By SCOTT CACCIOLA
ST. PAUL, Minn.—Jim O’Neill, the baseball coach at Cretin-Derham Hall High School, was mowing the outfield grass last month when he saw someone jump the fence and jog toward him.

It was one of his former players—Joe Mauer, the Minnesota Twins’ star catcher and the American League’s reigning Most Valuable Player.

Mr. Mauer had gotten his hair cut and his sideburns trimmed across the street at Schmidty’s Sports Barbers, where he’d paid the proprietor—John Schmidt, another former coach—his usual rate of $15. Mr. O’Neill said Mr. Mauer just wanted to say hello. “He’s a St. Paul guy,” he said.

As the city of Cleveland waits in angst-ridden anticipation for the middle of next week, when the Cavaliers’ LeBron James is expected to declare for free agency and—perhaps you’ve heard—entertain offers from other NBA teams, Mr. Mauer’s story is worth considering. It’s a case study in what might happen if Mr. James decides to stay.

Mr. Mauer, who is 27, and Mr. James, 25, share some striking similarities. Both rank among the very best athletes in their respective sports. Both were local heroes as teenagers who were drafted by their hometown teams straight out of high school and made their professional debuts there. While they’ve both won division titles, neither man has managed to lead his team to a championship.

Now Mr. James faces the same decision Mr. Mauer tackled this spring: whether to stay at home or to start a new chapter in a more glamorous town.

With one year left on his contract before he was eligible for free agency, Mr. Mauer signed an eight-year, $184 million extension to remain with the Twins. Minnesota has been reveling in Mauer-palooza ever since. The franchise, which is free of the fear of losing its favorite son, opened a spectacular new outdoor ballpark this season.

“I bet if he had left, there are people in this community who would’ve never gone to a Twins game again for the rest of their lives,” said St. Paul Mayor Chris Coleman. “They absolutely would’ve blamed the Twins—not Joe. Be clear on that one.”

Instead, Mr. Mauer and the Twins are thriving. Through Wednesday, Mr. Mauer was hitting .309 for the Twins, who were atop the A.L.’s Central Division with a 40-31 record. Target Field in downtown Minneapolis has been host to 33 consecutive sellouts and the stands are peppered with fans wearing shirts with Mr. Mauer’s No. 7. (Some of them actually belong to people named Mauer: His parents and grandparents attend nearly every home game.)

For a city that’s long accustomed to losing high-profile athletes to teams in bigger, bolder markets, keeping Mr. Mauer was a rare triumph. “For me, it all came down to where I’d be happy,” Mr. Mauer said.

After the 2009 season, one year before his contract was set to expire, Mr. Mauer met with his agent, Ron Shapiro, to weigh his options. Mr. Shapiro had prepared a flip chart that addressed Mr. Mauer’s curiosities about free agency. It was broken down by team—the Twins, New York Yankees and Boston Red Sox were presumed to be the key players—with pros and cons listed by topic, including his personal life (where could he expect the most privacy?), his desire to win titles (which team was best equipped to compete?) and, of course, his bank account. “Even if you’re Joe Mauer, you have to think about financial repercussions,” Mr. Shapiro said.

Mr. Shapiro had drawn up rough figures for the type of contract he believed each team could offer, though he cautioned his client that it was difficult to predict where the Red Sox and the Yankees—big-spending rivals who play in the same division—would wind up if they were to launch a bidding war. With both teams leaning on aging catchers, Mr. Shapiro was fairly certain the numbers could have gotten astronomical in what he considered an “irrational marketplace.”

As he began to negotiate with the Twins, the team made clear that it intended to pay Mr. Mauer fairly, according to Twins president Dave St. Peter, though not so much that the deal would hamstring its ability to surround him with other good players. “Joe agreed with that,” Mr. St. Peter said.

No matter where he wound up, Mr. Mauer would have been one of the highest-paid players in baseball. The contract he eventually signed with the Twins was the fourth-largest in baseball history. The same goes for Mr. James, regardless of where his journey ends.

But while Mr. James, under the NBA’s salary system, would actually make more money by staying in Cleveland, Mr. Mauer likely could have made millions more by leaving. So what was it that made the difference?

To some extent, it was his team’s forthright and aggressive attempt to retain him. But according to people who know him well, it came down to the intangible lure of home.

Had Mr. Mauer left, he might have dealt a severe blow to sales at Billy Mauer Chevrolet in suburban Inver Grove Heights. The proprietor, one of Joe’s two older brothers, opened the dealership in February—just one month before Joe re-signed. Billy Mauer, who pitched in the Twins’ minor-league system before retiring, converted the loading dock into an indoor batting cage for teaching kids. “I think it’s the best baseball school at any car dealership in the world,” Billy Mauer said.

Mr. Mauer said a lot of customers ask him if his brother drives a Corvette. The answer is no. “First of all, he can’t fit in it,” he said. “Second, they’re kind of attention-getters.”

Here’s the thing about Joe Mauer that the people of Cleveland should bear in mind: He drives a Tahoe. He gets cheap haircuts. He has a burger named after him at the Nook, a no-frills bar across the street from his old high school. He lives in a condo with roommates like Larry Nava, a friend since grade school who now sells cars for Mr. Mauer’s brother.

Sure the catcher has trouble going out in public here. He tends to get mobbed by fans who want an autograph, a photo or a handshake. He might enjoy the relative anonymity of a city where Derek Jeter and Alex Rodriguez top the marquee.

But when he was promoted to the big leagues in 2004, Mr. Mauer couldn’t even bring himself to move to Minneapolis instead of St. Paul. “People were telling him, ‘You can’t move across the river, that’d be terrible,’ ” his brother said. “I just think this is home for him.”

We’ll see if Mr. James feels the same way about Cleveland