Anticipation by basketball defenders: an explanation based on the three-dimensional inverted pendulum model

We previously estimated the timing when ball game defenders detect relevant information through visual input for reacting to an attacker's running direction after a cutting manoeuvre, called cue timing. The purpose of this study was to investigate what specific information is relevant for defenders, and how defenders process this information to decide on their opponents' running direction. In this study, we hypothesised that defenders extract information regarding the position and velocity of the attackers' centre of mass (CoM) and the contact foot. We used a model which simulates the future trajectory of the opponent's CoM based upon an inverted pendulum movement. The hypothesis was tested by comparing observed defender's cue timing, model-estimated cue timing using the inverted pendulum model (IPM cue timing) and cue timing using only the current CoM position (CoM cue timing). The IPM cue timing was defined as the time when the simulated pendulum falls leftward or rightward given the initial values for position and velocity of the CoM and the contact foot at the time. The model-estimated IPM cue timing and the empirically observed defender's cue timing were comparable in median value and were significantly correlated, whereas the CoM cue timing was significantly more delayed than the IPM and the defender's cue timings. Based on these results, we discuss the possibility that defenders may be able to anticipate the future direction of an attacker by forwardly simulating inverted pendulum movement.