BOSTON — On a concourse behind third base at Fenway Park, silent but for the periodic whoosh of the frigid wind, Dan Rea recently approached a display case devoted to the 1930s-era Red Sox. A ledger inside the case was opened to a page where an accountant once entered players’ salaries.

One entry was for Smead Jolley, best known for his “difficulty playing the incline” in left field, Rea said, until the field was leveled during a 1934 renovation.

Rea is one of two Red Sox employees who are also club historians. They belong to a small cadre of people with a passion for major league baseball lore who added such roles to their team jobs and later figured out what to do....