The film's writer, Nathaniel Benchley, is the son of famous author, humorist, actor, and raconteur, Robert Benchley. Nathaniel's son, Peter Benchley, would go on to write the novel, Jaws, as well as co-author the screenplay for the subsequent film.
The "P" on Tom Ewell's hat (and his assistant coach played by Dean Jone) is supposed to represent their team mascot "the Panthers." However, it's the script style "P" of the 1950s Philadelphia Phillies that Ewell and Jones wear. The Phils were known as the "Whiz Kids in the Fifties and had many fans around the country. Curiously, the kids on the team wear hats with a different "P" style on their hats. Maybe Ewell or Jones were Phils fans. However, Little League coaches often wear a Major League style cap different from their players as they available in adult sizes.
While other games are referred to, the only games shown are between the Tigers and the Panthers.
Playing for the Little League "Tigers", Dennis wears #4. During the timeframe of the film, #4 on the Detroit Tigers was worn by "Sunday" Charlie Maxwell, a popular player known for coming up big during the day games played on Sunday.
1956 was also the year that Ann Francis made her iconic appearance in the sci-fi classic, "Forbidden Planet".