EFPI: Elastic Formation and Position Identification in Football (Soccer) using Template Matching and Linear Assignment

Joris Bekkers

REVIEW 4 major objections 6 minor 12 references

EFPI: Elastic Formation and Position Identification in Football (Soccer) using Template Matching and Linear Assignment

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper claims that scaling player positions to template dimensions before linear-sum assignment lets a single transparent method label both formations and individual roles from spatiotemporal tracking data.

desk verdict Incremental template-matching method with a promising scaling fix that is not yet validated by any quantitative experiment. read the letter →

arxiv 2506.23843 v1 pith:RLZSK2RS submitted 2025-06-30 cs.LG

Joris Bekkers This is my paper · ORCID

classification cs.LG

keywords footballanalyticsformationrecognitionplayerrolelabelinglinearsumassignmentHungarianalgorithmspatiotemporaltrackingdatatemplatematchingtacticalanalysis

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

EFPI claims that a team's formation and each outfield player's role can be read off from tracking data in one step, by matching players to static formation templates. The method first scales actual player positions to the width and length of the template set, then solves a linear sum assignment for each of 65 templates and selects the lowest-cost one. The paper argues that this pre-scaling is what fixes the tactically wrong assignments that unscaled template matching produces, and that the same procedure works on single frames, possessions, or arbitrary time windows. The contribution is a transparent alternative to supervised role classifiers, needing no training labels, with an optional stability parameter to suppress noise in transition moments.

What carries the argument

The mechanism is the linear sum assignment problem, solved with the Hungarian algorithm, applied to a cost matrix of Euclidean distances between players and template positions. Before any cost is computed, all player coordinates are scaled to the maximum width and length of the 65-template set, which turns the matching into a shape comparison rather than a raw proximity fit. Assignment is run separately for each template, the lowest-cost template wins, and the player-to-position matching from that template supplies the role labels. An optional stability parameter $\epsilon$ blocks a template change unless the new cost is at least $\epsilon$ percent lower than the previous one.

What would settle it

Take a sample of match frames with human-annotated formations and roles, run EFPI with and without scaling, and compare agreement. If the scaled version disagrees with the annotations systematically in compressed or stretched situations—teams packed deep, attacking in wide spaces, or playing narrow—then the scaling does not preserve the geometry needed for correct assignment.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that scaling player coordinates to the bounding dimensions of the formation templates before cost computation makes template matching tactically coherent. In the paper's illustrative frame, unscaled matching labels a center back as a defensive midfielder and a central midfielder as a winger; after scaling, the same frame is labeled 4411 with roles the author treats as correct. The paper states that this scaling largely resolves the illogical assignment problem identified in earlier work, and that formation labels and player position labels can therefore be produced instantly and simultaneously for any time segment, from single frames to full periods.

Load-bearing premise

The load-bearing premise is that linearly scaling all player positions to the widest and longest formation template preserves the relative geometry that makes the lowest-cost template the tactically correct one in every game situation; this normalization is introduced without a sensitivity analysis.

Editorial extensions

If this is right

A single algorithm outputs both the formation label and individual role labels for every outfield player, without training data or manual annotation.
Because player locations can be averaged over any segment, the same code labels single frames, possessions, 5-minute windows, or full periods.
The stability parameter $\epsilon$ suppresses spurious formation switches during transitions while still allowing genuine changes when the cost improvement is large enough.
Templates for 8, 9, and 10 outfield players let the method keep working when red cards or injuries reduce a team's numbers.
The open-source implementation consumes standardized tracking data, so it can be applied to data from a wide range of providers.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The scaling step is implicitly a claim that formation geometry is scale-invariant across match situations; a natural extension would test rotation or shear alignment, which the paper does not do.
Frame-level labels from EFPI could serve as weak supervision for role-classification models, but that use would require checking EFPI's own accuracy against annotated ground truth first.
The stability threshold and segment length interact: a fixed $\epsilon$ may be too lax for long segments and too strict for short ones, so an adaptive threshold is a testable refinement.
A systematic comparison of EFPI's formation labels with human-annotated formations across varied match states would reveal whether the scaling truly resolves illogical assignments or only on the illustrated frame.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear colleague,

Short version: this is a clearly written, incremental method paper that ships code, but its central claim—that the scaling step fixes the assignment problem—is supported only by two qualitative examples. If it lands in a venue, it should be after a real evaluation.

