So the United States and its $11 trillion, sports-obsessed society sits atop the medal board in Athens. Big deal.

And China, which has won nearly as many gold medals as the United States? With about one-fifth of the world's population and a burgeoning economy, let's just say a vast gene pool and a fattened wallet provide plenty of opportunity to cultivate winners.

In an era of free markets and falling borders, it's time instead to celebrate the real champions of this year's Summer Games: Congratulations, Eritrea, with honorable mentions for Georgia, Ethiopia, Mongolia and Azerbaijan!

At least as of the end of competition yesterday, those nations ranked highest in terms of the number of medals won per dollars of gross domestic product -- a measure that helps show how well a nation is doing compared with its resources.

With a $734 million economy, Eritrea's capture of a bronze medal in the men's 10,000-meter race translates into 136 medals for each $100 billion of gross domestic product. Georgia's medal tally -- two golds and two silvers -- translates into 101.6 medals per $100 billion of GDP. Ethiopia is close behind, with a medals-to-GDP ratio of 90, while Mongolia is running fourth with 84, and Azerbaijan fifth with 70.

Other nations punching above their economic weight include Belarus, Bulgaria, Jamaica, Cuba, Russia and Australia. The United States, by contrast, is near the bottom among the 73 countries that have won at least one medal, with only about 0.83 medals per $100 billion of GDP. China's ratio is around 4, in the middle of the pack.

Other big losers? Oh, Canada: With $834 billion in GDP, the country has managed just nine medals, so its ratio is almost as disappointing as its giant neighbor to the south. India may be the biggest underachiever of all; despite a fast-growing economy and a billion people, the country has so far managed only a silver in double trap shooting.

There is little dispute that economic size wields major influence over how well a nation does at the Olympics.

Setting aside the now-fading market distortions of the former Eastern Bloc, which focused its centralized resources to grow hothouse athletes, wealthier countries enjoy substantial advantages in international athletic competition -- large pools of talent, enough leisure time for people to participate in sports, and extensive facilities, rewards and other support for athletes.

Academics who have studied past Olympics have found that GDP, the total value of goods and services that a nation produces, is probably the single best predictor of a country's success at the Games. "If you look just at economic power, you'll explain about 60 percent of the variation in medal totals," said Andrew B. Bernard, a professor at the Tuck School of Business at Dartmouth College.

Examining the relationship between GDP and medal rankings also offers some lessons on how globalization distributes rewards among countries.

On the positive side, the Olympic success of some developing nations appears to reflect rising living standards, which increase the likelihood that gifted athletes will get to exploit their talents. China is a vivid example: In 1988 the Chinese won just 28 medals, five of which were gold, but in 2000 they won 59 medals, 28 of which were gold. In Athens, the Chinese had won 57 medals as of yesterday, with three days of competition left.

Driving that improvement, Warner and other experts agree, is China's transformation from a largely peasant-based economy to an industrial powerhouse. That has bestowed better health on millions of Chinese and given the government in Beijing the resources to fund a nationwide network of sports schools; as an extra incentive, the government provides cash bonuses for medalists, with a gold worth $24,000, and potentially much more in corporate donations.

China's stellar record at Athens, to be sure, is something of a special case because the 2008 games are slated to take place in Beijing, "and any country that is going to host the Olympics starts ratcheting up their system before they get the bid," said David Wallechinsky, an author who has written books about the Olympics. "For China, this idea of doing well in the Olympics is massive; they're thinking, 'We're going to be proud of ourselves.' "

But even as some developing nations have garnered more Olympic glory, the rich have gotten richer -- medal-wise, just as they have in terms of GDP.

According to one study, the wealthiest 10 percent of countries have increased their proportion of medals, from 35 percent in 1952 to 42 percent in 2000. In part, that's because many of the new Olympic sports -- softball and beach volleyball, for example -- are not exactly typical Third World pursuits.

