PaperlayerView exact revision on arXiv

Source-linked AI summary

How Much Velocity Does Off-Ball Space Value Need? A Broadcast-Viewport Benchmark

Seongjin Choi

arXiv:2609.10801v1cs.CVcs.LG

TL;DR

Broadcast off-ball analysis must decide how to use velocity when players are hidden and visible velocities come from drifting calibration. The paper benchmarks four velocity regimes across imputation, control surfaces, and team verdicts, finding that velocity is nearly useless for imputation, first-order for surfaces, and much smaller for verdicts, with visible velocity providing most of the benefit.

  • Problem

    Broadcast pitch-control pipelines lack observable velocity for off-screen players, while visible velocities derive from positions affected by drifting calibration.

  • Method

    The paper scores four velocity regimes against a velocity-aware reference across imputation, control-surface, and team-verdict layers, with noise and viewport-width tests.

  • Results

    Velocity is nearly useless for imputation, first-order for the surface, and an order of magnitude smaller for verdicts; perfect occluded-player velocity adds only 2–6% of visible-channel gain.

  • Takeaways & Limitations

    Prioritize imputation on tight shots and visible-velocity quality on wide shots; occluded-player velocity is a low-return investment under the tested pipeline.

  • Takeaways & Limitations

    Hidden-zone scoring is simulated, while real-broadcast evaluation covers visible players from eleven clips of one match and includes reference and operator mismatch.

Abstract

from arXiv · show

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.

1 Introduction

The paper benchmarks where velocity matters in broadcast off-ball analysis, separating imputation, surface, and team-verdict layers. It finds that visible velocity drives most surface-level benefit, while hidden-player velocity contributes little.

  • Velocity is nearly useless for imputation, first-order for the control surface, and an order of magnitude smaller at the verdict layer.The benchmark measures distance from a velocity-aware reference surface rather than whether that reference is correct about football.
  • Perfect occluded-player velocity adds only 2–6% of the visible-channel gain, and no tested last-seen decay policy changes that result.
  • Per-cell time-averaged bias from omitting velocity stays at RMS ≤0.14 pp and never exceeds 0.4 pp, far below per-frame error.Imputation instead creates a 5–9 pp structured bias against the defending team in its deep zone.
  • At fixed velocity windows, eleven noise settings are ordered mainly by σv, with break-even near 1 m/s; real broadcast error retains a quarter to a third of the benefit.The real error includes frame-common and heavy-tailed components that differ from the i.i.d. controls.
  • Velocity’s value grows with viewport width, motivating imputation work on tight shots and velocity work on wide ones.

2 Related Work

Prior work provides velocity-aware pitch-control and EPV models, velocity completion, broadcast tracking accuracy measurements, and off-screen imputation protocols. This paper audits the velocity term under partial broadcast visibility rather than replacing those models.

  • The study audits velocity-aware pitch-control and EPV models by zeroing velocity in a Spearman-style model, rather than evaluating a velocity-free Voronoi implementation.
  • Prior velocity completion fills all 22 velocities from event snapshots, whereas this setting observes visible-player velocity and imputes only occluded-player velocity.The reported 2–6% occluded-channel result is a marginal effect at fixed imputed positions.
  • Published broadcast trackers report detected-player speed RMSEs from 0.35 to 1.19 m/s and undetected-player RMSEs from 0.78 to 2.0 m/s, but those figures are not directly comparable to this study’s per-axis vector-noise threshold.
  • The benchmark inherits an off-screen imputation protocol, imputation ladder, and block-bootstrap evaluation, while measuring velocity-related headroom for learned alternatives at fixed positions.

3 Benchmark Protocol

The benchmark uses three Metrica matches with a moving broadcast viewport, four velocity regimes, and three evaluation layers scored against a common velocity-aware surface. Noise, viewport width, and real-broadcast axes test how observed velocity degrades.

  • Three Metrica first-half matches are subsampled from 25 Hz to 5 Hz, while a ball-following virtual camera reveals a 44 m window and hides players outside it.The viewport sweep spans 36–60 m.
  • The protocol evaluates B2 centroid-relative-offset imputation, with B4 role-anchored voting noted where it differs.
  • Pitch control uses 0.7 s reaction time, Vmax = 7.8 m/s, and a logistic arrival-time difference with scale 0.45 s; velocity enters through the reaction-time projection.
  • All regimes are scored against the same surface built from true positions and velocities, with layer-specific errors and 95% one-minute block-bootstrap intervals.
  • The four estimated-side regimes are zero velocity, viewport-legal observed velocity, true velocity for visible players only, and true velocity for all 22 players.
  • All velocities are capped at 9 m/s, with the cap binding negligibly across the main 0.6 s ladder but affecting the 0.2 s-window point substantially.
  • The noise ladder perturbs visible positions with Gaussian, AR(1), or common-mode jitter across 0.2, 0.6, and 1.0 s velocity windows, while the real-broadcast axis scores matched visible players from eleven SoccerNet-GSR clips.The real-broadcast intervals resample clips from one match, not multiple matches, broadcasts, or trackers.

4 Results

Velocity matters primarily at the control-surface layer, especially through the visible channel, while imputation bias dominates verdict error. Noise, window length, and viewport width determine how much of the surface benefit survives deployment.

