Technical Summary: Blame is easier than praise: Measuring off-ball defensive performance in football

1. Problem Statement

Defensive performance in football is traditionally measured through discrete, active actions such as tackles, interceptions, and blocks. The authors argue that these metrics are insufficient because they are biased toward active participation and fail to capture the continuous, subtle impact of positional behavior and anticipation. A prime example cited is Virgil van Dijk, whose elite defensive reputation and Ballon d'Or ranking are not reflected in his percentile rankings for tackles or interceptions.

Current advanced metrics often focus on "pressing" or team-level organization but lack a robust method for attributing defensive responsibility to individual players, particularly when no explicit action (like a tackle) occurs. Existing approaches that attempt to identify "out of position" players often struggle to correlate these findings with defensive success. Consequently, negative defensive contributions—such as failing to cover a passing lane or leaving a zone unguarded—are largely absent from evaluation, creating a gap in understanding how defenders influence the outcome of an opponent's attacking play.

2. Methodology

The study proposes a framework that shifts the perspective from the defender's actions to the attacking team's passing outcomes. The methodology attributes "blame" or "credit" for changes in expected threat among defenders based on their spatial proximity and tactical roles. The pipeline consists of four main stages:

2.1 Data Sources

The model is validated on a unique, extensive cross-gender and cross-competition dataset comprising:

• Men's FIFA World Cup 2022: 64 matches (PFF FC tracking data).
• Frauen-Bundesliga (Women's German Bundesliga) 2023/24: 116 matches (STS/Track160 tracking data).
• Men's 3. Liga (German third tier) 2023/24: 336 matches (STS/Track160 tracking data).
  The dataset includes high-frequency optical tracking (25–30 fps) and manually recorded event data (passes, outcomes), totaling over 400,000 passing events.

2.2 Defensive Involvement (Spatial Proximity)

The model calculates the value of a pass using Expected Threat (xT), defined as the probability of scoring within the next few actions. The defensive value is termed Expected Defensive Threat (xDT):

• Successful passes: $xDT = -\Delta xT$ (a negative value indicating a defensive failure to stop a dangerous pass).
• Unsuccessful passes: $xDT = xT_{start}$ (a positive value indicating a successful defensive disruption).

To attribute this value to specific players, the authors define Defensive Pressure Areas (DPAs) based on the pass outcome:

1. Successful passes with negative xDT: DPAs cover the passer, receiver, and the pass lane (circles of radius $r=5$m and a connecting rectangle).
2. Successful passes with positive xDT (backward passes): DPA covers only the passer.
3. Unsuccessful passes out of play: DPA covers only the passer.
4. Interceptions: No DPA; the interceptor receives full credit.

For defenders within a DPA, involvement is calculated based on Euclidean distance to the pass. This yields metrics for Raw Contribution (successful pressure), Valued Contribution (weighted by threat reduction), Raw Fault (failure to stop a threat), and Valued Fault (failure weighted by threat increase).

2.3 Responsibility (Tactical Role)

To address the limitation that spatial proximity does not account for being "out of position," the authors introduce Responsibility.

• Formation Detection: A template-matching algorithm identifies team formations and assigns players to 20 distinct roles (e.g., Center Back, Full Back, Central Midfielder) across six role groups.
• Expected Involvement: Responsibility is defined as the average involvement observed for a specific triplet of (Passer Role, Receiver Role, Defender Role) across the competition.
• A defender assigned to a specific role receives a "responsibility" score for a pass based on their role, regardless of their actual physical location. This allows the model to penalize a defender who is far from the ball but should have been covering that zone.

2.4 Metric Aggregation

Metrics are aggregated at the match, player, and role levels. The authors found that fault-based metrics are more valid when aggregated per 90 minutes (accumulating mistakes), while contribution-based metrics are better aggregated per pass (normalizing for possession). To create a single performance indicator, they propose a fused metric that combines contribution (per pass) and fault (per 90 minutes) using a weighted equation.

3. Key Contributions

• Novel Attribution Framework: The paper introduces a method to distribute defensive responsibility for all passing events (successful and unsuccessful) among defenders, moving beyond simple action counting.
• Separation of Fault and Contribution: The model explicitly distinguishes between "fault" (preventing dangerous passes) and "contribution" (creating pressure), acknowledging that these require different aggregation strategies.
• Responsibility Modeling: By integrating automatically detected tactical formations, the model quantifies "expected involvement," allowing for the measurement of positioning errors (being out of position) rather than just active failures.
• Extensive Validation: The study provides the first comprehensive evaluation of individual defensive positioning metrics across three distinct datasets, covering elite men's and women's football as well as lower-tier men's professional football.

4. Results

The proposed metrics were validated against external benchmarks (market values and FIFA "Defensive Awareness" ratings) and internal robustness checks (repeatability and season-level stability).

• Validity: The fault-based metrics (specifically Valued Fault per 90 minutes and Valued Fault Responsibility) showed the strongest correlations with external ratings, outperforming traditional metrics like interceptions and tackles by approximately 1 standard deviation.
• Robustness: Responsibility-based metrics generally demonstrated higher stability and discriminatory power than proximity-based involvement metrics.
• Role Specificity: The study found that "fault" is a stronger predictor of defensive quality than "contribution." This aligns with the nature of defending, where a single mistake can be more costly than a positive action.
• Competition Differences: The new metrics significantly outperformed classic metrics in elite competitions (World Cup, Frauen-Bundesliga). In the men's 3. Liga, the performance gap was smaller, which the authors attribute to a narrower skill gap and a more combative playing style where active contributions are more valued.
• Fusion Success: The custom fused metrics (combining contribution and fault) performed significantly better than naive combinations or single-aggregation metrics.

5. Significance and Claims

The authors claim this work establishes the first published metric capable of reliably measuring positioning errors in football. By shifting the evaluation lens to the "blame" for conceding high-value actions, the study demonstrates that defensive performance is better captured by analyzing what defenders fail to prevent rather than just what they actively do.

The significance of the work lies in:

1. Quantifying the "Invisible": Providing a mathematical basis for the "off-ball" defensive skills that are often praised subjectively but rarely measured.
2. Cross-Domain Applicability: Validating these metrics across genders and competition levels, including a near-full season of women's data, which is underrepresented in sports analytics literature.
3. Reproducibility: The authors have made all underlying code publicly available to support further research in this under-studied area.

The paper concludes that while there is no "one-size-fits-all" solution (as optimal metrics vary by role and competition level), the involvement-responsibility paradigm offers a substantial improvement over state-of-the-art defensive evaluation.