For the Slovenian cross-country skier Petra Majdič, the unlikely key to Olympic glory was misdiagnosis.

While warming up for her first race at the 2010 Winter Games in Vancouver, Ms. Majdič skidded off an icy corner and fell more than 10 feet into a rocky creek bed. She dragged herself to an on-site medical tent for an ultrasound. “I don’t know,” the doctor said, “but it looks like everything is OK.”

Sure, she was in excruciating pain that made her shriek every time she exhaled. But the pain, she believed, was just in her head. As long as nothing was broken, her decision was clear. “Can I go?” she asked. The doctor said yes.

Later that evening, after gritting her teeth through a qualifying race, a quarterfinal, a semifinal and a final where she fought to an improbable bronze medal in the classic sprint, she finally went to the hospital—where she was diagnosed, correctly this time, with four broken ribs. The stabbing pain she’d felt during the semifinal? That was one of the broken ribs puncturing her lung, which then collapsed. She missed the rest of the Games and was in the hospital for nearly a week.

Such tales are a staple of Olympic lore, a stirring reminder of the heights to which athletes can rise with a medal on the line. In the coming weeks, as the world’s fleetest and toughest converge on South Korea for this year’s Winter Games, we will undoubtedly see more extraordinary feats of endurance. But how, exactly, do the athletes do it? Is it just a matter of physical prowess and training, or is there something else going on in these superhuman exertions?