NEW YORK — Here’s a piece of advice for any men hoping to have a successful US Open in an Olympic year: Don’t win the silver medal.

Carlos Alcaraz’s shock second-round defeat by Botic van de Zandschulp at Flushing Meadows on Thursday night was just the latest in a run of early exits for those who have come so close to winning gold at the Games down the years.

Since tennis was officially reintroduced into the Olympics in 1988 (when the Games were held after the US Open), Roger Federer is the only male silver medal winner to make it even as far as the quarterfinals, in 2012.

Three lost in the first round, including Juan Martin del Potro in 2016 and Karen Khachanov in 2021; three went out in Round 2; two exited in Round 3; and one made the last 16.

Speaking after his defeat Thursday night, Alcaraz said he didn’t feel that missing out on gold had played a part in his performance or affected him.

“Being so close [to] the gold medal, it was difficult for me in the few moments or one hour … [after] the match,” he said. “But once I realized what I have achieved, the silver medal, it was a great achievement. I was really proud about it and after … I didn’t think about it anymore.”

But after a packed summer in which he also won the French Open and Wimbledon, his performance in Cincinnati — where he lost his first match and smashed a racket on the court — and his below-par display in New York, suggest otherwise.

Even a bronze medal seems to make players happier than the just-missed-gold silver medal.

When tennis players lose a match, that’s normally that. Time to pack the bags and move on to the next week and the next opportunity. But at the Olympics, when you lose in the semifinals, there is a second chance, at least in tennis. Winning the bronze medal can almost feel better than silver, because of that chance for redemption.

“I’ve been told statistically that bronze medalists are happier than silver medalists,” Taylor Fritz said, with a smile, at the US Open earlier this week. Fritz and Tommy Paul won the bronze medal in the men’s doubles in Paris and, despite wanting gold, they left France happy.

“I would have loved to have a chance at gold with Tommy. We were playing really well,” he said. “We were pretty upset after the semifinal loss and immediately all I told him was, like, ‘Look, if we’re upset now, how bad are we going to feel if we don’t come back and win the bronze? Let’s make sure we focus back up and, you know, win the next one.’

“It was an awesome experience. My main goal there was to leave with a medal. I think if we would have lost that third, fourth playoff, it would have hurt a lot.”

Italian Lorenzo Musetti won the bronze medal in the men’s singles in Paris. Outplayed by Novak Djokovic in the semis, he took his second opportunity to claim the bronze.

“I was in such a sad mood [after the semifinal], the way I behaved on court, there were some things that I didn’t like about myself in the performance,” he said.

“But I had to analyze all these things and I had the chance to play the day after. It was something really kind of strange for us because when you lose, you’re home, but it was like a second chance. And I got it the hard way, so it was even more deserved in a way.”

World No. 1 Iga Swiatek won the bronze medal in Paris, after losing in the semifinal against China’s Zheng Qinwen, the eventual champion. Having that second chance, she said, allowed her to leave on a high.

“It was kind of bittersweet, and I didn’t understand what’s going on right after I won this match, because it doesn’t happen often in tennis,” she said. “In a normal tournament, finishing third wouldn’t be a good result for me, but the Olympics feels a little bit different.”

Silver medalists in the women’s event have performed better than the men at the US Open in an Olympic year, with Angelique Kerber winning the title in 2016 and only one woman, Marketa Vondrousova in 2021, going out before the last 16.

Donna Vekic, the Croatian who lost to Zheng in the Olympic final, said she left Paris elated at her achievement. “I’m really proud,” she said. “It’s a great feeling, something that I’ll have for the rest of my life.” Vekic is still in play at the US Open, and will get a chance for a rematch against Zheng on Sunday in the fourth round.

But speaking to WTA Insider earlier this month, Victoria Azarenka said she was “for sure the happiest on the podium” when she won the bronze in London in 2012.

“The bronze for me is so much better than silver,” she said. “It has to be gold or bronze. Silver, sorry, bye-bye. I don’t like it. Emotionally it’s very difficult. But the reward and the feeling of getting it was just beyond.”