I see great things in baseball, It will take our people out-of-doors, fill them with oxygen, give them a larger physical stoicism, tend to relieve us from being a nervous, dyspeptic set, repair those losses and be a blessing to us.
Source, in full
This has been widely attributed to Whitman, and no one else, but without definite source. It has sometimes been cited as being from the Brooklyn Daily Eagle (sometimes with a date of 23 July 1846), where Whitman had been an editor, but its presence on that date is not apparent in the online historical archives of that publication.
Notes from Wikiquote
Brian Cronin, in "Did 'Bull Durham' misquote Walt Whitman on baseball?", Los Angeles Times (28 March 2012), suggests that this is (loosely) paraphrased from a remark of September 1888 reported in Horace L. Traubel, With Walt Whitman in Camden, Vol. 2 | I like your interest in sports ball, chiefest of all base-ball particularly: base-ball is our game: the American game: I connect it with our national character. Sports take people out of doors, get them filled with oxygen generate some of the brutal customs (so-called brutal customs) which, after all, tend to habituate people to a necessary physical stoicism. We are some ways a dyspeptic, nervous set: anything which will repair such losses may be regarded as a blessing to the race. We want to go out and howl, swear, run, jump, wrestle, even fight, if only by so doing we may improve the guts of the people: the guts, vile as guts are, divine as guts are! | "Sports for a Dyspeptic Race", Intimate With Walt: Whitmans Conversataions With Horace Traubel, p. 261