Disruption Maps Reveal How Teams Break The Best Attacks
A Graph Neural Network framework combining xReceiver, xPass, and xThreat to quantify player availability, defensive impact, and how teams disrupt attacking decisions in real time
The following summary critically reviews the research paper titled “Making Offensive Play Predictable - Using a Graph Convolutional Network to Understand Defensive Performance in Soccer” by Michael Stöckl, Thomas Seidl, Daniel Marley and Paul Power. All data, figures, and analysis presented here are drawn from their original work; I do not claim any authorship or ownership of the content. This summary has been written to provide a concise and technically informed synthesis of the paper’s findings, methodologies, and implications, while maintaining fidelity to the authors’ intellectual contributions.
1. Introduction
1.1 Measuring defensive quality in soccer
The paper begins by reframing how defensive performance should be understood. Instead of focusing on observable actions such as tackles or interceptions, the authors argue that “the art of good defending is to prevent something from happening before it has even happened”. This immediately highlights a core limitation in traditional football analytics, where defenders like Virgil van Dijk are undervalued because their impact often lies in preventing passes or shots rather than executing visible defensive actions.
The central idea is that defending aims to make attacking play predictable. By restricting passing options and forcing attackers into less dangerous decisions, defenders shape the decision-making landscape of the opponent. If this predictability can be modeled, then defensive quality becomes measurable. The authors argue that with sufficient data, one can predict “where a player will pass the ball, the likelihood of that pass being completed and whether this pass will result in a scoring opportunity”.
I have previously explored research with the same idea:
To operationalize this idea, this paper introduces a Graph Convolutional Neural Network designed to model the interaction between attacking and defensive players in real time.
The framework consists of three core predictive models:
xReceiver, which estimates the probability of each player receiving the next pass
xThreat, which estimates the likelihood of a shot occurring within the next ten seconds
xPass, which predicts pass completion probabilities.
These models allow the authors to move beyond observed actions and instead quantify what was prevented.
Building on these outputs, the paper introduces new defensive concepts.
“Player Availability” measures how accessible each attacker is as a passing option.
“Defensive Impact” captures how defenders influence attacking decisions, including concepts like man-oriented or ball-oriented defending.
“Disruption Maps” provide a spatial summary of how a defense alters an opponent’s attacking structure.
Together, these components shift the focus from actions to influence.
1.2 Related Work
1.2.1 Dealing with unstructured data
Tracking data presents a major challenge due to its unstructured and variable nature. Traditional machine learning approaches require ordered, tabular inputs, which has led to methods such as aligning players to formation templates [1,2]. However, this introduces several issues. Different formations imply different positional meanings, making comparisons difficult, and these methods struggle when the number of players changes, such as after a red card.
Alternative approaches have used image-based representations of tracking data with convolutional neural networks [3,4]. While this removes the ordering problem, it introduces inefficiencies by converting low-dimensional spatial data into high-dimensional sparse images. This can be computationally expensive and unsuitable for real-time applications.
The authors propose Graph Neural Networks as a solution. GNNs naturally handle unordered, relational data and can accommodate varying numbers of players. They allow the model to learn both local and global spatial relationships directly, without requiring predefined structures or heavy feature engineering. This flexibility is crucial for modeling dynamic football interactions.
1.2.2 Evaluating and Predicting Future Actions in Sports
The paper situates its approach within existing work on valuing actions and predicting outcomes. Models such as xThreat and xPass have already been used to estimate pass success and scoring probabilities [2,4,6]. Additionally, prior work has explored valuing off-ball positioning and space control [2,3,9].
Here are some examples:
Other approaches include predicting future actions, such as the next pass destination [7,8], and modeling defensive influence on offensive outcomes [10]. Techniques like “ghosting” simulate defensive movements based on attacking behavior [11,12]. These methods highlight the growing interest in understanding not just what happens, but what could happen.
The contribution of this paper lies in integrating these ideas into a unified framework that models decision-making at the frame level. By combining predictions of receiver likelihood, pass success, and downstream threat, the authors create a system that captures both immediate and future consequences of actions, enabling a more complete evaluation of defensive behavior.
