Quantifying defensive pressure on the ball carrier in soccer based on minimum arrival time

Ikuya Sakamoto; Ken Yamamoto; Takuma Narizuka; Yoshihiro Yamazaki

arxiv: 2606.09452 · v1 · pith:FS6SWFVWnew · submitted 2026-06-08 · ⚛️ physics.soc-ph

Quantifying defensive pressure on the ball carrier in soccer based on minimum arrival time

Takuma Narizuka , Ikuya Sakamoto , Ken Yamamoto , Yoshihiro Yamazaki This is my paper

Pith reviewed 2026-06-27 14:10 UTC · model grok-4.3

classification ⚛️ physics.soc-ph

keywords soccerdefensive pressuretracking dataarrival timepressingball possessionmotion modelJapan league

0 comments

The pith

Defensive pressure on the soccer ball carrier equals the minimum time for any opponent to arrive at that spot using a physics motion model.

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

The paper defines defensive pressure directly as the shortest time any opponent would need to reach the current ball-carrier position, calculated from player positions and speeds via a simple physics model. The authors apply the measure to every possession interval across all 306 matches of the 2023 Japanese top division and track how the value changes over time. They report that the arrival time shortens while a team keeps the ball and lengthens after the ball is released, that possessions begun under shorter arrival times produce less forward progress, and that possessions ended under shorter arrival times end in turnovers more often for open-play passes. A reader would care because the approach supplies a single, transparent number grounded in physical motion rather than layered statistical assumptions.

Core claim

Defensive pressure is quantified as the opponent minimum arrival time to the ball-carrier location computed from a physics-based motion model. Using synchronized event and tracking data from 306 matches, the quantity decreases during a possession interval and rises again after ball release. Possessions that begin under shorter minimum arrival times produce smaller ball progression, and intentional open-play passes that end under shorter arrival times are more likely to be lost.

What carries the argument

Minimum arrival time to the ball-carrier location, computed from a physics-based motion model applied to tracking data.

If this is right

The minimum arrival time shortens while a team maintains possession and lengthens after the ball is released.
Possessions that start with shorter minimum arrival times produce smaller net ball progression.
For intentional open-play passes, possessions that end with shorter minimum arrival times are more likely to result in loss of the ball.
The quantity supplies a simple baseline for describing pressing intensity directly from tracking data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same arrival-time calculation could be applied to evaluate how individual players or teams alter pressure levels through positioning choices.
Coaches could test whether training drills that reduce opponent arrival times improve real-match outcomes.
The measure offers a way to compare pressing styles across leagues using only position and velocity data without additional modeling layers.

Load-bearing premise

A basic physics model of constant-speed straight-line motion gives an accurate enough picture of how fast any defender can actually reach the ball carrier.

What would settle it

Direct comparison of the model's predicted arrival times against the actual times defenders reach the ball carrier in the same match footage or higher-frequency GPS data; large systematic differences would falsify the claim that the quantity measures real defensive pressure.

Figures

Figures reproduced from arXiv: 2606.09452 by Ikuya Sakamoto, Ken Yamamoto, Takuma Narizuka, Yoshihiro Yamazaki.

**Figure 1.** Figure 1: For the possession-loss analysis in Subsection 3.4, we further restricted the release actions to intentional teammate-directed open-play passes, namely ordinary passes and through passes as labeled in the event data. Ball loss was defined as the situation in which possession switched to the opponent or play stopped after the action. The numbers of analyzed possessions and passes are reported for the ball-… view at source ↗

**Figure 2.** Figure 2: Distributions of the opponent and teammate minimum arrival times, [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Typical time series of the opponent minimum arrival time to the ball-carrier location, [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Temporal change in the opponent minimum arrival time during possession. (a) Nor [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: Change in the opponent minimum arrival time after ball release. (a) Normalized two [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 6.** Figure 6: Association between defensive pressure and ball progression. (a) Mean ball progression [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

