FORT MYERS, Fla. — Mookie Betts leaned forward in a chair and waited his turn to bowl. It was down to him and actor J.T. “Action” Jackson in the shootout portion of the Chris Paul Celebrity Invitational, and Betts oozed confidence from every pore.

“You better strike,” Betts hollered. “You better strike.”

Jackson has competed on the Professional Bowlers Association tour, making him something of a ringer on this night in January at Lucky Strike in downtown Los Angeles. Here, though, in the decisive 10th frame, he rolled a 7. Jackson was toast — and he knew it before Betts even stood up.

Betts clapped his hands together, then wriggled his middle and ring fingers into a purple and black ball. He swung his right arm back, angled his left shoulder to face the pins and unleashed a shot so perfect he didn’t need to watch it. Betts extended his arms and, gold chain hanging from his neck, walked off the lane as all 10 pins fell, just as Larry Bird looked away as he swished the winning shot in the 1988 NBA 3-point contest.

“He knew he aced it,” veteran pro bowler Sean Rash recalled by phone. “He knew it was going to hit the pocket. He knew it was going to win the event. It was funny. It was great for television.”

So great, in fact, that the PBA wishes Betts would go on tour permanently.

REST EASY, BOSTON. Betts isn’t about to quit his day job.

Not after last season, when the 24-year-old Red Sox right fielder was the best player in the American League not named Mike Trout. And certainly not with Betts’ first gargantuan payday approaching next year, when he becomes eligible for arbitration and could see his annual salary skyrocket toward $10 million.

Betts’ hands whip through the hitting zone at the speed of light. He covers so much ground in the outfield that you’d never guess he was an infielder until two years ago. The personality that he doesn’t often reveal in interviews comes through on the field, from his creativity in the Red Sox’s congratulatory outfield dances (“the Carlton?”) to sprinkling an imaginary pinch of salt after his first spring training hit last week.

But it’s Betts’ face that baseball really needs. And at a time when the sport is looking for young stars to replace recently retired Derek Jeter, David Ortiz and Alex Rodriguez, Betts’ smile is measured in megawatts.

Indeed, Markus Lynn Betts — yes, his initials really do spell out “MLB” — is the perfect player around which the league can market itself.

But Betts could easily be the face of bowling, too. No offense to Walter Ray Williams Jr., Pete Weber, Norm Duke and other accomplished PBA veterans, but bowling and baseball have a similar problem, specifically an aging fan base and a perception that the sport isn’t, well, cool.

“We need to introduce bowling to a different demographic, and usually younger is what we’re most interested in,” PBA commissioner Tom Clark said. “It’s really important to us to have people understand that [bowling] is cool, and Mookie is cool. He’s one of the best players in baseball. He’s young and he’s hip and he’s engaging. When you see him standing there at a bowling event, and he’s with pro bowlers, tell me bowling isn’t cool.”

Paul, the Los Angeles Clippers point guard, has been associated with the PBA for several years, hosting his annual event for charity. But although the nine-time NBA All-Star enjoys the sport, he’s much more of a recreational bowler than Betts, who has serious game.

Betts grew up in alleys, trailing his mother to various league events in suburban Nashville, and averaged a 240 score at John Overton High School. If not for the fact he batted .549 as a junior and .509 as a senior, he might have prioritized bowling over baseball.

“He’s one of the best players in baseball. He’s young and he’s hip and he’s engaging. When you see him standing there at a bowling event and he’s with pro bowlers, tell me bowling isn’t cool.”

PBA commissioner Tom Clark

“It’s something I definitely thought about,” said Betts, who has rolled seven 300 games. “I’ve been bowling for so long, and I really, really enjoy it. It definitely would’ve been something I pursued.”

Betts still bowls with his mom, Diana Benedict, in the offseason and practices in the two-lane alley in the basement of 19-year-old Wichita State phenom Kamron Doyle’s parents’ home in nearby Brentwood, Tennessee. There’s even a rivalry brewing between Betts and Red Sox ace David Price, who claims to have beat Betts at least once this winter.

Never mind that Betts has not yet played in baseball’s World Series. With the Red Sox’s permission, he competed in the 2015 PBA World Series of Bowling in Reno, Nevada.

It was hardly a publicity stunt. Other celebrities, including former NFL wide receiver Terrell Owens, have been invited to bowl in PBA events and were exposed as amateurs. But Betts rolled a 224 in his first game and had scores of 245 and 249 later in the tournament. He averaged 196 over nine games and finished 212th out of 240 bowlers.

“I just didn’t want to step on any toes,” Betts said. “I knew I was there to bowl, too, and I felt like I was good enough to maybe not compete but at least be out there. But I wanted to make sure I didn’t get in anybody’s way that was actually legit going to win the tournament.”

Said Tommy Jones, an 18-time PBA title winner who has earned more than $1.6 million on tour: “He was always asking, ‘Is this OK if I do this?’ That was cool. We just told him, ‘Go relax, have fun,’ and I think he did.”

CLARK LEARNED ABOUT Betts’ bowling affinity from an interview during a Red Sox telecast in which Betts said he dreamed of participating in Paul’s charity event.

Now, Betts might be poised to host his own PBA celebrity tournament.

Clark said he has put Betts and Benedict in touch with Paul’s family to discuss a potential spin-off event. Regardless, Betts has a standing invitation to come on tour with the PBA and said he would have returned to the World Series of Bowling last December if he hadn’t had arthroscopic knee surgery one month earlier.

“Oh yeah, I definitely would’ve done it,” Betts said. “I’ve got to make that an annual thing now. I was a little mad I missed it this year, but my knee, that definitely comes first.”

Baseball always comes first for Betts. But given his talent on the lanes, might we have a two-sport star in our midst?

“He’s legit,” Clark said. “If he worked on his game and could devote practice to it, he could be a legitimate contender in the Professional Bowlers Association.”

“Yeah, for sure he could be,” added Jones, who partnered with Betts to finish second in the team portion of Paul’s event. “He’s definitely got the ability, and he’s got the mindset, too.”

For now, Betts is content to mostly watch the PBA on television. Perhaps he will someday follow former Red Sox pitcher John Burkett, an avid bowler who joined the PBA’s senior tour last year.

One thing is for sure: Bowling is never far from Betts’ mind. When Jones took his family to Fenway Park last September for a Red Sox-Yankees game, Betts came over to say hello after batting practice.

“I hadn’t seem him for probably six months, and the first thing he does is ask me how the new bowling balls are,” Jones said. “He’s just a regular guy that’s in the spotlight in a spotlight town and plays for one of the best organizations in baseball, and I don’t think it’s really changed him. I’ll shoot him a text, and he’ll text me right back. That’s pretty cool. He’s having fun every day, whether it’s baseball or bowling, and that’s all it needs to be.”