Traditional approaches to measuring visual exploratory behavior in soccer rely on counting visual exploratory actions (VEAs) based on rapid head movements exceeding 125°/s, but this method suffer from player position bias (i.e., a focus on central midfielders), annotation challenges, binary measurement constraints (i.e., a player is scanning, or not), lack the power to predict relevant short-term in-game future success, and are incompatible with fundamental soccer analytics models such as pitch control. This research introduces a novel formulaic continuous stochastic vision layer to quantify players' visual perception from pose-enhanced spatiotemporal tracking. Our probabilistic field-of-view and occlusion models incorporate head and shoulder rotation angles to create speed-dependent vision maps for individual players in a two-dimensional top-down plane. We combine these vision maps with pitch control and pitch value surfaces to analyze the awaiting phase (when a player is awaiting the ball to arrive after a pass for a teammate) and their subsequent on-ball phase. We demonstrate that aggregated visual metrics - such as the percentage of defended area observed while awaiting a pass - are predictive of controlled pitch value gained at the end of dribbling actions using 32 games of synchronized pose-enhanced tracking data and on-ball event data from the 2024 Copa America. This methodology works regardless of player position, eliminates manual annotation requirements, and provides continuous measurements that seamlessly integrate into existing soccer analytics frameworks. To further support the integration with existing soccer analytics frameworks we open-source the tools required to make these calculations.