**Figure 7.** Figure 7: Association between defensive pressure at ball release, the relative safety of the realized [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

read the original abstract

Defensive pressure on the ball carrier is a fundamental component of soccer tactics. Existing pressure measures often involve additional modeling assumptions, which may reduce interpretability. In this study, we quantify defensive pressure as the opponent minimum arrival time to the ball-carrier location, computed from a physics-based motion model. Using synchronized event and tracking data from all 306 matches in the top division of the Japan Professional Football League during the 2023 season, we analyze the statistical characteristics and temporal evolution of this quantity during ball-possession intervals. The results show that the opponent minimum arrival time tends to decrease during possession and to increase again at the start of the next possession after ball release. We also find that possessions starting under stronger defensive pressure tend to yield smaller ball progression, and that, for intentional open-play passes, possessions ending under stronger pressure are more likely to be lost. These findings indicate that minimum arrival time provides an interpretable and physically grounded measure of immediate defensive pressure on the ball carrier. The proposed framework provides a simple and interpretable baseline for quantifying pressing dynamics from tracking data.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper defines defensive pressure via minimum arrival time from a physics motion model and links it to J-League possession outcomes, but skips any check that the model matches real player paths.

read the letter

The main takeaway is that this work treats the shortest time for an opponent to reach the ball carrier, computed from a basic physics motion model, as a direct pressure metric. They run it on synchronized tracking and event data from every 2023 J-League match and report that the time drops during a possession, rises after release, and that higher starting pressure predicts less ball progress while higher ending pressure predicts more turnovers.

What stands out is the use of a full league season of real data rather than small samples, plus the choice to keep the measure simple instead of layering on extra fitted parameters. That gives a clean baseline for pressing dynamics.

The soft spot is exactly where the stress-test note flags it. The paper never shows whether the model's predicted arrival times line up with when opponents actually reach the ball-carrier spot in the data. Without that check, or even the explicit equations and parameter values, the claim that the metric is physically grounded rests on an untested assumption about player motion. Direction changes, fatigue, or ball speed could easily break the proxy, and the abstract gives no error bars or sensitivity tests to judge how much that matters.

This is for analysts who already work with tracking data and want an interpretable pressure number they can compute quickly. It is not yet ready for direct use in coaching without the missing validation.

It deserves peer review because the data scale and the outcome correlations are concrete enough to be worth referee time, even if the methods section will need substantial work.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes quantifying defensive pressure on the soccer ball carrier as the minimum arrival time of opposing players to the ball-carrier location, derived from a physics-based motion model. Using event and tracking data from all 306 matches in the 2023 Japan Professional Football League, the authors analyze its statistical properties during ball possessions, finding that it tends to decrease during possession and increase after ball release. They also report that possessions starting under stronger pressure yield smaller ball progression, and possessions ending under stronger pressure are more likely to end in turnovers for intentional open-play passes.

Significance. If the underlying motion model is validated, the approach offers a simple, interpretable, and physically motivated baseline for assessing pressing dynamics directly from tracking data, avoiding some of the additional assumptions in existing pressure metrics. The empirical correlations with progression and turnover provide initial support for its relevance.

major comments (2)

[Abstract/Methods description] Abstract/Methods description: The physics-based motion model is referenced but not specified with explicit equations, parameter values, or error bounds. No validation is reported comparing predicted arrival times against observed player trajectories or actual times at which opponents reach the ball-carrier location. This is load-bearing for the central claim that the measure is 'physically grounded,' as unaccounted factors like direction changes or acceleration limits could introduce systematic mismatch.
[Results section (statistical characteristics and temporal evolution)] Results section (statistical characteristics and temporal evolution): The reported patterns (decrease during possession, correlations with progression and turnover) lack details on exact sample sizes, confidence intervals, or controls for confounders such as pitch location. This limits assessment of whether the data robustly support the interpretability claims.

minor comments (1)

Clarify data synchronization between event and tracking sources and any applied filters, as this affects reproducibility of the possession-interval analysis.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive comments, which highlight important areas for improving the clarity and robustness of our manuscript. We address each major comment below and will revise the manuscript to incorporate the suggested enhancements.

read point-by-point responses

Referee: [Abstract/Methods description] Abstract/Methods description: The physics-based motion model is referenced but not specified with explicit equations, parameter values, or error bounds. No validation is reported comparing predicted arrival times against observed player trajectories or actual times at which opponents reach the ball-carrier location. This is load-bearing for the central claim that the measure is 'physically grounded,' as unaccounted factors like direction changes or acceleration limits could introduce systematic mismatch.

