A physics-based simulation framework for evaluating goalkeeper positioning at every moment of an opponent's attack — not just at shot time. For each frame, the model computes: given the ball location, where should the goalkeeper stand to minimize goal probability across all possible shot destinations? The goalkeeper's movement is constrained by a realistic run radius (meters per second × time since last frame). The model compares the goalkeeper's actual position to the optimal simulated position, quantifying how much goal probability the goalkeeper gained or lost through positioning alone.
(1) Define 6 target points in the goal (top-left, top-center, top-right, bottom-left, bottom-center, bottom-right). Assume a "perfect striker" who can hit any target with equal probability (strong simplifying assumption). (2) For each frame during an opponent's attack, compute: for every realistic goalkeeper position within the run radius, what is the combined goal probability across all 6 targets? Account for defender shot-blocking (if a defender is between the shooter and a target, that target's probability is reduced). (3) The optimal position is the one that minimizes total goal probability. (4) Compare actual GK position to optimal: the gap is the positioning error. (5) Evaluate not just at shot time but continuously — a goalkeeper who is well-positioned 3 seconds before the shot but drifts out of position is still making an error.
Key constraint: goalkeepers can't teleport. The run radius (based on time between frames × maximum sprint speed) ensures only physically reachable positions are considered as alternatives.