Mike Trout, the best player in his sport, is the mostly unrecognizable face of baseball

You can take Mike Trout away from home, but you cannot take him away from his home teams.

He celebrated with the Philadelphia Eagles as they won the Super Bowl. He proudly wears his old-school “PHILA” 76ers jersey inside the Angels clubhouse and he has served a helping or two of trash talk to the Lakers fans among his teammates.

For a few hours there, a couple of Sundays ago, Trout dared to dream. LeBron James was meeting with the 76ers. Trout knew that James lived in Los Angeles in the summer. He had heard that James’ son might enroll in a local high school. But maybe, just maybe …

As Trout likes to say: Yeah, no. James signed with the Lakers. Trout might catch a few of their games, but there will be no purple and gold bleeding into his basketball loyalty.

“Obviously, Sixers,” Trout said. “But I root for guys with his talents. He’s the best.”

The best basketball player in the world and the best baseball player in the world now play for Los Angeles teams.

One is a marketing phenomenon. The other is Trout. Why is that?

“I have no idea,” Trout said with a laugh. “I don’t really think about it like that.”

That in itself is one reason. But Tuesday’s All-Star Game reminds baseball’s leaders that they have yet to discover how to turn the greatest player of his generation into an icon of popular culture.

Derek Jeter transcended baseball, and he might not have even been the best player on his New York Yankees teams. David Ortiz transcended baseball, and he rarely set foot in the field for the Boston Red Sox.

Trout ought to be a godsend to a national pastime losing ground to the NFL and NBA. He is supremely talented and unfailingly polite, a Norman Rockwell painting with a Roy Hobbs bat.

“Mike Trout is the one guy that everybody wants to see,” Ortiz said. “You can’t get any better as a player, and as a person. I don’t know which one he is better at.”

Jeter retired four years ago. Trout was supposed to replace him as the face of baseball.

“He is, without a doubt,” Ortiz said. “Maybe there is only one thing that would probably be against how big he is, and that is playing in L.A., three hours different from this side of the planet.”

Maybe Trout does not resonate because most of the country is asleep when he plays in Anaheim, or maybe the issue is that Trout has played in only three playoff games, winning none.

Jeter played in 158, Ortiz 85. NFL games are nationally broadcast all season; MLB games are nationally broadcast primarily in October.

“If Trout gets to the playoffs consistently, even if he doesn’t win a World Series, people will know who he really is,” said one of his mentors, former Angels outfielder Torii Hunter.

“Bryce Harper is a great hitter. Everybody knows who he is. He is very well-marketed. And he is a fun guy.”

Harper has played in 19 playoff games. He and the Washington Nationals, like Trout with the Angels, have yet to win a playoff series.

Harper said he does not necessarily buy the national story line that baseball cannot market young stars such as himself and Trout.

“I don’t know if I can say that about myself,” Harper said, citing his national sponsorship deals with Gatorade, Jaguar, T-Mobile and Under Armour.

“I think Major League Baseball and the players’ association does an OK job of trying to get their players out there. It can definitely get better. But I don’t think you’re ever going to have what the NFL or NBA has.”

The NFL is America’s most popular sport, and kids across the country buy the shoes that NBA players are paid handsomely to promote relentlessly.

James has appeared in eight consecutive NBA Finals, launched a Hollywood production company and taken on President Trump. He has 41.1 million followers on Twitter and 39.9 million on Instagram; Trout has 2.5 million and 1.4 million, respectively.

James embraces the spotlight. So did Jeter, who won four World Series championships in his first five seasons, made himself at home on late-night television shows and starred in a commercial with owner George Steinbrenner. So does Harper.

Trout does not. He takes questions at his locker every day, but he turned down profiles on “60 Minutes” and HBO, the kind of national publicity the league covets. In the winter, he would rather hunt, fish and cheer on the Eagles than fly from one commercial shoot to another.

“If Mike really wanted to, if he got a marketing team and everything, he would be the face of baseball,” Hunter said. “He doesn’t. He wants to be with his wife and keep it simple.

“It’s his choice. It’s not anybody else’s choice.”

That choice frustrates league officials, who cannot persuade their presumptive biggest star to participate in the home run derby at an All-Star game he already is attending, let alone to give up an off day in the interest of promoting the sport.

But Tony Clark, executive director of the players’ association, said the league should be able to sit down with Trout and figure out ways to maximize his exposure while minimizing his time commitment off the field — that is, to make him the face of baseball.

“It’s hard for me not to imagine that him not being recognized in that fashion is part and parcel of how we as an industry promote,” Clark said. “I believe there are opportunities to move our game and our players back into the forefront of the conversation, and to do so in such a way that benefits the industry as a whole.

“Mike is doing things that our game has rarely seen. It would be fantastic if more people knew about it.”

In the league office, that charge falls upon Chris Park, executive vice president of product and marketing. To Park, authenticity is more than a buzzword. In an era where players establish their own profile on social media, fans might reject any identity the league might try to fit onto a player.

“Their relationships with fans really start with themselves,” Park said.

In Trout’s case, the evidence of his stardom might not be readily apparent to the casual fans and non-fans that need to embrace him in order for him to transcend the sport.

He does not hit the ball 500 feet. He does not hit .400, or hit 50 home runs. He does not throw 100 miles per hour.

Tony Gwynn played in San Diego and went 12 years without a playoff appearance, but he shared his raucous laugh with every camera in sight and won eight batting titles. Even a fourth-grader can divide hits by at-bats to calculate a batting average.

Trout does everything well, but the formula for the measurement offered in support — wins over replacement (WAR) — is neither agreed upon by sabermetricians nor understood by casual fans.

“Some of what makes him great may be non-obvious,” Park said. “It then becomes a bit of a challenge for us to figure out how to take advantage of that, and how to help evangelize the world and community to a player’s greatness.

“I don’t think that’s unique to him, or to this sport. In your town, you could probably say the same thing about Aaron Donald,” the Rams’ defensive lineman and reigning NFL defensive player of the year.

“It’s OK that some things are easier to frame or distribute to the world. The non-obvious ones may be the best opportunities for us.”

Over time, Park hopes, Trout might embrace a larger national profile. The league is encouraged that he has agreed to wear a microphone and talk with Fox broadcasters during a half-inning of Tuesday’s game.

On the one hand, Trout is 26, and he has been elected to six All-Star starting lineups, the most of any player in Tuesday’s game. On the other hand, he fell out of the top 10 among the league’s most popular player jerseys this season.

Should the league do a better job of promoting him?

“I don’t know,” Trout said. “I’m not telling anybody to do that.”

bill.shaikin@latimes.com

Follow Bill Shaikin on Twitter @BillShaikin