up a 51-strike sophomore year.

But the first segment of Kucherov’s career promises his peak years should be very good. The Lightning would be best served locking him up for the next phase, just like they did with Stamkos.

Under general manager Steve Yzerman’s stewardship, the Lightning have drafted, signed, and developed excellent young players. As such, they are due raises. Like Kucherov, do-it-all left wing Alex Killorn will also be restricted on July 1. Jonathan Drouin, Tyler Johnson, and Ondrej Palat will reach RFA status on July 1, 2017, the same day Victor Hedman will be unrestricted. They are all must-sign players.

Accommodating all that talent might lead to chatter of bridge deals. Kucherov should not be in that company. At this point of his career, Kucherov is a sure thing, just like 2011 classmates Gabriel Landeskog, Brandon Saad, Ryan Nugent-Hopkins, and Andrew Shaw. They are the only four players drafted in 2011 who have more goals than Kucherov.

Landeskog (seven years, $39 million), Saad (six years, $36 million), and Nugent-Hopkins (six years, $42 million) scored big with their second contracts. Shaw will be restricted after signing a two-year, $4 million bridge deal. Chicago may not be able to afford to give Shaw the raise he deserves.

As painful as the Lightning will find it if Stamkos walks, they know they got bang for their buck on his second contract. The seven-year blockbuster Stamkos is sure to find elsewhere will most likely be inflated near the end of its term. The team would like to apply a similar model with Kucherov. He’s worth it.

ETC.

Will Blues bring back Backes?

David Backes gave the Blues everything they had. The captain led the way with his heart, grit, and strength in the regular season and playoffs. No team would want to say goodbye to such a leader.

The reality, however, is that Backes is 32 years old and about to be unrestricted. If he’s looking for a long-term deal, he’s not getting it in St. Louis, regardless of how he’s served the franchise. GM Doug Armstrong knows that bringing Backes back depends on what he can give the team in the future. At Backes’s age, it’s not as much as Jaden Schwartz, 23, has to offer.

“What you’ve seen around the league is that if you get too aggressive, those contracts are sometimes difficult to maneuver around in years pushing out,’’ Armstrong told St. Louis reporters of long-term extensions to veteran players.

Re-signing Backes at a player-friendly term would be an emotional decision. Armstrong is not an executive who’s ready to make moves with his heart. He knows that locking up young players such as Schwartz is a wiser alternative. It’s why re-signing Schwartz, who will be restricted, is Armstrong’s top offseason priority. By doing so, instead of going to arbitration for a one- or two-year extension, the Blues will have their foundational players in place: Schwartz, Vladimir Tarasenko, and Alex Pietrangelo, with Colton Parayko sure to join that group upon expiration of his entry-level contract after 2017.

If Backes walks, it won’t help the Blues in 2016-17. But they are expecting improvement from their next class of leaders. It will be Ken Hitchcock’s final season as an NHL coach. Hitchcock will not stand for a step back in his last kick at the can.

Go off ice for offside

I think the offside challenge is dreadful. It is wretched from every angle, from the nit-picking manner in which it second-guesses the linesmen to the tablets they have to squint at to judge the replays. But if the league is serious about retaining the challenge, it should do the right thing and deploy some of its off-ice officials to make the calls. It would be a lot easier for officials, positioned overhead or in fixed positions at each blue line, to judge whether a play goes offside. They wouldn’t have to battle with flying pucks or players. Views are unimpeded. They wouldn’t have to skate to catch up to the play. Linesmen are sometimes in the worst positions of all to make these calls.

Sweet deals in Pittsburgh

The Penguins are built for another deep playoff run in 2016-17, and not just because of their star players. Conor Sheary, Bryan Rust, Tom Kuhnhackl, Brian Dumoulin, and Matt Murray will all be 25 or younger when the puck drops on next season. They will all be better next year given their age and the experience they’ve gained during the playoffs. Now consider the collective cap hit for the five players: $3.26 million, according to www.generalfanager.com, a hair under Trevor Daley’s $3.3 million average annual value. It’s as good as you’ll find around the league in terms of bang for the buck. It’s why good young players on entry-level or inexpensive second contracts are critical to offset top-heavy superstars such as Evgeni Malkin and Sidney Crosby, who combine for $18.2 million per year. Pittsburgh’s trick will be to allocate the dollars when the young players are due for raises. But that doesn’t start until 2017-18.

Cizikas cashes in

Opponents have long considered the Islanders’ crash unit of Matt Martin, Casey Cizikas, and Cal Clutterbuck the best fourth line in the league. On Thursday, Cizikas signed a blockbuster that signified the Islanders think of him as more than a fourth-liner. According to Newsday, Cizikas’s five-year extension is worth $16.75 million. It’s a generous payday in both term and salary. While Cizikas is only 25 years old and has proven to be a durable player, his smashmouth style puts him at higher risk of injury than others. He is coming off a career-best 30-point season, but it’s unknown how much more production he can squeeze out of his role.

Loose pucks

On March 2, the eight World Cup teams named their preliminary rosters. In hindsight, they used ink on some players when pencil would have been a better alternative. Shea Weber and Niklas Kronwall, for example, should not have made the Canadian and Swedish rosters over P.K. Subban and John Klingberg. But they were locked in because they were among the first wave . . . Based on four playoff rounds, most teams have made the delay standard operating procedure to generate speed and gain clean entries on the power play. The puck carrier skates through center ice, then drops the puck to a trailing teammate. The new carrier has two options: skate it in himself, or make a cross-ice pass to a second trailer. It’s hard to defend because penalty killers have to maintain tight gaps while respecting all options . . . The Lightning were arguably the most aggressive postseason team in initiating neutral-zone regroups. Whenever they saw their opponents lined up in stout defensive formation, they did not hesitate to hinge the puck back to a trailer, either to switch the angle of attack or pick up more speed on entry. This forced defenders to reset their gaps . . . Based on his team’s defensive-zone setups, Mike Sullivan does not make challenging the points a priority. The Pittsburgh coach’s priority is on collapsing in the slot. This way, the Penguins eliminate everything down low between the dots. It also keeps them in tight formation when they win the puck. When they sprint the other way, they do so as a five-man unit . . . Old friend Rich Peverley, Dallas’s player development coordinator, joined his team’s amateur staff in Buffalo for the combine. Alex Goligoski, Jason Demers, Jordie Benn, Kris Russell, Travis Moen, Vernon Fiddler, and Patrick Eaves will become unrestricted. Not all will be back, meaning some of the prospects under Peverley’s watch, such as Julius Honka and Esa Lindell, could make the jump in 2016-17 . . . The Canadiens hired Kirk Muller as associate coach on Thursday, the same day Michel Therrien was spied buying every copy of Rosetta Stone French he could find.

Fluto Shinzawa can be reached at fshinzawa@globe.com. Follow him on Twitter @GlobeFluto. Material from interviews, wire services, other beat writers, and league and team sources was used in this report.