AI 中文总结
本研究通过广播视角基准，探究无球分析中速度在不同层面的价值，发现速度对插补无用、对控制面重要、对判定影响小，且可见速度是关键，并随视角宽度增加而更重要。
AI 中文摘要
速度感知的球场控制是标准做法，但在广播视角下，一半球员在画面之外，画面内的速度来自漂移校准。我们探究在广播无球分析的哪一层，速度会改变答案。继承我们的离屏插补协议（三场Metrica比赛，44米视角，块自助置信区间），我们评估四种速度模式——无速度、视角合法观测速度、可见球员真实速度、所有球员真实速度——对照速度感知的真实值，在三个层面：插补、控制面和团队判定。速度对插补几乎无用（相对于无速度表面的12–14个百分点MAE，仅-0.2个百分点），对控制面是一阶影响（-1.5至-1.8个百分点，占该MAE的11–15%），对判定则小十倍（-0.12至-0.19个百分点）。重要的速度是可见通道：完美的遮挡球员速度仅增加可见增益的2–6%，我们测试的所有最后可见衰减策略均未超过此值。省略速度会使控制面模糊（每帧|e|为2.2–2.6个百分点），但时间平均偏差较小（每单元≤0.4个百分点），而插补误差是对防守方深区的结构性偏差（5–9个百分点）。在固定速度窗口下，包含十一种抖动设置的噪声阶梯（包括sigma_v匹配对）按一阶由速度噪声轴sigma_v排序，盈亏平衡点约为1 m/s；来自同一场比赛的十一个SoccerNet-GSR片段通过我们的流程测得sigma_v=1.65 m/s，但仍恢复了24–36%的收益：43%的方差是帧共有的，控制面可容忍，其余部分是重尾且聚集的，而按分量RMS匹配的高斯控制无法复现（+0.03对比+0.36）。速度消除的无速度误差比例随视角宽度增加（36米时为7%，60米时为21%）：在紧凑镜头中修复插补，在宽镜头中修复速度。代码和日志已发布。
英文摘要
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.
Comments15 pages, 3 figures, 4 tables. Code, logs and data: https://github.com/nowayfootball/offscreen-impute (velocity/)
