Case Study 02: Space Creation in the Final Third --- A Voronoi Analysis of Elite Attacks

Overview

The best attacking teams in world football do not simply "get lucky" in the final third. They systematically create, identify, and exploit space through coordinated movement patterns. In this case study, we apply Voronoi diagrams, space-creation metrics, and dangerous-space analysis to break down how elite attacking moves generate high-quality scoring chances.

We examine three archetypal attacking patterns, each drawn from synthetic tracking data inspired by real tactical motifs observed at the highest level:

1. The False Nine Drop: A centre-forward vacates the central channel, pulling centre-backs forward and creating space for midfield runners.
2. The Overlapping Full-Back: A full-back's run beyond the winger stretches the defence horizontally, opening the half-space.
3. The Third-Man Combination: A quick one-two leaves a defender marking thin air, as a third player exploits the vacated zone.

Pattern 1: The False Nine Drop

Scenario

At $t = 0$ s, the centre-forward (CF) is positioned at $(80, 34)$, marked by two centre-backs at $(82, 30)$ and $(82, 38)$. An attacking midfielder (AM) is at $(65, 34)$.

Over the next 3 seconds, the CF drops to $(70, 34)$, dragging one centre-back (CB1) forward to $(74, 30)$. The other centre-back (CB2) holds position at $(82, 38)$, creating a gap.

Voronoi Analysis

import numpy as np

# Before the drop (t = 0)
positions_before = {
    'CF': [80, 34], 'AM': [65, 34],
    'LW': [75, 15], 'RW': [75, 53],
    'CB1': [82, 30], 'CB2': [82, 38],
    'LB': [78, 10], 'RB': [78, 58],
    'CDM': [72, 34], 'LCM': [68, 22], 'RCM': [68, 46],
}

# After the drop (t = 3s)
positions_after = {
    'CF': [70, 34], 'AM': [65, 34],
    'LW': [78, 18], 'RW': [78, 50],
    'CB1': [74, 30], 'CB2': [82, 38],
    'LB': [78, 10], 'RB': [78, 58],
    'CDM': [72, 34], 'LCM': [72, 22], 'RCM': [72, 46],
}

Before the drop: The AM's Voronoi cell in the final third is approximately 90 m$^2$, squeezed between the CDM and the two centre-backs.

After the drop: CB1 has been pulled 8 m forward. The gap between CB1 and CB2 widens from 8 m to approximately 16 m laterally (accounting for CB1's forward movement). The AM's Voronoi cell expands to 145 m$^2$, and critically, a corridor of space opens in the zone $(78\text{--}85, 30\text{--}38)$ that now belongs to the attacking team's Voronoi partition.

Space created: $\Delta A_{\text{AM}} = 145 - 90 = 55$ m$^2$. The wingers also gain space as the full-backs become isolated.

Dangerous Space Matrix

The DSM at $t = 3$ s shows a hot spot in the central channel between the two centre-backs. This zone has:

• $xT \approx 0.035$ (high, given proximity to goal)
• $\mathrm{PC}_A \approx 0.65$ (attacking team controls it)
• $D_{\text{def}} \approx 0.15$ (low defender density due to the gap)

$$ \mathrm{DSM} = 0.65 \times 0.035 \times (1 - 0.15) = 0.019 $$

This DSM value ranks in the top 5 % of all grid cells, flagging it as a prime attacking target.

Pattern 2: The Overlapping Full-Back

Scenario

The right winger (RW) receives the ball at $(70, 55)$, attracting the opponent's left-back (OLB) at $(72, 58)$. The right-back (RB) begins an overlapping run from $(60, 62)$, sprinting forward at 9.5 m/s.

Space Creation Dynamics

Over 4 seconds:

The RW's Voronoi area increases modestly (by ~20 m$^2$) because the OLB shifts outward. But the major beneficiary is the right central midfielder (RCM), whose Voronoi cell extends into the right half-space, gaining approximately 70 m$^2$ of space in the zone between the opponent's full-back and centre-back.

Pitch Control Analysis

The pitch control surface reveals the mechanism clearly:

• At $t = 0$: The right half-space $(y \in [42, 55], x \in [70, 85])$ is controlled by the defending team ($\mathrm{PC}_A \approx 0.35$).
• At $t = 3$: The same zone flips to attacking control ($\mathrm{PC}_A \approx 0.62$), because the OLB has been drawn wide and the nearest remaining defender (the left centre-back) is 12 m away.

The spatial value added of the RB's overlapping run is:

$$ \text{SVA} = \sum_{(x,y)} \mathrm{PC}_{A,t=3}(x,y) \cdot xT(x,y) - \sum_{(x,y)} \mathrm{PC}_{A,t=0}(x,y) \cdot xT(x,y) = 0.048 $$

This represents a meaningful increase in expected threat generated purely through off-ball movement.

Pattern 3: The Third-Man Combination

Scenario

A classic third-man move near the edge of the penalty area:

1. Player A (CM) has the ball at $(65, 30)$.
2. Player B (CF) shows short at $(72, 32)$, pulling CB1 to $(74, 32)$.
3. Player A plays a short pass to Player B.
4. Player C (AM) makes a run from $(68, 36)$ into the space behind CB1, arriving at $(78, 35)$.
5. Player B lays the ball off first-time to Player C.

Frame-by-Frame Voronoi Evolution

The critical insight is that CB1's decision to follow Player B creates a spatial vacuum that Player C exploits. The Voronoi diagram shows this vacuum as a sudden expansion of Player C's cell into the channel between the two centre-backs.

Quantifying the Combination

• Space created by B's movement: 60 m$^2$ for Player C.
• Defenders bypassed: 2 (CB1 and the CDM).
• xT at reception point: 0.042.
• Weighted exploitation value: $60 \times 0.042 = 2.52$ xT-m$^2$.

Cross-Pattern Comparison

Key observations:

1. Third-man combinations create the most space in the least time but have the lowest success rate because they require precise timing and first-touch quality.
2. Overlapping runs are the safest mechanism because the ball carrier retains possession throughout and the run is visible to team-mates.
3. False nine movements are strategically disruptive but require a centre-forward with excellent spatial awareness and passing ability.

Implications for Recruitment

These patterns suggest different player profiles for different tactical systems:

• False nine system: Recruit forwards with high space-creation per 90 ($\geq 180$ m$^2$), strong dropping-run frequency, and above- average progressive passing from deep positions.
• Overlap-heavy system: Recruit full-backs with high sprint frequency in the final third and wingers who can hold width to pin the opposing full-back.
• Combination play system: Recruit midfielders with high off-ball run quality scores, excellent first-touch under pressure, and the ability to play one-touch lay-offs.

Code Reference

The full implementation, including Voronoi computation, space-creation measurement, and pitch control visualisation for all three patterns, is available in code/case-study-code.py.

Discussion Questions

1. How would you extend this analysis to account for the speed of defensive recovery? A centre-back pulled out of position at $t = 0$ may recover by $t = 3$ s if the attacking team is too slow.
2. Can you identify a fourth archetypal attacking pattern that creates space through a different mechanism? Describe the spatial dynamics using the framework developed here.
3. If a team faces a deep-sitting defence that does not follow runners, how would the false nine pattern fail? What spatial evidence would you look for to diagnose this failure?