"There's a bit of trickle-down, because the pool of medals is getting larger, and a few drops of it are going to smaller nations," said Daniel K.N. Johnson, a Colorado College economist who co-authored the study. "But in percentage terms, the richest are grabbing an increasing share of those new medals. You can guess one of the reasons -- new sports are introduced by and large by the rich nations. We're not playing indigenous African games. We introduce things like trampoline, and curling."

The GDP factor is presumably even stronger now because during the Cold War the Soviet bloc nations spent lavishly on nurturing Olympic competitors to showcase the virtues of socialism. Their medal counts zoomed accordingly, even as their economies stagnated. In 1988, both the Soviet Union and East Germany topped the United States.

Much of that sports infrastructure has since fallen into disrepair, although to some extent the legacy remains -- Romania's continued excellence in gymnastics being a case in point. Russia's medal harvest at Athens is probably attributable in no small part to the efforts by President Vladimir Putin to resurrect his country's sports machine. Moscow has reportedly tripled spending on sports and offers bonuses of up to $50,000 for gold medalists.

Similar factors help explain why Cuba remains an overperformer, said Meghan R. Busse, a University of California at Berkeley professor who co-authored a study on Olympic results with Bernard. "They have political reasons to show they can do well," she said.

But old-fashioned capitalist wealth offers ample compensation. The government bonuses given to Russians and Chinese can't compare with the multimillion-dollar contracts that top American athletes get from endorsing commercial products, as witnessed by the ubiquitous Visa ads featuring swimmer Michael Phelps.

Less famous members of the U.S. team can take advantage of deals offered by U.S. companies, such as Home Depot, which pays 49 U.S. Olympic team members a full-time salary with benefits for 20 hours of work a week, allowing plenty of time for training. U.S. Olympic training centers are equipped with laptops, video cameras and sensors designed to give athletes minutely detailed feedback on their technique. The Germans, meanwhile, have developed high-tech boats, bikes and bobsleds to give their athletes an edge.

And for the ultimate illustration of how the Olympic field is tilted in favor of rich nations, there is the recent trend of athletes from impoverished lands "country hopping" to greener pastures. Asaad Said Saif Asaad -- the former Angel Popov -- is one of eight Bulgarian weightlifters whom the wealthy emirate of Qatar is funding for a reported $1 million to compete under its flag, according to the official Olympic Web site.

Perhaps even more important is the evolving market in coaches. "As the economies of the former communist nations melt down, a lot of the coaches who would have done very well in the old Soviet system in sports like gymnastics and figure skating are now moving to the United States," Wallechinsky said.

Still, a flourishing market economy can sometimes work against a country's Olympic interests. Assuming that every nation is endowed with a certain percentage of talented athletes, Wallechinsky said, "in the United States almost all these people are going to go into basketball, baseball, football and tennis" because that's where the money is. "In Russia, you can win a gold medal in weightlifting and be a national hero. In the U.S., you can win a gold medal in weightlifting and no one will hear about you a week later. We were great in weightlifting in the '50s, but the guys who used to be strong in weightlifting are becoming [football] linemen instead."

In some cases, societal factors may play as big a role as economics. India, for example, might be less of an Olympic laggard if the culture encouraged female athletes.

"I find it comforting that Olympic medals don't entirely follow GDP lines, because it supports my view that there's a lot more to life than GDP," Johnson said. "I wish that the ability to achieve athletic caliber were truly independent of economic or financial means. Think of the world records that could be broken if everyone had an equal opportunity to achieve their utmost. So I celebrate when Olympic medalists come from unexpected places."

But the cold, hard reality, he continued, is that economics often plays a decisive role, because "athletes need a support system. . . . If your main goal in life is to go out and make enough food to survive till tomorrow, you won't have a lot of time left for curling."

So far, China, with 57 medals, has won about four medals per $100 billion in GDP, while the United States, with 90 medals, has garnered about 0.83 and Canada has pulled in slightly over one per $100 billion in GDP with its nine medals.