Laverne DeFazio’s (Penny Marshall) clothes always had a large, distinctive “L” on the left breast, and her short-sleeve, beige baseball jersey was no exception. The “L” monogram was solely Marshall’s idea. When the show began certain facts about the characters were repeated to allow the audience to get to know them.
Instead of being addressed as “Laverne” every time, Marshall though the “L” monogram would let the audience know who she was and cut down on the repetition. (And, yes, both Laverne and Shirley played softball to hilarious results.)
It’s also worth pointing out that Laverne’s jersey bears a striking resemblance to the Rockford Peaches jerseys in the 1992 film “A League of Their Own,” which Marshall directed.