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The International Ice Hockey Federation Hall of Fame inducted a procession of hockey greats in May. The honorees included the former N.H.L. stars Joe Sakic, Teemu Selanne, Saku Koivu and Uwe Krupp as well as Angela Ruggiero, one of the most decorated players in women’s hockey.

But no one made as memorable an entrance as Tony Hand, who stepped toward the podium that night in Cologne, Germany, dressed in traditional Scottish Highland regalia — an argyle jacket, knee-high socks and a kilt.

Hand, who may be Britain’s lone hockey icon, received the Richard “Bibi” Torriani Award, which is given to players from lesser-known hockey nations.

But he might have become well known in North America if a 1980s tryout with the powerhouse Edmonton Oilers had panned out.

“I went and met the queen and had a chat, which was quite nice,” Hand, 50, said in a phone interview from Edinburgh, Scotland. “Even if you look at the career, over here I’ve been fortunate enough to have helped the sport any way I can. I have had a decent career and I’ve got a good family here and a lot of friends. So I’m not sitting back sulking. But it would have been nice to see what could have happened.”

Hand is an accomplished coach in the English Premier Ice Hockey League and with the national program, but his most impressive achievements came during an unrivaled 34-season playing career.

Growing up in Edinburgh, Hand headed to the local skating rink when he was 7 for peace and closure after the death of his father from a heart attack. Playing alongside his brothers, he was eventually discovered by a local team, the Murrayfield Racers, with whom he made his professional debut at 14.

By 17, Hand led the British Hockey League with 116 assists in 50 games to go with 99 goals. He surpassed the 100-goal mark in each of the next four seasons.

Those early years were the statistical high point of a pro career spanning more than three decades during which Hand collected 2,992 assists and 4,634 points, both British hockey records. Wayne Gretzky, the player to whom Hand is most frequently compared in Britain, established N.H.L. records considered unmatchable with 1,963 assists and 2,857 points.

“The goalies were bad; that’s what it was,” Hand said modestly when asked about his British hockey exploits.

Whatever the reason for his remarkable point totals, it was enough to gain the attention of the Oilers, who had built one of the great dynasties in league history when they selected Hand with the final pick in the 1986 draft, making him the first British player drafted by an N.H.L. team. By then, Hand had earned a tryout with Calgary, Edmonton’s biggest rival.

“Our league had a deal with Calgary — they would invite the young player of the year in Britain to the camp in Calgary,” Hand said. “It was a token gesture. I don’t think they realized there was a possible opportunity that one of the players could make the team.”

But his rights were officially owned by the Oilers, who had won consecutive Stanley Cups in 1984 and 1985, so Hand reported to Edmonton training camp in 1986. On a club that would win three more Cups in the next four seasons, Hand made an impression despite facing long odds to make the team.

“There was absolutely no question when he came over for that first training camp that he had enough hockey skill,” said Bill Tuele, the Oilers’ former director of public relations. “He had never been pushed to any great limit. He was a neat kid. He was a bit overwhelmed by the whole process. To be thrown into that caldron was almost an impossible task.”

With few roster spots available, Hand was sent to the Victoria Cougars of the Western Hockey League. After collecting 8 points in three games, a homesick Hand returned to Edinburgh to finish the season with the Racers.

He was invited back to Oilers camp the next season and was one of Edmonton’s final cuts. But Hand again decided to head home rather than report to Edmonton’s top developmental team in the American Hockey League.

He would not receive another invitation to an N.H.L. camp, instead flourishing in Britain and becoming the only hockey player to receive the prestigious Member of the British Empire award from Queen Elizabeth II.

His 82 points with the national team made him the country’s career leading scorer. After 14 seasons serving in a dual role as a player and coach with a number of British teams, Hand retired as a player in 2015 at age 47. He served as head coach of the Manchester Phoenix of the English Premier Ice Hockey League until the club ceased operations in January.

Now consisting of 12 teams, the league is entering what local officials believe could be a new golden age for the sport in Britain, with former N.H.L. players joining the league.

“In Tony’s day, he was the best player in the U.K. by far,” said Andy French, the general secretary of Ice Hockey U.K., the national governing body for the sport. “He was better than a lot of the imports. He had a vision that nobody else had. He’s now passing that quality that he had down through to the younger generation of players. I’m hoping that we can produce another Tony Hand.”

For all the success he enjoyed at home, Hand still, three decades later, sometimes thinks about his decision to leave Edmonton.

“It wasn’t like I was unambitious,” he said. “I just didn’t know. I had never been away. Obviously when you’re young you make these decisions, and I had never had a father figure to sort of guide me. I don’t sit and regret it. But did I make the right decision? Probably not.”

Since ending his playing career, Hand has contributed as a scout and coach to the British national team, which in April won the 1B division of the world championships to earn promotion to Division 1A, one level below the top tier.

Hand’s hope is that Britain’s accomplishments in international hockey can help him find the kind of opportunity in the N.H.L. he never quite pursued in an otherwise illustrious hockey career.

“I think I’ve got a lot to offer teams,” Hand said. “I’ve got a lot of experience. I’ve got a lot of knowledge. I haven’t really put my name out anywhere. I thought I would just wait and see what comes.”