P3: Potential Penetrative Passing Analysis
- P3 is a football analytics concept defined to quantify potential penetrative passes when the ball is with a player and a teammate is positioned within the opponent convex hull.
- It employs a geometric method with convex hull analysis and a CNN-based image classification model to determine whether a pass becomes effectively penetrative.
- The P3% metric normalizes pass conversion by available opportunities, enabling nuanced tactical evaluations for both players and teams.
Potential Penetrative Pass (P3) is a football analytics concept for evaluating penetrative passing relative to the set of situations in which such a pass was available. A P3 is defined at a passing moment in open play when the ball is at a player’s foot, the pass origin is outside the team’s defensive third and outside the opponent’s final quarter, and at least one teammate is positioned in front of the ball and inside the convex hull formed by the opposing outfield players, with the goalkeeper excluded. The framework therefore quantifies both opportunity and conversion: it first detects moments in which a depth-breaking pass is available, then estimates whether the observed pass actually becomes penetrative, and finally aggregates the results into an opportunity-normalized KPI, (Sotudeh, 2023).
1. Definition and analytical rationale
P3 is motivated by a basic asymmetry in conventional passing statistics: completed penetrative passes are observable, but the number of times a team or player could have attempted one is not usually measured. The P3 concept addresses this by defining a “Potential Penetrative Pass” as any moment in open play satisfying three conditions. First, the ball is at a player’s foot in a passing moment. Second, the origin of the pass lies outside the team’s defensive third and outside the opponent’s final quarter, described equivalently as not in the first $1/3$ or last $1/4$ of the pitch. Third, there exists at least one teammate “in front of the ball” and inside the convex hull formed by the opposing outfield players.
The central rationale is that penetrative passing should be normalized by its opportunity set rather than evaluated only through realized actions. In this sense, P3 measures not only how often a team completes depth-breaking passes, but how many times it had the potential to do so. A common misunderstanding is to treat as a raw passing-volume statistic; by construction, it is instead an opportunity-normalized measure of conversion.
2. Geometric and probabilistic formulation
The geometric core of the framework is the convex-hull criterion. Let denote the coordinates of the opponent outfield players in front of the ball, and let denote the coordinates of teammates, excluding the passer. The opponent hull is
A passing moment is flagged as a P3 opportunity if
This geometric definition is then coupled to a binary classification problem. The model input is a feature representation of the P3 moment consisting of a CNN-image that combines 360 data, Voronoi or pitch-control layers, and the convex hull overlay. The output is a binary target $1/3$0 indicating whether the pass actually becomes penetrative. The trained model is
$1/3$1
Threshold selection is based on the ROC curve. The validation threshold $1/3$2 is chosen by minimizing the Euclidean distance to the ideal operating point $1/3$3:
$1/3$4
The selected threshold is $1/3$5 (10.38%). Aggregation is then performed through the KPI
$1/3$6
This formalization separates three distinct objects: the opportunity set, the realized penetrative events, and the conversion rate from one to the other.
3. Computational pipeline
The computational workflow begins with data preparation. StatsBomb event data and 360° freeze-frame data are loaded for each match, and each pass event is filtered by the spatial rule that the passer’s location must not be in the first third or last fourth of the pitch. Opportunity detection then identifies all opponent outfield player positions in front of the ball, computes the convex hull of those players, identifies teammates excluding the passer, and flags the event as a P3 opportunity if any teammate lies inside the hull.
The image representation step converts each detected opportunity into a half-pitch crop in the direction of play. In that representation, blue dots indicate ball-team players visible via 360 data, red dots indicate opponent players, the passer is a black dot, Voronoi or pitch-control shading is rendered for both teams, and the hull $1/3$7 is shown as a green polygon. The resulting image is the input to the classification model (Sotudeh, 2023).
Model inference uses a pre-trained ResNet-34 initialized from ImageNet and fine-tuned for 8 epochs on approximately 79,000 P3 images, of which 88% are non-penetrative. The model outputs $1/3$8, and a pass is classified as penetrative when $1/3$9 with $1/4$0. Aggregation then counts total P3 opportunities and successful penetrative passes for each player or team and computes $1/4$1.
