"round object," Old English *beal, from or corresponding to Old Norse bollr "ball," from Proto-Germanic *balluz (cf. Old High German ballo, German Ball), from PIE root *bhel- (2) "to blow, inflate, swell" (see bole).
Meaning "testicle" is from early 14c. Ball of the foot is from mid-14c. A ball as an object in a sports game is recorded from c.1200; To have the ball "hold the advantage" is from c.1400. To be on the ball is 1912, from sports. Ball-point pen first recorded 1946. Ball of fire when first recorded in 1821 referred to "a glass of brandy;" as "spectacularly successful striver" it is c.1900.