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Unified Pitch Graphs for Diagnosing Pitching Strategy

Kichang Lee, JeongGil Ko

arXiv:2609.03810v1cs.IR

TL;DR

Pitching-strategy representations can collapse physically distinct executions or fragment when they include detailed context and long pitch histories. UPG represents exact pitch events in a traceable, multi-scale graph and adapts path detail to repeated support. Its evaluation reports improved held-out coverage and execution reconstruction, while keeping its conclusions retrospective rather than causal or predictive.

  • Problem

    Common representations collapse physically distinct executions or fragment into sparsely repeated patterns when they add trajectory, location, context, and longer histories.

    Source: §1 · p. 1, §2.1 · p. 2

  • Method

    UPG builds a hierarchical graph that preserves exact pitch events and sequence relations, organizes events across semantic and temporal scales, and backs off when repeated support is insufficient.

    Source: §1 · p. 1, §2.3 · p. 2

  • Results

    Support-adaptive backoff raises held-out path coverage from 18.9% to 94.9% while improving execution reconstruction from R^2=0.495 to 0.685.

    Source: §1 · p. 1

  • Takeaways & Limitations

    UPG supports traceable multi-scale diagnosis and retrospective change localization that discrete pitch-mix and sequence representations cannot detect.

    Source: §1 · p. 2, §6 · p. 9

    Recurrence and held-out consistency are observational and do not establish causal effects or guarantee future persistence.

    Source: §3.5 · p. 5

Abstract

from arXiv · show

Pitching strategy in baseball is expressed through both physical execution and the ordered context in which pitches are used, yet common representations collapse pitches into discrete types or aggregate statistics. We present Unified Pitch Graphs (UPG), a hierarchical graph representation for retrospective analysis of sequential spatiotemporal events. UPG preserves each pitch as an exact event with reconstructed three-dimensional trajectory and context, connects consecutive pitches through directed sequence edges, and organizes the same events across semantic and temporal resolutions. A support-adaptive mechanism backs off from fine, long sequences when repeated evidence is insufficient, while retaining exact event lineage. We evaluate UPG on 3.94 million MLB Statcast pitches from 2021 to 2026. Nominally identical pitch sequences exhibit distinct physical executions, and ordered structure becomes increasingly evident in longer context-conditioned paths. Support-adaptive backoff increases held-out path coverage from 18.9\% to 94.9\% while improving execution reconstruction from $R^2=0.495$ to $0.685$. UPG also reliably localizes controlled execution changes that discrete pitch-mix and sequence representations cannot detect. These results demonstrate that UPG provides a traceable, multi-scale representation for identifying recurring strategy patterns without conflating retrospective associations with causal or future-performance claims.

1 Introduction

Pitching strategy depends on physical execution, pitch order, and context, but coarse or highly specific representations struggle to preserve physical fidelity while retaining reliable support. UPG addresses this trade-off with a traceable, support-adaptive graph; evaluation shows improved path coverage and execution reconstruction, and identifies structure missed by discrete representations.

1 Introduction

  • Pitching strategy depends on execution, prior pitches, and context, so nominal pitch labels alone do not capture the relational meaning of a pitch.Two fastballs with the same label may differ physically, and the same sequence may vary in meaning by count, matchup, location, and physical relationship.Source: §1 · p. 1
  • Coarse pitch states collapse distinct executions, while highly detailed long sequences fragment into sparsely repeated patterns.Aggregate representations can also obscure the games, plate appearances, and pitches supporting a pattern.Source: §1 · p. 1
  • UPG preserves exact pitch events and their continuous execution, organizes them across semantic and temporal resolutions, and backs off when repeated support is insufficient.The hierarchy retains links to original pitches and plate appearances, allowing analysis at a supported resolution without discarding its underlying events.Source: §1 · p. 1
  • Support-adaptive backoff raises held-out path coverage from 18.9% to 94.9% while improving execution reconstruction from R^2=0.495 to 0.685.UPG also localizes execution changes that pitch-mix and discrete sequence representations cannot detect, while retaining lineage to supporting games, plate appearances, and pitches.Source: §1 · p. 1
  • UPG reveals execution and ordered structure that discrete representations miss, supporting traceable multi-scale diagnosis and retrospective change localization.The authors frame it as a diagnostic representation, not a causal or future-performance prediction model.Source: §1 · pp. 1–2

2 Background and Problem Formulation

Pitch-tracking data are hierarchical event sequences whose strategic meaning combines physical execution, pitch order, and context. The formulation motivates a graph that preserves exact events and their lineage while adapting the resolution of recurring patterns to available support.

