Not to suggest Andreychuk, 40, is an old dog. Or that he is getting by on trickery this late in his hockey life.
But long after most of his peers have faded into retirement or ceased to be factors in a young man's game, Andreychuk's ability to embrace an entirely different way of playing has been one of the most important lessons learned by a team that for the first time has legitimate Stanley Cup dreams and indeed is one of the compelling stories of this playoff season.
Head coach John Tortorella credits Andreychuk with no less than helping teach the Lightning to be a team, to become professionals.
"Three years ago, our locker room did not know how to conduct itself as a locker room," Tortorella said.
And that had nothing to do with how it conducted itself on the ice, he added.
Talented young players knew no other way; they needed direction that didn't necessarily come from the mouth of a young coach trying to sell a new system based on a lot of hard work and self-sacrifice.
Andreychuk embraced Tortorella's philosophy and imparted it to his young teammates by working harder at it than many of them had ever seen anyone work at anything.
"That's when you start to break down the bad habits," Tortorella said. "That's when I think David started touching on his role with this team."
"I just thought that was huge," added general manager Jay Feaster, who inherited the veteran center when he took over as GM midway through the 2001-02 season. "And if that's all he'd done, that would have been enough."
But there was more.
Not only did Andreychuk work hard and share his insights with the young players and help sell a system, he thrived in that system. He became the consummate two-way player. Instead of seeing his ice time slowly diminish and quietly vanishing from the team itself, Andreychuk has gotten stronger and better.
"John doesn't give you anything. It's not a gift," Feaster said of the 17-plus minutes a night Andreychuk logged during this his 22nd NHL season. "Dave's earned this, and I think this is a positive message."
In hockey, talk is cheap. Coaches know that; veteran players know that; and even young players still learning their way come to understand that.
"If you're coming out here and playing six minutes a night and struggling in those six minutes," Feaster said, "it's hard to make the message stick."
Instead, Andreychuk has proven to be the perfect teaching tool. As a player who used to be focus solely on scoring (20-plus goals in 14 straight seasons), he is now illustrating how two-way hockey can be fun and rewarding, said assistant coach Craig Ramsay, who played alongside a much younger Andreychuk in Buffalo some 20 years ago,
"These kids have a chance not just to hear about it but to visualize it, to see it," said Ramsay, listing the attributes Andreychuk possesses, the skills he displays on a nightly basis -- blocking shots, killing penalties, winning faceoffs, scoring key goals, playing crucial minutes.
"He really has become that symbol of two-way hockey," Ramsay said.
It is one thing for a veteran player to adjust to a diminished role; it is quite another to assume a greater, more pivotal role, especially closing in on 40. Three straight years in Tampa, Andreychuk's delivered 20-goal seasons when all anyone wanted to know was when he was going to quit coming to the rink.
This season, Andreychuk, a captain for the first time in his career, didn't score his second goal of the season until Dec. 4 and still closed out the Lightning's best-ever campaign with 21, his fourth straight 20-goal season and 19th overall.
He also played all 82 games, the second time in three years as a Bolt he has gone the distance.
In recent weeks, he has looked 20, not 40, Feaster said: "There are times he's taken this club on his back and carried it."
Perhaps wary of mythologizing the graying forward, Tortorella points out that Andreychuk hasn't always been so dedicated. He recalls that Andreychuk, as a young man, had some pretty disagreeable habits when it came to fitness and preparation.
"He was no day at the beach as far as his act was concerned," said Tortorella, who was an assistant coach in Buffalo when Andreychuk was a Sabre. "He has gone the full gamut of understanding. He's gone through the full cycle."
Many of Andreychuk's teammates were still in diapers when the Hamilton, Ontario, native played his first playoff game in 1983. Drafted 16th overall, he became one of the most successful power forwards in the game.
Tortorella recalled a day in Buffalo when Andreychuk took him aside after practice, asking questions about a particular drill or concept.
"He knew the answers. He was testing me and trying to figure out a little bit about me," Tortorella said.
He has done the same with his young teammates, testing them, pushing them. As the Lightning practiced Wednesday in preparation for their first game with the New York Islanders, Andreychuk was in the thick of things, cajoling and encouraging his teammates. And if Andreychuk has earned the right to test those young players, they certainly tested him early on, too.
According to Brad Richards, the young players wondered what Andreychuk's deal was.
"Is he on vacation to finish out his career here? Or is he a grumpy old man that doesn't want to talk to anyone?" recalled Richards, who ended up rooming with Andreychuk for a time and becoming not just a protégé but also a close friend. "He still goes out there every night like it's his first NHL season. That's the biggest kind of leadership."
Half an hour after practice, Richards added, "he is still out there banging pucks around. That's exciting to see. It's what brings this room together."
Andreychuk signed as a free agent in Tampa in summer 2001 because he knew the people involved -- Tortorella, Ramsay and former GM Rick Dudley, now the Florida Panthers' GM, who had coached Andreychuk in Buffalo.
And he liked the talent he saw, the potential, even if it meant changing his own priorities.
"Maybe it wasn't about scoring goals anymore," Andreychuk said. "Maybe it was something else."
When the trade deadline approached in 2002 and the Lightning were out of playoff contention once again, Feaster out of courtesy approached Andreychuk about moving to a contending team. He already had gone that route; he missed winning the Stanley Cup in New Jersey by a year and then went to Colorado with Ray Bourque in 2000, only to see his close friend win it with the Avalanche the following year.
Tampa Bay was his seventh stop, and while the lure of a championship was strong, Andreychuk remained committed to the Lightning and declined the offer.
"I just felt my job wasn't done here," Andreychuk said. "We came together as a team. It made my decision pretty easy to stay."
The Lightning missed the playoffs that spring, only the seventh time since 1983 that Andreychuk hasn't played in the playoffs. But last season the Lightning won their first-ever division title and followed that up this season with 106 points and the top seed in the Eastern Conference.
Feaster points to a handful of young players crucial to the Lightning's legitimate Stanley Cup dreams -- Richards, Pavel Kubina, Vincent Lecavalier, Martin St. Louis -- as players who have learned well at Andreychuk's knee and are tangible examples of Andreychuk's importance.
"I take pride in what happens around this room. Watching them mature into good players," said Andreychuk, whose 139 playoff games without a Stanley Cup ring is second only to Steve Thomas of Detroit (168) among active players. (Adam Oates, who announced his retirement at the end of this regular season, had played 163.)
He admits that the time away from the rink, away from a family that includes three daughters, continues to remind him that he is indeed 40 -- and will be 41 if there's another training camp on the horizon.
"That's when you start to feel, 'When is this all going to end?' " he said. "But when I'm here at the rink, I don't feel very old."
Feaster and Andreychuk have an offseason ritual they have followed each of the last three years. Andreychuk comes into the office, and Feaster asks him whether he's coming back for another season. Andreychuk wearily says he'll have to take a few weeks and talk it over with his wife, Susan, and think about whether he still has it in him ... and then he comes back and scores 20 more goals.
Said Feaster, who may or may not have been kidding: "I think he'll play forever."
Scott Burnside is a freelance writer based in Atlanta and is a frequent contributor to ESPN.com.