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

This study introduces a physically grounded metric based on opponent minimum arrival time to quantify defensive pressure in soccer, demonstrating its effectiveness in analyzing possession dynamics and predicting outcomes like ball progression and turnover risks using 2023 J-League tracking data.

Original authors: Takuma Narizuka, Ikuya Sakamoto, Ken Yamamoto, Yoshihiro Yamazaki

Published 2026-06-09

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Takuma Narizuka, Ikuya Sakamoto, Ken Yamamoto, Yoshihiro Yamazaki

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a soccer match not just as a game of kicking a ball, but as a high-speed dance where 22 people are constantly trying to either grab a partner or keep them safe. This paper is about measuring how close the "danger" is to the person holding the ball.

Here is the breakdown of the study in simple terms:

The Core Idea: The "Time-to-Grab" Meter

The researchers wanted a simple way to measure how much pressure a defender is putting on the player with the ball. Instead of using complex math that guesses what might happen, they used a "physics-based motion model."

Think of it like this: Imagine every player on the field has a stopwatch. When a player gets the ball, the researchers calculate: "How many seconds would it take for the fastest opponent to run over and grab the ball?"

They call this the Minimum Arrival Time.

Low number (e.g., 0.5 seconds): The defender is right on top of you. You are in deep trouble.
High number (e.g., 3.0 seconds): The defender is far away. You have plenty of time to think and act.

How They Did It

They looked at data from 306 professional soccer matches in Japan's top league (the J1 League) from the 2023 season. They used high-speed cameras that track every player's position 25 times a second. They plugged this data into their "physics engine" to calculate that "time-to-grab" number for every single moment a player held the ball.

What They Discovered

1. The "Squeeze" Gets Tighter Over Time
When a player first gets the ball, they usually have a little breathing room. But as they hold onto it, the defenders swarm closer.

The Metaphor: Imagine holding a hot potato. At first, you have a second to decide what to do. But the longer you hold it, the more people reach out to grab it. The study found that the "time-to-grab" number gets smaller and smaller the longer a player keeps the ball, until they finally pass or lose it.

2. The "Relief" After a Pass
Once the ball is passed to a teammate, the pressure on the new person usually starts lower than it was for the person who just passed it.

The Metaphor: It's like a relay race. The runner handing off the baton is being chased hard. The runner catching the baton gets a fresh start with the chasers a bit further back, giving them a momentary advantage.

3. Pressure Kills Progress
The study found a clear link between pressure and how far the ball moves.

The Finding: If a player starts their turn with the ball under heavy pressure (low "time-to-grab"), they usually don't move the ball very far down the field.
The Metaphor: If you are trying to walk through a crowded hallway while someone is already pushing your shoulder, you are likely to take small, hesitant steps rather than sprinting forward.

4. Pressure Increases Mistakes
When a player tries to pass the ball while under heavy pressure, they are much more likely to lose possession (have the ball stolen).

The Finding: The study looked at intentional passes. If the passer was being chased hard, the ball often ended up in a spot where the receiving teammate was also about to be grabbed by a defender.
The Metaphor: Throwing a ball to a friend while being tackled is risky. Often, the ball lands in a spot where the friend is already surrounded, making it easy for the other team to steal it.

Why This Matters

The authors argue that this method is better than other complex ways of measuring pressure because it is simple and honest.

It doesn't guess what a player might do.
It simply asks: "Based on how fast they can run, how long until they get here?"

The Bottom Line

This paper proves that we can use simple physics to measure the "heat" on a soccer player. It shows that when the heat is too high, players move less and make more mistakes. This gives coaches and analysts a clear, easy-to-understand tool to see exactly how defensive pressure changes the flow of the game.

Note: The authors specifically mention that their data comes from a private company and cannot be shared publicly, but they have made their code available for other researchers to check their work.

Technical Summary: Quantifying Defensive Pressure on the Ball Carrier in Soccer Based on Minimum Arrival Time

Problem Statement
Defensive pressure on the ball carrier is a fundamental component of soccer tactics, influencing outcomes such as ball progression, possession retention, and shot creation. While recent advances in synchronized event and tracking data have enabled high-resolution quantitative analysis, existing methods for quantifying pressure often rely on additional modeling assumptions, geometric heuristics, or supervised learning. These approaches can transform arrival-time information into elaborate composite scores, potentially reducing interpretability and introducing indirectness in the physical meaning of the metric. The study addresses the need for a simple, interpretable, and physically grounded baseline measure to quantify immediate defensive pressure directly from player kinematics.

