Abstract: Protective covers for preventing damage to ball bats during batting practice are comprised of an impact force absorbing elastic sleeve which has through its length bore and a V-shaped notch extending forward from a rear transverse edge of the sleeve, dividing a rear length of the sleeve into opposed flaps, thus providing an enlarged entrance opening which facilitates insertion of a bat into the sleeve bore. A strap extending radially from one flap is releasably attachable by a closure fastener to the other flap, enabling the flaps to be cinched around and secured to a bat inserted into the sleeve bore. The protective covers may optionally have weights and/or friction strips positioned within the sleeve, and may optionally include an inertial sensor or impact force sensor and radio transmitter for transmitting signals representative of bat motions or impact forces exerted on the bat.