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REVIEW 5 major objections 5 minor 1 cited by

Pressing Intensity: An Intuitive Measure for Pressing in Soccer

T0 review · 5 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper claims that pressing intensity in soccer can be measured frame by frame as the probability that any defender intercepts an attacker or the ball, based only on positions, velocities, reaction time, and a logistic transform.

desk verdict The central intercept-time formula has mismatched units, so the paper's main metric is not computable as written—but the underlying idea is a reasonable extension of pitch-control work. read the letter →

arxiv 2501.04712 v2 pith:NTBFYMDU submitted 2024-12-30 stat.AP cs.LG

Joris Bekkers This is my paper · ORCID
classification stat.APcs.LG
keywords pressingintensitysocceranalyticstimetointerceptpitchcontrolpositionaltrackingdatadefensivepressurelogisticfunctionframe-levelmetric
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

This paper tries to establish that pressing in soccer can be quantified at the level of a single tracking frame: the pressure on any attacker is the probability that at least one defender can intercept that attacker or the ball before the play moves on. The authors build a time-to-intercept for every defender-attacker pair from positions, velocities, a reaction-time delay, a maximum running speed, and a direction penalty, then convert those times into probabilities with a logistic curve. Combining the probabilities across defenders gives one readable number, the pressing intensity, which they argue captures how every player's movement creates pressure somewhere on the field and is more informative than event-based proxies such as passes-against-defensive-actions.

What carries the argument

The carrying object is the modified time-to-intercept $T_{i,j}(t) = \tau_r + \tau_{i,j}(t) + \tau_\beta(t)$, where $\tau_{i,j}(t) = \|\vec{d}\| / v_{\max}$ is the time to cover the distance between the defender's post-reaction position and the attacker's extrapolated position, and $\tau_\beta(t)$ penalizes defenders running away from the target. Each intercept time is passed through a logistic function with width $\sigma = 0.45$ and horizon $T = 1.5$ seconds to give a probability, and the probabilities are combined as $P_j = 1 - \prod_i (1 - p_{i,j})$, a product rule that the paper notes assumes independence across defenders. This mechanism converts raw tracking coordinates into a continuous pressure field whose values are directly interpretable as the chance that pressure arrives in time.

What would settle it

Take a single tracking frame and recompute the pressure values after converting all velocities from meters per second to kilometers per hour; a literal implementation of the direction-penalty term changes the intercept time by the conversion factor, so the pressure values change for an identical physical scene. A valid metric must give the same answer under both unit systems.

Watch

Extended reading notes

Core claim

The central claim is that Equations 1 to 5 define a valid, interpretable measure of pressing intensity. For each attacking target $j$, the pressure is $P_j = 1 - \prod_i (1 - p_{i,j})$, where $p_{i,j}$ is the logistic function of the time $T_{i,j}$ estimated for defender $i$ to intercept target $j$. The intercept time is built from a reaction-time delay, the distance between extrapolated positions divided by a maximum speed, and a penalty for defenders whose velocity points away from the target; the logistic scale is set with $\sigma = 0.45$ and a horizon of $T = 1.5$ seconds. The authors state that this captures how every player's movement influences pressure on the field, works at the individual frame level, and offers an improvement over rule-based and event-based pressing measures because it uses full positional tracking data.

Load-bearing premise

The entire metric rests on the intercept-time formula producing a true time in seconds; if the direction penalty and the position-plus-velocity extrapolation are not unit-corrected, every pressure probability inherits an arbitrary scale.

Editorial extensions

If this is right

  • Coaches and analysts get a continuous pressure value for every attacker at every tracking frame, instead of only for players within a fixed radius of the ball.
  • The speed-threshold filter turns the raw values into a measure of active pressing, suppressing pressure from defenders who are nearby but not moving toward the ball.
  • Because the pressure is defined for every defender-attacker pair, a team can sum or average it to describe whole-team pressing behavior and compare it across matches.
  • The same intercept-time machinery can be pointed at pass lanes, giving a pressing intensity for space rather than only for players.
  • Boundary behavior remains incomplete: near the sideline the model can report zero pressure in situations where defenders are herding an attacker out of play.

