Expert sports players extract anticipatory visual cues effectively to overcome spatiotemporal constraints on them. The purpose of this paper is to explain what information the experts pick up and process from the moving ball and the opponent's movement kinematics to make accurate predictions of forthcoming events. In particular, we discuss mathematical analysis of visual information processing of the moving ball and the expert's ability to intercept a ball at the right time and the right place

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... n baseball. We also discuss principal component analysis (PAC) as a method of discriminating the opponent's movement kinematics between shot directions in tennis. Finally, we show relations between the kinematics of the opponent's motions and the expert player's ability to make accurate predictions.