A cage used in a ball bearing assembly is rendered to be of a ring shape having a plurality of pockets defined therein to hold a corresponding number of balls in a circumferential row. The radius of a bore of a circumferentially extending body of the cage as measured from the geometric center of the bore to an inner peripheral surface area of the circumferentially extending body aligned with each of the pockets is chosen to be greater than the radius as measured from the geometric center of the bore to a different inner peripheral surface area of the circumferentially extending body intermediate between the neighboring pockets.