The final races have been run, the Olympic cauldron has been doused, the athletes have returned home to endorsement deals or fourth-place oblivion. Now we can focus on the question about the Olympics that is truly on everyone’s mind: What does the final medal tally reveal about contemporary theories of international relations?

First things first. Those worried about the decline of U.S. power can exhale. This is still a world of American primacy; the United States is first among unequals. As has been the case in every Summer Olympics since 1996 — except Beijing in 2008, when the host country came away with more gold than anyone else — American athletes won the largest number of medals overall, as well as the most gold.

But primacy is not dominance. The United States earned 104 medals, 11 percent of the total; with 46 golds, Americans won 15 percent of all gold medals. Athletes representing 84 other countries won 89 percent of the total medals and 85 percent of the gold. In 1988, only 52 countries earned medals of any kind. Olympic power, like economic, military and diplomatic power, is increasingly diffused. Nonpolarity, not unipolarity, not even multipolarity, defines the 21st century.

And yes, China is clearly on the rise. At the 1988 Seoul Olympics, China won 28 medals, just five of which were gold. Today, a quarter-century later, China came in second to the United States with 88 medals overall, 38 of them gold. This does, however, represent something of a falling-off from four years ago.

The decline could be attributed to China’s loss of home-country advantage, or it might be further evidence that a difficult political and economic transition is sapping the nation’s energy and focus. Economic growth in China is slowing; Olympic results seem to be a lagging indicator. Those arguing for containment of China might want to spend more time reading the sports section and less with op-eds.

Even worse, for many Chinese, the London Olympics were just the latest instance of the world ganging up on them. There was outrage across China over charges that the swimmer Ye Shiwen won her gold with an improbably fast (and much improved) time because of doping; over the disqualification of its badminton team for appearing to throw a match to improve its chances in the next round; and over the judging in gymnastics that awarded one of China’s best athletes silver rather than gold. It is a reminder that nationalism could become more of a force in China if and when popular frustration grows as the economy cools and freedom is curtailed. Thank God the Olympics have nothing to do with politics.

Russia did extremely well by coming in third overall and fourth in gold, especially when you consider that it is a country of 143 million people, less than half the population of the United States and only 11 percent of China’s. For what it is worth, if you combine Russia’s tally with that of Ukraine, Kazakhstan and the other former Soviet republics, the old U.S.S.R. would have won the most medals and nearly equaled the United States in gold. This is more evidence that we are fortunate the Cold War ended when it did.

If the Olympics are any measure, Germany has not weathered the end of the Cold War and the country’s unification all that well. In 1988 in Seoul, the two Germanys won a combined 142 medals, including 48 gold. This time, a unified Germany won 44 medals, 11 of them gold. It would appear that the private sector has not stepped up to replace the role of the East German state in training athletes. The two Koreas, which won a combined 34 medals (17 gold), are no doubt taking notice.

The 17 euro-zone countries, including Germany, had a strong showing: 168 medals, 41 gold. Here, at least, there is little link between financial disarray and athletic achievement. But this is unlikely to persuade the British to end their opposition to joining the euro zone; they are doing just fine on their own, thank you. Indeed, Great Britain’s remarkable 65-medal haul (with 29 gold) equals more than one medal per every million inhabitants. At that rate, China or India would have taken every medal awarded and then some.

The British performance — close to a 50 percent improvement compared with the Beijing Games four years ago — can in part be chalked up to the traditional home-team advantage. The likelihood that the British will match this outcome in Rio in four years is about as great as that of its empire rising again.

Of course, Britain’s success this year bodes well for Brazil, the host of the 2016 Summer Games. Brazil won 17 medals (three gold) this year, and if form holds, it will earn considerably more next time. It had better: What good is it being an emerging market if you never emerge?

And what of the rise of the rest? Jamaica and Kenya are proof that even small countries can be world-class. By contrast, India was one of the least-successful competitors, winning only two silver medals and four bronze ones in London despite a population of more than 1.2 billion. This reinforces the view that India is not quite ready to join the ranks of the major powers.

Japan, meanwhile, garnered its highest-ever number of medals, 38, but fell down on the gold with seven medals, far short of the 16 golds it won in both 1964 and 2004. Like its economy, Japan’s Olympic showing is more drift than direction.

The Middle East continues to do abysmally, much worse than any other region. The area pays a price, at the Olympics and everywhere else, for poor governance and a lack of opportunities available to women. That said, the Middle East can be accorded some slack, since people there have been busy lately ousting repressive governments. Those taking up residence in Tahrir Square can be forgiven for not making it to Trafalgar Square.

Richard N. Haass is the president of the Council on Foreign Relations and the author of “War of Necessity, War of Choice: A Memoir of Two Iraq Wars.”

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