Inning

wiktionary

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Back-formation from  innings, mistaken to be plural of the time period, not the entries of the batters/batsmen. 

inning

etymonline

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inning (n.)

Old English innung "a taking in, a putting in," gerundive of innian "get within, put or bring in; lodge; include; fill up, restore," from inn (adv.) "in" (see in). Meaning "a team's turn in action in a game" first recorded 1735, usually plural in cricket, singular in baseball.