Home-Field Advantage (1920)

“With the score of games all even at two each and three games still to play on their home field, the advantage should rest with the Indians.” Arkansas Gazette, October 10, 1920, p17

“With the home field advantage, the Hills are favored to win.” Saginaw News Courier, May 13, 1921, p20 (First baseball use of full phrase)

Earlier example from football

“Home Field Advantage. {Subhead}. ‘Washington always goes two or three touchdowns better on Denny Field than away from home,’ cautioned May. ‘So you see one doesn’t want to accept comparative scores as a standard without inquiring into conditions.'” Morning Oregonian, November 16, 1914, p10

Variation: Home Ground Advantage 

“Shaking off all possibilities of a home-ground advantage the game was staged at the Trenton High School field….” Trenton Evening Times, August 23, 1919, p11
NOTE: Like “home-field advantage” this was used earlier for football, but this baseball use (about a Trenton Boys League game) is earlier than the first baseball use of “home-field advantage.