A ball game apparatus comprises a control device (14, 24, 52, 60) which defines a predetermined range of allowable movements of a ball (10, 20, 40, 70) over space and time, sensing means (12, 22, 42) for detecting the actual movements of a ball, comparison means for comparing an actual movement to the predetermined range of allowable movements, and indicating means (16, 34, 54, 62) for indicating the output of the said comparing. The sensing means (12, 22, 42) comprises a multi-axis accelerometer contained in the ball and having accelerometer, gyroscope and/or magnetometer functions. The ball may be activated by an internal magnetically-operated switch (17, 22, 47). The control device and indicating means can be incorporated in the ball itself or in a separate portable computing device.