Jeff Daniels adjusted his reading glasses and bent close to peer at a framed baseball card from 1909 featuring Honus Wagner, a legendary shortstop for the Pittsburgh Pirates.

“It’s so small,” he said of the card, on display at the Metropolitan Museum of Art.

The Emmy-winning actor (for HBO’s “The Newsroom”) shook his head in bemusement, aware that Wagner cards have sold for $1 million and higher. “You imagine a kid with the Wagner in 1909 using it to put his gum in and then throwing it away,” he said.

Mr. Daniels, 61 and warily amiable, is a lifelong baseball fan. How passionate is he? He wrote and recorded a jokey lament about his beloved Detroit Tigers called “Tiger Fan Blues.” He waxed rhapsodic about opening day in a promotional video for Major League Baseball.

And, years ago, he piled his wife, Kathleen Treado, and their three young children into a 28-foot R.V., which he drove from their home in tiny Chelsea, Mich. (population 5,000), to Cooperstown, N.Y., to visit the Baseball Hall of Fame.

His love of the game is why, looking rumpled in jeans and a short-sleeved plaid shirt, he dragged himself on a recent Friday afternoon across Central Park to view this vest-pocket-size exhibition of vintage baseball cards at the Met.

It’s a rare break for Mr. Daniels, who is starring on Broadway in “Blackbird,” an intense drama he first performed Off Broadway in 2007. His role, as a child abuser confronted by his victim, now an adult (played by Michelle Williams), is difficult and exhausting. Most days, when not at the theater, he stays close to his apartment on the Upper West Side.

“Tired? I am,” he said. “But it means that we’re doing it right. There’s only one way to do this show, and that’s all in. It’s got to hurt every time.”

At the Met, he spotted a card featuring Babe Ruth and Lou Gehrig. “You wonder if they knew, the people watching at the time?” he asked. “Are we able to recognize greatness when we’re looking right at it?”

A few cards down, Mr. Daniels’s face lit up. “Al Kaline, that’s my guy!” Mr. Kaline, a Hall of Famer, played for the Tigers for 22 seasons before retiring in 1974. “He was the only guy I ever saw who could make the ball come to him,” said Mr. Daniels, stretching an arm and bending low to mime Mr. Kaline scooping up a grounder.

Mr. Daniels included that line in “The Vast Difference,” one of 16 plays he has written. He and Mr. Kaline became friends after his hero attended a performance of “Vast” at the Purple Rose Theater Company in Chelsea, a 168-seat theater devoted to new works that the actor founded in 1991 and continues to oversee.

Mr. Daniels grew up in Chelsea, which is an hour’s drive west of Detroit. After his junior year at Central Michigan University, he moved to New York to become an actor.

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He found a refuge from professional anxieties at Yankee Stadium. “You could kill a whole night,” he said. “For a young actor who wasn’t getting work, you’d sit in the upper deck drinking a beer and watching batting practice and then the game, and just escape.”

Such escape wasn’t necessary for long. He soon found success on stage and in films like “Terms of Endearment” and “The Purple Rose of Cairo.” Along the way, in 1979, he wed Ms. Treado, a hometown girl he began dating while he was a struggling actor in New York. In 1986, the couple moved back to Chelsea to raise their growing family.

After touring the exhibition, Mr. Daniels sat at one of the Met’s cafes for a chat. He mentioned that he has a wee baseball memorabilia exhibition of his own at his Manhattan apartment: balls signed by Mr. Kaline, Roger Maris and Mickey Mantle. Mr. Daniels talked about playing first base in high school (he earned letters in basketball and football, too) and in the Broadway Show League (a softball theater league) in his 20s.

“In the Broadway league, if you’re at all coordinated, you’re gold,” he said. “The theater scene is not exactly known for people who excelled at high school sports.”

Now he mostly watches. As soon as “Blackbird” finishes its run on June 11, Mr. Daniels is heading home to Chelsea, where he has Tigers season tickets waiting.

“I have four seats, 11 rows behind the Tiger dugout,” he said, adding proudly that he has occupied the same seats for nearly 30 years. “I’m never getting rid of them. Ever.”