home half (1883)

“In the home club’s half this inning they did some very heavy batting.” “Won by a Run,” Philadelphia Inquirer, May 5, 1883, p3

“Cleveland scored a single run in the home half of the inning.” “The Grooms in Cleveland,” The World (New York), September 27, 1890, p1

No earliest use given in 2009 Dickson Baseball Dictionary