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Spatio-Temporal Analysis of Team Sports -- A Survey

Joachim Gudmundsson, Michael Horton

arXiv:1602.06994v1cs.OH

TL;DR

Team-sports performance analysis requires methods that account for players’ movements and interactions, while available tracking data has enabled research across many disciplines. This survey categorizes computational approaches using spatio-temporal data and identifies open research questions.

  • Problem

    Player and team performance in invasion sports cannot be fully analyzed without considering the movements and interactions of all players as a group.

  • Method

    The survey organizes recent research using spatio-temporal team-sports data as input and non-trivial computational models into a coherent framework.

  • Results

    The survey identifies diverse techniques and research problems across team-sports spatio-temporal analysis, while reporting little consensus on key questions or techniques.

  • Takeaways & Limitations

    The framework provides a concise introduction and a structured classification for researchers entering the field.

  • Takeaways & Limitations

    Modeling player motion faithfully while remaining computationally tractable remains an open problem because physiological constraints and prior momentum are often ignored.

Abstract

from arXiv · show

Team-based invasion sports such as football, basketball and hockey are similar in the sense that the players are able to move freely around the playing area; and that player and team performance cannot be fully analysed without considering the movements and interactions of all players as a group. State of the art object tracking systems now produce spatio-temporal traces of player trajectories with high definition and high frequency, and this, in turn, has facilitated a variety of research efforts, across many disciplines, to extract insight from the trajectories. We survey recent research efforts that use spatio-temporal data from team sports as input, and involve non-trivial computation. This article categorises the research efforts in a coherent framework and identifies a number of open research questions.

1 Introduction

Team-based invasion sports share competitive structures that make group movement and interaction central to performance analysis. This survey organizes growing, multidisciplinary research using spatio-temporal sports data and identifies open questions.

  • Invasion sports involve two teams competing for possession while simultaneously attacking the opposition goal and defending their own.
  • Human observation can be unreliable, with expert observers recalling significant match events as little as 42%.
  • Automated tracking systems have expanded sports-analysis research, but adoption and research-data availability vary across sporting codes.
  • The survey covers team-based invasion sports whose primary input is spatio-temporal data and whose models perform non-trivial computation.
  • Research spans machine learning, network science, GIS, computational geometry, computer vision, complex systems science, statistics, and sports science.
  • Player trajectories offer small spatial and temporal ranges, dense sampling, few agents, cooperative and adversarial interactions, and latent structure.
  • The survey framework covers data types, spatial subdivision, event networks, data mining, performance metrics, and visualization.

2 Representing Sports Play using Spatio-Temporal Data

Team-sports spatio-temporal analysis uses timestamped player or ball trajectories alongside semantically richer event logs. These complementary representations support geometric and computational analyses of play.

  • 2.1 Object Trajectories: Object trajectories record timestamped player or ball locations as sequences of points in the plane.
  • 2.1 Object Trajectories: Tracking systems generate dense trajectory samples at uniform frequencies of 10 to 30 Hz.
  • 2.1 Object Trajectories: Trajectory data availability varies by league and team, with league-wide datasets enabling controls for weather, injuries, and home or away play.
  • 2.2 Event Logs: Event logs record player events such as passes and shots alongside technical events including fouls, time-outs, and period boundaries.
  • 2.2 Event Logs: Trajectories and events can be converted into geometric representations, including player geometry at a time-step and pass geometry from involved players.
  • 2.2 Event Logs: Unlike dense trajectories, event logs are sampled only when events occur but carry semantic details such as event type and involved players.
  • The surveyed models use object trajectories, event logs, or both as their primary input.

3 Playing Area Subdivision

The survey describes spatial subdivision as a common preprocessing step for converting trajectories and events into interpretable regional summaries, while also covering player-dominance regions and low-rank representations. These approaches support analyses of spatial behaviour, shooting styles, passing, team performance, and computationally tractable dominance estimation.

