The money, though, did little to relieve Bell’s cascading health problems. There were the seizures and migraine headaches and chronic pain that doctors treated with opioids such as Vicodin and OxyContin. He became addicted, which contributed to the demise of his marriage. In 2014, Bell killed himself. It was his second attempt. He was 42.

“In reality, he died the day that crash happened,” Chuck Bell said. “He never recovered from it.”

The Crash That Might Have Saved a Life

Sisson cannot remember thinking about Bell or his crash before or after his own fateful run down a track in St. Moritz in early 2002. He can’t remember anything from that time. Six weeks of his life are blank. He pieced together details of the crash, which occurred during a practice run, as a forensic scientist would: by studying the helmet and the sled, and talking with teammates, officials and the doctors who treated him.

He had stayed up until 4 a.m., local time, the night before the crash, watching the Super Bowl. He overslept and rushed to the track for training. Pressed for time, he neglected to check the sled before pushing off. He quickly realized that the steering mechanism had frozen, making a crash almost inevitable.

He avoided disaster for eight turns. On the ninth turn, a nasty horseshoe-shape curve, his luck ran out.

The black helmet Sisson wore that day, along with two other scraped and dented ones from his career, sit atop a cabinet in his classroom at Morgan High School, where he teaches geography, history, psychology and weight training. As he cradled it and pointed to the dings and peeled paint, he explained how he thinks an initial impact, between the edge of the wall and his helmet’s chin covering, knocked him unconscious. A whack to the back left side of the head caused further damage.

The sled flipped, and Sisson slid hundreds of yards more, his head wedged between the wall and the 400-pound sled, until the sled finally slowed in the finish area. He was airlifted to a trauma center 50 miles away.

Back home in Wyoming, his parents got a phone call saying not to come to Switzerland because it was unlikely he would survive. His mother, father and stepfather scrambled to get passports that day and got on the first available flight.

The doctors who evaluated Sisson at the hospital in Chur, Switzerland, gave him a score of five on the Glasgow Coma Scale, which starts at three for patients who are essentially unresponsive and goes as high as 15 for less severe victims of head injuries.

“Five is very low,” said Dr. Gian-Reto Kleger, the specialist who supervised Sisson’s treatment in Switzerland.

A CT scan revealed bleeding in multiple areas of the brain, though the lesions were not large enough to require removal. Instead, Kleger drilled a hole in Sisson’s skull to treat the potentially damaging effects of swelling, drain excess fluid and insert a device to monitor the pressure. Doctors kept him in a coma for four days.

Twenty years later, Kleger still does not know why the pressure in Sisson’s skull remained low given the severity of the crash. He thinks Sisson’s brain may not have sheared the way brains often do when the skull rotates violently during a high-speed crash, causing lesions throughout the brain tissue rather than the targeted bleeding that can occur in a head-on impact.

Sisson’s age — his “young brain” — also most likely played a role. Doctors classify brains older than 25 to 30 as “old.”

“It’s a fascinating thing,” the doctor said. “A young brain is just so much better at healing.”

A week after his crash, Sisson and his mother flew back to Salt Lake City, the host city for the 2002 Winter Olympics, on a special medical jet. He checked into the brain rehabilitation unit of the L.D.S. Hospital, where Dr. Andrew Dodds, the attending physician, took over his care.

In those first days, Sisson was confused about where he was. His eyes and facial expression had the flat affect of someone who is there but not really there. He struggled with memory and balance. He tired easily. Noise and bright lights overstimulated and agitated him, though Misti Timpson, a physical therapist who helped with his rehab, said he never lashed out the way brain injury patients often do.

“He was the nicest agitated person I have ever met,” Timpson said. “He would say: ‘Excuse me, ladies, I am getting agitated. I suggest you step away.’ And only then would he scream or strike out or cover himself with a blanket.”

After a little more than a week, Dodds cleared him to attend an Olympic medal ceremony in Salt Lake City with an aide.

Bell was there. Sisson has a photo of the two of them embracing that night, though he has no memory of the moment.

After another week, Sisson had improved enough to go home, though doctors monitored him for a year, slowly clearing him to use knives and kitchen appliances, then to drive and enroll in some college classes that did not involve math or languages or much memorization.

“I’m convinced that Joe was saved because he was 21 and didn’t have the cumulative trauma from sliding injuries that his friend probably had,” Dodds said.

A little less than two years later, Sisson asked Dodds if he could try bobsledding again. The doctor was hesitant, and consulted with a neurosurgeon, but Sisson seemed back to normal, so he cleared him.

The comeback was short-lived. In January 2005, Sisson flipped his sled on one of the last turns on the track in Lake Placid, N.Y. The crash spooked his wife, who told him his career as an elite bobsledder was over.

He still loves the sport, still takes the occasional joy ride down the track in Park City. Sometimes he takes players from his football team.

His goal now is to pass the test that will give him the certification he needs to work as a strength and conditioning coach at the college level. The test requires learning a lot of scientific terms, which remains a challenge. It also costs $400. He signed up for it in December.

“That’s the kind of money I don’t have to take a test if I am going to fail it,” he said.

Dodds is semiretired. A few years after he cleared Sisson to try bobsledding again, the doctor did something he had never done: He folded his 6-foot-5 frame into the back of a sled at the Park City track.

Within seconds, the doctor said, he was in excruciating pain, his body and head slamming around as the sled careened down the hill. He underwent an examination to make sure he did not have a spinal cord injury.

When he next saw Timpson, the physical therapist, at the hospital, he told her he had made a big mistake. If he had known what the body and the brain endured during a bobsled run, he never would have cleared Sisson to compete again.