An Etymological Dictionary of the German Language/Annotated/Ball
Ball, (1.) masculine, ‘challenge (of hounds),’ belongs to the stem of bellen.
Ball (2.), masculine. ‘ball,’ from the equivalent Middle High German bal (genitive balles) or balle, ballen, masculine Old High German ballo, masculine, balla, feminine; Anglo-Saxon *bealla is wanting; English ball (Middle English balle) is borrowed from the Romance word French balle, which was obtained from German. Old Icelandic bǫllr, ‘ball,’ presupposes Gothic *ballus. The root bal- appears also with a further gradation in Bolle (in Bolster too?); compare further Bellen.
Ball (3.), masculine, ‘dancing entertainment,’ from French bal, ‘ball’; Old French baller, ‘to dance,’ and its Romance cognates have been derived from Greek βαλλίξω, ‘I dance.’