Roger Kahn's "The Boys of Summer" is still one of the best literary looks at the Game and what it meant in the Era -- on the surface it's the story of one man's attachment to the Brooklyn Dodgers thru childhood, young adulthood, and ultimately his career as a newspaper beat writer actually covering the team. The second half of the book finds the author revisiting the players he knew twenty years later, revealing how baseball -- and leaving baseball -- affected their lives. The book was published in 1972, and has never been out of print since.
Also, as flawed as it is in a lot of ways, and as annoying as I find the filmmaker himself, Ken Burns's "Baseball" is worth seeing if you haven't already.
Kahn's approach to baseball in the book reveals something very important about understanding its appeal. It's a game of generations, not of the moment, and you have to have grown up with it -- as most Americans in the Era did -- grown up in a baseball oriented family, to truly understand why it matters. In the Era, you were a Dodger fan or a Red Sox fan or a Cardinal fan in the same way you were a Methodist or a Catholic or a Baptist or a Jew: it was part of your identity, and part of your heritage, and no matter where you go in life or how you evolve and change, it remains an essential element of who you are.
Without gambling, basketball and football would lose their entire reason for existence. Baseball transcends the game on the field to become a part of your very being.