New Metric Based on the Centroid to Measure Rational Space Occupation in Football

11 Oct New Metric Based on the Centroid to Measure Rational Space Occupation in Football

This research introduces a new metric that objectively measures the rational occupation of space by players on the field. The metric is based on the centroid, which is the midpoint of the positioning of the 10 outfield players (excluding the goalkeeper), and the projection of this centroid through both the amplitude (horizontal axis) and depth (vertical axis). This analysis offers an innovative way to understand how teams occupy space and how to optimize their tactical layout during matches.

What does the metric consist of?

1. Team centroid: The centroid is the midpoint calculated from the positioning of the 10 outfield players, excluding the goalkeeper. This point represents the team’s center and determines how lines are projected to divide the field into areas for analysis.
2. Projection of lines from the centroid:
   • Amplitude line (horizontal): A horizontal line is drawn from the centroid, splitting the field into two zones: right and left. This line reflects the lateral distribution of the team. Importantly, the centroids of both teams tend to be laterally similar, so this horizontal line is almost the same for both teams, meaning that the field is divided similarly into right and left halves for both sides.
   • Depth lines (vertical): From the centroid, two vertical lines are drawn that divide the field according to proximity to the goals. These lines mark areas of influence and help analyze how the team organizes itself in relation to depth, i.e., the distance to its own or the opponent’s goal.
3. Division of the field into 6 areas: Based on these projections, the field is divided into six areas:
   • Two attacking areas (closer to the opponent’s goal).
   • Two central areas (midfield zones).
   • Two defensive areas (closer to the team’s own goal).
   This division allows for the analysis of how players distribute themselves across these areas and whether there is numerical superiority or inferiority in each sector.

The rationale behind the metric

The study is based on the hypothesis that while amplitude (right or left side of the field) tends to be similar for both teams due to the proximity of their centroids, the key differences lie in the depth lines since a team’s centroid is usually closer to its own goal. This creates differences in how teams occupy space vertically, offering a detailed way to understand the spatial organization of players on the field.

Practical applications for coaches

This new metric can help coaches plan and adjust their tactical strategy more effectively, both in training and during matches. Key applications include:

1. Measuring rational space occupation: This metric allows coaches to analyze whether players are logically and efficiently distributed across the six areas of the field. For example, in an attacking scenario, coaches can observe whether players are occupying the areas near the opponent’s goal with enough numbers or leaving defensive areas vulnerable.
2. Optimizing defensive strategy: By knowing how the centroid projects and how players are distributed in defensive areas, coaches can better adjust player positioning to avoid numerical inferiority in critical areas such as the team’s own penalty box or nearby sectors.
3. Real-time analysis: During a match, coaches can use this metric to detect spatial imbalances in the team, such as areas that are overpopulated by players or, conversely, sectors that are left empty and exposed to counter-attacks.
4. Improving transitions: Understanding how the centroid moves and how players are distributed across the sectors is crucial for managing defensive-to-offensive transitions and vice versa. This allows for better tactical adjustments depending on the phase of play and ball position.
5. Ball distribution from the back: In situations where the opposing team applies a high press, this metric can help the team in possession identify areas where they have numerical superiority to safely play out from the back, avoiding turnovers in dangerous areas.

Conclusion

The new metric based on the centroid and the division of the field into six areas is an innovative tool to accurately measure the rational occupation of space by players. Its ability to identify numerical superiority and inferiority in various sectors of the field provides coaches with clear, data-driven insights to make better tactical decisions and optimize team performance in different match contexts.