Wide Open Gazes: Quantifying Visual Exploratory Behavior in Soccer with Pose Enhanced Positional Data

Imagine you are watching a soccer game. You see a player waiting for a pass. In the old days, analysts tried to figure out how "smart" that player was by counting how many times they whipped their head around quickly. If they spun their head fast enough, they got a point for "scanning."

But this method had a few big problems:

It was too simple: It was like a light switch (on or off). It didn't measure how much the player was looking, just if they moved their head fast.
It was biased: It mostly counted midfielders because they move their heads the most. It ignored defenders or strikers who might be scanning differently.
It didn't predict success: Just because a player spun their head fast didn't mean they would make a great play next.

This paper introduces a brand new way to measure "seeing" in soccer. Instead of counting head spins, they built a digital "Super-Vision" map for every single player on the field.

The Core Idea: The "X-Ray Goggles"

Think of the new method as giving every player a pair of X-Ray goggles that see the whole field at once, but with a twist: the goggles know exactly what the player can actually see based on where their head and shoulders are pointing.

Here is how they built this system, broken down into simple steps:

1. The "Flashlight" (Field of View)

Imagine a player holding a flashlight. The beam isn't just a perfect circle; it gets dimmer the further away it goes, and it gets fuzzier the further it is to the side.

The Innovation: The researchers used new camera tech (Pose Estimation) to see exactly where a player's head and shoulders are pointing. They created a mathematical "flashlight" that shows exactly what percentage of the field a player can see at any given second.
The Speed Factor: If a player is running super fast, their "flashlight" gets narrower (like when you drive fast and only look straight ahead). If they are standing still, the flashlight is wide open.

2. The "Crowd Blocker" (Occlusion)

Now, imagine that flashlight beam hits a wall. In soccer, the "walls" are other players.

The Innovation: The system calculates if another player is standing in the way. If a defender is standing right in front of your player, they block the view of the goal behind them. The system draws a "shadow" on the map where the player cannot see.
The Shoulder Trick: It even looks at the other player's shoulders. If an opponent is facing sideways, they block less of the view than if they are facing you directly.

3. The "Value Map" (Pitch Control & Value)

Next, they overlaid this "Vision Map" onto two other famous soccer maps:

The "Who Owns This?" Map: This shows which team controls which part of the field.
The "Gold Mine" Map: This shows which parts of the field are most valuable (usually closer to the opponent's goal).

The Experiment: Waiting for the Pass

The researchers looked at a specific moment: The "Awaiting Phase." This is the split second before a player receives a pass. They asked: What did this player see while waiting?

They compared two groups of players:

The Old Way: Players who just spun their heads fast (Traditional VEA).
The New Way: Players who had a high-quality "Vision Map" (they saw a lot of the field, especially the dangerous spots controlled by the defense).

The Results: Seeing is Believing

The results were a game-changer:

The Old Way Failed: Counting head spins had zero ability to predict if the player would make a good move next. It was like guessing the weather by looking at a broken thermometer.
The New Way Succeeded: Players who had a "clear view" of the defensive players and the valuable space while waiting were much more likely to make a brilliant move (dribble into open space) after they got the ball.

The Big Takeaway

Think of it like driving a car.

The Old Method was like counting how many times you whipped your head left and right. It doesn't tell you if you actually saw the car coming around the corner.
The New Method is like having a dashboard that tells you exactly how much of the road ahead you can see, and if your view is blocked by a truck.

In short: This paper proves that it's not about how fast you look; it's about what you see. If a player can mentally map out the defense and the open space before they even touch the ball, they are much more likely to succeed. And now, thanks to this new math, coaches can finally measure that "mental map" without needing to hire a team of people to watch videos and count head movements.

1. Problem Statement

Traditional methods for measuring visual exploratory behavior (VEB) in soccer rely on counting Visual Exploratory Actions (VEAs), defined as rapid head movements exceeding 125°/s. The authors identify several critical limitations in this approach:

Positional Bias: VEAs are heavily skewed toward central midfielders, failing to capture behavior across all player roles.
Annotation Challenges: Manual annotation is labor-intensive and suffers from high inter-observer variability.
Data Limitations: Standard 25 FPS tracking data is often insufficient to reliably detect rapid head movements.
Binary Constraints: The method is binary (scanning vs. not scanning), failing to capture the continuous nature of visual attention.
Lack of Predictive Power: Studies show VEA frequency does not significantly correlate with performance metrics (e.g., pass success) or distinguish between elite and super-elite players.
Incompatibility: Traditional VEA metrics do not integrate well with advanced spatial analytics frameworks like Pitch Control and Pitch Value.

2. Methodology

The authors propose a novel formulaic continuous stochastic vision layer that integrates pose-enhanced tracking data with spatial modeling.

