This informant is my roommate, who grew up in Laguna Hills. He played baseball up until high school, when he quit to play lacrosse.
Baseball has a ton of superstitions and lots of players do weird shit, like never wash their socks if they are on a winning streak or something, but the “Rally Cap” is known by all players. It doesn’t matter if you are in Little League or the Majors but if your team is losing and you need a good inning everyone wears their hats upside-down, which is suppose to make your team play better or hit homeruns or something.
I know from my few years in Little League that the rally cap is a very prominent folk belief in baseball regardless of how effective it really is. While neither my informant nor myself know how it originated, I can guess that it stuck into the baseball culture because of the “hat’s” importance to the sport. Many people refer to hats as “baseball caps,” regardless of the embroidering on them and hats really aren’t worn in any other sport, making them unique to baseball. From this perspective it sort of makes sense that a folk belief like this stuck for good. Altering an item of clothing that embodies baseball seems natural, especially when a hats appearance is so easy to change by flipping it.