Perhaps more than anyone on earth, Monica Puig understands the enormous stakes in play for these four Olympic singles semifinalists.

Five years ago, an unseeded 22-year-old from Puerto Rico came whistling out of obscurity to win the women’s singles gold medal in Rio de Janeiro.

She defeated in succession Garbiñe Muguruza, Petra Kvitova and Angelique Kerber – today all multi-Grand Slam champions – and drastically altered her trajectory. In a single week, Puig achieved the milestone that will dominate her resume and, going forward, her life.

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Of the eight gold medals awarded for women’s singles in the modern Olympics, Puig and Elena Dementieva were the only players who did not win more than one major. 

It’s a well-worn cliché to call it a life-changing event, but Puig lived it. Tuesday, in a phone conversation from Scottsdale, Arizona, she explained what that medal, what that moment meant.

“Just seeing my name in textbooks in the schools in Puerto Rico, just knowing I’m going to be taught in history class for future generations,” Puig said, laughing. “It’s humbling and it’s an honor that people see me as this person.

“I try and see myself as the same Monica, who grew up in Miami, loving to play tennis. Just being who I am, my most authentic self. It’s amazing to see how far I’ve come and what that meant to Puerto Rico.”

Not one of the final four –Elina Svitolina, Belinda Bencic, Elena Rybakina or Marketa Vondrousova – have ever won a Grand Slam singles title. It’s veterans Svitolina and Bencic versus a pair of 22-year-olds, the age Puig was when she broke through in Rio.

This is their legacy moment. Win two matches in three days and you’re in the history books.

No.9 Belinda Bencic vs. No.15 Elena Rybakina

What’s at stake for Bencic:

Switzerland, a nation known for its obsession with precision, has produced some spectacularly fine tennis. Roger Federer has won 20 Grand Slam singles titles and took home gold with Stan Wawrinka (three majors) at the Beijing Olympics in 2008. Martina Hingis amassed a collection of 25 Grand Slam titles – including the doubles calendar Slam in 1998 – and won a silver medal with Timea Bacsinszky in Rio.

This one would put the 24-year-old on the board.

Her best effort in the majors is reaching the semifinals of the 2019 US Open, where she lost to Bianca Andreescu.

This is a tricky one for Bencic, for she’s never played Rybakina. To beat her, she’ll have to clean up her service game. In the quarterfinals against Anastasia Pavlyuchenkova, there were 11 double faults to go along with five aces. Bencic will have to improve her numbers both on first (32-for-45) and second serve (23-for-34) if she wants to get to the final.

What’s at stake for Rybakina:

Born on June 17, 1993, Rybakina is 11 days older than Vondrousova and seems destined to make a significant impression on the WTA Tour. It’s worth noting that her two best Grand Slam efforts came this year – the quarters at Roland Garros and the fourth round at Wimbledon.

A medal in Tokyo would continue the Kazakhstan player’s upward arc.

Rybakina had the most impressive performance in the quarterfinals, taking down two-time major champion Muguruza 7-5, 6-1. She hammered 17 forehand winners and eight from the backhand side; Muguruza managed only four and five, respectively.

If she continues to be aggressive (six aces), she can hang with Bencic, whom she’s never played.

No.4 Elina Svitolina vs. Marketa Vondrousova

What’s at stake for Svitolina:

Along with Karolina Pliskova, Svitolina is the most accomplished player not to have a major title in her trophy case. She’s come close, reaching the semifinals at 2019 Wimbledon and the US Open. This, for a number of reasons, is her best chance to put a powerful asterisk on her resume.

After three consecutive matches that went the distance, the 26-year-old from Ukraine had a relatively sedate 6-4, 6-4 outing against Camila Giorgi. She was opportunistic, breaking Giorgi’s serve four times.

The key for Svitolina? Forget where you are and what’s in play. Easier said than done, of course.

The week before Tokyo, Svitolina married French tennis star Gael Monfils, amid much pomp and circumstance. There might be a connection between that event and Svitolina’s run through the draw in Tokyo. After the stress of the wedding and all the related last-minute travel logistics, maybe tennis-as-usual has had a steadying effect.

A number of great players before her managed to take one monstrous title in their career – Mary Pierce (200 French Open), Ana Ivanovic (2008), Francesca Schiavone (2010 French Open), Marion Bartoli (2013 Wimbledon) and Flavia Pennetta (2015 US Open), to name a few.

Svitolina made the quarterfinals in Rio, losing to eventual bronze medalist Petra Kvitova. This is her chance to make a big statement in a big moment, the ultimate wedding present to herself.

What’s at stake for Vondrousova:

Vindication.

When the qualifying deadline came down last month, Vondrousova was on the wrong side of the cut. Fellow Czech Republic players ahead of her were Karolina Pliskova, Barbora Krejcikova, Petra Kvitova and Karolina Muchova. Vondrousova opted to use a protected ranking  – going back to pre-pandemic wrist injury and subsequent surgery – and Muchova didn’t make the trip to Tokyo.

The 22-year-old lefty heard her share of criticism, but she’s the last Czech standing in the singles draw. Like Rybakina, she has a promising future. Vondrousova reached the final at Roland Garros in 2019, losing to Ashleigh Barty in straight sets. This would be another early marker of that vast potential.

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In the quarterfinals against Badosa, Vondrousova was down 3-1 and rallied to win the next five games. Badosa, who retired before the second set began, left the court in a wheelchair, apparently overcome by the heat.

Vondrousova must overcome history here; Svitolina holds a 3-1 career edge.

Here’s a grand opportunity to take those last few steps to a breakthrough victory.