What's new: EFPI applies linear sum assignment (Wei et al.'s idea) to formation labeling with two additions: per-frame scaling of player positions to the template collection's max width/length before cost computation, and a hysteresis threshold on cost differences to stabilize labels across segments. The implementation is open source and works across several tracking data providers via Kloppy. That is genuinely useful for practitioners who want a transparent, low-parameter alternative to supervised classifiers like Pleuler's.

The paper's main illustration is honest about the problem: Figure 2 shows the unscaled assignment mislabeling a center back as a defensive midfielder, and the scaled version gives the expected 4411 and more sensible labels. That's a nice demonstration that the scaling can help in at least this frame. The Portugal-Switzerland case study is also a reasonable qualitative use-case.

The soft spot is exactly what the stress-test note says: the scaling is load-bearing and unvalidated. The scale factors depend on the current bounding box, so the same nominal formation can map to different normalized shapes depending on whether the team is compact or stretched. The cost surface is not invariant under this transformation, so there is no guarantee the lowest-cost template after scaling corresponds to the true formation. The paper provides no ablation of scaling, no comparison against unscaled assignment on a labeled dataset, no baseline (e.g., Wei et al., or a simple majority classifier), and no sensitivity analysis for epsilon or the scaling itself. The phrase 'largely resolves' is not backed by evidence. Also, the evaluation is entirely qualitative; there is no ground-truth formation/role labeling, so accuracy is unknown. The stability parameter is reasonable but also unexamined—how sensitive are segment-level labels to epsilon?

These are fixable. The method is simple enough that a careful comparison on a few matches with manually annotated formations and roles would settle it. I'd like to see that before trusting the results, but the paper is coherent and the code is public, so it deserves a proper review rather than a desk reject.

My recommendation: if you're refereeing, return it with a request for quantitative validation and sensitivity analyses. If you're just scanning the literature, it's worth a skim for the scaling idea, but don't cite it as a validated method until those numbers exist.

Referee Report

4 major / 6 minor

Summary. The paper introduces EFPI, a rule-based method for football formation recognition and per-player role labeling from spatiotemporal tracking data. For each frame or time segment, player coordinates are linearly scaled to the maximum width and length of a fixed set of 65 static formation templates, a linear sum assignment solver matches players to template positions for each template, and the lowest-cost template is selected. An optional stability parameter suppresses formation changes when the relative cost improvement is below a threshold. The method is illustrated on a single frame and on Portugal's 2022 World Cup match against Switzerland, and the implementation is released through the open-source unravelsports Python package.

Significance. If the scaling step can be shown to preserve the relevant geometry of player arrangements, EFPI would provide a simple, transparent, and computationally cheap baseline for dynamic formation and role labeling, complementing supervised and change-point approaches such as those of Pleuler (2024) and Kim et al. (2022). The open-source implementation and support for multiple tracking-data providers through Kloppy are clear practical strengths, as is the use of an openly available dataset for the code example. However, the paper currently offers no quantitative evidence for its central claim that the method 'functions effectively': there is no ground-truth comparison, no error metric, no sensitivity analysis, and no baseline comparison. The contribution is therefore a plausible algorithmic recipe whose practical validity remains unestablished.

major comments (4)

