Beyond the Shot: A Relational Graph Framework for Contextually Accurate Expected Goals in Association Football

Abstract Expected Goals (xG) has become foundational in football analytics, yet most reproducible shot models remain predominantly event-centric and context-limited. This paper proposes a relational framework for contextual xG and introduces an explicit evidence-tier structure to align claims with data conditions. Three claim tiers are used. Claim A (validated): adding relational context derived from event data and freeze-frame structure improves probabilistic shot modeling relative to a standard event-centric baseline. Claim B (incremental): lightweight exogenous context (e.g., weather) can provide additive gains beyond event + freeze-frame features when temporal and spatial merges are reliable. Claim C (proposed): full dynamic player-state and graph-relational architectures are conceptually appropriate for football's interdependent structure but require richer tracking and physical data for definitive validation. The empirical strategy combines exploratory and confirmatory evidence. A three-match, 104-shot exploratory analysis is retained for mechanism illustration and hypothesis generation; primary validation is conducted on a larger 8,130-shot dataset with temporal holdout and probabilistic evaluation. Results support A-level gains and bounded B-level increments in the current implementation, while C-level claims are explicitly positioned as future work. The contribution is a scientifically scoped bridge: contextual improvements that are implementable now, and a disciplined roadmap toward richer entity-centric xG modeling.