A defence can shift together while nearby defenders also move within the unit. This project measures that second geometry: movement by defenders nearest an off-ball attacker relative to the wider defensive unit. It compares the average accumulated defender-relative path of the nearest three defenders with that of four middle-ranked defenders, with ranks fixed before the defender interval.
Main finding: movement away from the pitch centreline (“outward”) was associated with greater subsequent localized defensive reorganization than comparable movement toward goal.
For the prespecified comparison of straight 5 m outward versus straight 5 m goalward movement, holding modeled path magnitude and starting context equal, the contrast was approximately 28 cm in IDSSE, 24 cm in the original SkillCorner cohort, and 28 cm in the prospective additional SkillCorner cohort. These are differences in the near-minus-middle group-average defender-relative path—not extra movement by each defender.
The directional difference appeared in separate analyses of seven IDSSE and nine original SkillCorner matches, then prospectively replicated in ten additional nonoverlapping SkillCorner matches. Every match contrast was positive. The cohorts and tracking environments were not pooled.
The measurement could organize candidate passages for later video review; its football interpretation and review usefulness remain unvalidated. It does not establish causation, marking responsibility, tactical effectiveness, or attacking value.
Reproduce and inspect: start with REPRODUCE.md, or browse the frozen protocols, public result summaries, and tests.
Primary evidence — separate directional analyses
Separate estimates are shown for IDSSE, original SkillCorner, and the prospective additional SkillCorner cohort: all 7/7, 9/9, and 10/10 match-level outward-minus-goalward contrasts are positive. No cross-provider or pooled 19-match estimate was calculated. The figure reports observational geometry, not value.
| Environment | Outward minus goalward | 95% CI | Direction consistency |
|---|---|---|---|
| IDSSE | 0.056856 m/m | [0.051358, 0.062430] | 7/7 match; 7/7 leave-one-match-out positive |
| SkillCorner Open Data | 0.048883 m/m | [0.042940, 0.054707] | 9/9 match; 9/9 leave-one-match-out positive |
| SkillCorner prospective additional cohort | 0.055007 m/m | [0.050064, 0.060021] | 10/10 match; 10/10 leave-one-match-out positive |
The IDSSE modeled comparison corresponds to approximately 0.284 m greater near-minus-middle group-average accumulated defender-relative path for a 5 m outward rather than 5 m goalward displacement, under equal path magnitude and context. Defensive reorganization was therefore not simply aligned with movement toward goal. This does not mean outward movement is better, more valuable, or a preferred tactical action.
Raw defender movement combines collective unit shift and movement within the unit. The measurement separates these by expressing each outfield defender's movement relative to the contemporaneous movement of the other nine defending outfield players. D1–D3 and D4–D7 are proximity groups fixed before the defender interval, not inferred marking assignments. Attacker movement is measured over the preceding two seconds; defender-relative path over the subsequent two seconds.
Supporting evidence — temporal association and reverse-time comparison
Panel A illustrates one fixed passage; panels B–C report statistical evidence. The fixed Metrica Game 2 passage contrasts absolute defender paths with net defender-relative displacement over the same subsequent interval. The statistical outcome is accumulated defender-relative path, not the illustrated net arrows.
This six-second Metrica Game 2 replay illustrates the fixed passage used in Figure 1. It shows tracking geometry only; it is not human validation or independent evidence of tactical meaning.
Run or reproduce locally: use the output-free tracking replay notebook with the public Game 2 files available locally.
Tracking data: Metrica Sports sample data. Animation rendered by Moving the Defense; no original match video is included.
This retrospective analyst replay colors defenders by accumulated movement relative to the other nine defenders over the trailing two seconds. Values are raw metres shown on one fixed 0–6.25 m scale. Attackers remain blue while only defender marker fill uses the yellow-to-red score scale; the team meter is the arithmetic mean across all ten supported defenders. The centered smoother requires raw tracking just after the displayed time, so this is not a live detector. Missing ten-player support is shown as unavailable rather than interpolated.
The replay describes tracking geometry only. It does not diagnose defensive quality, tactical error, marking, or causal attacker influence. Reproduce it with the output-free defender-relative replay notebook and the public Metrica Game 2 files.
