The origin of “Big Apple” was explained in the 2010 Canadian comedy-drama film Barney’s Version, with a screenplay by Michael Konyves. This dialogue does not appear in the novel Barney’s Version (1997) by Mordecai Richler (1931-2001).
   
Barney Panofsky (played by Paul Giamatti) explains to Miriam Grant (played by Rosamund Pike), while walking through Manhattan’s Central Park:
 
“You know, I’m always surprised that people from New York don’t know this. ‘The Big Apple’ is actually an old racetrack term, credited to John Fitzgerald - a sports writer for the herald in the 30’s.  He’d heard old stable hands from Mississippi use it when referring to the New York racetracks.  Getting to race in New York was considered hitting the big time - getting a bite of that “Big Apple” and I’m just going to keep talking because I’m afraid if I stop…”
 
This is essentially correct, but there are several mistakes. John J. Fitz Gerald wrote for the New York (NY) Morning Telegraph, not the New York (NY) Herald. His “Big Apple” columns were mostly in the 1920s, not the 1930s. Also, the stable hands were from the Fair Grounds racetrack in New Orleans, Louisiana—not Mississippi.
   
     
Wikipedia: Barney’s Version (novel)
Barney’s Version is a novel written by Canadian author Mordecai Richler, published by Knopf Canada in 1997.
 
Wikipedia: Barney’s Version (film)
Barney’s Version is a 2010 Canadian comedy-drama film directed by Richard J. Lewis, based on the novel of the same name by Mordecai Richler. The film was nominated for the Golden Lion at the 67th Venice International Film Festival.
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Directed by Richard J. Lewis
Produced by Robert Lantos
Written by Michael Konyves
Based on Barney’s Version
by Mordecai Richler
 
Barney’s Version: The Big Apple (video)
Barney’s Version—Clip—The Big Apple (video)
Barney Panofsky (played by Paul Giamatti) to Miriam Grant (played by Rosamund Pike) while walking through Central Park in Manhattan.
     
Barney’s Version (script)
Pg. 81:
BARNEY
“The Big Apple” is actually an old racetrack term, credited to John Fitzgerald - a sports writer for the herald in the 30’s.  He’d heard old stable hands from Mississippi use it when referring to the New York racetracks.  Getting to race in New York was considered hitting the big time - getting a bite of that “Big Apple” and I’m just going to keep talking because I’m afraid if I stop (MORE)