“Do your talking on the field/court” means that one should concentrate less on the sportswriters and concentrate more on the performance, letting that speak for itself. “He prefers to do his talking on the football field” was cited in print in 1915. “He will do his talking on the ball field” was cited in 1917.
 
   
7 August 1915, Denver (CO) Post, “A. C. Miles, of Denver, Says Navy Has an Excellent Chance to Win From the Army in Annual Football Struggle” by Clem Crowley, pg. 7, col. 3:
Captain Miles is naturally very reticent in regard to the Army-Navy game Thanksgiving day. He prefers to do his talking on the football field and it is this characteristic that has made him so popular at the Navy.
 
3 May 1917, Trenton (NJ) Evening Times, “Big Opening At Morrisville Sat.,” pg. 15, col. 1:
Ray Egner, manager of the Empire Tire club, is not saying much, but says he will do his talking on the ball field.
(A baseball game.—ed.)
 
14 August 1942, Augusta (GA) Chronicle, “McCarthy Annoyed Because Self-Appointed Managers Trying to Run Champions” by Edward W. Cochrane (INS), pg. 12, col. 6:
He (New York Yankees Manager Joe McCarthy—ed.) does his talking on the ball field and makes no predictions.
 
Google News Archive
14 July 1976, Miami (FL) News, “Towle want to show last year was n fluke” by Charlie Nobles, pg. 1C, cols. 2-3:
“It’s also a natural feeling to keep your mouth shut and do your talking on the field.”
(Miami Dolphins linebacker Steve Towle.—ed.)
 
20 January 1979, State-Times (Baton Rouge, LA), “Super Bowl Rhetoric at a Peak: It’s Time to Back Up All Those Words” by Frank Wilson, pg. 1-C, col. 4:
“It’s far better to do your talking on the football field, not while surrounded by sports writers with pencils poised.”
(Pittsburgh Steelers running back Franco Harris.—ed.)
 
Google News Archive
6 August 1981, Eugene (OR) Register-Guard, “People in Sports,” pg. 5C, col. 1:
“I don’t think anyone can think about the Heisman right now,” he (Georgia running back Herschel Walker—ed.) says. “You have to do your talking on the field.”
   
Sports Illustrated
Originally Posted: March 3, 1986
Miamian without a vice
Miami O.‘s Ron Harper can do it all, and NBA scouts are panting
BY ROGER JACKSON
(...)
“Some players are just good players, and some players talk trash,” Harper says. “Talk is cheap. You have to do your talking on the floor.”
 
Google News Archive
15 September 1991, Gadsden (AL) Times, “Cowboys eye battle with Philadelphia, McMahon” (Associated Press), pg. B3, col. 4:
“I’m not a big talker. I believe you do your talking on the football field.”
(Philadelphia Eagles coach Rich Kotite.—ed.)
 
Google Books
Then Belichick Said to Brady…:
The Best New England Patriots Stories Ever Told
By Jim Donaldson
Chicago, IL: Triumph Books
2009
Pg. ?:
“I said, ‘No, I wasn’t. But now that you’re here, I’d like to point out that you’re getting your ass handed to you. You should do your talking on the field, instead of in the papers.’”
     
Empire Writes Back
December 20, 2014  
David Harris Ready To Reach Milestone For New York Jets
by Joe Pietaro
(...)
“Do your talking on the field” is an old saying but fits perfectly with Harris’s style. He leads by example and more.
 
Twitter
7uLiET
‏@juliet4yuu
@Lakers LIN should just quit with the on-liners. Just shut-up and do your talking on the court.
11:41 AM - 20 Dec 2014