The first use of '110 percent' I found, from 1916, was a sports use referring to competitive rowing. The next two, from 1919, referred to worker loyalty (Sept) and patent medicine formulation (Nov). The latter purported to quote the 19th century US humorist, Artemus Ward (pseudonym of Charles Farrar Browne, 1834-1867), and attributed the '110 percent' trope to that source:
The Palm Beach Post (West Palm Beach, Florida), 28 Nov 1919.
I was unable to verify the attribution to Artemus Ward. A careful search of his work did not turn up the phrase. It is possible the quote was an off-the-cuff remark, however, and certainly the earlier uses of the trope suggest it was already established in the early 1900s. Yet no uses turned up in publications from the 19th century, or from anytime before 1916.
Of the three uses I found in 1923, the first use showed what later became a frequently repeated element of mild humor, here repeated from the first use in 1916 but almost wholly absent in contemporary sports applications. The second repeated the theme of nationality — in this case straightforward nationalism — from the 1920 instance. The second and third uses established another theme by using the trope to refer to special effort.
The theme of reference to special effort dominates contemporary sports uses of the figure; the element of mild humor is generally absent in those contemporary uses; the reference to nationality or nationalism is now rare.
A 1924 use concerning a basketball team repeats the sports application first seen in 1916, and also emphasizes special effort, as seen in the two later instances from 1923.
A 1925 use in a review of a vaudeville show repeats the established themes of mild humor (from 1919, 1923, and 1925), special effort (from 1923 and 1924), and theatrical competence (from 1923 and 1925) underlying the figurative reference to '110 percent'.
In 1929, after four years of waiting in the wings, the trope reappears in another reference to nationality/nationalism. This reference recurs in 1933 and 1939. Interspersed among those are uses with reference to special effort (1930), fakery (1935), theatrical competence (1935), and political orthodoxy (1937).
A ten year gap in the historical evidence is interrupted by a semi-humorous use referring to the amount of attention gotten by a man who emphasizes a point by pounding a gun on a dinner table (1949).
Through the 1950s and 1960s, every use I found related to sports. That dominance continues in contemporary use.
The evidence I found does not support the primacy of any one context of origin. Sports contexts eventually won out (in the 1950s and 1960s), but early patterns and frequencies of use suggest the more likely origin was in a theatrical context, or in the context of nationality/nationalism.
Similarly, the areas of use suggest no single regional source, although with more information something might be made of the early uses appearing primarily in the US east and midwest. Canada is represented by two uses in The Winnipeg Tribune, from Manitoba, 1937 and 1939. Both those appearances are, however, datelined out of London.
Too much could easily be made of the number of early uses in The Brooklyn Daily Eagle (4 of 17, nearly one-quarter). Although I checked to see if those uses were all from articles by one reporter, I could not verify they were. The variety of subjects covered suggests a variety of authors. Perhaps one reporter or editor at The Brooklyn Daily Eagle was fond of the '110 percent' trope, and spread it 110 percent among his colleagues. The span of dates involved (1923-35) does suggest the tenure of a single journalist, or of that journalist's influence on a newsroom.
First use found, 1916:
Mount Carmel Item (Mount Carmel, Pennsylvania) 12 Sep 1916.
Another use in 1919. See also the 1919 clipping in the Analysis, above:
Reports that the United States Steel Corporation would shut down its plants in the Pittsburgh district unless there was 110 percent loyalty shown by the workers was denied today at the office of the Carnegie Steel Co., a subsidiary.
The Portsmouth Herald (Portsmouth, New Hampshire), 20 Sep 1919.
Use in 1920, first of the several early uses referrring to nationality:
Jackson Daily News (Jackson, Mississippi), 16 Jun 1920.
The 1923 appearances:
The Brooklyn Daily Eagle (Brooklyn, New York), 16 Sep 1923.
The Fort Wayne Sentinel (Fort Wayne, Indiana), 08 Dec 1923.
Dixon Evening Telegraph (Dixon, Illinois), 23 Nov 1923.
The 1924 application repeating the sports reference of the 1916 use:
The Daily Chronicle (De Kalb, Illinois), 01 Feb 1924.
In a 1925 use reviewing a vaudeville show, mild humor, special effort, and theatrical competence all underlie the figurative reference to '110 percent':
Battle Creek Enquirer (Battle Creek, Michigan), 27 Mar 1925.
In 1929, nationalism rears up again:
The Brooklyn Daily Eagle (Brooklyn, New York), 11 Aug 1929.
In 1930, special effort:
The Brooklyn Daily Eagle (Brooklyn, New York), 16 Feb 1930.
In 1933, more nationalism:
Reading Times (Reading, Pennsylvania), 21 Nov 1933.
In 1935, fakery and theatrical competence:
Moberly Monitor-Index (Moberly, Missouri), 07 Feb 1935.
The Brooklyn Daily Eagle (Brooklyn, New York), 01 Dec 1935.
The two appearances in The Winnipeg Tribune, from 1937 and 1939, are datelined out of London, but refer variously to political orthodoxy and acquired nationalism:
The Winnipeg Tribune (Winnipeg, Manitoba, Canada), 26 Jun 1937.
The Winnipeg Tribune (Winnipeg, Manitoba, Canada), 17 Mar 1939.
A 1949 outlier, where the "rod" is a gun:
The Daily Reporter (Greenfield, Indiana), 04 Apr 1949.