There were failures all over the Super Bowl field. They were everywhere you looked, the losers, drifters and discards. There were the guys who went undrafted, the guys who had been cut, or traded, or lowballed. There were the coaches who knew how it felt to be fired. What that should tell you is to never underestimate the virtues of failing.

Winning coated it all with such a false patina, the shine on the sterling of the Lombardi Trophy covering all that came before. Which was a sort of shame, because underneath the spectacularity of the Kansas City Chiefs’ 31-20 victory over the San Francisco 49ers there was a dull yet invaluable truth to be found, something of use to any ordinary person trudging through a long day: namely, how to manage defeat and turn that demon around. They did it not with dazzlement but by being what Coach Andy Reid called “dirty tough-minded.”

If “success is the ability to go from one failure to another with no loss of enthusiasm,” as Winston Churchill once said, then surely the 61-year-old Reid qualifies as a success, with his first championship in 21 years of trying. But then so does the hard-yarder Damien Williams, whose journey to Super Bowl champion included clawing through junior college, getting kicked out of Oklahoma, going undrafted and an unappreciated stint with the Miami Dolphins. “I’m not going to be stopped,” he told the Chiefs in the huddle just before he tore outside for his second touchdown to ensure the victory. Williams had talked all week about the value of his old failures. “I’ve had a long, long road,” he said.

Williams was one of 28 undrafted free agents in the game. Think about that for a second. More than a quarter of the players on the field were considered unworthy at one point in their careers.

Even within the game, critical players at times looked like terrible blunderers, only to rebound. For three quarters, Chiefs quarterback Patrick Mahomes was headed toward the most ignominious failure of his young career. With his team down by 10 early in the fourth quarter, he was just 18 for 31 with two interceptions and, “It looked rocky, man,” defensive end Frank Clark said. Mahomes admitted, “It was a bad situation.” But Reid steadied his quarterback with a fascinating piece of advice. He told him: “Keep firing. Keep believing what your eyes are seeing.” What he meant was, trust your experiences, even if it means we go down.

What these people demonstrate is that to win, you have to be willing to lose — badly. Even hurtfully. Reid entered the Super Bowl with a 14-14 playoff record. He had finished every single postseason as a head coach with a loss, left wanting. Time after time, he came back for more, willing to experience the radiological exposure of failure.

So many people, at the early stage of disappointment, flinch. We want to know just enough about ourselves and no more. We don’t want to think the worst — that we’re failures — and that means we never get close to our best, either. If there is one characteristic that any day laborer can draw from a pro coach or athlete, if there is any way in which an ordinary person can emulate them, it’s in the ability to lose without losing heart.

Failure is a seriously under-analyzed experience. There are shelves upon shelves of books about how to succeed, but precious few of them make the vital connection that failure is an essential precondition for success. Nor do they acknowledge that reversal, a negative experience, a frustration, an obstacle, is the far, far more common work experience. About 3 million Americans lost a job for one reason or another between 2015 and 2017, according to the Bureau of Labor Statistics. Their plant closed or their company moved, their shift was cut, their position was abolished or their boss simply wanted someone fresh. Running back Raheem Mostert has that in common with them. He was laid off by six different teams before he landed with the 49ers. “I finally have a place to call home,” he said.

One reason coaches and athletes deal so resiliently with setback is that they understand something most people don’t: You can’t improve something until you’ve stressed it. You have to probe for your own weaknesses to correct them. If NFL coaches have anything in common with any other profession, it might be with engineers. As Kevin Kelly, founding editor of Wired magazine, has observed: “Great engineers have a respect for breaking things that sometimes surprises non-engineers, just as scientists have a patience with failures that often perplexes outsiders. But the habit of embracing negative results is one of the most essential tricks to gaining success.”

Renowned research chemist Richard N. Zare put it similarly: His lab failures can be comedies of errors, he says, but “failures are nature’s way of guiding us to what really works.” But maybe nobody put it more simply than Thomas Edison.

“I can never find the thing that does the job best until I find the ones that don’t,” he said.

Reversing failure takes more than just sheer resilience, of course. Everyone perseveres. What separates headbanging from an actual change in your circumstances is the ability to patiently diagnose and learn. According to an interesting 2019 study titled “Quantifying the Dynamics of Failure Across Science, Startups and Security” that appeared in Nature magazine, it’s not just the ability to keep trying that matters, but the ability to keep trying in an organized, well-directed way. The study, which looked at failure data in a variety of fields, including 46 years of venture-capital start-ups, concluded that the eventual succeeders made “critical refinements to systematically advance towards success,” whereas others who encountered repeated failure reacted in a more disjointed way, especially making rash changes, tearing things up prematurely.

A lot of NFL teams could learn something from that observation.

If the Chiefs had a signature quality this season, it was their ability to deal with failure in an organized way. This was undoubtedly the leadership of Reid, the veteran of so many playoff years with the Philadelphia Eagles when he was “so close” before he was fired in 2012. Last year, after the Chiefs suffered their bitter overtime loss to the New England Patriots in the AFC championship game, Reid went back to work without surrendering to the self-doubts over his sub-.500 career playoff record.

So many teams respond to a disheartening loss by regressing, but Reid told the Chiefs they were “just four inches off.” Four inches was the distance of an offside penalty that negated the interception that could have won them the game. A single four-inch mistake. “We decided we could all do four inches better,” Reid said. It was the difference between another failure and the ultimate success.

For more by Sally Jenkins, visit washingtonpost.com/jenkins.