Authors: We agree that the physics-based motion model requires more explicit specification to support the claim of being physically grounded. In the revised manuscript, we will add the explicit equations of the motion model, the parameter values (including maximum speed and acceleration), and associated assumptions or error bounds. We will also include a dedicated discussion of the model's limitations, such as the effects of direction changes and acceleration constraints, and how these may affect predicted arrival times. Direct validation against observed arrival times was not performed in the original submission because the available tracking data does not allow straightforward matching of predicted versus actual opponent arrival events at the ball-carrier location; we will transparently note this limitation while explaining why the model still provides a useful baseline. revision: yes
Referee: [Results section (statistical characteristics and temporal evolution)] Results section (statistical characteristics and temporal evolution): The reported patterns (decrease during possession, correlations with progression and turnover) lack details on exact sample sizes, confidence intervals, or controls for confounders such as pitch location. This limits assessment of whether the data robustly support the interpretability claims.

Authors: We acknowledge that additional statistical details are needed to strengthen the results section. In the revised manuscript, we will report the exact sample sizes for the analyzed ball-possession intervals, include confidence intervals or standard errors for the reported temporal trends and correlations, and add controls for pitch location (for example, by stratifying the analyses by pitch zones or including location as a covariate). These revisions will provide a clearer basis for evaluating the robustness of the observed patterns. revision: yes

Circularity Check

0 steps flagged

No circularity: measure defined from external physics model and tested on independent data

full rationale

The paper defines defensive pressure directly as opponent minimum arrival time computed from a physics-based motion model applied to tracking data. No parameters are fitted to the outcome variables (progression, turnovers); the model is treated as an external input. Statistical associations are then reported on the 2023 J-League dataset without any self-referential loop or renaming of fitted quantities as predictions. No self-citations are load-bearing for the core definition, and the derivation chain does not reduce any claimed result to its own inputs by construction. This is the normal non-circular case for a physics-derived proxy tested against match events.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the appropriateness of the physics-based motion model for arrival times and the representativeness of the single-league dataset; no explicit free parameters or invented entities are described in the abstract.

free parameters (1)

motion model parameters
The physics-based motion model for computing arrival times likely requires parameters such as maximum speed or acceleration, though none are specified in the abstract.

axioms (1)

domain assumption The minimum arrival time computed from the motion model directly quantifies immediate defensive pressure.
This definition is the load-bearing premise of the entire framework.

pith-pipeline@v0.9.1-grok · 5727 in / 1282 out tokens · 26426 ms · 2026-06-27T14:10:16.038272+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

18 extracted references · 13 canonical work pages

[1]

Andrienko, G., Andrienko, N., Budziak, G., Dykes, J., Fuchs, G., von Landesberger, T., Weber, H.,
[2]

Data Mining and Knowledge Discovery 31, 1793–1839

Visual analysis of pressure in football. Data Mining and Knowledge Discovery 31, 1793–1839. doi:10.1007/s10618-017-0513-2

work page doi:10.1007/s10618-017-0513-2
[3]

An integrated dataset of spatiotemporal and event data in elite soccer

Bassek, M., Rein, R., Weber, H., Memmert, D., 2025. An integrated dataset of spatiotemporal and event data in elite soccer. Scientific Data 12, 195. doi:10.1038/s41597-025-04505-y

work page doi:10.1038/s41597-025-04505-y 2025
[4]

