YANQING, China — Not very long ago, the leaders of Alpine skiing in the United States believed they had built something lasting, that the record medal haul Americans achieved at the 2010 Vancouver Games signaled a machine capable of churning out champions for years.

A dozen years later, at the Beijing Games, American Alpine skiers are in danger of posting their lowest medal tally in 20 years.

Ryan Cochran-Siegle surged to a silver medal in the super-G, but Mikaela Shiffrin, who has largely trained outside the U.S. system, has had the most disappointing Olympics of her career, with one last chance to win an individual medal in Thursday’s combined event after failing to finish a single run in her two best events.

The machine that had nurtured a golden generation of skiers who became repeat Olympic medalists, including Bode Miller, Lindsey Vonn, Ted Ligety and Julia Mancuso, has fallen victim to — depending on whom one asks — some unlucky injuries, the choice to go all-in on the present rather than invest in the future, or some combination of both.

“We tried to do a lot of different things, including helping people win on the World Cup level,” Sasha Rearick, the head men’s coach for the men’s Alpine team from 2008 to 2018, said of the U.S. Ski and Snowboard Association. The organization oversees Alpine skiing and six other disciplines.

“In the end we had less clarity,” he added. “We were not as steadfast on a clear mission.”

Not so, according to Tiger Shaw, who has led the organization since 2014 and will depart after the Beijing Games.

Names to Watch

• Kamila Valieva: The doping case surrounding the Russian figure skater, who will be allowed to compete but won’t be able to receive medals, echoes another dark Olympic era.
• Kaillie Humphries: The bobsledder, who left Canada after accusing her coach of mental abuse, won gold for the U.S. in monobob.
• Erin Jackson: The speedskater’s gold ended a U.S. drought and made her the first African American to medal in the sport.
• Chris Corning: The American snowboarder, who is more calculating and quiet than his competitors, thinks his sport has an image problem. He wants to fix it.

Shaw compared the association to a private equity firm, with annual revenues of about $38 million a year, that places high-risk bets and provides expertise in the form of coaching.

“It’s a resource allocation game,” Shaw said. “You’re trying to do the right thing in many areas, trying to give everyone a chance and at the same time support the very best athletes.”

What is not up for debate are the results: The team the United States brought to Beijing has struggled to compete with the best skiers in the world on the sport’s biggest stage.

The Americans have just one medal through eight races, and have failed to have a skier in the top 10 in four races. The American men did not have an entrant in the men’s combined event for the first time since it was reintroduced to the Olympic program in 1988.

After finishing fourth in the giant slalom, River Radamus, a 24-year-old from Colorado, said he was well aware of the large ski boots to be filled. “I hope we can live up to the legacy,” he said.

The team was weakened on the eve of the Games when Breezy Johnson, thought to be a medal contender in the women’s downhill, withdrew with an injury.

Also, ski racing can be incredibly random, especially in the pressure cooker of an Olympics, and on the new hill in China where the top skiers have never competed. World champions (Shiffrin) can slip. Long shots like Austria’s Johannes Strolz, who tunes his own skis and won the combined, can prevail.

Still, the more skiers a team has with a history of success, the better its chances of winning medals. But while the team was building its medal collection from 2006 to 2014, there was less emphasis on building depth within the next generation of racers.

With a gifted collection of skiers at the peak of their careers, the U.S. Ski and Snowboard Association decided to invest heavily in elite performance. At the top level, few expenses were spared. The organization hired top coaches from Europe, a director of sports science from Australia, and another specialist, a former surgeon and physiologist named Jim Stray-Gundersen, who had spent years working with Norway’s Olympic development program, which is widely considered the best in the world.

The organization opened a gleaming headquarters and training center in Park City, Utah, and spent as much as $1 million a year on research for elite athletes, not just in Alpine but in all disciplines. Those investments have helped the U.S. maintain its supremacy in snowboarding and become competitive in women’s cross-country skiing.

For the top Alpine skiers, there were also off-season training camps in Chile and New Zealand. The organization even paid to have the training slopes prepared in the same fashion as the hard and icy World Cup tracks, a move that several teams in Europe have since copied.

A handful of top skiers had all their travel and training expenses covered. Younger skiers, though, had to cover costs that can stretch as high as $30,000 a year.

When Cochran-Siegle was finishing high school as a nationally and internationally ranked amateur, he got an email congratulating him for being selected to the U.S. Ski Team’s development squad, or D-Team, a big step toward the highest levels of the American ski racing hierarchy. It included an invoice for training and coaching for $5,000.

His mother, Barbara Ann Cochran, an Alpine gold medalist in 1972, wrote back and declined the invitation, in part because she didn’t have the money. The ski team replied that it had found some funding — in the form of grants and scholarships — that would allow Ryan to join the team. But his early career also relied on the generosity of the extended Cochran ski racing family, which provided regular lodging at national ski team training settings.

Still, the sport’s expenses made trying to advance from promising junior skier to world-class competitor a risky, and expensive, proposition. A full scholarship to a top college with a competitive ski team became a far safer path, though few at the top of the sport would argue it provides the training necessary for a career as a top professional skier.

Financing for developing skiers was not restored until 2018.

“At the time, it was exactly the right strategy,” Luke Bodensteiner, the former director of sport for the organization, said of investing in the best of the best.

“What we were saying was, ‘Give Lindsey and Bode and Ted and Julia everything they would get if they were from Austria,’” Bodensteiner said.

That gamble paid off in medals, but at a cost. American coaches suspect the organization may have missed out on a handful of prospects who might now be entering their prime.

Bodensteiner said if he could go back, he might have been more patient and tried to figure out how to build a lasting foundation for Alpine success, knowing that the payoff might not arrive for several more Olympic cycles.

“We knew we had amazing athletes,” Bodensteiner said. “The choice boiled down to, do we compromise them and try to continue with some things that will not pay off for 12 years or go all in on them to make it happen?”

Bill Pennington contributed reporting.