"People have a tendency to compare their state of the world and what happens to them with what could have been. ... The term for that is counterfactual thinking," McGraw said.
So, "there`s this spontaneous in-the-moment reference point, or counterfactual, which is that for silver, you think, `Oh, I could have won the gold,` and for bronze, it`s `At least I got a medal,` " he said. "What`s happening is, there is no one formula; there`s just a natural tendency for people to try to get a feel for the good and bad of the situation and what could have happened and how close the match was. It creates this sort of cocktail that might push people around in such a way that you can find bronze medalists who are happier than silver medalists."
Thomas Gilovich, professor of psychology at Cornell University, co-authored a study on counterfactual thinking and satisfaction among Olympic medalists, published in the Journal of Personality and Social Psychology in 1995.
Gilovich and his colleagues videotaped all of the NBC coverage of the 1992 Summer Olympic Games in Barcelona, Spain, and analyzed how bronze and silver medalists reacted to winning their medals.
Then, the researchers showed 25 shots of post-competition reactions and interviews to a panel of 20 college students who indicated that they were either uninterested or uninformed about the Olympic Games. Those students were asked to evaluate the Olympians` reactions and emotions in the video clips, without knowing who won bronze or silver.
When assessing the athletes` immediate reactions, participants indicated that bronze medalists appeared happier on average than their counterparts who won silver.
Additionally, the researchers interviewed 115 bronze and silver medalists at the 1994 Empire State Games in New York, a prominent amateur athletic event. After completing their events, the athletes were asked to rate their thoughts about their performance on a 10-point scale.
The researchers found that, following a competition, athletes who won bronze appeared to be significantly happier on average and that silver medalists tend to focus more than bronze medalists on what they failed to achieve.
"They compare themselves to the gold medalist and thereby think of what they didn`t achieve; the bronze medalists also focus on what didn`t happen: They didn`t come in fourth and fail to get a medal," Gilovich said.
In other words, counterfactual thinking influences how satisfied each athlete feels.
What`s another example of counterfactual thinking for those of us who are not Olympic athletes? "College admissions," McGraw said. "Do you get your first choice? Do you get your second choice? It took me three tries to get into graduate school, and I only got into one, and so I was so much happier to be there than my peers who turned down three other schools."
Olympic viewers might not notice this difference in how happy bronze and silver medalists really are, unless they take a close look at how the athletes smile, according to a 2006 study published in the Journal of Personality and Social Psychology.
The study used photos of 84 gold, silver, bronze and fifth-place winners at the judo competition at the 2004 Olympic Games in Athens. (There are two bronze medals given out at the Olympics in judo.)
The spontaneous facial expressions of athletes immediately after they had just won or lost a medal match were examined, such as facial muscle movements and eye positions.
"We found that bronze medalists tended to have more of the `genuine` smiles, known as Duchenne smiles," said David Matsumoto, professor of psychology at San Francisco State University and lead author of the study.
"These are smiles that involve not only the smiling muscle that pulls the lip corners up but also the muscle around the eyes, which lifts the cheeks, narrow the eyelids and produces crow`s feet wrinkles. Most silver medalists did not smile at all, having just lost their match," said Matsumoto, who is also a former Olympic judo coach. "On the podium later, all athletes smiled. ... The silver medalists, however, had non-Duchenne social smiles, which did not include the muscle around the eyes. That indicated that they were smiling to be polite but were not really happy."
Matsumoto added that he was initially surprised by the research findings but then thought about his own experiences as a coach.
"We all believe that silver medal performances are an amazing accomplishment, and no doubt they are. But the findings made it clear that the silver medalists were not really happy at the time they won," he said. "When I looked back at my own experiences dealing with many other athletes over the years, I realized it was true, and that some silver medalists maintain their feelings for years."
For instance, American track and field star Allyson Felix narrowly lost gold and was awarded silver in the women`s 400-meter final on Monday when Shaunae Miller of the Bahamas dove over the finish line.
Allyson Felix beaten by Shaunae Miller in 400m final 00:52
Felix wrote on her Facebook page on Tuesday that she felt disappointed.
"Last night didn`t end the way I had dreamed. I`m disappointed. I was quickly reminded of countless reasons to be proud, thankful and grateful," Felix wrote.
"Bobby [Kersee, Felix`s coach,] told me this is the most proud he has ever been of me. That resonated with me. Everything went wrong this year, but some way I made it here and won a silver medal. I fought as hard as I could and gave my all. I`m most proud of never giving up on my dreams in the face of adversity. I`m extremely humbled to now be the most decorated female Olympian in USATF history. All glory to God!"
McGraw said one way to manage these emotions would be to lower your expectations. Then, disappointment can be mitigated.
"But the problem with that is that expectations often motivate us," he said. "If you`re an athlete, wanting to win the gold is a good thing because it helps you train harder. Running is painful, and it helps you try to overcome pain. There`s the psychological component that comes with it that hard work pays off."
McGraw has his own personal connection with the Olympic bronze. Emma Coburn, one of his former students, made history when she won the bronze medal in the women`s 3,000-meter steeplechase at the Olympic Games on Monday, becoming the first American to win a medal in that event.
"I remember one time, she came to see me to talk about careers," McGraw said.
"She was asking about doing marketing research, and I responded, `Aren`t you a pretty good runner?` She said, `Yeah.` And I asked, `Don`t you have a shot to go to the Olympics?` And she said, `Uh, yeah.` And so I was like, `Then don`t even bother thinking about this stuff. Go build your brand, win Olympic medals. You have a whole career ahead of you!` And she said, `OK, thanks!` So, now, years later, seeing her win a bronze medal obviously makes me feel like I had the right reaction to her question, which was `Go see where this running thing takes you first.` "