TOKYO — At the intersection of gimmicky Olympic innovation and questionable American lineup strategy stood the world’s fastest swimmer Saturday morning. Tabbed to swim the anchor leg of the first mixed-gender medley relay final in Olympics history, and needing a gold medal to keep alive his hopes for a historic meet, Caeleb Dressel dove in and attempted to chase down seven female swimmers whose head starts ranged from about eight seconds to about 2½.

It was an incongruous sight — and ultimately, too much to ask of Dressel. Over his 100 meters of freestyle, he managed to track down three of the women, but he couldn’t catch the other four. As a result, Team USA finished fifth in a relay for which it once had designs on gold — the latest disastrous result for a nation unaccustomed to being shut out of the medal stand in Olympic relays.

“We’re not happy with how we finished, certainly not,” said Dressel, who has won two individual golds and one relay gold at the Tokyo Olympics, with chances left for one more of each on Sunday’s final session of the meet. “Fifth place is unacceptable for USA Swimming, and we’re very aware of that. Our standard is gold. And we didn’t execute well … I think everyone swam as good as they could in that moment, and there were teams better than us. It stings.”

Britain won the inaugural Olympic gold in the 4x100-meter mixed medley relay, in a world record time of 3 minutes 37.58 seconds. The event has been contested at world championships since 2013 but had never been included in the Olympic meet program until this year. Teams can use any swimmers for any of the four strokes as long as they deploy two women and two men.

The American quartet of Ryan Murphy (backstroke), Lydia Jacoby (breaststroke), Torri Huske (butterfly) and Dressel (freestyle) performed more or less as expected, with Murphy (52.23), Jacoby (1:05.09) and Dressel (46.99) all coming within .14 of their medal-winning times in the 100-meter races in their individual strokes, and Huske (56.27) coming within .54 of hers. Jacoby’s solid effort came despite the fact her goggles slipped off and were down by her mouth for much of her race.

Nonetheless, Team USA’s time of 3:40.58 was more than three seconds off the Brits’ gold medal winning time, and more than a second and a half off the time it would have taken to make the medal stand.

“We’ve put a ton of time into how to put together the best possible relay to go compete for a medal. There’s different trains of thoughts with using mathematics [versus] using gut instinct,” U.S. head women’s coach Greg Meehan said. “And unfortunately it didn’t all come together. We’ve had lots of different [lineup] iterations. And … we felt like maybe we’d be a little bit better with that crew.”

“Maybe in a way we overthought it,” head men’s coach Dave Durden said. “It wasn’t from a lack of analysis. Maybe at some point we got too analytical with that and just needed to roll four athletes out there and let them go.”

In weighing the lineup possibilities, Meehan and Durden had to weigh factors such as each swimmer’s daily schedules (freestyle sprinter Abbey Weitzeil, for example, had just six or seven minutes between her heat of the 50 free and the start of the relay), plus their recent performances and relay history — as well as an intangible factor that might be described best as trust.

But the U.S. coaches appear to have ignored one simple mathematical reality in constructing this lineup: the fact the gap between elite men and elite women in the breaststroke is the largest of any of the four strokes — roughly 7½ seconds on average at this meet.

The gap between individual men’s 100 breast gold medalist Adam Peaty of Britain (57.37) and women’s winner Jacoby (1:04.95) at these Olympics, for example, was 7.58 seconds. By comparison, the gap between men’s 100 free champion Dressel (47.02) and women’s counterpart Emma McKeon of Australia (51.96) was only 4.96 seconds.

There was a reason China, Australia, the Netherlands, the Russian Olympic Committee and Israel chose men in the breaststroke leg to match up against Britain’s Peaty, arguably the most unbeatable swimmer in the world across 100 meters of his stroke. Only the U.S. went with a female, the 17-year-old Jacoby. Peaty out-split her by more than eight seconds.

The Americans weren’t lacking in options for men to swim the breaststroke leg. In theory, that list would begin with Michael Andrew, who is No. 3 in the world rankings this year at 100 meters based on the 58.13 he swam at Olympic trials. But Andrew also has had a disappointing meet to this point, swimming a 58.84 to finish fourth in the 100 breast final, then collapsing during the freestyle leg of his 200-meter individual medley to finish fifth.

Asked about Andrew’s underperformance, Durden said, “It’s the challenge of the Olympic Games, the weight and the gravity of it, and certainly Michael as a first time Olympian, you feel that in some different ways.”

Until Tokyo 2020, Team USA had medaled in every relay in Olympics history in which it had an entry. But this week, they have failed to make the podium twice: in the men’s 4x200 free relay and now the mixed medley. In Rio 2016, the Americans won gold in five of the six relays, taking silver in the other. Here, they have won just one — the men’s 4x100 free — with the men’s medley and women’s medley Sunday.

There are critical decisions to be made in both. The Americans only can hope those decisions work out better than the one they made Saturday.