Ball striking devices, such as golf clubs, have a head that includes a face having a striking surface configured for striking a ball, and a body connected to the face and extending rearwardly from the face, with the body having a crown, a sole, a heel side, and a toe side, such that the face and the body combine to define an enclosed internal cavity. A damping member is connected to the body and includes a post extending inwardly into the cavity from an inner surface of the body, a first arm extending from the post toward the heel side of the body, and a second arm extending from the post toward the toe side of the body. The damping member is configured to produce a mass damping effect upon an impact on the face.