Methodology
The study utilizes synchronized event and tracking data from all 306 matches of the 2023 J1 League (Japan Professional Football League) season. The tracking data provides absolute coordinates for all players at 25 Hz, while event data includes time-stamped on-ball actions.

Motion Model: The authors employ the Fujimura–Sugihara physics-based motion model to describe player movement. This model treats players as agents governed by a constant driving force and viscous resistance ( $m\ddot{\vec{x}} = F\vec{n} - k\dot{\vec{x}}$ ). Under the assumption that the driving force direction can change freely, the set of reachable locations after time $t$ forms a circle defined by a center $\vec{c}_p(t)$ and radius $r_p(t)$ .
Metric Definition: The core metric is the opponent minimum arrival time ( $\tau_{opp}$ ), defined as the minimum time required for any opponent to reach the ball-carrier's location ( $\vec{x}_b$ ) at a specific time $t$ . This is computed by numerically solving the reachability equation for all opponents and selecting the minimum. A corresponding teammate minimum arrival time ( $\tau_{same}$ ) is also calculated but excluded from the ball carrier.
Data Processing: Ball-possession intervals are identified from the synchronized data, defined as continuous periods where a single player controls the ball. Goalkeeper possessions are excluded. The study analyzes $\tau_{opp}$ at the start of possession ( $t_{get}$ ) and at ball release ( $t_{rel}$ ).
Outcomes Analyzed: The study correlates $\tau_{opp}$ $τ_{o pp}$ with two key outcomes:
1. Ball Progression: The decrease in distance from the ball carrier to the opponent goal between possession start and end.
2. Possession Loss: Specifically for intentional open-play passes (ordinary and through passes), the probability of losing possession after the action.

Key Results

Distribution Asymmetry: The distribution of $\tau_{opp}$ is concentrated at shorter times compared to $\tau_{same}$ , reflecting the tactical reality that opponents actively pressure the ball carrier while teammates often maintain formation.
Temporal Evolution: During a possession interval, $\tau_{opp}$ tends to decrease, indicating that defensive pressure builds up on the current ball carrier. Conversely, at the start of the subsequent possession (after ball release), $\tau_{opp}$ tends to increase, suggesting a partial relief of immediate pressure on the new ball carrier.
Pressure and Ball Progression: Possessions starting under stronger defensive pressure (lower $\tau_{opp}$ at $t_{get}$ ) are associated with smaller ball progression. This relationship holds across different field zones (defined by distance to the opponent goal), indicating it is not solely an artifact of field location.
Pressure and Possession Loss: For intentional open-play passes, possessions ending under stronger pressure (lower $\tau_{opp}$ $τ_{o pp}$ at $t_{rel}$ $t_{r e l}$ ) have a higher probability of resulting in possession loss.
- The study further analyzes the "relative safety" of the pass end location using the difference $\tau_{opp}(\vec{x}_{end}) - \tau_{same}(\vec{x}_{end})$ . It finds that passes released under higher pressure tend to end at locations where teammates have less time advantage over opponents.
- Consequently, a smaller time advantage for teammates at the realized pass-end location correlates with a higher probability of ball loss.

Key Contributions

Interpretable Baseline Metric: The paper proposes the opponent minimum arrival time as a direct, physically grounded measure of immediate defensive pressure. Unlike composite scores, it is defined strictly by player kinematics and a validated motion model, offering a transparent "first-arrival-time" perspective.
Empirical Characterization: The study provides a comprehensive statistical characterization of how defensive pressure evolves temporally during possession intervals and how it transitions between consecutive possessions.
Outcome Association: It establishes clear statistical associations between immediate defensive pressure and critical possession outcomes (progression and loss), demonstrating that higher pressure constrains offensive utility and increases turnover risk.

Significance and Claims
The authors claim that the opponent minimum arrival time serves as a simple and interpretable baseline for quantifying pressing dynamics from tracking data. By avoiding complex transformations of arrival-time data, the proposed framework allows for a more direct interpretation of defensive interactions. The results indicate that this quantity captures meaningful temporal structures in the game and is significantly associated with subsequent possession outcomes.

The paper maintains a modest scope, acknowledging limitations such as the use of fixed kinetic parameters in the motion model, the exclusion of contextual factors like body orientation and coordinated team movement, and the reliance on a single league (J1 League) for validation. The analysis of pass outcomes using realized end locations is explicitly framed as a post hoc explanation of observed results rather than a predictive tool available at the moment of ball release. Nevertheless, the study concludes that the framework successfully relates local defensive pressure to possession outcomes, providing a foundation for future work that may incorporate broader contextual information.