Winter has led some of the most influential research on the connection between sleep and athletic performance. A 2013 study, for instance, piggybacked on early Major League Baseball research to look into the relationship between fatigue and career longevity in the league. It found that the more tired players were - on a self-reported sleepiness scale - the less likely they were to still be in the league at the three-year follow-up point.
"If you're an athlete who has a long season - like MLB or NBA players - the season catches up to you, particularly if you're not sleeping well," Winter says. "Sleep impacts everything."
For some athletes, checking sleep hygiene boxes a la Brady pays off. For others, however, restorative sleep can be hard to get.
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Becky Wade, 29, is among the country's top female marathoners - the runner will be lining up at next year's Olympic trials for the fourth time. When in heavy training, Wade, who lives in Boulder, Co., logs 100-plus miles per week. She knows all the right things to do to keep her body healthy, such as eating well and balancing her training, and is diligent about them. She finds a good night's sleep elusive, however.
"It became problematic in high school," Wade says. "The pressures of school, training and my goals all began to escalate. I had a hard time both getting to sleep and staying asleep." And she felt it then - and now - in her training. "I can get through an easy day, but if it's a tough workout, I definitely struggle."
Wade is well aware of the science behind sleep and performance and admits that, sometimes, that's part of the problem. "It is stress inducing," she says. "I feel like because I don't get the sleep I need, I'm skimping on maximal training."
Natasha Cloud, a 26-year-old point guard with the WNBA's Washington Mystics, says she's always been a poor sleeper but she really noticed its impact when she got to the WNBA. "I really struggled my first three years in the league as a result," she says. "It's tough to recover after a bad night's sleep. On the court, I was drowsy, slow and had poor reaction times."
After a consult with Winter, Cloud made changes to her routine, including limiting late-night use of her cellphone and other devices, and dedicated herself to getting the rest she needed. It paid off.
"This has been my best year yet," she says. "I've established a bedtime routine that helps my body signal it is time to sleep. I've learned to stay off my phone at night and aim for an early bedtime whenever possible."
Winter says that the vicious cycle of needing sleep, worrying about it and then getting even less, like Wade described, is common among top athletes. "You've got hyper-focused athletes who want to do everything right," he says. "But that can be a liability when it comes to sleep."
Coaches can sometimes contribute to the issue. "When a coach drills it into an athlete's head that he or she needs to get a good night's sleep, it can backfire," Winter explains.
Wade says she has explored many avenues to improve the quality of her sleep. Over time, she says she has developed workarounds to help offset the detrimental impact of lost sleep.
"I do all the right things with regards to sleep hygiene and that helps to some extent," she says. "I also take naps when I can because I'm better at napping than sleeping through the night."
This napping approach may actually mean Wade, and others like her, get more sleep than they realize, says Winter, mitigating the negative effects of nighttime insomnia on performance.
"These are the people who, when they track their sleep, find that they do better than they think," he says. "They might struggle four nights out of 30, but it's the four nights that they focus on."
And Wade's results suggests that her napping may be compensating for her nighttime sleep issues, even if her daytime quality of life can be affected by her fatigue.
"I recover well from hard workouts, have made progress and have run six marathons in a row without injury," she says. "I'd be more worried if I was in a constant state of breakdown."
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Smith sees plenty of players who don't get enough sleep. "I don't know that there are many players who don't have some sleep issue," he says. "You've got a fast-wired, driven group and after a game or practice, they need to shut it down and sleep. That can be hard."
One study also found that team-sport athletes are "particularly susceptible to reductions in both sleep quality and sleep duration after night competition and periods of heavy training
Like many regular people, elite athletes multiply their issues by spending too much time on devices. "The blue light damages their circadian rhythms," says Smith, meaning that their body's natural sleep-wake cycle can get out of whack. "We've given them blue-light blocking glasses and ask them to take a break from their devices before bed."
The Wizards take other steps to improve sleep, as well, including scheduling travel for away games across time zones "to optimize sleep," Smith says. "We've also added sensory deprivation tanks, education, and staff members who send reminders about sleep. We've thrown everything at it, both high-tech and low-tech."
One thing the athletes generally do not do is use sleep aids, either over-the-counter ones, such as melatonin, or prescription pills such as Ambien. "Instead of handing them a pill, which doesn't solve their long-term problems, we like to give them tools to deal with their issues," Winter says.
It's not hard, says Smith, to predict which athletes will be in the NBA for the long haul. Like Brady in the NFL, they're the ones who take sleep seriously. "The guys who have a sleep routine and appreciate the value of it are the ones who will make it," he says. "If they don't, given equal talent, they will have a shorter career."
As a performance coach, sleep is the one issue Smith wishes all his athletes took seriously. "It's the magic pill," he says. "For an athlete, it simply cures most ills."