For 10 years, Andre Iguodala slept terribly. Back in college, the Golden State Warriors forward would play videogames late into the night. Eventually he'd crash, sometimes as late as 4 am, only to wake up a few hours later for practice. Then came class. When he was lucky, he'd squeeze in an afternoon nap. Later that night, it'd be back to videogames—either that or Fresh Prince reruns.

Iguodala's brutal sleep habits followed him to the NBA. Only in 2013, after joining the Warriors, did he manage to connect with Cheri Mah, a physician scientist at the UC San Francisco's Human Performance Center.

"Sleep duration is important, but we also focused on the quality and timing of Andre's sleep," says Mah, who consults with teams in the NFL, MLB, NHL, and NBA—including the Warriors—on sleep and recovery strategies. "We worked on his caffeine intake, his nutrition, his wind-down routine. Big picture, we worked on his whole approach to sleep, to make it more of a priority."

Did it work? Sample size of one and all that, but boy, did it ever seem to: With more sleep, Iguodala's three-point-shot percentage doubled. His points-per-minute spiked 29 percent. His turnover and foul rates fell 37 and 45 percent, respectively. His coaches gave him more game time, and, in the 2015 Finals, tasked him with guarding Cleveland Cavaliers powerhouse LeBron James. The Warriors went on to win the series. Iguodala received the Most Valuable Player award.

Mah, who has been studying the relationship between sleep and performance in elite athletes for more than a decade, is modest about her role in Iguodala's rise to MVP status. She's cagey, too, about her work with individual players and teams. She declines to discuss, for example, Iguodala's recovery strategy these past few weeks. When a knee injury sidelined him during the Western Conference finals last month, some speculated that Iguodala would sit our the remainder of the playoffs. But in Wednesday's Game 3 NBA finals matchup against Cleveland, he was back—a bit slower than usual, but not too slow to make things difficult for James, or to drive for a dunk in the game's final minutes to give the Warriors a three-point lead.

So was it sleep that brought Iguodala back, or something else?

Realistically, it was probably some combination of nutrition, physical therapy, and rest. But to hear other athletes tell it, sleep makes for especially strong medicine. Two weeks ago, when reporters asked James how he planned to prepare for Game 7 of the Eastern Conference finals, he said: "Try to get as much sleep as I can … that's the best recovery that you can possibly get." (This from a man who reportedly spends some $1.5 million a year on training, diet, and physical therapy.)

Mah puts it in even starker terms: "The comparison most of us make, when talking about the importance of sleep, is to performance-enhancing drugs," she says. "All these athletes are looking for that extra 1 percent boost in performance. But when you look at the research, it suggests a solid foundation of rest and recovery is worth way more than 1 percent."

How much more? In a seminal study from 2011, Mah got members of Stanford's men's basketball team to up their nightly sleep sessions by an average of 110 minutes. After five to seven weeks, Mah found the extra shut-eye correlated with a 9 percent boost in both their free-throw and three-point accuracy and a 0.7-second improvement on a grueling 282-foot sprint drill. She was shocked, and the athletes were, too. "These aren't amateurs—a 9 percent improvement isn't the kind of thing you typically see in players at this level," she says.