⚡ electrical engineering

Data-Driven Framework of Player Spatial Ownership in Football

This paper introduces a fully data-driven framework for quantifying player spatial ownership in football by estimating individualized movement parameters from optical tracking data to calculate arrival times and assign control of field regions without relying on generalized movement assumptions.

Original authors: Daniel Castro, Jan-Anders Mansson

Published 2026-08-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Daniel Castro, Jan-Anders Mansson

Original paper licensed under CC BY 4.0 (https://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

In the modern game of football, the story is often told through the ball. We celebrate the striker who scores, the midfielder who threads a perfect pass, or the defender who intercepts a dangerous cross. These moments are easy to see and easy to count. Yet, a vast amount of the game happens without the ball ever touching a player's feet. It happens in the spaces between players, in the runs made to create an opening, and in the positioning that forces an opponent to hesitate. For decades, coaches and analysts have struggled to measure this invisible influence. How much space does a player actually control at any given second? Who could reach a specific patch of grass faster than anyone else? Answering this question requires more than just watching; it requires a way to translate the chaotic motion of twenty-two athletes into a clear map of who owns the field.

For years, researchers have tried to solve this by drawing imaginary lines on the pitch, dividing the ground into territories based on where players are standing. These models, known as dominant region models, assume that if a player is closer to a spot than anyone else, they own it. However, this approach treats all players as if they move in exactly the same way. It ignores the fact that one player might be a sprinter who accelerates instantly, while another might be a powerful runner who turns slowly. It also assumes everyone reacts to the game with the same speed, ignoring that some players are quicker to spot a change in play than others. This simplification misses the unique physical signature of every athlete on the field.

A new study from Purdue University offers a different way to look at the game, one that builds a map of space based on how real people actually move. Instead of assuming everyone is the same, the researchers developed a system that learns the specific movement habits of every single player from the data collected during matches. They used optical tracking data, which records the exact position of every player and the ball twenty-five times every second. From this stream of numbers, the team extracted a unique profile for each athlete. They calculated how fast each player could accelerate, how quickly they could slow down, their top speed, and exactly how they handle turning. Perhaps most importantly, they figured out each player's reaction time—the split-second delay between seeing the ball move and starting to run toward it.

The researchers then used these individual profiles to simulate a race across the entire field. They divided the pitch into a grid of small squares, each fifty centimeters wide, roughly the size of a player's lateral reach. For every single square on the field, the system asked a simple question: if a player needed to get to this spot right now, how long would it take? To answer this, the model ran two different scenarios for every player. In the first scenario, the player kept moving forward while constantly adjusting their direction, like a car steering around a curve without ever stopping. In the second scenario, the player slowed down to a halt, turned their body to face the target, and then accelerated toward it. The system calculated the time for both strategies and kept the faster one.

By running these calculations for every player and every square on the field, the researchers created a dynamic map of "Player Spatial Ownership." This map shows which player can reach any given spot the fastest, taking into account their specific speed, their turning ability, and their personal reaction time. The study found that when you account for these individual differences, the picture of who controls the space changes significantly compared to older models. A player who might seem far away on a static map could actually be the first to reach a spot because they react faster or turn more efficiently than their opponents.

The team tested this method using data from actual football matches provided by FIFA. They found that the system could process the entire field in a way that is both fast enough to be used in real-time and detailed enough to capture the nuances of individual movement. Unlike previous methods that required complex, non-reproducible math or assumed everyone moved identically, this framework is built entirely on observed data. It does not guess how a player moves; it learns from how they have moved in the past. The result is a tool that can show, with precision, how a team creates space, how a defender covers an area, and how a player's unique physical traits influence the flow of the game.

This approach does not just tell us who is closest to the ball; it tells us who has the physical capacity to dominate the space around it. It reveals that spatial control is not a fixed territory but a fluid competition of speed, agility, and reaction. By treating every player as a unique individual with their own movement signature, the study provides a clearer, more realistic view of the game. It suggests that the true value of a player often lies not in what they do with the ball, but in how they move without it, shaping the field in ways that were previously impossible to measure. This new framework offers a foundation for understanding the invisible geometry of football, turning the chaotic motion of the game into a story of individual capability and tactical control.

Technical Summary: Data-Driven Framework of Player Spatial Ownership in Football

Problem Statement
Current football analytics primarily evaluate players based on ball-centric metrics (goals, assists, passing accuracy), leaving a significant gap in quantifying a player's ability to create and control space without the ball. While "Dominant Region" models have historically addressed spatial control, existing approaches suffer from several limitations: they often assume identical physical capabilities across all players, utilize simplified movement behaviors that ignore turning dynamics, rely on computationally demanding non-parametric representations, and fail to explicitly incorporate individualized reaction times. Consequently, there is a need for a framework that estimates spatial ownership using only optical tracking data while accounting for the unique kinematic profiles of individual players.

