How Much Velocity Does Off-Ball Space Value Need? A Broadcast-Viewport Benchmark
Seongjin Choi
Abstract
Velocity-aware pitch control is standard, but under a broadcast viewport half the players are off screen and on-screen velocities come from a drifting calibration. We ask at which layer of broadcast off-ball analysis velocity changes the answer. Inheriting our off-screen imputation protocol (three Metrica matches, 44 m viewport, block-bootstrap CIs), we score four velocity regimes -- none, viewport-legal observed, true-for-visible, true-for-all -- against a velocity-aware ground truth at three layers: imputation, the control surface, and team verdicts. Velocity is nearly useless for imputation (-0.2 pp against a 12--14 pp velocity-free surface MAE), first-order for the surface (-1.5 to -1.8 pp, 11--15% of that MAE), and ten times smaller for verdicts (-0.12 to -0.19 pp). The velocity that matters is the visible channel: perfect occluded-player velocity adds 2--6% of the visible gain, and no last-seen decay policy we tested exceeds that. Omitting velocity blurs the surface (per-frame |e| 2.2--2.6 pp) with small time-averaged bias (per cell <=0.4 pp), whereas imputation error is a structured bias against the defending team's deep zone (5--9 pp). At a fixed velocity window, a noise ladder of eleven jitter settings, including sigma_v-matched pairs, is ordered to first order by one velocity-noise axis sigma_v with break-even ~1 m/s; eleven SoccerNet-GSR clips from one match through our pipeline measure sigma_v=1.65 m/s yet recover 24--36% of the benefit: 43% of the variance is frame-common, which the surface tolerates, and the residual is heavy-tailed and clustered, which Gaussian controls matched on component RMS do not reproduce (+0.03 vs. +0.36). The share of velocity-free error that velocity removes grows with viewport width (7% at 36 m, 21% at 60 m): fix imputation on tight shots, velocity on wide ones. Code and logs are released.