Preceding attacker movement was associated with greater subsequent defender movement relative to the defensive unit among the nearest defenders than the middle group. Here, m/m expresses the near-minus-middle group-average accumulated defender-relative path contrast in metres per metre of attacker movement, not additional movement by every defender.
| Environment | Near-minus-middle association | Interval |
|---|---|---|
| Metrica Games 1–2, pooled | 0.05029 m/m | [0.03433, 0.06858] |
| IDSSE, seven matches | 0.06115 m/m | [0.05579, 0.06681] |
| IDSSE forward-minus-reverse difference | 0.02455 m/m | [0.01932, 0.02985] |
All seven IDSSE primary estimates and all seven forward-minus-reverse differences were positive. Reverse-time structure also remained positive: the evidence is that the correctly ordered association exceeded the reverse-time comparison, not that shared temporal structure disappeared.
The measurement could organize candidate passages for later video review. Its football interpretation and review usefulness remain unvalidated. It can describe local movement separately from a shared defensive shift, but does not automatically assign tactical labels, rank players, or measure value.
The contribution is not a new centroid or generic tracking primitive. It is a prospectively tested and externally replicated temporal measurement of internal defensive reorganization, combined with a replicated directional difference in the defensive geometry associated with outward versus goalward off-ball movement—without requiring inferred marking assignments or a value model.
Goalward movement showed a strong secondary, nonclassifying association with collective defensive translation: the frozen 5 m goalward-versus-outward contrast was 2.962709 m [2.870720, 3.048322], positive in 7/7 match and 7/7 leave-one-match-out fits.
The proposed inward-versus-outward narrowing mechanism was MIXED: 0.134003 m [−0.006622, 0.273430], with 5/7 positive match contrasts. Different geometric response scales are visible, but the mechanism behind the directional difference remains unresolved.
Localized reorganization tended to be larger when attackers started closer to the ball and less far goalward relative to the defensive unit.
| Starting relationship | Association | 97.5% CI |
|---|---|---|
| Attacker goalward position relative to the unit | −0.010161 m/m | [−0.011805, −0.008499] |
| Attacker–ball distance | −0.007533 m/m | [−0.008864, −0.006245] |
Both relationships had the same direction in all 7/7 match and leave-one-match-out fits, and passed their predeclared trims. They characterize where the observed geometry was larger; they do not explain why defenders moved.
The evidence does not establish attacker causation or influence; defender attention, marking, assignment, or responsibility; tactical success; space creation; player quality; gravity; or off-ball value.
A direct consequence test was negative: Opportunity Redistribution in Metrica
Game 1 estimated beta_D = -0.02407 [−0.09392, 0.04776]. Under that test,
localized defensive reorganization did not imply improved nearby teammate
separation. A context-adjusted retrieval model also remained MIXED after
missing its predeclared application threshold. Negative and mixed findings are
retained in the claim-status ledger and
research log, not tuned away.
Descriptive secondary result — IDSSE only
An additional descriptive map summarizes the contrast by attacker starting location.
The scientific primary remains h=7.5 m, selected by human review of response-blind support and frozen before response access. Shown here is the predeclared h=10 m sensitivity as a near-complete-support presentation view; its Conservative support covers 99.89% of the legal pitch. Its tighter display scale is presentation-only and does not change the scientific primary. This is not a significance map or a hotspot test.
A prospectively frozen SkillCorner follow-up
in the already-used nine-match sample found a positive lateral-starting-position
association (
| Data source | Role |
|---|---|
| Metrica Sample Game 1 | Open/public development environment |
| Metrica Sample Game 2 | Open/public heldout validation and real explanatory example |
| IDSSE / DFL XML | Seven-match public research release; IDSSE/DFL Figshare dataset, CC BY 4.0 |
| SkillCorner Open Data | Open third, broadcast-derived environment for the original directional replication and prospective ten-match nonoverlapping replication |
| Metrica Sample Game 3 | Untouched |
Current publication policy excludes raw provider files and new reconstructive provider-linked row artifacts without explicit approval; historical tracked artifacts retain their governed provenance. Compact governed results, code, figures, protocols, configurations, and provenance ledgers are public.
| Goal | Start here |
|---|---|
| Reproduce the paper | REPRODUCE.md |
| Inspect technical reproduction detail | Technical reproducibility guide |
| Audit research history and claim limits | Claim-status ledger and research log |
| Continue the research | Research roadmap |
| Understand the football question | Project explainer |
| Inspect protocols and results | Documentation guide |
The next scientific challenge is semantic and applied: determine what these replicated geometric patterns correspond to in football practice and how analysts should use them without converting observable reorganization into unsupported claims of influence or value. Artificial-transition work is a post-Sloan extension, not a current mechanism search.
Figure sources use closed governed artifacts. Code and documentation are released under the MIT License.