Optimal performance in time-constrained and dynamically changing environments depends on making reliable predictions about future outcomes. In sporting tasks, performers have been found to employ multiple information sources to maximize the accuracy of their predictions, but questions remain about how different information sources are weighted and integrated to guide anticipation. In this paper, we outline how active inference, a unifying account of perception and action, explains many of the prominent findings in the sports anticipation literature. Active inference proposes that perception and action are underpinned by the need to minimize prediction errors and optimise a predictive model of the world. To this end, decision making approximates Bayesian inference and actions are used to minimize future prediction errors. Using a series of Bayesian neurocomputational models based on a partially observable Markov process, we demonstrate that key findings from the literature can be recreated from the first principles of active inference. In doing so, we formulate a number of novel, empirically falsifiable hypotheses about human anticipation capabilities which could guide future investigations in the field.