Nearly a century ago, American middle-distance runner Abel Kiviat entered the Stockholm Olympics as the odds-on favorite to win the 1,500-meter race, an event in which he held the world record. Kiviat had the lead 1,492 meters into the race but was passed in the final eight meters by Britain’s Arnold Jackson.

Kiviat was devastated. Years later, he recalled the loss as one of the lowest points in his life. Even after he turned 90 — decades and decades after that 1912 race — Kiviat said he would wake up in the middle of the night, asking himself how he could have lost.

The Olympics mean many things to many people. For those who study human behavior, the games provide a remarkable Petri dish in which to study a paradox in human behavior.

Why, for example, do the silver medalists usually look gloomier than those who win bronze, a step lower on the stand?

Researchers Victoria Husted Medvec, Scott Madey and Thomas Gilovich once systematically examined the reactions of Olympic medalists after they had won a silver or bronze medal. They tracked down video footage of dozens of second- and third-place finishers in sports including swimming, wrestling, gymnastics, and track and field. They also obtained footage of medal ceremonies. The psychologists then showed the video to volunteers who were uninterested in sports and asked them to rate how happy the athletes looked.

The volunteers concluded that, indeed, the bronze medalists looked significantly happier than the silver medalists.

The psychologists also obtained television interviews with the medalists and asked volunteers to rate the athletes’ comments immediately after they had finished their events. Silver medalists, the researchers found, obsessively spoke about what they could have done differently to have won gold. Bronze medalists, by contrast, tended to focus on how lucky they were to have won a medal at all.

Medvec, Madey and Gilovich later interviewed athletes. They tracked down 115 medalists at the Empire State Games, an amateur competition in New York.

Again, they found that the silver medalists couldn’t get the gold medalists out of their heads, whereas the bronze medalists compared themselves with athletes who didn’t win anything. Again, the bronze medalists seemed happier than the silver medalists.

“If you win a silver, it is very difficult to not think, ‘Boy, if I had just gone a little faster at the end …’” said Gilovich, who works at Cornell University. “The bronze-medal winners — some of them might think, ‘I could have gotten gold if I had gone faster,’ but it is easier to think, ‘Boy, I might not have gotten a medal at all!’”

In a separate study, photographer Bob Willingham took thousands of photographs of judo competitors during the 2004 Olympics in Athens, capturing images of athletes in the seconds after they had won or lost a medal. Researcher David Matsumoto then coded the photographs according to the athletes’ expressions.

The duo found that the bronze-medal winners looked nearly as happy as the winners of the gold medal, whereas the expressions of the silver medalists more closely resembled the athletes who placed fifth.

Silver medalists at the Olympics seem to perform what psychologists call an upward counterfactual — they compare themselves against someone better off than them. Bronze medalists seem to perform downward counterfactuals — they tend to compare themselves with people who did worse.

Olympic athletes are not the only ones who make such comparisons, of course. People use counterfactual thinking all the time to weigh how they feel about their jobs and salaries, about their relationships and their life.

Madey, a psychologist at Shippensburg University in Pennsylvania, said counterfactual reasoning is closely related to people’s expectations. A student who expects a B in a test would be delighted to get a B-plus, but if it turns out he nearly got an A, he is now likely to focus on what he missed.

“Initially, they wanted only a B, but getting close to an A leaves them unsatisfied,” Madey said.

In general, Gilovich said, comparing ourselves against people who do better than us can help us do better. When the silver medalist replays the race in her mind and imagines getting off the starting blocks faster, or finishing more smartly, it can help her improve her performance.

The problem, however, is that comparisons with those who do better than us can carry on long after they have ceased to play a useful role. For example, Abel Kiviat’s recurring regret over the 1912 Olympics only caused him pain.

“The key to understanding happiness is not to think about it as a trait but as a talent,” Gilovich said, quoting a colleague. “Happy people have a talent — they are able to argue life is a glass half full. They are able to say, ‘I have gone over this enough, now let me be happy I got a silver medal.’”

Psychology can help people see how the unconscious choices they make influence how they feel, but it is not very good at telling people what choices they ought to make.

“One of life’s many dilemmas is where you set that bar to create the optimal balance between achievement and satisfaction,” Gilovich added. “That’s where you leave the science of psychology and get to the art of living.”