FORT MYERS, Fla. — There is a hotel of sorts near Kenmore Square so exclusive that you can’t make a reservation. There’s only one small room, but it does sleep four comfortably if you don’t mind bunk beds.
The bathroom is out in the hallway, which can be an inconvenience. But the location makes up for that: It’s inside the Red Sox clubhouse at Fenway Park.
The “sleep room’’ is just that, a 145-square-foot room where the players and even an occasional member of the coaching staff can grab a nap before a game. It has become so popular that the Red Sox recently entered into a sponsorship agreement with a bedding company that will include a full renovation of the room along with high-tech sheets, blankets, and pillows for the players to use at home.
It’s part of an effort to chase even the smallest competitive advantage. In an era where teams are taxed for spending too much on player salaries, a comfortable bed is one of the new battlegrounds.
“Every little edge you can get on your competition, if it’s one game or even an extra out, it matters,’’ said Brad Pearson, the team’s head athletic trainer. “We’re always looking for ways to get better. This is one way.’’
Strength and conditioning coaches and sports psychologists have been around baseball for decades. Hiring a team nutritionist gained prominence in recent years and now healthy meals are prepared in clubhouse kitchens by professional chefs.
Sleep is a new frontier in the never-ending chase for a championship. For Eugene Alletto, it’s a market that came to him.
Alletto founded Bedgear in 2009. The New York-based company sells what it calls “performance bedding.’’ Pillows come in models designed for specific body types and sleep habits and are vented to stay cool. Sheets have the ability to wick away heat and moisture.
Vic Black, who pitched for the Mets from 2013-14, purchased some of the products off Bedgear’s website. That led to an unexpected surge of business.
“He fell in love with it,’’ Alletto said. “The baseball community is relatively small and he mentioned it to other pitchers. We started to get calls.’’
The company eventually made sponsorship deals with the Mets, San Diego Padres, and Detroit Tigers along with the NFL’s Denver Broncos, the NBA’s Dallas Mavericks, and the NHL’s New York Islanders.
Alletto’s original business plan did not include sports marketing. But unprompted social media posts from athletes helped generate sales to fans.
“It’s made a huge impact,’’ he said. “This was something that allowed players to a build a relationship with a smaller company. When players are engaged, the fan base notices.’’
Bedgear contacted the Red Sox through president of baseball operations Dave Dombrowski, the former Tigers president and a Bedgear user. Dombrowski passed the message along to team president Sam Kennedy. From there, executive vice president of partnerships Troup Parkinson made a deal.
It was the first time in his 15 years with the Red Sox that Parkinson negotiated a sponsorship that directly benefited the players. Manager John Farrell was a supporter from the start.
“We have the wherewithal to be able to provide the latest and best technology that might be out there,’’ Farrell said. “This is maybe not the most publicized area, but it’s something that we do delve into. You want every advantage you can get.’’
Pearson and other members of the medical staff tried the products first. Their approval mattered.
“I get e-mails to vet products all the time. This was one they sent to us asking if this was something worth pursuing and if it would help the players,’’ said Pearson, who has been with the Red Sox for 15 years. “If it was a disaster, it wouldn’t have gone off. But we liked what they were doing.’’
Last Wednesday, Bedgear representatives met with Sox players before a spring training workout. In a hallway outside the clubhouse, players tested mattresses, were measured for pillows, and lined up to choose from a variety of sheets and blankets.
Of the 58 players in camp, 45 selected at least one item. An additional 36 coaches, team staffers, and front office personnel participated.
Hanley Ramirez asked that a new mattress be shipped to the home he is renting during spring training. It’s on the way.
“The one I had was too soft,’’ Ramirez said. “How many hours can I sleep without waking up, that is the big thing for me. It changes the way you play. It’s unbelievable. When you’re young you don’t think about stuff like that.’’
Shana Rocheleau, Bedgear’s vice president of strategic development, met with the Sox players during their fitting. Selling them on the idea of improving their sleep wasn’t difficult.
“In your own life, if you wake up tired there’s just no way you’re getting the muscle reaction time or memory recall,’’ she said. “It affects everybody . . . The trainers have made this part of the players’ routine. It’s a key component.’’
With 81 road games that cross time zones, sleep can be fleeting for baseball players. If their bed at home can be made more comfortable, it could translate to the field. Not every game time for the coming season has been determined, but the Sox are scheduled for at least 27 day games after night games. It’s taxing.
“In this line of work, you have to get good sleep,’’ righthanded reliever Matt Barnes said. “If you don’t, it can be a long day. It’s crucial. The effects can hit you and it takes a few days to catch up.’’
But for some players, luxury sheets and comfortable pillows only go so far.
“I have three kids. If one of them gets up, I’m getting up,’’ Dustin Pedroia said. “But I get it, we need to get good sleep.’’
The renovated sleep room at Fenway Park will be ready by Opening Day. The room, which is on the second floor of the clubhouse, will have oak flooring, exposed brick, and a selection of pillows. The old room also had four beds, but just standard models.
The Sox may adjust their travel habits, too. For years, the next day’s starting pitcher has traveled four or five hours ahead of the team while on road trips. It’s something all teams do so that player can get a full night of sleep.
The Sox have discussed having their pitchers travel two days ahead so they will be even better rested.
“Pitchers don’t want to leave the team and feel displaced,’’ Farrell said. “But the more you talk about the value of sleep, guys will be open to it.’’
Outfitting the players with high-end bedding may not lead directly to a better record. But when combined with other small advantages, it could make a difference.
“Sleep is probably the most important thing we talk to them about,’’ Pearson said. “It’s critical to their recovery. You pick the low-hanging fruit first, the simple things. You create a stable base and build on that.
“When we won the World Series in 2013, I thought a lot of little things added up. That’s what we’re trying to do again.’’
Peter Abraham can be reached at pabraham@globe.com. Follow him on Twitter @PeteAbe.
