He added with a laugh, “I’m not doing push-ups at midnight before I go to sleep. You train a bit later, and the whole routine is pushed back a little bit. But you also want to get a good night’s sleep so your biological rhythm keeps going in the right way.”

Djokovic has one strategy, grudgingly adopted, that helps him sleep longer and sounder during tournaments: he leaves his two small children at home. He may be on to something. Norah Simpson, a clinical assistant professor at Stanford who studies the role of sleep on athletic performance, recommends that players get good, quality sleep in the days before matches so they don’t go into a late-night match already sleep-deprived.

“It’s very challenging to navigate the variable schedule in respect to both your internal clock and the amount of sleep you’re able to obtain,” Simpson said in a telephone interview.

The potential for late-night matches is part of tournaments with stadium lights and no curfews. Madison Keys played mostly night matches on her way to the final at the 2017 United States Open, and recalled going to bed after 4 a.m. many mornings, waking up around noon and taking power naps whenever she could. “It’s not natural,” she said, adding, “If I know I’m playing a night match, I sleep as much as I can the day before.”

Anastasia Pavlyuchenkova’s coach, Simon Goffin, encouraged her to stay up until 1 a.m. the night before playing Stephens to help reset her body clock.

“I pushed her to watch a movie, do something, even after midnight, to be used to this kind of late match,” said Goffin, who also insisted that she sleep in until noon. “It’s important for the body and the mind to have this routine.”

Still, Pavlyuchenkova said she felt sluggish. “It was so, so strange because I was like ‘Come on, I have to make rallies!’” she said. “My energy level was on and off as well. I was trying to get as many energy drinks and gel packs as I could take.”

After ingesting all that caffeine, how did Pavlyuchenkova plan to get to sleep? “I don’t know honestly,” she said, adding, “Try to take chamomile tea?”