Data-driven detection of counterpressing in professional football

Bauer, P., Anzer, G., 2021. Data-driven detection of counterpressing in professional football. Data Mining and Knowledge Discovery 35, 2009–2049. doi:10.1007/s10618-021-00763-7. 9

work page doi:10.1007/s10618-021-00763-7 2021
[5]

Pressing intensity: An intuitive measure for pressing in soccer

Bekkers, J., 2025. Pressing intensity: An intuitive measure for pressing in soccer. arXiv preprint arXiv:2501.04712. doi:10.48550/arXiv.2501.04712

work page doi:10.48550/arxiv.2501.04712 2025
[6]

Measuring skill via player dynamics in football dribbling

Brink, L., Ha, S.K., Snowdon, J., Vidal-Codina, F., Rauch, B., Wang, F., Wu, D., López-Felip, M.A., Clanet, C., Hosoi, A.E., 2023. Measuring skill via player dynamics in football dribbling. Scientific Reports 13, 19004. doi:10.1038/s41598-023-45914-6

work page doi:10.1038/s41598-023-45914-6 2023
[7]

Official website.https://www.datastadium.co.jp/en

DataStadium Inc., 2026. Official website.https://www.datastadium.co.jp/en. Accessed: 2026- 03-14

2026
[8]

Wide open spaces: A statistical technique for measuring space creation in professional soccer, in: Proceedings of the MIT Sloan Sports Analytics Conference, pp

Fernandez, J., Bornn, L., 2018. Wide open spaces: A statistical technique for measuring space creation in professional soccer, in: Proceedings of the MIT Sloan Sports Analytics Conference, pp. 1–19

2018
[9]

The keys of pressing to gain the ball – characteristics of defensive pressure in elite soccer using tracking data

Forcher, L., Forcher, L., Altmann, S., Jekauc, D., Kempe, M., 2024. The keys of pressing to gain the ball – characteristics of defensive pressure in elite soccer using tracking data. Science and Medicine in Football 8, 161–169. doi:10.1080/24733938.2022.2158213

work page doi:10.1080/24733938.2022.2158213 2024
[10]

Geometric analysis and quantitative evaluation of sport teamwork

Fujimura, A., Sugihara, K., 2005. Geometric analysis and quantitative evaluation of sport teamwork. Systems and Computers in Japan 36, 49–58. doi:10.1002/scj.20254

work page doi:10.1002/scj.20254 2005
[11]

and Horton, M

Gudmundsson, J., Horton, M., 2017. Spatio-temporal analysis of team sports. ACM Computing Surveys 50, 1–34. doi:10.1145/3054132

work page doi:10.1145/3054132 2017
[12]

Off-ball behavior in association football: A data-driven model to measure changes in individual defensive pressure

Herold, M., Hecksteden, A., Radke, D., Goes, F., Nopp, S., Meyer, T., Kempe, M., 2022. Off-ball behavior in association football: A data-driven model to measure changes in individual defensive pressure. Journal of Sports Sciences 40, 1412–1425. doi:10.1080/02640414.2022.2081405

work page doi:10.1080/02640414.2022.2081405 2022
[13]

Measuring the effectiveness of pressing in soccer

Merckx, S., Robberechts, P., Euvrard, Y., Davis, J., 2021. Measuring the effectiveness of pressing in soccer. Proceedings of the 8th Workshop on Machine Learning and Data Mining for Sports Analytics

2021
[14]

Validation of a motion model for soccer players’ sprint by means of tracking data

Narizuka, T., Takizawa, K., Yamazaki, Y., 2023. Validation of a motion model for soccer players’ sprint by means of tracking data. Scientific Reports 13, 865. doi:10.1038/s41598-023-27999-1

work page doi:10.1038/s41598-023-27999-1 2023
[15]

Space evaluation in football games via field weight- ing based on tracking data

Narizuka, T., Yamazaki, Y., Takizawa, K., 2021. Space evaluation in football games via field weight- ing based on tracking data. Scientific Reports 11, 5509. doi:10.1038/s41598-021-84939-7

work page doi:10.1038/s41598-021-84939-7 2021
[16]