Reading between the lines

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

  • One testable extension is to compare the per-frame pressure values with expert labels of pressured touches; a stable optimal threshold would validate the logistic calibration.
  • The unit inconsistency in the intercept-time formula implies the metric should be repaired and re-validated before use; if fixed, the product structure could transfer to any sport with similar intercept geometry.
  • The sideline example suggests a natural modification: adding a repulsive 'touchline potential' that shortens the effective intercept time when the attacker is near the boundary; this is an editorial extension, not yet in the paper.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. The paper introduces Pressing Intensity, a frame-level metric that quantifies defensive pressure on each attacking player by converting an estimated defender-to-attacker interception time into a probability via a logistic function and combining probabilities over defenders with a product rule. The metric is implemented in an open-source Python package and illustrated with tracking-data snapshots, and extensions to pass-lane pressure and smart pressing are sketched. The central mathematical object, however, is not well defined as written because the defining equations contain unit inconsistencies.

Significance. If the dimensional issues were corrected, the metric would be a plausible and interpretable addition to pressing measurement in sports analytics, and the open-source implementation plus the conceptual link to Spearman's pitch control are strengths. The paper is not circular: the metric is defined directly from the equations and no parameters are fitted to pressing outcomes. Nevertheless, the current formulation does not evaluate to a well-defined probability, and the manuscript offers no quantitative validation or comparison with existing metrics, so the practical claims are unsupported.

major comments (5)
  1. [Section 2.1, Eq. (2)] The vector d_j is defined as r_j(t) + v_j(t), adding a position (meters) to a velocity (meters/second). Because there is no time horizon multiplying v_j, d_j is not a position and d = d_j - d_i is not a length. Consequently tau_i,j = ||d||/v_max is not a time, and the intercept-time interpretation fails at the first step.
  2. [Section 2.1, Eq. (3)] In the definition of u, (r_i(t) + v_i(t)) - r_i(t) simplifies algebraically to v_i(t), so ||u|| has units of speed. Since beta is an angle, tau_beta(t) = ||u|| beta/pi has units of m/s rather than seconds. Equation (1) therefore adds a reaction time, a term with units of speed, and tau_i,j whose units are already broken; T_i,j is not a valid duration.
  3. [Section 2.2-2.3, Eqs. (4)-(5)] Because T_i,j is not a well-defined time, p_i,j is not a well-defined probability and P_j inherits this problem. The paper's central claim that Eqs. (1)-(5) produce a frame-level pressure field is therefore not supported by the manuscript as written; please provide corrected equations, for example with an explicit prediction horizon for the attacker's position, and verify the resulting units.
  4. [Section 2.4] The treatment of the ball carrier switches from the product in Eq. (5) to a maximum over defenders, described only as an improvement. This changes the metric without a formal definition or rationale, and makes the reported pressure on the ball carrier inconsistent with the general formula.
  5. [Sections 2-3] The manuscript contains no quantitative validation, error analysis, sensitivity analysis, or comparison with existing pressing metrics such as PPDA [13], StatsBomb pressure events [6], or the models of [5] and [10]. The included figures are illustrative snapshots; as a statistical application paper this leaves the practical usefulness unestablished.
minor comments (5)
  1. [Abstract/Introduction] There are typos: 'intepretable', 'inherit lack', and 'the the Pressing Intensity' in the implementation note; please proofread the manuscript.
  2. [Section 3.1 and Figures] The text says Figure 2 shows unfiltered pressure and Figure 4 shows filtered pressure, but Figure 2's caption reads 'Filtered Pressing Intensity' and no Figure 4 for filtering exists; Section 4.1 uses Figure 4 for pass lanes. The figure numbering should be corrected.
  3. [Section 2.1-2.2] The notation switches between 'Formula' and 'Equation', and T is used both as the time horizon in Eq. (4) and inside T_i,j; please use distinct symbols such as T_horizon to avoid ambiguity.
  4. [Section 3.1] The active-pressing threshold of 2 m/s is introduced without justification or sensitivity analysis, and it conflicts with the abstract claim that every movement influences pressure; please discuss its effect and how it was chosen.
  5. [General reproducibility] No information is given about the tracking data source, sampling frequency, coordinate system, or velocity estimation method; these details are needed for reproducibility beyond the open-source code reference.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the pressing intensity metric is defined directly from stated physical formulas and fixed constants, and the cited self-references are only code-availability pointers.

