According to TMC, Ronald Reagan had lobbied hard to play the title role in Un homme change son destin (1949) but Warner Bothers didn't want to take a chance on a baseball film and passed on the project. After "The Stratton Story" became a huge hit, the studio picked up the Grover Cleveland Alexander story about another player who made a comeback after being forced from professional baseball.
Before making this film together, Doris Day and Ronald Reagan had dated in real life. After he hesitated about asking for her hand in marriage, Day accepted a proposal from her manager at the time, Martin Melcher, to whom she remained married until his death in 1968.
Because Doris Day's most popular movies were usually musicals, Warner Brothers wanted her to sing in this film. The result has Day performing "Old Saint Nicholas" when her family celebrates Christmas while Grover is recuperating from his head wound. But when Warners released the film in June of 1952, rather than the holiday season, the song got far less airplay (and sold far fewer copies) than Day recordings of the time usually did.
Per Wikipedia, Grover Cleveland Alexander "has the unique distinction of being named after one U.S. president and being played on-screen by another."
The opening credits show Grover Cleveland Alexander's plaque at the Hall of Fame in Cooperstown, New York. It is accurate in all respects except one: it shows Ronald Reagan's likeness instead of the real Grover Cleveland Alexander.