Training-Free Off-Screen Player Imputation for Broadcast-Based Spatial Football Analytics

Spatial football metrics such as pitch control assume access to the positions of all 22 players, yet the most widely available source of positional data -- the broadcast main camera -- shows only 10-16 of them at any moment. We quantify the resulting distortion with an open, reproducible benchmark: a simulated broadcast viewport applied to open full-pitch tracking data (Metrica Sports; three matches, one held out from method development). Ignoring off-screen players -- the visible-only baseline implied whenever a video-based game-state-reconstruction (GSR) pipeline adds no imputation layer -- inflates hidden-zone pitch-control error to 25.1-26.9 percentage points and a mean absolute control-share error of 11.1-13.4 points across the three matches. We then evaluate a ladder of training-free, online imputation baselines that use only observations from the match being analysed. The best overall on these decision-relevant metrics, role-anchored centroid voting (each visible player votes for the full-team centroid by subtracting its running role offset, attenuating the viewport-induced subset bias), roughly halves hidden-zone error (to 12.2-13.8 points) and cuts control-share error to 28-48% of the ignore policy at every viewport width from 36 m to 60 m in all three matches. For occlusions <=9.6 s -- the regime of the closest learned prior work -- it reaches binwise median position errors of 3.3-8.9 m; but 50-57% of hidden-player observations lie beyond that regime. Integrated end-to-end into a broadcast-video GSR pipeline, imputation moves a downstream possession-quality score (Space-Creation Index) by 15.6 and 17.2 points on two real World Cup broadcast windows, flipping the verdict class in one.