Joe Sakic and Patrick Roy have learned their lesson. I’m convinced they never again will allow a coveted player to remain with the team beyond the trading deadline if he can be an unrestricted free agent on July 1. They did that with Paul Stastny … and they got burned.

It’s very clear — and this will affect Ryan O’Reilly, among others, moving forward — that Sakic and Roy are sincere when they speak of a “structure,” and it’s about more than money. It’s about buying in, being committed, wanting to be here and backing it up. The Avalanche has displayed the commitment to the model with lucrative long-term extensions, and will try to avoid even getting into the Stastny position again.

Sakic can’t get too huffy. In August 1997, he agreed to a front-loaded, three-year, $21 million offer sheet from the Rangers. The cash-short Avalanche ownership of that era had to scramble to be able to write the initial $15 million check. Sakic was a restricted, not unrestricted, free agent.

Four years later, Roy, Sakic and Rob Blake agreed to long-term deals with Stanley Cup champion Colorado a few hours before they could hit the market as UFAs. Blake had joined the Avalanche in February 2001 after the Los Angeles Kings realized they wouldn’t be able to re-sign him before he was a UFA. The Avalanche did.

But Sakic’s and Roy’s perspectives are different now.

The day before the NHL trading deadline in March, Stastny and I chatted in Chicago. It seemed almost certain that he would enter the offseason with the chance to become a UFA on July 1. But he said he hoped to stay with the Avalanche for the rest of the season and beyond.

“You can obviously go somewhere and get more money somewhere else,” Stastny said. “But if you have something good and you want to stick with it, that hometown discount is obviously something that everyone’s aware of and is important to do. You want both sides to be happy. You don’t want to (mistreat) the team and you want the team to be put in a good situation where they can kind of compete down the road as well.”

The “hometown” issue came into play, but that meant St. Louis, where Paul moved when he was 7 years old and his father, Peter, joined the Blues.

Stastny got the best of both worlds: a) his real hometown, rather than Denver, where he played 10 seasons with the University of Denver and with the Avalanche; and, b) a raise, from the $6.6 million he made the previous five seasons with Colorado, to $7 million for the next four seasons with the Blues.

If the team making the outlandish offer was anyone other than St. Louis, Stastny might have accepted a Colorado offer that was less than he could have gotten elsewhere and been back. But the point is, the Avalanche — meaning Sakic and Roy — gauged the situation and decided it was worth the risk.

Trading Stastny at the deadline in a remarkable season would have been ripped as sending the “wrong” message. But I doubt Sakic and Roy will worry about that again.

Colorado is nudging up toward the NHL salary cap, which was inevitable when the extensions kicked in. But with attendance down, this team also has been operating on a “budget” the past few seasons. Ownership has accepted the increasing payroll, especially since the playoff flameout can’t obscure the progress in the past year.

So, again, the issue here isn’t just money. Sakic and Roy, among the best in the game as players, worked the system themselves. But they believe they are building something, including a culture that involves an acceptance of a generous but “fair” salary hierarchy within the cap system. In that sense, “structure” is synonymous with “culture.”

Thanks to the Stastny Lesson, I’m convinced that from now on, it’s going to be …

You’ll prove that you’re with us.

Or we’ll see that you’re not.

Terry Frei: tfrei@denverpost.com or twitter.com/TFrei