Pass Networks

Definition

A graph-based visualization where nodes represent players (positioned at their average location on the pitch during possession) and edges represent passing connections between them. Edge thickness or opacity encodes passing frequency, and node size often encodes total pass involvement.

History & Origins

Pass networks draw from graph theory and social network analysis (SNA), disciplines with roots going back to the 18th century (Euler's bridges of Königsberg, 1736) and formalized in sociology in the 1930s–1950s.

The application of network analysis to football was pioneered in academic research in the late 2000s and early 2010s. Javier López Peña and Hugo Touchette published an early influential paper, "A network theory analysis of football strategies" (2012), applying Network Centrality Metrics|centrality metrics from SNA to passing data. They showed that network metrics like betweenness centrality (how often a player sits on the shortest path between two other players) and closeness centrality could identify key players in a team's structure.

David Sumpter, mathematician and author of Soccermatics (2016), helped popularize pass networks among a broader audience by connecting them to accessible explanations of how teams self-organize.

Javier Fernández (later at FC Barcelona's analytics department, see EPV - Expected Possession Value|EPV) and others extended pass networks into more sophisticated frameworks, incorporating temporal dynamics and weighting edges by pass value rather than just frequency.

In media, pass networks became a standard part of match analysis around 2015–2018, appearing in outlets like The Athletic, StatsBomb, and Between the Posts. Karun Singh and others in the analytics Twitter community produced influential visualizations.

How It Works

For each player, compute their average position during possession phases (either from event coordinates or tracking data)
Count pass frequency between each pair of players
Draw nodes at average positions, sized by involvement (total passes)
Draw edges between connected players, with thickness proportional to pass count
Optionally apply a minimum threshold (e.g., ignore connections with fewer than 3 passes) to reduce clutter

Network Metrics

See Network Centrality Metrics for full detail. Key metrics applied to pass networks include:

Degree centrality — number of unique passing connections
Betweenness centrality — how often a player bridges passing paths between teammates
Closeness centrality — how quickly a player can reach all others through passes
Clustering coefficient — how interconnected a player's passing partners are (triangular play)
Eigenvector centrality — importance based on the importance of connected players
Graph density — ratio of actual connections to possible connections (passing diversity)

Variants

Weighted pass networks — edges weighted by pass value (xT - Expected Threat|xT, VAEP - Valuing Actions|VAEP) instead of frequency
Temporal pass networks — showing how the network evolves over different match phases (first half vs. second half, in possession vs. building from the back)
Opponent-adjusted networks — comparing a team's pass network against their average to highlight how they adapted to a specific opponent
Directional networks — using directed edges to show pass direction, revealing asymmetries (e.g., a fullback receives from the CB but passes to the winger, not back)

Key Properties

Reveal team shape and structure in a way that formation labels (4-3-3, etc.) don't fully capture
Identify the most central players in a team's possession game
Can expose tactical changes: a substitution that reshapes the network, or a half-time adjustment

Limitations & Debates

Average position fallacy: a player's average position can be misleading if they move a lot — a midfielder who alternates between dropping deep and pushing forward will show up in the middle, which misrepresents both roles
Doesn't capture timing: a quick one-touch combination and a slow recycling of possession look the same in a static network
Possession bias: pass networks only reflect time on the ball — a team that presses brilliantly (see PPDA - Passes Allowed Per Defensive Action|PPDA) but has little possession will have a sparse network that undersells their performance
Threshold sensitivity: the choice of minimum pass count to display an edge significantly changes the visual output
Increasingly sophisticated alternatives: some researchers argue that static pass networks are being superseded by sequence-based and trajectory-based models that capture temporal dynamics

Related Metrics

Network Centrality Metrics — the mathematical metrics used to analyze pass networks
xT - Expected Threat — can weight network edges by value instead of frequency
VAEP - Valuing Actions — alternative edge weighting

Related Visualizations

Pass Maps — individual pass arrows vs. the aggregated network view
Heat Maps — complementary spatial view of player activity

Key People

Javier López Peña & Hugo Touchette — early academic work on SNA in football
David Sumpter — popularized network thinking in football analytics (Soccermatics)
Javier Fernández — advanced network approaches at FC Barcelona
Karun Singh — influential pass network visualizations

Notable Implementations & Resources

mplsoccer (Python) — pass network plotting
NetworkX (Python) — general graph analysis library used for computing Network Centrality Metrics|network metrics
López Peña & Touchette, "A network theory analysis of football strategies" (2012)
Sumpter, Soccermatics (2016)

Tags: #football #analytics #visualization #passing #network-analysis

History & Origins

How It Works

For each player, compute their average position during possession phases (either from event coordinates or tracking data)

Count pass frequency between each pair of players

Draw nodes at average positions, sized by involvement (total passes)

Draw edges between connected players, with thickness proportional to pass count

Optionally apply a minimum threshold (e.g., ignore connections with fewer than 3 passes) to reduce clutter

Network Metrics

See Network Centrality Metrics for full detail. Key metrics applied to pass networks include:

Degree centrality — number of unique passing connections

Betweenness centrality — how often a player bridges passing paths between teammates

Closeness centrality — how quickly a player can reach all others through passes

Clustering coefficient — how interconnected a player's passing partners are (triangular play)

Eigenvector centrality — importance based on the importance of connected players

Graph density — ratio of actual connections to possible connections (passing diversity)

Variants

Weighted pass networks — edges weighted by pass value (xT - Expected Threat|xT, VAEP - Valuing Actions|VAEP) instead of frequency

Temporal pass networks — showing how the network evolves over different match phases (first half vs. second half, in possession vs. building from the back)

Opponent-adjusted networks — comparing a team's pass network against their average to highlight how they adapted to a specific opponent

Directional networks — using directed edges to show pass direction, revealing asymmetries (e.g., a fullback receives from the CB but passes to the winger, not back)

Limitations & Debates

Average position fallacy: a player's average position can be misleading if they move a lot — a midfielder who alternates between dropping deep and pushing forward will show up in the middle, which misrepresents both roles

Doesn't capture timing: a quick one-touch combination and a slow recycling of possession look the same in a static network

Possession bias: pass networks only reflect time on the ball — a team that presses brilliantly (see PPDA - Passes Allowed Per Defensive Action|PPDA) but has little possession will have a sparse network that undersells their performance

Threshold sensitivity: the choice of minimum pass count to display an edge significantly changes the visual output

Increasingly sophisticated alternatives: some researchers argue that static pass networks are being superseded by sequence-based and trajectory-based models that capture temporal dynamics

Notable Implementations & Resources

mplsoccer (Python) — pass network plotting

NetworkX (Python) — general graph analysis library used for computing Network Centrality Metrics|network metrics

López Peña & Touchette, "A network theory analysis of football strategies" (2012)

Sumpter, Soccermatics (2016)

Tags: #football #analytics #visualization #passing #network-analysis