I find it hard to avoid the conclusion that the United States is doing very well at the international Great Game under President Barack Obama.

Now, you may think U.S. hegemony is a good thing or a bad thing (personally I prefer it to the alternatives currently on offer). And you may disapprove of Obama's methods, which include the scary advent of drone warfare. But in terms of pure realpolitik, Obama seems to be very far from the weak, ineffective statesman that the Republicans try to portray him as.

Let's try to take an unbiased look at the scoreboard. The U.S. has one military enemy (international jihadists) and three geopolitical rivals - China, Russia, and Iran. All have suffered setbacks during the Obama years.

Global Sunni Islamist jihadism is on the back foot. Osama bin Laden sleeps with the fishes. Most of al-Qaida's leaders have been killed or captured - the single remaining villain of 9/11 is Ayman al-Zawahiri, a cantankerous old man who has notably done nothing to boost the dying terrorist organization. The new kids on the jihadist block are the Islamic State, which is locked in a death struggle with one of our rivals, Iran.

That's worth repeating. If Obama had intervened in Syria, as many wanted him to, it would be American bodies interposing themselves between the bullets of the Sunni and Shiite combatants - much as it was in the later days of the war in Iraq, only worse. Instead, our main enemy and one of our rivals are at each other's throats. The people of the Middle East are suffering - and that's bad - but U.S. power and prestige are enjoying a much-needed respite.

As for Russia, it took Crimea, that's true. But in the process it transformed Ukraine from a client state to an enemy, whose trade links with the European Union will probably draw it further and further from Russia's orbit. Russia then tried to foment a rebellion in Ukraine, perhaps thinking it might split off the Russian-speaking eastern areas, but the rebels utterly failed to gain popular support. Now Vladimir Putin's hired goons can barely hold onto two cities in a tiny and shrinking region on the Russian border. Meanwhile, Russia's economy, already suffering from stagnant oil prices, is taking a beating from sanctions. It seems hard to believe that a U.S. military intervention could have produced a better outcome.

Finally, China, by far the most powerful rival, has experienced some minor setbacks. With its enormous size and hypercharged growth, China looked in the 2000s as if it was poised to dominate Asia. Maybe it still will, but its charm offensive has evaporated as it has engaged aggressively in territorial disputes with almost every country in its vicinity. Myanmar, one of its few regional allies, has defected from China's camp, opening up to the West and taking steps toward democracy.

Speaking of democracy, the idea that it's the U.S.'s responsibility to promote our system of government may have gone out of fashion, but we still generally think it's beneficial when democracy spreads. On this front, things are looking good, with Tunisia going democratic, Indonesia showing that Muslim-majority countries have no problem with durable democracy and Myanmar reforming substantially. A couple of countries, such as Thailand and Turkey, have backslid, but not as a result of the influence of the U.S.'s rivals.

Now note that during all this, the U.S.'s prestige in the world has increased, while the prestige of Russia and Iran have fallen (China's has remained unchanged).

What about the idea that our president is a wimp, not sufficiently feared by our enemies and rivals? For a supposed milquetoast, Obama sure managed to cow Syrian President Bashar Assad, who agreed to dispose of his entire arsenal of chemical weapons in the middle of a civil war. That is a pretty unprecedented feat of intimidation.

The idea that Democrats are wimps is a standard old Republican saw. They've used it constantly since World War II, usually flying in the face of facts to the contrary. Former Secretary of State Dean Acheson, for example, who in the 1950s implemented the policy of containment that ultimately won the Cold War, was ridiculed by Richard Nixon for his "College of Cowardly Communist Containment." Don't believe this line - it's pure partisan noise.

It seems to me that the presidents who have done the most to advance U.S. power and prestige aren't the ones who charge forward firing their guns randomly - as George W. Bush did - but those who keep their powder dry and wait until they see the whites of the enemy's eyes. Richard Nixon withdrew from Vietnam and allied with China against the Soviet Union; Ronald Reagan built up U.S. strength and avoided major military adventures even as he signed arms control treaties with the Soviets. In both cases, the U.S. came out on top of our rival.

Today, the growth of China and the U.S. recession have put America in a much trickier situation. But Obama's quiet, inexorable strategy - whatever you think of his methods - are defying the odds and paying dividends for American hegemony.

• Noah Smith is an assistant professor of finance at Stony Brook University. He maintains a personal blog, called Noahpinion.