Ball striking devices, such as golf club heads (including putter heads), have a high moment of inertia about their center, to help prevent twisting and mis-hits, particularly when the ball striking device hits the ball at a somewhat off-center position. The ball striking head of the ball striking device may be structured and/or weighted (optionally with separately attachable weight elements) to have a moment of inertia about a center of the ball striking surface of at least 10,000 g/cm2, and in some examples, the moment of inertia may be at least 11,000 g/cm2, or even at least 12,000 g/cm2. In some examples, the moment of inertia may be at least 20,000 g/cm2, or even at least 25,000 g/cm2 or at least 28,000 g/cm2.