RENTON, Wash. >> The players filed past a table and picked up the electronic wristbands as casually as any of other piece of equipment designed to make the Seattle Seahawks perform at their peak.

But rather than protect or help them power through a game, this new one, distributed to the players at practice on Monday, is aimed at a more subtle effect. Very subtle.

“Get your nine hours of sleep!” receiver Doug Baldwin shouted to Trevone Boykin, the backup quarterback, as Boykin fiddled with his band, a motion-sensing monitor designed to ensure he does just that.

The Seahawks want to become sleeping giants.

NFL teams obsessively track almost everything they can about a player: weight, muscle mass, hand-eye coordination and more.

Yet in recent years, in the never-ending search for an edge, teams have opened their eyes to sleep as a priority, backed up by science that increasingly points to its importance for physical and mental health. A solid night in the sack particularly helps players recover from the inevitable wear and tear of a taxing season.

Several other teams besides the Seahawks have also been focusing on sleep. And it has caught on in other sports — some NBA players, for instance, take naps during the day to remain fresh for night games. Basketball and hockey teams adjust their flight schedules to allow their players more time to sleep. And New England Patriots quarterback Tom Brady made waves two years ago when he said he goes to sleep at 8:30 p.m.

Few teams, however, have cozied up to the idea as much as the Seahawks

It is partly out of necessity. The Seahawks are hours by plane from their nearest rivals and regularly log more miles than any other NFL team. On Friday, for example, they flew five hours to New Jersey for their game against the New York Jets.

The focus on sleep also flows from the team’s holistic approach to player health, which encompasses, among other things, blood tests, meditation and yoga. The team has been among the best in the NFL in recent years, including a Super Bowl win in 2014.

“I’ve always had a belief that sleep is one of the main ways your body recovers,” said Sam Ramsden, the Seahawks’ director of player health and performance. “Some of the best players on the team are the best sleepers.”

The bands the players collected Monday are the latest version of those the team first tried in 2011 but had to stop using last season after the players’ union raised concerns about the intrusiveness of a device used outside games and practices. In July, the league and players settled their differences and allowed the bands if the teams received the union’s approval.

The devices used by the Seahawks, called Readibands, are made by a Canadian company called Fatigue Science and include motion sensors that calculate how long and how deeply the players have slept. Another algorithm, developed by the U.S. military and others, converts the sleep data into a number correlated to the player’s alertness.

The wristbands send the data to the players’ smartphones, allowing them to monitor their sleep better and make adjustments on their own.

A player with a score of around 90 on the 100-point scale has about a 10 percent reduction in alertness — nothing serious. A player with a score of 70, by contrast, will have a 43 percent reduction in reaction time — a significant impairment to his performance.

“It’s not enough to know how much or how well you are sleeping, but to understand the relationship between sleep and performance,” said Jacob Fiedler, a sales director at Fatigue Science, which works with about 40 sports teams around the world as well as miners, train engineers and other workers who need to stay alert on the job for long periods. “If the timing of my sleep is inconsistent, we’ll pay a health price, a safety price, a performance price.”

Many Seahawks say they are now getting to bed before 10 p.m. during the week, and credit the sleep bands with keeping them on track.

“I’m the type of guy, I try to get an advantage any way I can and stay ahead of the game and keep my body right and limit my risk of injury to make my performance better,” said DeShawn Shead, a cornerback. “I know I’m a great sleeper, but now I can physically see it and monitor it so I can put that to the test as well.”

To underscore the importance of sleep, Ramsden told the players about a passage in one of the Jason Bourne spy novels in which the protagonist Bourne called sleep “a weapon.”

Ramsden said: “Everything that’s happening to this guy, and he thinks sleep is important. I like that because it helps players understand how important it is.”

Old habits die hard, however.

Russell Wilson, the quarterback, has used the hashtag “#NoTime2Sleep” on his Twitter account and said that he is fine with five or six hours of sleep even though doctors recommend several hours more.

Pete Carroll, the Seahawks’ coach, also had to come around to the idea that his players need their rest.

“I always thought that sleep was overrated, and I had to kind of be knocked in the head to understand,” Carroll said. “Like so many things, once it gets on the radar screen, it makes sense and you ask, why didn’t we pay attention before?”

Some players have spoken publicly about the benefits of sleep. Richard Sherman, a cornerback, said before the team’s Super Bowl victory in 2014 that “sleep science has paid off for several guys.”

“We’re all tough guys, that’s proven,” said K.J. Wright, a linebacker. But “you have to be smart, and on Sunday it shows which team has prepared the best, which team is moving the best.”