[Section 2.1] The per-frame scaling of player positions to the maximum width and length of the template set is the load-bearing novelty of the method, but it is neither justified nor validated. The scaling factors depend on the current bounding box of the team, so the same real formation can map to different normalized shapes in a compact low block versus a stretched high press, and the assignment cost in Eq. (1) is not invariant under this normalization. The paper provides no comparison of scaled versus unscaled assignment costs, no ablation of the scaling, and no sensitivity analysis. The single illustrative frame in Figure 2 cannot establish that the lowest-cost template after scaling corresponds to the true formation. The claim that scaling 'largely resolves the illogical assignment problem pointed out by Poppeliers (2025)' therefore needs quantitative support, for example by comparing assignment accuracy against ground-truth formation and role labels on a labeled dataset.
[Entire manuscript (especially Abstract and Figures 2, 4, 5)] The central claim that EFPI 'functions effectively on individual frames' is not supported by any quantitative experiment. The paper reports no accuracy, precision, recall, or error rates for formation identification or player-role assignment, and it compares against no baseline method such as Wei et al. (2013), Pleuler (2024), or SoccerCPD. The qualitative Portugal-Switzerland case study (Figures 4-5) and the single-frame example (Figure 2) cannot substantiate the claim. Because the paper's stated goal is a usable tactical-analytics tool, the authors should evaluate EFPI on the openly available dataset cited as [1], using ground-truth labels (e.g., starting lineups and known formation annotations), and report frame-level and segment-level metrics against at least one baseline.
[Section 2.3, Eq. (3)] The stability parameter is a free parameter, yet the paper provides no sensitivity analysis. The only demonstration is a single 24-second sequence in Figure 3, which is insufficient to show that the threshold reliably separates genuine formation changes from noise. Additionally, Eq. (3) uses C_{t-1} for the cost of the previously assigned template but does not specify what happens if that template was not the lowest-cost template at time t-1, or how the parameter interacts with the 'change after possession' option shown in Codeblock 1. A systematic robustness study over a range of epsilon values, and over multiple matches and game situations, is needed before the stability mechanism can be considered a validated component.
[Section 2.2] The segmentation procedure that averages player positions over a segment (Eq. (2)) is presented without validation. Averaging over a full period or a five-minute window can obscure genuine tactical transitions and is sensitive to substitutions and out-of-possession excursions. The statement that segments are 'partitioned by attacking and defending periods' is not operationalized, and it is unclear how this interacts with possession data. The paper should compare frame-level vs segment-level assignments and report how often the segment-level label differs from the majority of frame-level labels, especially in transition-heavy intervals.

minor comments (6)

[Figure 2 caption] The caption refers to '31231' while the text and figure describe '31213'; the caption also contains the typo 'identifeied'. Please correct both.
[Eq. (3)] The expression should be written as (C_{t-1} - C_t)/C_t > epsilon, and each symbol should be defined at first use, including the distinction between the cost of the previously assigned template and the cost of the best template at time t.
[Section 2.2] The phrase 'partition these segments by attacking and defending periods' needs a precise definition, including how attacking and defending are determined from tracking or event data.
[References] Reference [7] is incomplete: no publication venue, arXiv identifier, or year-consistent citation details are given. Please provide a complete citation or remove it if it is not publicly available.
[Codeblock 1] The heading 'Model Configuration and Training' is a misnomer because the method has no training phase. Also, the 'change_threshold' parameter is not explicitly connected to the stability parameter epsilon in the text.
[General] There are several typographical and phrasing issues, including 'the the' in Section 2.4, 'individually players' in the introduction, and variable naming inconsistencies (N and q in Eq. (2)). A careful proofread is recommended.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: EFPI is an open-loop template-matching procedure; no fitted parameter or self-citation is load-bearing.

full rationale

The paper's derivation chain is straightforward: Eq. 1 solves a linear sum assignment against 65 predefined static templates, and the only novel ingredient is a pre-scaling of player coordinates to the maximum template width and length before computing costs. This scaling is a heuristic introduced in Section 2.1, not derived from the output, and the assignment cost is simply minimized over templates. The result is always one of the predefined templates by construction of the method, which is a model-selection property rather than a circular prediction. There is no fitted parameter that is later relabeled as a prediction: no ground-truth labels are used for fitting, and the stability parameter epsilon is user-chosen and is not itself used to generate the template assignments it filters. The self-citations ([2], [3]) point to the software package and prior work by the same author, but they are implementation references, not load-bearing premises for the assignment math. External citations provide the assignment solver and the template library. The claim that scaling 'largely resolves' Poppeliers's illogical-assignment problem is an empirical assertion that is not validated with ground truth, and this is a correctness or validation concern, not circularity. Therefore no significant circularity is present.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim relies on three domain assumptions about template coverage, data quality, and the validity of cost as a tactical proxy. The only user-controlled free parameter is the stability epsilon, with the scaling normalization acting as an unvalidated modeling choice. No new physical or conceptual entities are introduced.

free parameters (2)

stability parameter epsilon = 0.1 (example, user-chosen)
Threshold in Eq. (3) that controls when a formation change is accepted. It is not fitted to data but directly affects the temporal stability of the output.
scaling to maximum template width and length
Player positions are rescaled to the maximum dimensions of the template set before cost computation. This is a modeling choice that changes all distances and can alter assignments; it is not justified or validated.