2.1 Pitching as Sequential Event Data

  • A plate appearance is an ordered, variable-length sequence nested within games and longer temporal windows, while adding physical and contextual detail can fragment the state space.Pitch events combine nominal identity, continuous execution, pre-pitch context, and post-pitch annotations.Source: §2.1 · p. 2

2.2 Related Work

  • Prior pitch prediction and decision models use prior actions and context, while sequence graphs capture order but commonly use discrete states that merge distinct executions.Increasing state detail or path length can recover specificity at the cost of statistical support; trajectory and outcome analyses alone do not expose recurring ordered structures and temporal contexts.Source: §2.2 · p. 2
  • Table 1 compares representative pitching analytics by which aspects they model explicitly, partially, or not centrally.UPG's positioning is joint analysis of sequence structure, physical execution, context, outcome pathways, and event-level traceability.Source: §2.2 · p. 2, Table 1 · p. 3

2.3 Problem Formulation

  • The formulation defines a pitcher-period attributed hierarchical graph whose nodes represent exact pitch events, semantic indices, and temporal scopes, with edges encoding order, membership, and containment.The edge sets are sequence, semantic, and temporal relations.Source: §2.3 · p. 2
  • Exact pitch events remain canonical: continuous trajectory and location stay attached, while semantic and temporal nodes support aggregation and drill-down.Post-pitch outcomes are annotations rather than part of event identity or semantic state construction.Source: §2.3 · p. 2
  • When highly detailed or long paths have too little repeated evidence, UPG backs off to shorter or coarser descriptions instead of treating near-unique executions as stable patterns.The diagnostic task retains support and lineage to games, plate appearances, transitions, and pitches.Source: §2.3 · p. 2
  • UPG is designed for event fidelity, support-adaptive resolution, and multiscale traceability, not causal identification or a universally superior predictive model.Prediction and post-execution modeling serve only as auxiliary evaluations under task-specific information constraints.Source: §2.3 · pp. 2–3

3 System Design

UPG keeps exact observed pitches as the event backbone, linking their within-PA order while indexing the same events across physical and temporal resolutions. Its support-adaptive paths vary reported sequence specificity with recurrence while retaining event-level lineage.

3 System Design

  • UPG represents strategy as a hierarchy over exact observed pitch events, separating physical event fidelity from the resolution used to report recurring patterns.Consecutive pitches within a PA form directed sequence edges; semantic and temporal links organize the same events at multiple scales.Source: §3 · p. 3

3.1 Exact Pitch Events and Sequence Relations

  • Each valid pitch remains a one-to-one event with nominal identity, continuous execution, and pre-pitch context; directed within-PA edges preserve order and pairwise execution.Aggregate structures index this event-and-edge backbone while retaining links to the original pitches.Source: §3.1 · p. 3

3.2 Continuous Execution and Semantic Hierarchy

  • Semantic levels range from pitch type through trajectory and location refinements to exact events, while trajectory strata use frozen within-type reference thresholds.Count, handedness, base-out state, inning, and score remain conditioning attributes rather than default semantic-state components.Source: §3.2 · pp. 3–4

3.3 Multi-Scale Strategy Graphs

  • Changing semantic resolution alters physical detail, while temporal scope selects the events summarized; aggregate patterns remain traceable to constituent events and sequence edges.Temporal levels include plate appearances, games, rolling windows, and seasons; rolling-window analyses use only completed games available within each window.Source: §3.3 · p. 4

3.4 Support-Adaptive Strategy Paths

  • For 2–4-pitch within-PA paths, UPG tests trajectory-refined then pitch-type candidates against occurrence and distinct-game thresholds, backing off to shorter suffixes or target pitch type.Backoff changes the statistical resolution of a claim, not stored information: supporting pitches retain trajectories, locations, contexts, temporal occurrences, and exact sequence edges.Source: §3.4 · p. 4

3.5 Diagnostic Evidence and Reporting

  • A motif is a recurring path reported in pitcher-level analysis; UPG records its support, timing, contextual usage, execution, and exact event lineage.Reports distinguish outcome-linked motifs, recurring patterns without strong effectiveness claims, and distinctive executions lacking recurrence; evidence remains observational and does not establish causality or future persistence.Source: §3.5 · p. 5

4 Evaluation

The evaluation tests UPG’s representation fidelity, adaptive resolution, reliability, traceability, change localization, and uses across players, time, and contexts. It uses MLB Statcast data and compares UPG with discrete and fixed-order alternatives.