Methodology
The proposed framework estimates Player Spatial Ownership (PSO) by determining which player can reach any given region of the field first, based on individualized movement capabilities derived from historical optical tracking data. The methodology proceeds through the following stages:

Data Input and Preprocessing:
- The system utilizes optical tracking data sampled at 25 Hz, recording $(x, y)$ coordinates and instantaneous speed for all players, referees, and the ball.
- The field is discretized into a uniform grid of 28,560 square regions (50 cm $\times$ 50 cm), corresponding to the average lateral reach of a player.
Individualized Movement Profile Estimation:
- Unlike previous models that assume uniform parameters, this framework extracts specific kinematic limits for each player from historical data.
- Linear Dynamics: Estimates maximum/minimum speed ( $v_{i,MAX}, v_{i,MIN}$ ), acceleration/deceleration ( $a_{i,MAX}, a_{i,MIN}$ ), and the rates of change for acceleration.
- Angular Dynamics: To mitigate noise, angular velocity ( $\omega$ ) and acceleration ( $\alpha$ ) are estimated from trajectories sampled every 0.4 s. The model captures maximum/minimum angular velocity and acceleration, along with their rates of change.
- Reaction Time ( $t_{r,i}$ ): Instead of using a fixed constant, individualized reaction times are estimated by identifying moments when the ball undergoes a velocity change ( $\ge 10$ m/s). The time elapsed until a player within a specific angular sector exhibits a significant change in linear or angular acceleration is recorded as a reaction event.
Movement Simulation Models:
To estimate the arrival time to a target region, the framework simulates two complementary movement strategies and retains the shortest time:
- Continuous Accelerated Movement (CAM): The player continuously adjusts their direction while maintaining forward motion, accelerating toward the target without stopping.
- Staged Reactive Movement (SRM): The player first decelerates to a stop while changing direction, potentially completes a turn in place, and then accelerates toward the target.
- Simulation Steps:
  1. Reaction Phase: The player continues current motion for the duration of their individualized reaction time ( $t_{r,i}$ ).
  2. Turning Phase: The player adjusts orientation toward the target. The target direction is defined by the centroid and edge midpoints of the region. Angular deceleration is applied to prevent overshooting.
  3. Linear Phase: The player advances in a straight line to the target.
  - In SRM, if the player is not aligned after stopping, an additional "turn in place" step is simulated before the linear advance.
Optimization and Assignment:
- For every grid region, the framework calculates the arrival time for all players.
- To ensure computational efficiency, players are ordered by Euclidean distance to the target. Simulations are discarded early if a player's current estimated time exceeds the best time found so far for that region.
- The region is assigned to the player with the minimum arrival time.

Key Contributions

Fully Data-Driven Parameterization: The framework eliminates the need for manual parameter tuning or assumptions of identical player capabilities by deriving acceleration, deceleration, turning dynamics, and reaction times directly from optical tracking data.
Dual-Movement Strategy: By evaluating both continuous acceleration (CAM) and staged reactive movement (SRM), the model captures a broader range of realistic player behaviors, particularly regarding turning agility and stopping mechanics.
Individualized Reaction Time: The method introduces a novel procedure to estimate player-specific reaction times based on ball velocity changes and subsequent player acceleration responses, addressing a gap in previous dominant region models.
Computational Efficiency: Through vectorized operations and early-exit simulation logic, the framework is designed to be reproducible and capable of real-time application without requiring wearable sensors.

Results and Claims
The paper presents the methodology as a complete framework rather than a study of specific match outcomes or a comparative benchmark against other models using external datasets. The authors demonstrate the workflow through illustrative examples (e.g., Figure 3) showing how CAM and SRM trajectories differ for a single player targeting a specific region.

The authors claim that this methodology provides:

A realistic estimate of spatial control that accounts for individual physical limitations and reaction times.
A reproducible and interpretable system that relies solely on standard optical tracking data.
A foundation for future analyses regarding passing opportunities, off-ball movement, and tactical decision-making.

Significance
The paper positions PSO not as a final performance metric, but as a fundamental spatial representation upon which advanced tactical and performance analyses can be built. By moving away from geometric simplifications toward individualized kinematic modeling, the framework aims to enable a deeper understanding of how players and teams create, maintain, or lose control of space. The authors note that while the current implementation is limited to 2D movement and data-derived reaction times, the approach is adaptable to other invasion sports and can be extended to account for dynamic factors like fatigue.

Technical Summary: Data-Driven Framework of Player Spatial Ownership in Football

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