VANCOUVER, British Columbia  No gold is awarded to the nation that takes home the most medals at the Vancouver Games, yet for a few countries, the battle to rack up the most golds, silvers and bronzes can be one of the most competitive sports at the Olympics.

After winning two medals Saturday, the United States is assured of breaking the record for the most medals ever won at a Winter Games, with 36 and one more ensured in men’s hockey. But in proclaiming the accomplishment, the American officials made no mention of the fact that many of the athletes who have contributed to the medal haul are those who have gone their own way, sometimes barely linked to United States Olympic team programs.

In speedskating, Shani Davis, winner of a gold and a silver, has such a strained relationship with U.S. Speedskating, the sport’s national governing body, that he does not allow his biography to be posted on its Web site. Lindsey Vonn, who won a gold and a bronze in Alpine skiing, was cultivated in the U.S. Ski Team system but now receives intensive independent training.

The snowboarder Shaun White, who won a gold, prepared for the winter season by training privately on a halfpipe that was financed by Red Bull, his sponsor.