Decomposing every pass into two independent dimensions: risk (probability of interception, [-1, +1]) and gain (change in expected position value, ΔEPV). Plotting all passes in risk-gain 2D space reveals four distinct quadrants: (1) high risk, high gain — breakthrough passes near goal, (2) low risk, low gain — safe recycling backward, (3) high risk, low gain — bad passes that risk turnover without advancing, (4) low risk, high gain — nearly empty, because opponents prevent safe high-gain passes. The risk parameter is computed kinematically by simulating ball trajectory and defender/teammate interception probability from 360 data; the gain is ΔEPV from start to end zone.
(1) Risk calculation: for each pass, simulate the ball trajectory (start → end). For each defender in 360 data, compute time to intercept based on distance to trajectory and assumed movement speed. Do the same for attacking teammates. Risk = P(defender intercepts) - P(teammate receives). Normalize to [-1, +1]: +1 = certainly intercepted, -1 = certainly received by teammate. (2) Gain calculation: compute EPV at pass destination minus EPV at pass origin. Positive = advanced toward goal, negative = retreated. (3) Plot in 2D: each pass is a point in risk × gain space. The cloud shape reveals the team's passing character. (4) Aggregate per player: average risk, average gain, risk decision parameter, gain decision parameter.
Key finding: the majority of completed passes cluster in the low-risk, slightly-positive-gain zone. The high-risk/high-gain quadrant contains the breakthrough passes that create chances. The low-risk/high-gain quadrant is nearly empty — defenses ensure safe passes don't produce high gain.
In risk × gain 2D space, the low-risk/high-gain quadrant is nearly empty. Defenses are organized specifically to ensure safe passes don't produce high gain. There is no free lunch: high gain requires high risk. Any model claiming "safe and dangerous" passes is miscalibrated.