4.1 Evaluation Questions and Protocol

  • The evaluation asks whether UPG preserves physical execution and ordered structure, adaptively retains useful sequence detail, yields reliable, traceable motifs, and supports retrospective diagnostics across players, time, and context.It uses 3.94 million MLB Statcast regular-season pitches from 2021 through July 3, 2026; the partial 2026 season is denoted 2026*.Source: §4.1 · p. 5

4.3 Support-Adaptive Resolution

  • Variable-order backoff raises held-out path coverage to nearly 95% while improving execution reconstruction, with most paths reported at coarse orders two to four.Allowing trajectory-qualified substates adds only a small additional reconstruction gain; the principal benefit comes from adapting path length to available support.Source: Figure 3 · p. 6, §4.3 · p. 6

4.2 Representation Fidelity and Ordered Structure

  • Order shuffling reduces recurrence for three-pitch, four-pitch, and context-conditioned paths, while having little effect on isolated attributes or single transitions.A collision example also shows distinct trajectories assigned the same discrete pitch, zone, and count sequence.Source: Figure 2 · p. 5, §4.2 · p. 6, Figure 2A

4.4 Reliability, Confidence, and Multi-Scale Traceability

  • Full-season motifs largely retain top-ten membership and outcome direction after their strongest game is removed; UPG traces patterns to exact pitches and downgrades unstable claims.In partial 2026*, stable evidence is less common and most motifs are labeled limited evidence.Source: §4.4 · pp. 6–7, Figure 4 · p. 6

4.5 Retrospective Change Localization

  • With pitch type, zone, and count held fixed, multiscale UPG achieves near-perfect discrimination of a controlled execution change that pitch mix and SGT miss.It also identifies affected dimensions and supporting plate appearances; natural-boundary results are retrospective and do not establish persistence or future improvement.Source: Figure 6 · p. 7, §4.5 · p. 7

4.6 Player-Level, Longitudinal, and Contextual Diagnosis

  • Player cases illustrate cross-pitcher comparison, Ohtani’s longitudinal reorganization, and Yamamoto’s handedness-conditioned changes in pitch use and trajectory strata.These cases distinguish changes in repertoire and sequence structure from changes in execution.Source: §4.6 · p. 8, Figure 7 · p. 8, Figure 8 · p. 8
  • The multi-player style summaries contrast Misiorowski’s concentrated fastball backbone with broader, less concentrated repertoires, while retaining a common style vocabulary.The analyses keep aggregate graph patterns linked to the exact events that produced them.Source: §4.6 · p. 9, Table 3 · p. 9

5 Discussion

UPG supports retrospective diagnosis by linking observed trajectories, pitch order, game context, and outcomes, but its observational data do not establish causes. The discussion also bounds the method’s biomechanical explanation, coaching utility, and transfer evidence.

5 Discussion

  • Trajectory motifs associated with whiffs or favorable contact are associations, not proof that the motifs caused those outcomes.Pitch outcomes may also depend on factors not fully observed in pitch-tracking data, including batter anticipation, pitcher condition, umpire decisions, catcher coordination, and game-specific plans.Source: §5 · p. 9
  • UPG characterizes pitch travel and deployment, but does not fully explain the biomechanics producing a trajectory.The discussion points to biomechanical or pose-tracking measurements as possible additions and cautions against treating current results as prescriptions for mechanical changes.Source: §5 · p. 9
  • The evaluation measures representation quality and diagnostic specificity, but does not establish whether reports improve coaching or player-development decisions.The authors call for evaluation with pitchers, coaches, and analysts, and prospective studies of changes based on identified motifs.Source: §5 · p. 9
  • Transfer across competition levels and tracking systems remains to be clarified through broader league-wide, cross-season, and cross-league evaluations.Source: §5 · p. 9

6 Conclusion

UPG is a hierarchical graph framework for retrospective pitching-strategy analysis, preserving exact pitch events and continuous execution across semantic and temporal scales. On 3.94 million MLB Statcast pitches, it supported multi-scale diagnosis and retrospective change localization, while remaining an observational rather than causal or predictive framework.

6 Conclusion

  • UPG preserves exact pitch events and continuous execution, organizes them across semantic and temporal scales, and uses support-adaptive paths to balance sequence specificity with repeated evidence.Source: §6 · p. 9
  • Using 3.94 million MLB Statcast pitches, UPG supported reliable multi-scale drill-down, retrospective change localization, and player-level diagnosis with exact event traceability.The authors report that discrete sequence representations can miss meaningful execution and ordered structure.Source: §6 · p. 9
  • The framework is intended for observational diagnosis, not causal inference or future-performance prediction.The authors suggest its principles may be useful in other sequential-event domains combining continuous observations with recurring discrete structure.Source: §6 · pp. 9–10
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