full rationale

The derivation chain is self-contained in the sense relevant to circularity. Equation (5) defines total pressure as one minus the product of individual intercept probabilities, and Equations (1)-(4) define those probabilities from stated quantities: reaction time, maximum velocity, a direction penalty, and a logistic transform with fixed parameters (sigma = 0.45, T = 1.5 s). No parameter is fitted to any pressing outcome, no quantity is predicted from a subset of data and then compared to that same subset, and the metric is not claimed to be validated empirically. The citations to the author's own code [14] and related paper [3] are statements about where an implementation can be found, not load-bearing justifications for the formula. The serious dimensional inconsistency in Equations (2) and (3), where a position is added to a velocity and the resulting quantity is treated as a time, is a correctness and interpretability flaw, but it is not circular: the formula does not reduce to its own inputs, it merely appears not to evaluate to a well-defined physical time as written. Therefore the paper should not receive a circularity penalty.

Assumptions & free parameters 6 free parameters · 5 assumptions · 2 invented entities

The metric is built almost entirely on Spearman/Shaw/Pleuler pitch-control components plus hand-set parameters. No data fitting or external validation appears; the only invented quantity is the pressure scalar itself. Practical constants v_max and tau_r are referenced as 'similar' but never given values.

free parameters (6)
  • logistic spread sigma = 0.45
    Set in Section 2.2, taken from Spearman's pitch control, not estimated from pressing data.
  • time horizon T = 1.5 s
    Set in Section 2.2; controls the logistic curve and is not calibrated.
  • active pressing speed threshold = 2 m/s
    Section 3.1; defenders slower than this contribute zero pressure. Presented as noise filter without sensitivity analysis.
  • maximum player speed v_max = not stated
    Needed in Eq2; the paper says 'similar maximum running velocity' but does not give the value.
  • reaction time tau_r = not stated
    Needed in Eq1 and Eq2; the paper says 'similar reaction time parameter' but does not give the value.
  • epsilon = 1e-5
    Added in Eq3 as a small positive value to avoid division by zero.
assumptions (5)
  • domain assumption The Spearman/Shaw/Pleuler time-to-intercept model transfers unchanged to pressing contexts.
    The derivation starts from these models in Section 2 and applies them to defenders pressing moving attackers without recalibration.
  • domain assumption Interception probabilities of different defenders are independent.
    Section 2.3 explicitly states 'we make the naive assumption that all these probabilities are independent.'
  • ad hoc to paper Defenders moving slower than 2 m/s exert zero pressure.
    Active Pressing filter in Section 3.1 sets all intercept probabilities to zero below this threshold; the threshold is chosen by inspection of figures.
  • domain assumption The pitch has no boundaries, so a player forced toward the sideline experiences no extra pressure from the boundary.
    Section 3.2 admits the model assumes an infinite playing surface and treats near-sideline situations as pressure-free.
  • ad hoc to paper The attacker's future intercept point is its current position plus its current velocity vector with an implicit unit time.
    Eq2 uses d_j = r_j(t)+v_j(t). This is the source of the unit inconsistency and is essential to all subsequent probabilities.
invented entities (2)
  • Pressing Intensity scalar P_j(t)
    purpose: Quantifies the total pressure on an attacking player or the ball at each frame as 1 minus the product of non-interception probabilities.
    This scalar is new to the paper and is not validated against any external measure or labelled pressing outcome; Figures 1 and 2 illustrate it but provide no quantitative ground truth.
  • Frame-level pressure field across the pitch
    purpose: Extends the scalar to a visual map showing how every defender's movement changes pressure anywhere on the field.
    Described in Section 2.4 and shown in figures; no test or calibration is offered.

