The story
Back-formation from innings, mistaken to be plural of the time period, not the entries of the batters/batsmen.
Etymology from Wiktionary, CC BY-SA 4.0.
inning
Today it means: A period of play in which members of a visiting baseball team attempt to hit a baseball pitched by the opposing home team until three players are called out, followed by a similar attempt by members of the home baseball team against the visiting team's pitching. There are nine or more innings in a regulation baseball game. Full definition →