Batting

google

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late Old English batt ‘club, stick, staff’, perhaps partly from Old French batte, from battre ‘to strike’.

wiktionary

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From bat +‎ -ing, batt +‎ -ing(“material, collection”).

From bat +‎ -ing(“action”).

etymonline

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batting (n.1)

"sheets of cotton fiber," 1875, variant of obsolete bat "felted mass of fur, wool, etc." (see bat (n.1)), on notion of "beaten" fabric.

batting (n.2)

"action of striking with a bat," 1610s, verbal noun from bat (v.2). In cricket, from 1773. Baseball batting average is from 1867.