The archetypal image of a baseball umpire originated in Norman Rockwell’s 1948 painting Tough Call, which depicts three signal-callers looking skyward as rain starts to fall during a game. The real-life umpires shown—Larry Goetz, Beans Reardon and Lou Jorda—had an average age of about 53, establishing the standard for what the men responsible for maintaining law and order on a major-league field should look like.

“That’s in our psyche, that the ump is this older, mature, sometimes rotund person,” said Mark T. Williams, a lecturer...