  • 4.1 Velocity is a surface-layer input: 1.5–1.8 pp of control MAE is lost by omitting velocity at the surface, versus only −0.12 to −0.19 pp at the verdict layer.The surface loss is 11–15% of B2 error and seven to eight and a half times the imputation-layer term; threat weighting does not change the surface effect.
  • 4.2 The velocity that matters is the visible channel: True visible-player velocity reproduces nearly the full surface gain, while exact occluded-player velocity contributes only −0.04 to −0.09 pp, or 2–5%.Last-seen velocity decay policies remain within the same 2–6% occluded-channel bracket.
  • 4.3 Why velocity does not reach the verdict: blur far more than bias: Per-frame velocity omission reaches 2.25–2.63 pp, but spatial and temporal cancellation leaves per-cell time-averaged bias at no more than 0.4 pp.Imputation instead produces a structured 5–9 pp deep-zone bias against the defending team, making it the larger verdict-relevant error.
  • 4.4 How much velocity noise the surface tolerates: At a fixed 0.6 s window, recovery is ordered mainly by σv, with break-even near 1 m/s across the noise ladder.Common-mode error is more tolerable than i.i.d. error, but it neutralizes damage rather than creating a gain; larger σv can make verdicts significantly worse.
  • 4.6 Velocity matters in proportion to what you can see: A 0.2 s velocity window is catastrophic, whereas longer windows trade reduced variance against lag; the velocity benefit also grows with viewport width.The 1.0 s window loses 25–28% of the clean benefit to lag, so window choice is a deployment parameter.
  • 4.5 The real-broadcast axis: Real broadcast velocity has σv = 1.65 m/s yet retains 24–36% of the surface benefit, because frame-common and heavy-tailed clustered errors differ from matched-RMS Gaussian controls.The observed pipeline still yields −2.08 pp on true positions and −1.60 pp on pipeline positions relative to zero velocity.

5 Discussion: what this means for a deployed pipeline

The deployment priority is visible-player velocity and calibration stability before occluded-player velocity. Imputation remains the main source of structured bias, while velocity errors largely average out at the verdict layer.

  • Order of investment: True visible velocity removes only 7–11% of velocity-free surface error on 36–44 m shots, while imputation is the only source of structured bias.The recommended order places imputation first, followed by the visible velocity window and calibration stability, with occluded-player velocity last.
  • Re-reading earlier indices: The index is more exposed to the deep-zone imputation bias, which favors the attacking side of every deep zone.Velocity error largely averages out of the scalar index under the stated regimes, whereas the imputation bias persists structurally.
  • Learned occluded-player models: A velocity model for occluded players adds only 2–6% of the visible gain at imputed positions, so exact hidden velocities have limited marginal value.This fixed-position result does not bound joint position–velocity prediction, because stale velocity can sometimes compensate positional lag.

6 Limitations •

The evidence is bounded by a small set of matches, one control-model family, a static xT approximation, and simulation-only hidden-zone ground truth. The real-broadcast evaluation covers one pipeline and eleven clips from one match, with wide bootstrap intervals and limited generalizability.

  • Data and coverage: The benchmark uses one provider, first halves of three matches, and defines “every match” or “every width” only over the tested settings.The decay sweep is limited to match 1.
  • Control model: Results apply to one Spearman-style control-model family; layer and channel conclusions were tested across reaction times and logistic scales, but Vmax and learned influence surfaces were not varied.The break-even σv is conditional on Treact.
  • Threat weighting: Threat weighting uses a static xT grid that ignores ball position and phase, so “value” is an xT approximation rather than EPV.
  • Imputation interpretation: The interpretation that imputation compresses anchors toward visible teammates is a hypothesis consistent with maps but not separately tested.
  • Real-broadcast evaluation: Hidden-zone scoring exists only in simulation; the real-broadcast axis evaluates visible players on eleven clips from one match, with nominal-at-best interval coverage and no cross-match or tracker variation.The reference surface is itself imperfect, and team-assignment errors are excluded.

7 Reproducibility

The released benchmark and scripts expose the experiments, diagnostics, noise and viewport sweeps, real-broadcast analyses, figures, logs, and reproduction commands. Downstream numbers can be recomputed from the released code and tracks.

  • Benchmark commands: The released benchmark command reproduces the four velocity regimes, paired intervals, zone diagnostics, frame series, noise ladders, decay sweeps, viewport widths, and sensitivity tests.
  • Real-broadcast pipeline: The real-broadcast analyses use released SoccerNet-GSR test-clip tracks, with logs for every number and reproduction commands mapping each log to its generating command.The repository also includes the scripts for decomposition, structure analysis, matched-RMS controls, and figures.

8 Conclusion

The broadcast pipeline needs velocity primarily at the control-surface layer, while observed velocity is usually sufficient and imputation errors remain the main threat-weighted weakness. Investment should prioritize imputation on tight shots, then velocity window and calibration stability, with occluded-player velocity last.

  • Conclusion: Observed velocity reproduces the control surface, while verdicts need an order of magnitude less velocity and occluded-player velocity contributes only 2–6% of the visible gain.The useful velocity channel is already available from the camera.
  • Conclusion: A 5–9 pp under-crediting of the defending team’s deep zone makes imputation error the main exposure of threat-weighted verdicts.
  • Conclusion: For broadcast pipelines, invest in imputation first on tight shots, velocity window and calibration stability second, and occluded-player velocity last.Observed velocity can exceed the approximately 1 m/s i.i.d. noise threshold yet still recover a quarter to a third of the benefit because errors include a frame-common component and heavy-tailed residuals.
Loading 2609.10801v1…