Baseballs autographed by six Presidents. 'Big Train's' gift to Baseball Hall of Fame. Washington, D.C., April 29. Walter Johnson's contribution to the National Baseball Museum at Cooperstown, New York, will be these six baseballs autographed by six presidents: Theodore Roosevelt, William H. Taft, Woodrow Wilson, Warren G. Harding, Calvin Coolidge, and Herbert Hoover. With the exception of the ones autographed by Presidents Theodore Roosevelt and Herbert Hoover, the balls are those which were thrown out at opening games pitched by Johnson during his regime as star pitcher for the Washington Senators. The ball autographed by President Hoover was presented to Johnson while he was manager of the Washington team while the one with the signature of Theodore Roosevelt was a special gift to the Big Train