Several assumptions and hyperparameters are explicit. The opponent set excludes the goalkeeper. Only camera-visible players are used. The training split uses 80% of Bundesliga matches, with validation on the final 20%, corresponding to approximately 15,976 images. The loss is binary cross-entropy. Reported losses are train loss $1/4$2 and validation loss $1/4$3, with no serious overfitting noted. Because of class imbalance, the evaluation metric is AUC-ROC.
4. Validation and comparative performance
The framework is validated by comparing image-based modeling against event-only baselines. A baseline machine-learning approach using event features only achieves a best AUC of approximately $1/4$4, with ExtraTrees as the strongest baseline. By contrast, the CNN using images, 360 data, and pitch control attains a validation AUC of $1/4$5 (Sotudeh, 2023). Within the paper’s setup, this establishes that the spatialized image representation carries substantially more predictive signal than event features alone.
At the decision threshold $1/4$6, the reported confusion matrix is asymmetric, reflecting the class distribution and the thresholding choice. True non-penetrative events correctly classified number 9,351 (58.5%), true penetrative events correctly classified number 1,244 (7.8%), false positives are 4,780 (29.9%), and false negatives are 601 (3.8%). The selected threshold is therefore not a balanced-accuracy threshold; it is the ROC-derived operating point minimizing distance to the ideal corner.
Calibration is assessed through a quantile-based reliability curve, which is reported to show good alignment of predicted probabilities. This is important because the framework does not use the model only for ranking; it also relies on stable probabilistic outputs before thresholding and aggregation.
5. Derived indicators and case studies
The principal derived indicator is $1/4$7, computed for players or teams over a defined period. Because the denominator is the number of P3 opportunities rather than the number of total passes, the KPI evaluates how often available penetrative moments are converted into successful penetrative passes. This makes league-wide comparisons interpretable even when opportunity volume differs across tactical structures.
The paper reports 2020–21 LaLiga rankings for several groups, together with team-level attack and defense summaries (Sotudeh, 2023).
| Category | Reported results |
|---|---|
| Defenders (min. 1140 min, ≥30 pens) | Umtiti 48%, Berchiche 43%, Ruíz 39% |
| Midfielders (min. 1140 min, ≥36 pens) | Torreira 42%, Kroos 39%, Busquets 39% |
| U23 players (min. 1140 min, ≥11 pens) | Rodrygo 54%, Lainez 42%, João Félix 38% |
| Team-level attack P3 % | Barcelona 32%, Villarreal 30%, Atlético 27% |
| Team-level defense P3 opp per match | Sevilla concede 52 opp P3s (best), Real Sociedad 58 |
These case studies illustrate that the framework can be used from multiple perspectives. At player level, it can rank defenders, midfielders, or age-constrained cohorts by conversion of penetrative opportunities. At team level, it can characterize both attacking execution and defensive concession of P3 opportunities per match. A plausible implication is that the same geometric-opportunity definition can support both offensive and defensive profiling without changing the underlying formalism.
6. Scope, limitations, and proposed extensions
The framework has several stated limitations. The convex hull is computed only on camera-visible players, which introduces bias when some defenders are off-screen. The model has no body-orientation data, so it may overestimate passability against backwards-facing players. The 360 data do not cover the full freeze-frame, and future work is proposed to use full on-ball freeze-frames (Sotudeh, 2023).
The paper also identifies several extension paths. One is experimentation with alternate image representations. Another is an interactive tool that would vary player positions and allow observation of the sensitivity of $1/4$8. The same methodology is also proposed for generalization to “potential crosses” or “potential counter-attacks.”
These limitations clarify what P3 is and is not. It is not a full tracking-based model of passing feasibility under complete observability; it is a principled opportunity model built from event data, partial 360 context, spatial geometry, and CNN classification. Its significance lies in converting a previously implicit tactical concept—the availability of a depth-breaking pass—into an automated and explicitly normalized analytical object.