“Sometimes their eyes go back a little so that their whites show, and it’s really kind of creepy,” Erin Hamlin, the American bronze medalist in the luge, said of her fellow competitors. “Some people get really into it, and because we paddle to start, they’ll paddle really hard on the bench and all of the sudden you’ll be sitting there really quiet and someone will hit the bench really hard, and it will kind of startle you.”

The Winter Olympics are full of events that are contested in controlled, fairly predictable environments. Consider aerials and ski jumping. The wind or weather patterns may shift. The crowd noise may vary. But there is no direct competitor to change the dynamic, and in contrast to Alpine skiing events, no setting of gates to change the geometry.

But the most predictable Olympic environment is the sliding track. There are limited training runs during the Olympics, but Rush said that before competing, he had mentally driven the Sochi course hundreds of times from start house to finish.

“I’ve tried to keep the track in my mind throughout the year,” he said. “I’ll be in the shower or brushing my teeth. It just takes a minute, so I do the whole thing or sometimes just the corners that are more technical. You try to keep it fresh in your head, so when you do get there, you are not just starting at square one. It’s amazing how much you can do in your mind.”

Leading Winter Olympic nations clearly agree. The Canadian team came to Sochi with eight sports psychologists. The Norwegians came with three, including Britt Tajet-Foxell, who has worked with the cross-country star Marit Bjorgen as well as dancers at the Royal Ballet in London.

The French Olympic team, perhaps more inclined to self-analysis, came with none, according to one of its press officers, although its athletes do work with sports psychologists based at the national high-performance institute in Paris.