One afternoon this spring, John McCarthy walked into rehearsal for a new play about baseball and smoked a line drive to the back wall of the midtown Manhattan studio. He wanted the cast members he was training to see what a good swing might produce and what adhering to his core hitting principles could do. His three B’s of hitting are breathe, balance, be here.

They are paramount when batting. To April Matthis, who plays the title character of the off-Broadway play “Toni Stone,” they also can double as three B’s of life.

“He was a tremendous help,” Matthis said of McCarthy, a 50-year-old youth baseball instructor who was brought on to help the play’s actors look the part. “Not only did he make it so I wouldn’t look like I was choking the bat, but he helped me focus on the current show I’m in, not the other seven shows I have this week.”

“Toni Stone” tells the journey of the first woman to play professionally in the Negro leagues. It debuted last month and runs through Aug. 11 at Roundabout Theatre Company’s Laura Pels Theatre in Manhattan. The production, partially sponsored by Major League Baseball and the MLB Players Association, is scheduled to run next year at Arena Stage in Washington.

Because several members of the cast are from the Washington area, they call themselves “the DMV.” Another D.C. connection: McCarthy, the man who taught the cast how to play baseball, has lived in the nation’s capital nearly his entire life.

The play, written by Lydia R. Diamond, is based on Martha Ackmann’s 2010 biography, “Curveball: The Remarkable Story of Toni Stone, the First Woman to Play Professional Baseball in the Negro League.” It tells the story of how Stone was signed by the Indianapolis Clowns in 1953 not to play but to help with ticket sales. Ultimately, she took the roster spot of a promising young star — Hank Aaron, who had left the team for the Milwaukee Braves.

For research, the cast visited the Negro Leagues Baseball Museum in Kansas City, Mo. But they needed a lesson in playing the sport they had to represent. Cast members said it was not easy at first, even embarrassing, to depict themselves as high-level baseball players, given many of them had little to no experience playing the sport. But the play’s producer, Samantha Barrie, knew whom to call. Her son had participated in McCarthy’s youth baseball camp.

McCarthy pitched for a rookie league affiliate of the Baltimore Orioles in 1992. Two years later, he launched Home Run Baseball Camp at Friendship Park, across the street from where he grew up in Northwest Washington. It has grown into a full-time gig. McCarthy holds camps and clinics for several hundred boys and girls ages 4 to 12 and will hold a clinic for mothers this fall.

His session with the cast of “Toni Stone” was a twist on his usual camps: He taught the nine-person ensemble class how to mimic baseball players. The actors learned how to grip a bat, field groundballs and run the bases, even how to spit on the field and dig into the batter’s box. While no baseballs are hit or thrown in the play, the actors still exhibit common baseball movements.

“The bat is an extension of your hands,” he told them during the two-hour session. “You have to have the body language that says, ‘I’m here to play hardball,’ ” he implored. “Be loose, be relaxed” at the plate and in the field.

“They turned into players,” Barrie said. “This was out of their comfort zone.”

When McCarthy met with the cast of “Toni Stone,” he demonstrated the major aspects of the game, encouraging them to square up the middle of a baseball with the thickest part of the bat. That includes how a batter looks at the pitcher and the swagger a confident hitter exudes at the plate — shoulders back, chin up, loose hands. McCarthy emphasized body language and composure — “remember to breathe,” he said.

“They had to make the baseball believable, authentic and entertaining,” McCarthy said of the actors. “I told them, ‘Let’s not get down after a swing and a miss. Focus on positive growth. Missing a pitch puts you one step closer to making contact.’”

Afterward, Matthis, playing Stone as the show’s star second baseman, made weekly trips to the batting cages at Chelsea Piers in New York. She set the machine to 30 mph and hit for about an hour each session, focusing on the fundamentals McCarthy had instilled.

“April is a night-and-day better swinger,” said Ezra Knight, 56, an actor in the play who grew up in Arlington, Va. “Now people can go, ‘Okay, I’ll believe that she can swing a bat.’ You don’t want someone in a sports story who can’t play the sport. It can be disruptive and distracting.”

Before McCarthy left the cast, he ended practice with motivation. “You’re coming together,” he told them. “You’re not there yet, though. You’ll know you’re there when someone recognizes you on the street and says they were impressed with your effort, glad they learned about the story of Toni Stone.”

McCarthy made the cast vow to find “the next Toni Stone,” he said. “Find me some ballplayers out there on the margins who don’t get a chance to play baseball. Find me a young girl out in the five boroughs.”

Matthis, the cast’s lead, said they’re off to a good start. A few weeks ago, she met a 9-year-old girl who enjoys baseball. After an evening show, the girl asked the cast to sign her copy of the book that inspired the play. Then she asked for a hug.

Correction: An earlier version of this story incorrectly reported that Hank Aaron played for the Milwaukee Brewers.

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