2. Method
2.1 Data
The models are trained on a large dataset of tracking data from 1,200 matches across top European leagues, sampled at 10 Hz. Each frame contains positional data for all players and the ball, along with contextual information such as time and match events. In total, the dataset includes approximately one million passes, split into training and testing sets.
For the xThreat model, only frames corresponding to pass events are used. For xReceiver and xPass, additional temporal context is included by incorporating frames up to one second before the pass. This temporal augmentation acts as a form of “semantic regularization,” preventing the model from overfitting to the exact moment of the pass where the outcome may already be implied.
2.2 Graph Convolutional Network
To represent tracking data, the authors construct a graph where nodes correspond to players and the ball, and edges encode relationships between them. This formulation avoids the need for ordering players and allows the model to naturally capture interactions.
The graph is defined as G(V,E,U), where nodes V represent entities on the pitch and edges E capture pairwise relationships. No global features U are included. Each edge connects a sending node to a receiving node, enabling directional relationships.
The GNN architecture consists of two main components: an edge block and a node block. The edge block updates edge representations based on the features of connected nodes, while the node block updates node representations by aggregating information from incoming and outgoing edges. Aggregation is performed using permutation-invariant functions such as summation or averaging.
Each block is implemented as a multilayer perceptron, and the same overall architecture is used across all three tasks. This design allows the model to learn complex spatial and relational patterns directly from the data. Unlike traditional approaches, where relationships are predefined, the GNN learns them dynamically.
The final output assigns predictions to each node. For each player, the model estimates the probability of receiving a pass, the likelihood that a pass to them would be completed, and the probability that such a pass would lead to a shot within ten seconds.
2.3 Features
The feature set is intentionally lightweight, relying on fundamental spatial and motion characteristics. Node features include position, speed, acceleration, direction of movement, distance and angle to goal, and distance to the ball carrier. A binary flag identifies the ball carrier.
Edge features encode relationships between players, including whether they are teammates or opponents, their distance, and differences in movement direction. This combination allows the model to capture both individual behavior and interactions between players.
2.4 Training
Separate GNN models are trained for each task. During training, defensive players are masked out, focusing the learning process on attacking dynamics and potential receivers. For xReceiver, the true receiver is given a higher weight than other players to balance the signal.
The training strategy reflects the difficulty of the task, where only a small subset of players are realistic passing options at any given moment. By weighting examples appropriately, the model learns to distinguish meaningful signals from background noise.
2.5 Model Training Results
The GNN models are compared to baseline multilayer perceptrons that rely on handcrafted features. Across all tasks, the GNN achieves equal or better performance, with notable improvements in xReceiver accuracy.
An important insight is that the GNN achieves these results with fewer engineered features. For example, the baseline model explicitly uses pass-specific features such as speed and angle, whereas the GNN infers these dynamics implicitly from player movements and interactions.
This demonstrates the strength of the graph-based approach. By learning relational structures directly, the model captures the complexity of football without requiring extensive feature design. Additionally, inference is fast, taking approximately 0.05 seconds per frame, making the approach suitable for near real-time applications.
3. Measuring the Unmeasurable
The core contribution of the paper is the concept of Defensive Impact, a framework for quantifying how defenses disrupt attacking play. Rather than measuring interceptions or tackles, the approach evaluates how defenders alter the set of possible actions available to the opponent.
The xReceiver model plays a central role. When applied at the frame level, it can predict not only who will receive the ball, but also when a player changes their intended decision. This allows the model to capture decision-making dynamics and identify moments where defensive actions force attackers to reconsider their options.
By combining xReceiver, xPass, and xThreat, the framework evaluates both realized and unrealized outcomes. It measures not only what happened, but what could have happened and was prevented. This shift from outcome-based to opportunity-based evaluation is fundamental to the paper’s contribution.
3.1 Disruption Maps
To summarize these effects, the authors introduce Disruption Maps. These are spatial representations that show where a defense has altered the opponent’s attacking behavior.