assumptions (4)

domain assumption The 65 predefined templates from mplsoccer sufficiently represent all plausible formations and role layouts in a match.
The method can only select among these templates. If a team plays a formation not in the set, the output will be the closest template, which may be tactically wrong. Introduced in Section 2.1 and Appendix A.
domain assumption Player tracking positions are accurate, and the goalkeeper's role label from the data provider is correct.
The method excludes goalkeepers and relies on provider labels for them. Errors in tracking or goalkeeper labels would propagate. Stated in Section 2.1.
domain assumption The minimum assignment cost over templates is a valid proxy for the true formation and player roles.
The method always selects the lowest-cost template. This assumes that spatial proximity to a template is the correct criterion for tactical truth, which is not proven. Implicit throughout Section 2.1.
standard math The Hungarian algorithm solves the linear sum assignment problem optimally.
Use of the Hungarian algorithm in Eq. (1) relies on its proven optimality for minimizing assignment cost. This is a standard result from Kuhn (1955).

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Cite this review

Pith. "Pith review of EFPI: Elastic Formation and Position Identification in Football (Soccer) using Template Matching and Linear Assignment." pith.science (2026). https://pith.science/paper/RLZSK2RS

@misc{pith2026250623843,
  author       = {Pith},
  title        = {Pith review of: EFPI: Elastic Formation and Position Identification in Football (Soccer) using Template Matching and Linear Assignment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RLZSK2RS}},
  note         = {Machine review of arXiv:2506.23843}
}

read the original abstract

Understanding team formations and player positioning is crucial for tactical analysis in football (soccer). This paper presents a flexible method for formation recognition and player position assignment in football using predefined static formation templates and cost minimization from spatiotemporal tracking data, called EFPI. Our approach employs linear sum assignment to optimally match players to positions within a set of template formations by minimizing the total distance between actual player locations and template positions, subsequently selecting the formation with the lowest assignment cost. To improve accuracy, we scale actual player positions to match the dimensions of these formation templates in both width and length. While the method functions effectively on individual frames, it extends naturally to larger game segments such as complete periods, possession sequences or specific intervals (e.g. 10 second intervals, 5 minute intervals etc.). Additionally, we incorporate an optional stability parameter that prevents unnecessary formation changes when assignment costs differ only marginally between time segments. EFPI is available as open-source code through the unravelsports Python package.

Figures

Figures reproduced from arXiv: 2506.23843 by the authors.

**Figure 2.** Dynamic Position Labeling using the Hungarian algorithm to fit the lowest cost predefined static formation and its position labels to a scaled frame of tracking data. Direction of play is left to right. These assignment issues occur because the actual formation (see Figure 2a) is not at the same scale as the formation templates. To resolve this issue, we scale the original player positions to the maximum width and l… view at source ↗

**Figure 3.** A 24 second sequence of play for a single team transitioning from defense to attack, showing the effect of the stability parameter on formation template assignment [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: Portugals’ formations against Switzerland during World Cup 2022 Depending on the data source Portugal, in their 6-1 victory over Switzerland during the 2022 World Cup, played in a ”4312”1 or ”433”2 with Bruno Fernandes either playing as a Central Attacking Midfielder (…

**Figure 5.** Figure 5: Bruno Fernandes’ playing positions against Switzerland [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: mplsoccer Formation Templates 1 - 25 8 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: mplsoccer Formation Templates 26 - 50 9 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: mplsoccer Formation Templates 51 - 65 10 [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

12 extracted references · 11 canonical work pages

[1]

An integrated dataset of spatiotemporal and event data in elite soccer

Manuel Bassek et al. “An integrated dataset of spatiotemporal and event data in elite soccer”. In: Scientific Data 12.1 (2025), p. 195 (cit. on p. 6)

work page 2025
[2]

J. Bekkers. unravelsports [GitHub]. Version 1.1.0. 2024. url: https://github.com/UnravelSports/ unravelsports (cit. on pp. 1, 2, 6)

work page 2024
[3]

A Graph Neural Network deep-dive into successful counter- attacks

Joris Bekkers and Amod Sahasrabudhe. “A Graph Neural Network deep-dive into successful counter- attacks”. In: arXiv preprint arXiv:2411.17450 (2024) (cit. on p. 2)

arXiv 2024
[4]

SoccerCPD: Formation and role change-point detection in soccer matches using spatiotemporal tracking data

Hyunsung Kim et al. “SoccerCPD: Formation and role change-point detection in soccer matches using spatiotemporal tracking data”. In: Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining . 2022, pp. 3146–3156 (cit. on p. 1)

work page 2022
[5]