A rule-based approach to classify counterpress- ing – analysis of its risks and relationship with rest defence

Peters, A., Parmar, N., Davies, M., James, N., 2026. A rule-based approach to classify counterpress- ing – analysis of its risks and relationship with rest defence. International Journal of Performance Analysis in Sport 26, 206–222. doi:10.1080/24748668.2025.2473799

work page doi:10.1080/24748668.2025.2473799 2026
[17]

Physics-based modeling of pass probabilities in soccer, in: Proceedings of the MIT Sloan Sports Analytics Conference, pp

Spearman, W., Basye, A., Dick, G., Hotovy, R., Pop, P., 2017. Physics-based modeling of pass probabilities in soccer, in: Proceedings of the MIT Sloan Sports Analytics Conference, pp. 1–14

2017
[18]

TacticAI: an AI assistant for football tactics

Wang, Z., Veličković, P., Hennes, D., Tomašev, N., Prince, L., Kaisers, M., Bachrach, Y., Elie, R., Wenliang, L.K., Piccinini, F., Spearman, W., Graham, I., Connor, J., Yang, Y., Recasens, A., Khan, M., Beauguerlange, N., Sprechmann, P., Moreno, P., Heess, N., Bowling, M., Hassabis, D., Tuyls, K., 2024. TacticAI: an AI assistant for football tactics. Natu...

work page doi:10.1038/s41467-024-45965-x 2024

[1] [1]

Andrienko, G., Andrienko, N., Budziak, G., Dykes, J., Fuchs, G., von Landesberger, T., Weber, H.,

[2] [2]

Data Mining and Knowledge Discovery 31, 1793–1839

Visual analysis of pressure in football. Data Mining and Knowledge Discovery 31, 1793–1839. doi:10.1007/s10618-017-0513-2

work page doi:10.1007/s10618-017-0513-2

[3] [3]

An integrated dataset of spatiotemporal and event data in elite soccer

Bassek, M., Rein, R., Weber, H., Memmert, D., 2025. An integrated dataset of spatiotemporal and event data in elite soccer. Scientific Data 12, 195. doi:10.1038/s41597-025-04505-y

work page doi:10.1038/s41597-025-04505-y 2025

[4] [4]

Data-driven detection of counterpressing in professional football

Bauer, P., Anzer, G., 2021. Data-driven detection of counterpressing in professional football. Data Mining and Knowledge Discovery 35, 2009–2049. doi:10.1007/s10618-021-00763-7. 9

work page doi:10.1007/s10618-021-00763-7 2021

[5] [5]

Pressing intensity: An intuitive measure for pressing in soccer

Bekkers, J., 2025. Pressing intensity: An intuitive measure for pressing in soccer. arXiv preprint arXiv:2501.04712. doi:10.48550/arXiv.2501.04712

work page doi:10.48550/arxiv.2501.04712 2025

[6] [6]

Measuring skill via player dynamics in football dribbling

Brink, L., Ha, S.K., Snowdon, J., Vidal-Codina, F., Rauch, B., Wang, F., Wu, D., López-Felip, M.A., Clanet, C., Hosoi, A.E., 2023. Measuring skill via player dynamics in football dribbling. Scientific Reports 13, 19004. doi:10.1038/s41598-023-45914-6

work page doi:10.1038/s41598-023-45914-6 2023

[7] [7]

Official website.https://www.datastadium.co.jp/en

DataStadium Inc., 2026. Official website.https://www.datastadium.co.jp/en. Accessed: 2026- 03-14

2026

[8] [8]

Wide open spaces: A statistical technique for measuring space creation in professional soccer, in: Proceedings of the MIT Sloan Sports Analytics Conference, pp

Fernandez, J., Bornn, L., 2018. Wide open spaces: A statistical technique for measuring space creation in professional soccer, in: Proceedings of the MIT Sloan Sports Analytics Conference, pp. 1–19

