We previously compared following of the same trajectories with eye movements, but either as an isolated targets or embedded in a naturalistic scene-in this case, the movement of a puck in an ice hockey game. We observed that the oculomotor system was able to leverage the contextual cues available in the naturalistic scene to produce predictive eye movements. In this study, we wanted to assess which factors are critical for achieving this predictive advantage by manipulating four factors: the expertise of the viewers, the amount of available peripheral information, and positional and kinematic cues. The more peripheral information became available (by manipulating the area of the video that was visible), the better the predictions of all observers. However, expert ice hockey fans were consistently better at predicting than novices and used peripheral information more effectively for predictive saccades. Artificial cues about player positions did not lead to a predictive advantage, whereas impairing the causal structure of kinematic cues by playing the video in reverse led to a severe impairment. When videos were flipped vertically to introduce more difficult kinematic cues, predictive behavior was comparable to watching the original videos. Together, these results demonstrate that, when contextual information is available in naturalistic scenes, the oculomotor system is successfully integrating them and is not relying only on low-level information about the target trajectory. Critical factors for successful prediction seem to be the amount of available information, experience with the stimuli, and the availability of intact kinematic cues for player movements.