Parameterized potential-field framework for quantitative tactical analysis of football passing: a diagnostic analysis of the under_pressure annotation

Abstract Background Quantitative tactical analysis of football passing needs transparent spatial frameworks whose assumptions and limitations can be evaluated across competitions. Event annotations are widely used as ground truth in this literature, yet what they measure is rarely tested directly. Methods We rebuilt our dataset end to end from the raw StatsBomb 360 open-data JSON files at a pinned repository commit, yielding 133,639 attacking-half passes from 320 contributing matches across seven competition-seasons. We specified a parameterized potential-field framework comprising goal attraction, defensive repulsion and teammate attraction, and used it to test what the StatsBomb under_pressure annotation encodes. The defensive exponent β was refitted from scratch on a match-level split with a held-out test set of 71 matches. Model comparisons use generalized linear ladders and crossed random-intercept models for player, team and match, with AIC, BIC and held-out discrimination reported together. Three derived summaries (ATI, DEI, EQI) were tested for external validity against downstream shot, expected-goal and goal outcomes on held-out matches, with match-clustered bootstrap intervals on the incremental discrimination. Results The under_pressure annotation behaves as a threshold on the single nearest visible defender. Adding the additive power-law defensive field on top of a flexible spline in nearest-defender distance changes held-out AUC by 1.4 × 10⁻⁸ and worsens AIC by 1.27; the same contrast in the crossed random-effects model gives the same answer. Refitting β gives β̂ = 0.9745 (1.92-log-likelihood interval 0.9609–0.9883), close to but not equal to inverse-distance decay. R₁ and R₂ are not identified: two directional criteria select disjoint one-standard-error regions, a conditional-logit choice model is uninformative to nine decimal places, and both criteria exclude the working value R₁ = 1.7. Of the three summaries, only ATI shows a positive held-out increment (+ 0.0030 to + 0.0073 AUC across four shot windows, all intervals excluding zero), and it arises from ATI’s ratio functional form rather than from new information; EQI adds + 0.00022 AUC (interval spanning zero) in the possession-to-shot comparison, while adding EQI to the controlled pass-completion model improves AIC by 80.99 and held-out AUC by 0.00135; DEI shows no external validity for shots, expected goals or goals conceded once competition and pass volume are controlled. Conclusions The primary contribution of this work is diagnostic. The under_pressure annotation is a noisy nearest-defender threshold rather than an accumulating multi-defender pressure measure, which is a construct mismatch that no choice of exponent can repair. The potential-field framework provides a transparent way to organize spatial components of passing and to derive consistently defined summaries, but its balance parameters are under-specified and its three indices are exploratory summaries, not performance metrics. The pipeline is openly deposited; its extraction stage was verified on a prespecified six-match subset, while downstream result files were checked numerically rather than rerun in that clean-room test.