"The Mighty Casey" is the 35th episode of The Twilight Zone, first broadcast in June of 1960. It starred Jack Warden as baseball manager McGeary, Robert Sorrels as Casey, and Abraham Sofaer as Dr. Stillman.
McGeary's baseball club is dead last in the standings, and it looks like he might lose his job. Until a young man walks on to the field and pitches superhumanly. Literally: it turns out that Casey was a robot created by Dr. Stillman. That isn't the twist of the episode, that is the set-up. But when its discovered that Casey is a robot, the commissioner of baseball insists that to play baseball, he needs to have a heart. But what will having a heart installed do to Casey's pitching game?
I feel almost as silly writing that as you did reading it.
Somewhat ironically, this episode followed "The After Hours", which had a mostly-female cast. This episode has an all-male cast, with not even a background appearance of a female character, something that I can think of only one other example of amongst Twilight Zone episodes. And while the previous episode was suspenseful, this episode is comedic. I can't say I got that much from this episode, but I did appreciate the comedy, which as usual, makes a nice break in the series.