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Cite this review

Pith. "Pith review of Pressing Intensity: An Intuitive Measure for Pressing in Soccer." pith.science (2026). https://pith.science/paper/NTBFYMDU

@misc{pith2026250104712,
  author       = {Pith},
  title        = {Pith review of: Pressing Intensity: An Intuitive Measure for Pressing in Soccer},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NTBFYMDU}},
  note         = {Machine review of arXiv:2501.04712}
}
read the original abstract

Pressing is a fundamental defensive strategy in football, characterized by applying pressure on the ball owning team to regain possession. Despite its significance, existing metrics for measuring pressing often lack precision or comprehensive consideration of positional data, player movement and speed. This research introduces an innovative framework for quantifying pressing intensity, leveraging advancements in positional tracking data and components from Spearman's Pitch Control model. Our method integrates player velocities, movement directions, and reaction times to compute the time required for a defender to intercept an attacker or the ball. This time-to-intercept measure is then transformed into probabilistic values using a logistic function, enabling dynamic and intuitive analysis of pressing situations at the individual frame level. the model captures how every player's movement influences pressure on the field, offering actionable insights for coaches, analysts, and decision-makers. By providing a robust and intepretable metric, our approach facilitates the identification of pressing strategies, advanced situational analyses, and the derivation of metrics, advancing the analytical capabilities for modern football.

Figures

Figures reproduced from arXiv: 2501.04712 by the authors.

Figure 1
Figure 1. A visual representation of the pressure applied by every defender to every attacker 3.1 Active Pressing To account for this we introduce an Active Pressing speed threshold such that any chance of intercepting an attacking player is set to zero when a defending players’ speed is below this threshold [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Filtered Pressing Intensity with a speed threshold set at 2 m/s 4 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. No pressure in the system - even though we would expect it - because players are being forced toward the sideline, but are impossible to catch up to. 4 Future Work This Pressing Intensity model can be extended for other use cases, two of these are outlined below. 4.1 Pressing / Closing Down Pass Lanes By replacing the locations and velocities of the attacking players by the closest point (and their respective veloci… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: A simple sketch of the closest point (in orange) for the pressing player (in red) to block passing options of the Blue team [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: An example of pressing passing lanes, instead of players. In this example T=1 second. 4.2 Smart Pressing Because Pressing Intensity is measured at the individual tracking frame level we could try to measure smart pressing, or efficient pressing, by considering the amou…
Figure 6
Figure 6. Figure 6: Pressure on the ball carrier by some player (left) and their expended energy during the same time period (right) References [1] Gennady Andrienko, Natalia Andrienko, Guido Budziak, Jason Dykes, Georg Fuchs, Ta￾tiana Von Landesberger, and Hendrik Weber. Visual analysis …

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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

    physics.soc-ph 2026-06 unverdicted novelty 6.0 of 10

    Opponent minimum arrival time from a validated physics motion model is an interpretable defensive-pressure measure that decreases during possession and associates with less progression and more turnovers.

Reference graph

Works this paper leans on

14 extracted references · 13 canonical work pages · cited by 1 Pith paper

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    Pascal Bauer and Gabriel Anzer. Data-driven detection of counterpressing in professional football: a supervised machine learning task based on synchronized positional and event data with expert-based feature extraction. Data Mining and Knowledge Discovery, 35(5): 2009–2049, 2021

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