The method involves comparing a team’s typical “spatial identity” with its behavior in a specific match. By subtracting these two distributions, the model identifies areas where the defense increased or decreased threat, pass success, or player availability.
As shown in the visualizations, these maps reveal where a team successfully disrupts the opponent’s strategy. They provide a compact and interpretable way to analyze defensive performance at both team and player levels.
3.2 Lazio’s “Stellungsspiel” – Defensive Position Play
The paper illustrates the framework using a match between Lazio and Juventus. Despite losing, Lazio significantly disrupted Juventus’ attacking structure. The Disruption Maps show a reduction in xThreat in key attacking zones, particularly on Ronaldo’s side.
The analysis reveals that while Juventus players occupied threatening positions, the probability of successful passes into those areas was reduced, and the likelihood of those actions leading to goals was lower. This demonstrates how defensive positioning can neutralize attacking threats without direct interventions.
At the player level, the maps show that Ronaldo’s availability as a passing option was significantly reduced, especially in the first half. Similarly, Dybala occupied dangerous spaces but was rarely considered a viable passing option. This distinction between positioning and availability highlights the added value of the framework.
4. Going Deeper – Measuring Decision Making
The paper extends the analysis to decision-making processes. Defensive strategies such as ball-oriented and man-oriented defending are difficult to quantify, as they involve coordinated movements and off-ball actions.
Using xReceiver outputs, the authors define the “primary target” as the player with the highest probability of receiving the ball at each frame. Changes in this primary target indicate that a significant event has occurred, such as a defensive action or an attacking run.
Because labeled data for these situations is scarce, the authors use a programmatic labeling approach. Domain experts define simple rules that approximate different defensive contexts. For example, man-oriented defending is defined as a defender moving closer to the primary target to reduce their availability.
This approach allows the identification of complex tactical behaviors without manual annotation, enabling scalable analysis of defensive strategies.
4.1 Ronaldo: Null and Void
4.1.1 Targeting the Supply Line
The analysis of Ronaldo focuses on how Lazio disrupted the players who typically supply him with passes. By examining previous matches, the authors identify key passers and measure how often Ronaldo is selected as a target.
In the Lazio match, these connections are significantly reduced, particularly with Matuidi. This indicates that Lazio’s strategy targeted the supply chain rather than Ronaldo directly, limiting his involvement.
4.1.2 Targeting Ronaldo in Possession
When Ronaldo does receive the ball, Lazio applies a combination of ball-oriented and man-oriented defending. Defenders simultaneously pressure Ronaldo and his potential passing options, reducing both his immediate choices and the success probability of those choices.
The analysis also considers Ronaldo’s own behavior. Although he makes several active runs, only a few are forward, high-impact movements.
Compared to Lazio’s attackers, his runs are less effective in creating dangerous opportunities.
These insights demonstrate how the framework captures both defensive actions and attacking responses, providing a holistic view of the interaction.
5. Summary
The paper concludes by emphasizing the advantages of the GNN-based approach. By modeling tracking data as a graph, the method avoids the need for player ordering and heavy feature engineering, enabling efficient real-time predictions.
The introduction of Defensive Impact and Disruption Maps provides new tools for evaluating defensive performance. These tools capture how defenses influence attacking decisions, rather than simply measuring outcomes.
Finally, the framework enables the detection of complex tactical behaviors, such as man-oriented defending and off-ball runs, using programmatic labeling. This opens the door to more advanced analyses of team strategies and player interactions, bridging the gap between data and tactical understanding.
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References
Stöckl, M., Seidl, T., Marley, D., & Power, P. (2021, April). Making offensive play predictable-using a graph convolutional network to understand defensive performance in soccer. In Proceedings of the 15th MIT sloan sports analytics conference(Vol. 2022). United States: MIT sloan sports analytics conference.
https://www.sloansportsconference.com/research-papers/making-offensive-play-predictable-using-a-graph-convolutional-network-to-understand-defensive-performance-in-soccer