bald as a coot/billiard ball

Very bald indeed. The coot is a black water bird whose white bill extends up to the forehead, making it appear to be bald. Indeed, this bird was already being called a balled cote in the thirteenth century. The later simile, to a billiard ball, has been less recorded, but since billiards was already popular in Shakespeare’s day it cannot be of very recent origin.