Matt Centrowitz wins Olympic gold in the men's 1,500 meters. (Jonathan Newton/The Washington Post)

It doesn’t matter how many years athletes dream of it, how many times they fantasize about it, how many times they play it out in their heads. In the race of emotions, disbelief has a way of outpacing exhilaration.

So even though Matthew Centrowitz led from the start of the Olympic men’s 1,500-meter race Saturday and only briefly allowed another runner to pull in front of him, he still crossed the finish line a bit uncertain about what had just happened.

“I literally was still looking at the board, like, did somebody go by me? Did I really just win? Did I really just hold that caliber of a field off in the Olympic final?” Centrowitz said later. “I could not have scripted it any better.”

Someday the shock might wear off, but the wave of emotions that swept over Centrowitz will linger for a long time. The Arnold native won the race with a time of 3:50.00 to become the first American to claim Olympic gold in the 1,500 in 108 years.

“I thought on the best day I could maybe get a silver medal,” Centrowitz said later. “Sure, in the back of my head I thought I could get a gold. But I would’ve been very, very happy with a silver.”

After crossing the line, the 26-year-old Centrowitz took an American flag and circled the track, slowly processing how far he had come: a five-time All-Met at Broadneck High in Annapolis, a promising middle-distance runner at the University of Oregon, a runner who dealt with the frustration of just missing the podium four years ago at the London Games. He spotted his father, Matt Centrowitz, the former Olympic runner who coaches cross-country and track at American University, in the stands and yelled, “Are you kidding me?”

“Are you [expletive] kidding me?!” the elder Centrowitz yelled back.

“We just kind of went back and forth,” the runner recalled later with a chuckle. “I don’t think any of us believed it.”

The surprising win marked the United States’ first gold medal in the 1,500 since Mel Sheppard’s victory in the 1908 Olympics. Centrowitz employed a smart strategy that netted him gold but also resulted in the slowest winning time since the 1932 Games in London.

Centrowitz said he had a handful of strategies he had been mulling over, and he didn’t settle on his approach until reaching the starting line. “Spur of the moment,” he said. He raced to the front of the pack right away and showed he was in no hurry to race around the track. His 400-meter split was all of 66.83 seconds. The second lap was even slower — 2:16.59 after 800 meters — but he was still in front.

It was a strategic tactic, a gamble that he would conserve enough energy to fend off a late kick from the top challengers. The field was considered solid, featuring each of the past two Olympic winners: Algeria’s Taoufik Makhloufi, who won in London, and Kenya’s Asbel Kiprop, the 2008 Olympic winner.

“The alphas in the race, the ones who have the credentials, are people who traditionally aren’t front-runners,” said New Zealand’s Nick Willis, the bronze medal winner who finished 0.24 seconds behind Centrowitz. “There wasn’t anyone out there who was likely to go push the race.”

Centrowitz’s slow pace might have benefited runners with a good late kick, but it frustrated others.

“It’s like youth level, really. . . . It was beyond slow,” said Great Britain’s Charlie Grice, who finished in 12th.

As the pack circled the track, Centrowitz maintained the lead except for one brief stretch, running on the inside and holding position. The slow pace turned the race into a physical one, bumps, shoves and blocks helping determine positions on the track. Early in the race, Kenya’s Ronald Kwemoi tumbled and had to sprint to rejoin the group.

“Once I was in the lead for so long, I was kind of like, ‘All right, now we’re getting in the later stage of the race where I can’t give this lead up,’” Centrowitz said.

Centrowitz was still in front heading into the final lap. He didn’t need to slam on the gas, instead steadily increasing the pace. Kiprop had been patient and finally made his move to front but was unable to pass Centrowitz heading into the final curve.

“I wasn’t confident. I was thinking someone was going to try to come by me on the backstretch,” Centrowitz said. “No one did. I was happy to have it going into the last curve, and then that last homestretch was a long 100.”

While the runners started sprinting, Centrowitz showed he had plenty left in the tank and no other runner — not Kiprop, not Makhloufi — had any hope of closing the gap. He won gold with a time that was a full 15 seconds slower than he posted four years ago at the London Games.

At those Olympics, a 22-year-old Centrowitz turned in a fourth-place finish. It’s the position closest to the podium but, for many athletes, the furthest from a sense of true accomplishment.

“It was a disappointment, but I can’t say that was motivation coming into this,” Centrowitz said. “. . . I came into this championships with a different mind-set. Thought to myself, I’m in great shape. Just run to my capability. It wasn’t a redemption thing for London. It was about being the best I could be on this day.”