A fundamental problem in motor control is the coordination of complementary movement types to achieve a common goal. As a common example, humans view moving objects through coordinated pursuit and saccadic eye movements. Pursuit is initiated and continuously controlled by retinal image velocity. During pursuit, eye position may lag behind the target. This can be compensated by the discrete execution of a catch-up saccade. The decision to trigger a saccade is influenced by both position and velocity errors, and the timing of saccades can be highly variable. The observed distributions of saccade frequency and trigger time remain poorly understood, and this decision process remains imprecisely quantified. Here, we propose a predictive, probabilistic model explaining the decision to trigger saccades during pursuit to foveate moving targets. In this model, expected position error and its associated uncertainty are predicted through Bayesian inference across noisy, delayed sensory observations (Kalman filtering). This probabilistic prediction is used to estimate the confidence that a saccade is needed (quantified through log-probability ratio), triggering a saccade upon accumulating to a fixed threshold. The model qualitatively explains behavioral observations on the frequency and trigger time distributions of saccades during pursuit over a range of target motion trajectories. Furthermore, this model makes novel predictions that saccade decisions are highly sensitive to uncertainty for small predicted position errors, but this influence diminishes as the magnitude of predicted position error increases. We suggest that this predictive, confidence-based decision-making strategy represents a fundamental principle for the probabilistic neural control of coordinated movements. This is the first stochastic dynamical systems model of pursuit-saccade coordination accounting for noise and delays in the sensorimotor system. The model uses Bayesian inference to predictively estimate visual motion, triggering saccades when confidence in predicted position error accumulates to a threshold. This model explains saccade frequency and trigger time distributions across target trajectories and makes novel predictions about the influence of sensory uncertainty in saccade decisions during pursuit.