The Hungarian method for the assignment problem

Harold W Kuhn. “The Hungarian method for the assignment problem”. In: Naval research logistics quarterly 2.1-2 (1955), pp. 83–97 (cit. on p. 2)

work page 1955
[6]

Frame by Frame Position

Devin Pleuler. Frame by Frame Position . https : / / github . com / devinpleuler / research / blob / master/frame-by-frame-position.md . Accessed: 2025-03-25. 2024 (cit. on p. 2)

work page 2025
[7]

Automatic discovery of buildup tactics using football match data

Pieter-Jan Poppeliers. “Automatic discovery of buildup tactics using football match data”. In: (2025) (cit. on pp. 1, 2)

work page 2025
[8]

mplsoccer: A python package for plotting soccer/football charts in matplotlib

Andrew Rowlinson. mplsoccer: A python package for plotting soccer/football charts in matplotlib . htt ps://github.com/andrewRowlinson/mplsoccer. Version 1.5.0. 2021 (cit. on p. 2)

work page 2021

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[9]

Dynamic analysis of team strategy in professional football

Laurie Shaw and Mark Glickman. “Dynamic analysis of team strategy in professional football”. In: Bar¸ ca sports analytics summit13 (2019), pp. 1–13 (cit. on p. 1)

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[10]

SciPy 1.0: fundamental algorithms for scientific computing in Python

Pauli Virtanen et al. “SciPy 1.0: fundamental algorithms for scientific computing in Python”. In: Nature methods 17.3 (2020), pp. 261–272 (cit. on p. 2)

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[11]

Kloppy: standardizing soccer tracking and event data [GitHub]

Koen Vossen. Kloppy: standardizing soccer tracking and event data [GitHub] . 2020. url: https:// github.com/PySport/kloppy (visited on 02/03/2024) (cit. on p. 6)

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[12]

Large-scale analysis of formations in soccer

Xinyu Wei et al. “Large-scale analysis of formations in soccer”. In: 2013 international conference on digital image computing: techniques and applications (DICTA) . IEEE. 2013, pp. 1–8 (cit. on pp. 1, 2). 11

2013

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

An integrated dataset of spatiotemporal and event data in elite soccer

Manuel Bassek et al. “An integrated dataset of spatiotemporal and event data in elite soccer”. In: Scientific Data 12.1 (2025), p. 195 (cit. on p. 6)

work page 2025

[2] [2]

J. Bekkers. unravelsports [GitHub]. Version 1.1.0. 2024. url: https://github.com/UnravelSports/ unravelsports (cit. on pp. 1, 2, 6)

work page 2024

[3] [3]

A Graph Neural Network deep-dive into successful counter- attacks

Joris Bekkers and Amod Sahasrabudhe. “A Graph Neural Network deep-dive into successful counter- attacks”. In: arXiv preprint arXiv:2411.17450 (2024) (cit. on p. 2)

arXiv 2024

[4] [4]

SoccerCPD: Formation and role change-point detection in soccer matches using spatiotemporal tracking data

Hyunsung Kim et al. “SoccerCPD: Formation and role change-point detection in soccer matches using spatiotemporal tracking data”. In: Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining . 2022, pp. 3146–3156 (cit. on p. 1)

work page 2022

[5] [5]

The Hungarian method for the assignment problem

Harold W Kuhn. “The Hungarian method for the assignment problem”. In: Naval research logistics quarterly 2.1-2 (1955), pp. 83–97 (cit. on p. 2)

work page 1955

[6] [6]

Frame by Frame Position

Devin Pleuler. Frame by Frame Position . https : / / github . com / devinpleuler / research / blob / master/frame-by-frame-position.md . Accessed: 2025-03-25. 2024 (cit. on p. 2)

work page 2025

[7] [7]

Automatic discovery of buildup tactics using football match data

Pieter-Jan Poppeliers. “Automatic discovery of buildup tactics using football match data”. In: (2025) (cit. on pp. 1, 2)

work page 2025

[8] [8]

mplsoccer: A python package for plotting soccer/football charts in matplotlib

Andrew Rowlinson. mplsoccer: A python package for plotting soccer/football charts in matplotlib . htt ps://github.com/andrewRowlinson/mplsoccer. Version 1.5.0. 2021 (cit. on p. 2)

work page 2021