2018

[9] [9]

The keys of pressing to gain the ball – characteristics of defensive pressure in elite soccer using tracking data

Forcher, L., Forcher, L., Altmann, S., Jekauc, D., Kempe, M., 2024. The keys of pressing to gain the ball – characteristics of defensive pressure in elite soccer using tracking data. Science and Medicine in Football 8, 161–169. doi:10.1080/24733938.2022.2158213

work page doi:10.1080/24733938.2022.2158213 2024

[10] [10]

Geometric analysis and quantitative evaluation of sport teamwork

Fujimura, A., Sugihara, K., 2005. Geometric analysis and quantitative evaluation of sport teamwork. Systems and Computers in Japan 36, 49–58. doi:10.1002/scj.20254

work page doi:10.1002/scj.20254 2005

[11] [11]

and Horton, M

Gudmundsson, J., Horton, M., 2017. Spatio-temporal analysis of team sports. ACM Computing Surveys 50, 1–34. doi:10.1145/3054132

work page doi:10.1145/3054132 2017

[12] [12]

Off-ball behavior in association football: A data-driven model to measure changes in individual defensive pressure

Herold, M., Hecksteden, A., Radke, D., Goes, F., Nopp, S., Meyer, T., Kempe, M., 2022. Off-ball behavior in association football: A data-driven model to measure changes in individual defensive pressure. Journal of Sports Sciences 40, 1412–1425. doi:10.1080/02640414.2022.2081405

work page doi:10.1080/02640414.2022.2081405 2022

[13] [13]

Measuring the effectiveness of pressing in soccer

Merckx, S., Robberechts, P., Euvrard, Y., Davis, J., 2021. Measuring the effectiveness of pressing in soccer. Proceedings of the 8th Workshop on Machine Learning and Data Mining for Sports Analytics

2021

[14] [14]

Validation of a motion model for soccer players’ sprint by means of tracking data

Narizuka, T., Takizawa, K., Yamazaki, Y., 2023. Validation of a motion model for soccer players’ sprint by means of tracking data. Scientific Reports 13, 865. doi:10.1038/s41598-023-27999-1

work page doi:10.1038/s41598-023-27999-1 2023

[15] [15]

Space evaluation in football games via field weight- ing based on tracking data

Narizuka, T., Yamazaki, Y., Takizawa, K., 2021. Space evaluation in football games via field weight- ing based on tracking data. Scientific Reports 11, 5509. doi:10.1038/s41598-021-84939-7

work page doi:10.1038/s41598-021-84939-7 2021

[16] [16]

A rule-based approach to classify counterpress- ing – analysis of its risks and relationship with rest defence

Peters, A., Parmar, N., Davies, M., James, N., 2026. A rule-based approach to classify counterpress- ing – analysis of its risks and relationship with rest defence. International Journal of Performance Analysis in Sport 26, 206–222. doi:10.1080/24748668.2025.2473799

work page doi:10.1080/24748668.2025.2473799 2026

[17] [17]

Physics-based modeling of pass probabilities in soccer, in: Proceedings of the MIT Sloan Sports Analytics Conference, pp

Spearman, W., Basye, A., Dick, G., Hotovy, R., Pop, P., 2017. Physics-based modeling of pass probabilities in soccer, in: Proceedings of the MIT Sloan Sports Analytics Conference, pp. 1–14

2017

[18] [18]

TacticAI: an AI assistant for football tactics

Wang, Z., Veličković, P., Hennes, D., Tomašev, N., Prince, L., Kaisers, M., Bachrach, Y., Elie, R., Wenliang, L.K., Piccinini, F., Spearman, W., Graham, I., Connor, J., Yang, Y., Recasens, A., Khan, M., Beauguerlange, N., Sprechmann, P., Moreno, P., Heess, N., Bowling, M., Hassabis, D., Tuyls, K., 2024. TacticAI: an AI assistant for football tactics. Natu...

work page doi:10.1038/s41467-024-45965-x 2024