TOKYO — There’s an old saying around the Olympics that silver is the saddest medal.

The gold medalist is always over the moon. The bronze medalist is happy, too, because she is on the podium. The second-place finisher — well, she is not first. Coulda, woulda, shoulda.

For the first time Monday in her Olympic career, dating back to 2012, Katie Ledecky did not win an individual race. Australia’s Ariarne Titmus won the women’s 400-meter freestyle, arguably the most anticipated race of the Games, in a race that proved two things.

One, Katie Ledecky is a class act. In not winning, Ledecky showed everyone that silver shines, too, that silver is proudly one of three best in the world, that accepting silver when you’ve given your best — and your best, right now, is all you can ask of yourself — can yield a master turn in sportsmanship and good grace. 

Two, Ariarne Titmus in 2021 — at least at 400 meters and very likely at 200 as well — is, as an athlete, what Katie Ledecky was at the Rio Games in 2016, and the race Monday underscored how swimming has, over the past five years changed, and significantly.

Because of Katie Ledecky.

At distance, meaning 400 meters and up, Ledecky has always had one key trait. 

Ledecky would go out hard and seize such a lead that by 200 meters she would essentially, like one of the dementors in the Harry Potter books and films, crush the souls of the other women in the pool.

In the races to come here still this week, this is almost surely what Ledecky will do in the 800 and 1500, the 1500 to be run for the first time as a women’s event at the Games. 

But not at the 400, not here, not Monday.

In Rio in 2016, Ledecky was the second-youngest swimmer in the 400-meter free final, one of only two younger than 21. On Monday in Tokyo, Ledecky was the oldest by two years in the 400m free final. There were five teens in the race.

Consider: reflecting a generational turnover on the U.S. swim team, the Americans sent 11 teenagers to Tokyo, 10 of them female, including 17-year-old Lydia Jacoby of Seward, Alaska, who Monday morning won the first of the two women’s 100 breaststroke semifinals. 

Consider, too: 14-year-old Summer McIntosh of Canada, who made Monday’s finals, just like Ledecky did in London in 2012. When Ledecky was 15.

McIntosh finished fourth Monday. Bronze went to China’s Li Bingjie, 19, in 4:01.08.

In this respect, Ledecky is now something like Phelps was in Rio in 2016. Remember: Joseph Schooling of Singapore got Phelps in the 100 fly. As Ledecky, 24, has gotten “older,” she had more or less hit a plateau. The rest of the world took aim, and Titmus, in particular, surged past, at least at 400 and — to be seen later this week — most probably at 200, too.

In London in 2012, France’s Camille Muffat won the women’s 400 free in 4:01.45.

Four years later, in Rio, Ledecky won in 3:56.46. That’s still the world record. 

Five seconds in four years at this distance is — huge.

That’s how much Ledecky changed things.

Before Monday’s race, eight of the Top 10 women’s 400 were Ledecky times. 

But: all came between 2014 and 2018. 

The other two — Titmus, at the 2019 Gwangju world championships and 3:56.9 at the Australian Trials a month ago.

On Monday, in typical fashion, Ledecky went out hard.

Titmus knew to expect this. She was not intimidated. Farthest thing from.

Actually, no one was.

McIntosh had actually gone out harder. She was first at 50 meters, third at 100 and all the way through 350, then just couldn’t hold on over the last lap, Li rolling past for third. 

Ledecky took the lead by 100 and tried — tried — to extend it through 200. No dice. Titmus stayed within a second.

At 300 meters, Titmus had closed to within 16-hundredths.

And by 350, Titmus flipped first, 22-hundredths ahead. 

From then on, it was a sprint to the finish. Here the numbers reveal the cold, hard truth. Ariarne Titmus closed in 28.67 seconds. Katie Ledecky’s last lap was 29.12. 

Titmus touched in 3:56.59. 

That’s the second-fastest, ever, and as the world has by now seen, in a clip that instantly went viral, her coach, Dean Boxall, made like Mick Jagger in the stands. 

Ledecky: 67-hundredths back, 3:57.36.

Immediately after the race, the two hugged on the pool deck. “I was able to beat a great champion,” Titmus said. “That makes it even more satisfying.” 

Consider, also: Ledecky’s time made for her second-fastest time ever, her first time under 3:58 since 2018.

“I can’t be disappointed,” she said moments after the race. “It was a good time for me.” 

Referring to Titmus, Ledecky said, “We’re really friendly. She said she couldn’t have done it without me. I can say the same about her.”

A couple of hours later, at a news conference, Ledecky reflected:

“I just came into this race very much at peace with the work I've done.”

She went on:

“I knew no matter the outcome I was going to put up a fight and put up a great race. And even if I didn’t win, I was still going to be happy for whoever won gold. I know what it takes. To come out on top is amazing.

“… I found a lot of joy and happiness and love coming into that race, and carried that with me.

“I think,” Katie Ledecky said, “that’s the biggest win of all.”