A. Data Source

Dataset: 32 games from the 2024 Copa América.
Tracking Data: Broadcast tracking data (25 FPS) enhanced with human pose estimation (head, shoulder, and hip rotation angles) provided by Respo.Vision.
Event Data: Synchronized with StatsPerform (Opta) event data to identify specific phases: the Awaiting Phase (waiting for a pass) and the subsequent On-Ball Phase (dribbling after reception).
Preprocessing: Missing angles are interpolated using Euler's formula to handle the cyclical nature of angles.

B. The Vision Model

The core innovation is a 105x68 grid representing the pitch, calculating a Total Vision Map ( $V_i$ ) for each player $i$ at every frame. This map is the product of two probabilistic components:

Probabilistic Field of View ( $V_{\rho}$ ):
- Based on a 120° binocular vision assumption.
- Modeled as a Gaussian distribution that decays based on distance ( $d$ ) and angular deviation ( $\theta$ ) from the head orientation.
- Speed Dependency: The model accounts for player speed ( $v$ ). Higher speeds result in a narrower focus and reduced spatial awareness (sharper decay rates).
- Formula: $V_{\rho} = R \odot A \odot V_{\beta}$ , where $R$ and $A$ are radial and angular decay functions.
Probabilistic Occlusion Map ( $V_{\Phi}$ ):
- Calculates how other players ( $j$ ) block player $i$ 's view.
- Uses shoulder rotation ( $\theta_s$ ) to determine the apparent width of the obstructing player. A player facing sideways blocks less vision than one facing directly.
- Models a "probabilistic ray" from player $i$ through player $j$ , scaled by distance and apparent angular width.
- The total occlusion map is the element-wise product of all individual player occlusions.
Total Vision Map:
- $V_i = V_{\rho} \odot V_{\Phi}$ (Element-wise multiplication).
- This results in a continuous probability map of what a player can see at any given moment.

C. Integration with Spatial Analytics

The Vision Map is combined with established frameworks from Fernández & Bornn (2018):

Imminent Pitch Control ( $PC_{0.5}$ ): A modified pitch control model where the influence radius is scaled down to represent space a player can reach in a very short time.
Pitch Value ( $V_l$ ): A neural network-derived map estimating the strategic value of pitch locations based on defensive positioning.
Synthesis: The vision map is overlaid on these surfaces to calculate metrics like "percentage of defended area observed" or "observed pitch value."

3. Validation & Experimental Design

Objective: Determine if visual metrics during the Awaiting Phase predict the change in Pitch Value gained during the subsequent On-Ball Phase.
Modeling: Four XGBoost Binary Classification models were trained to predict if a player would significantly increase or decrease their controlled pitch value.
1. Baseline: Distance to goal only.
2. Traditional VEA: Adds counts of rapid head movements (1s, 2s, and specific intervals).
3. Regular: Adds spatial features (distance to goal/center), velocity vectors, and player position labels.
4. Vision Model: Adds aggregated features derived from the Vision Map (e.g., % of defensive space observed, ratio of defense vs. attack observed).
Labels: Defined by the ratio of pitch value at the end of the on-ball phase vs. the awaiting phase.

4. Key Results

Predictive Power: The Vision Model achieved the highest performance with an AUC of 0.788, significantly outperforming the Regular model (0.744).
Failure of Traditional VEA: Adding traditional VEA counts to the Baseline model resulted in no performance improvement (AUC dropped slightly to 0.654), confirming that rapid head movement counts are not reliable predictors of on-ball success.
Key Predictive Features (SHAP Analysis):
- Positive Correlation: Players who observed a higher percentage of total defensive occupied space and a higher ratio of defense-to-attack space while awaiting a pass were more likely to gain valuable pitch value afterward.
- Negative/Neutral Correlation: Simply observing more of the field (total area) or observing more attacking space did not correlate with success.
- Position Independence: The model works regardless of player position (unlike VEA counts which favor midfielders).

5. Key Contributions

Novel Stochastic Vision Layer: A formulaic, continuous method to quantify visual perception using pose-enhanced tracking, replacing binary manual annotation.
Integration with Pitch Control: Successfully bridges the gap between visual behavior and spatial analytics (Pitch Control/Pitch Value), allowing for the measurement of "observed value."
Empirical Evidence: Demonstrates that quality of observation (what is seen) matters more than frequency of movement (how often the head turns). Specifically, identifying defensive gaps is a stronger predictor of success than general scanning.
Open Source: The authors have open-sourced the tools and code on the U.S. Soccer Federation GitHub to facilitate reproducibility and further research.

6. Significance

This research fundamentally shifts how visual behavior is analyzed in soccer analytics. By moving away from the flawed "count the head turns" metric, it provides a continuous, position-agnostic, and context-aware framework. The findings suggest that elite players are distinguished not by how often they look around, but by what they choose to look at (specifically, identifying defensive vulnerabilities) before receiving the ball. This methodology is applicable to other invasion sports (e.g., basketball, American football) as pose-estimation data becomes more ubiquitous.