Emma Coburn celebrates after winning the bronze medal in the women's 3000-meter steeplechase. (David J. Phillip/Associated Press)

After she ran the steeplechase faster than any American woman ever has, Emma Coburn raised her arms as high as fatigue would allow. She made it to shoulder level and stopped. Enough. Her body had too little left to express joy.

Until the pain subsided, you would have to feel it for her. The steeplechase is 3,000 meters of middle-distance mayhem, a running, jumping, splashing ordeal. Until the pain subsided, you would have to comprehend the beauty of Coburn’s feat, which went beyond a dash in the latter half of the race to earn the final spot on the medal stand.

In the Olympics, in all sports, it’s easy to be so obsessed with winning and losing and predetermined measurements of success that you forget to appreciate growth. You forget that the old “Faster, Higher, Stronger” Olympic motto isn’t an excuse for dopers to cheat but an articulation of the will to improve, to max out, to make limits bend. It doesn’t always take gold to recognize that spirit. As Coburn showed Monday morning, sporting breakthroughs are so much more versatile.

Ruth Jebet, a 19-year-old born in Kenya who competes for Bahrain, ran the second-fastest women’s steeplechase ever, finishing in 8:59.75, just off the world record of 8:58.81. She dominated the field. She won by a Katie Ledecky margin. She was more than seven seconds faster than silver medalist Hyvin Jepkemoi of Kenya, nearly eight seconds faster than Coburn. For more than half the race, the chaos that a tightly bunched steeplechase can cause became a non-factor. Four runners separated from the pack, and there were also huge gaps separating several of those four.

“It was just a crazy, weird race,” said American runner Colleen Quigley, who finished in eighth place but posted a personal-best time of 9:21.10. “It went out really slow and then picked up really quick, and I didn’t plan for that.”

Here are 10 members of the U.S. track and field team you should know as they compete in the Rio Olympic Stadium. (Lee Powell/The Washington Post)

No one had planned for it. So the runners had to improvise. Basically, they had to concede first place to Jebet so that they wouldn’t surrender their best effort. The inclination is to expend too much energy keeping pace, keeping alive the far-fetched hope of catching Jebet, which would have been a formula for fading near the end and ultimately running a slower time. Instead, the women had to maintain the discipline to run a complete race. And here’s the catch: Even with that discipline, it was understood that there would be some kind of Jebet effect, that she was about to take everyone to a place that most of their bodies hadn’t known, if they could take the punishment.

Coburn handled the stress perfectly. She led the first two laps, but after Jebet’s surge, she was in fourth place, well behind Kenya’s Beatrice Chepkoech. Coburn was in a pickle. She prefers to close the gap slowly, leaving more for her finishing kick. But when Jebet took the lead, she caused every gap to open quickly. Coburn stalked the third-place Chepkoech carefully, running faster but still nibbling at the gap, before sprinting ahead with about 500 meters remaining. The final stage of the race would be about guts.

“Okay, hold on to this,” she told herself. “Hold on to this.”

Coburn beat Chepkoech by over eight seconds. She nearly caught Jepkemoi. It’s common, too common, to talk about an athlete settling for a bronze medal. Coburn didn’t settle. She set an American record with a time of 9:07.63, trimming a record that she already held by more than three seconds. It was the 13th-fastest time in women’s steeplechase history.

Coburn became the first American to win a medal in the women’s steeplechase, which has been an Olympic sport since 2008. Include the men’s steeplechase, which has been going since 1920, and Coburn is the first American medalist since Brian Diemer won a bronze in 1984.

But for Coburn, the medal wasn’t the honor. The medal was the reward for exceeding limitations and establishing a new standard for her sport in the United States.

“I’m very motivated with or without a record, a medal, whatever the case is,” Coburn said. “It wasn’t a big motivating factor in my training. The goal, the reason for competing, is so much greater than that.”

Coburn makes an important point that needs to be considered. Think about this: Russia had dominated the women’s steeplechase in the 2008 and 2012 Olympics, though Yuliya Zaripova’s gold in the latter was stripped earlier this year. If the Russian track and field team hadn’t been banned from the Rio Games for its doping scandal, it’s possible Coburn could have run the same race and finished, say, fifth. If that happened, if Coburn had still lowered an American record by three seconds, if she had maxed out and finished fifth, were we supposed to look at her with empathy and say “sorry”?

“It’s frustrating in little moments like that, when you know you’ve done your best and announcers or media don’t know quite how to approach you about it,” Coburn said.

If the top five finishers were awarded medals during the Olympics, there would be a lot more success stories. Three is a rather random number we are conditioned to accept without much consideration. It’s tradition. It was decided long ago. That’s just how it is.

And, of course, I’m offering these words after choosing to praise a bronze medalist instead of another Olympian, such as Quigley, who also reached a new level while finishing eighth — in the world. So there’s room for everyone to think harder about success. There’s room to think twice before casting an also-ran participating in the final of an international competition as a failure while heaping excessive praise on the rock-star Olympians who never seem to lose.

The image of gymnast Aly Raisman crying after her floor routine in the all-around last week keeps coming to mind. She was crying to celebrate that she had done all she could. She knew Simone Biles was going to win the gold medal. She knew silver was her summit, and when she reached it, her emotions overwhelmed her. Don’t tell her that second place is the first loser.

“This was the very best I could do,” Raisman said proudly.

On Monday, it was Coburn’s turn to win a medal for the anonymous competition purists who make the Olympics special. Let Quigley verify it.

After Quigley finished with a personal best that was 21 seconds slower than the gold medalist’s time and more than 13 seconds off Coburn’s, she fell to the track in agony. Then she looked at the scoreboard and saw an American flag next to third place. That’s when she realized what Coburn had done.

“I was in my own pit of pain,” Quigley said, “and I just forgot about the pain. She really deserved it. That was really a silver lining. Or a bronze lining.”

It’s a lining that should supersede color.