A ball striking device, such as a golf club head, has a head that includes a face configured for striking a ball and a body connected to the face. A brace extends from an inner surface of the body or from a perimeter weight system to a contact point on the rear surface of the face. This brace may extend from the sole or a sole oriented perimeter weight member to the rear surface of the face. The brace applies force to the face (at least when the face is flexed by a threshold amount) such that the area of the face surrounding the contact point has less flexibility relative to other areas of the face located away from the contact point. The brace and club head may include structures that allow one to control and customize the force applied to the face.