Scale from Priors, Location from Pixels: The Limits of Monocular Pitch Reconstruction

Professional baseball measures pitch trajectories with multi-camera tracking systems. Most games have only one broadcast camera behind the pitcher. We ask how much of a pitch's 3D trajectory this single view can recover, and where the accuracy of a working system comes from. We build a leakage-audited benchmark of 12,140 MLB pitches from OpenCommand, with solved camera poses and Statcast-derived reference trajectories. For the constant-acceleration trajectory models used in practice, metric depth has an exact scale ambiguity from a fixed camera. Gravity does not resolve it, because pitched baseballs are not gravity-only projectiles. For these models, absolute scale must come from prior information. Anchoring depth at the release and plate planes brings median 3D error from tens of meters to about one meter and plate-crossing error to 7 cm. We then measure what the observed ball track adds once calibration, temporal support, and priors are held fixed. A learned population prior with no pixel coordinates already beats the anchored physics fit in depth. In matched ablations tested once in each of the 31 MLB venues, adding the track cuts plate error from 30 to 5.4 cm and speed error from 3.6 to 1.9 mph. Depth error falls from 71 to 47 cm. Every venue improves on all three. These figures use the camera calibration supplied with the dataset. For the anchored physics fit, a reference-free audit with calibration and cohort built from inputs alone gives 8.7 cm median plate error. Priors set the scale, and the pixels set the location.