  • 3.1 Intensity Matrices and Maps: Discretizing the playing area assigns trajectory or event locations to regions, enabling spatial summaries based on event frequencies or player dominance.Intensity maps visualize counts of events in regions, whereas dominance-based subdivisions represent areas controlled by particular players.
  • 3.1 Intensity Matrices and Maps: Spatial subdivisions include expert-designed regions, equal-sized rectangles, unit squares, and polar grids aligned with a goal, basket, or ball-carrier.These choices can reflect domain knowledge or accommodate abrupt changes in player behaviour across locations.
  • 3.1 Intensity Matrices and Maps: Counting visits, passes, and shots within regions produces intensity matrices and discrete spatial distributions for players and match events.The resulting counts can represent player visits, passes, or shots across the playing area.
  • 3.2 Low-rank Factor Matrices: Non-negative matrix factorization compresses shooting intensity matrices into a small number of spatial bases, modelling each player’s shooting habits as a mixture of those bases.The non-negativity constraint encourages sparse, interpretable bases corresponding to coherent court regions.
  • Dominant Regions: Reachable polygonal regions provide an approximation strategy for speeding dominant-region computation, claiming a factor of 1000 improvement with roughly a 10% accuracy drop.The method iterates over time steps and combines partial dominant regions constructed from each player’s reachable regions.
  • Dominant Regions: Dominant-region methods estimate where players can arrive before others, with applications including team-area analysis, weighted contribution measures, and pass-reception evaluation.The survey reports correlations between dominant-region structure and offensive or defensive performance, while weighted regions were proposed to better model player contribution.

4 Network tools for team performance analysis

Network analysis models player interactions to study team playing style and individual importance. The survey focuses on passing and transition networks, which encode sequences of passes and outcomes for network-based performance analysis.

  • Player interactions can reveal a team’s playing style and help assess individual players’ importance to the team.
  • Passing and transition networks are the two dominant network types in the research literature on team sports.
  • Passing networks represent players as vertices and passes between them as directed, weighted edges.
  • Researchers compute network measures to quantify passing performance and other properties of team interaction.

4.1 Centrality

Centrality measures are used in team-sports network analysis to identify key players and estimate interactivity among teammates. The section introduces centrality, prestige, and passing-network examples as tools for interpreting player roles.

  • Passing-network centrality is applied to player connections, while transition-network analysis can incorporate possession outcomes.
  • Centrality measures aim to identify key players or estimate interactivity between team members.
  • In directed passing networks, out-degree is usually called centrality, while in-degree is usually called player prestige.
  • Degree centrality counts the edges incident to a vertex and distinguishes incoming from outgoing connections in directed networks.

Degree centrality

Degree-based network measures quantify player connectivity and the concentration of interactions in team play. Applications include basketball transition graphs and football analyses linking interaction structure with team performance.

  • Fewell et al. computed centrality on basketball transition graphs containing player positions, possession origins, and possession outcomes.
  • Freeman centralization compares the most central node with all other nodes using normalized differences in degree centrality.
  • High interaction centralization was shown to decrease team performance in Grund’s Premier League experiments.
  • Central midfielders and central defenders generally show higher degree centrality, whereas goalkeepers and forwards generally show the lowest.
  • Betweenness centrality counts how often a node lies on shortest paths between other nodes.

Betweenness Centrality

Betweenness, flow, closeness, eigenvector centrality, and PageRank interpret different aspects of ball movement and player influence in passing or transition networks. These measures connect network position with accessibility, possession likelihood, and dependence on particular players.

  • Betweenness Centrality: Betweenness centrality has been interpreted as measuring how ball flow depends on a player and the impact of that player’s removal or isolation.
  • Flow Centrality: Flow centrality measures the proportion of flow between two vertices that occurs on paths containing a given vertex.
  • Flow Centrality: Duch et al. applied flow centrality to transition networks using pass fractions and shooting accuracy to study paths leading to shots.
  • Closeness Centrality: Closeness centrality was interpreted as how easily the ball can reach a player, with higher scores indicating stronger team connectivity.
  • Eigenvector Centrality and PageRank: PageRank estimates possession likelihood after a fixed number of passes while accounting for teammates’ scores.
  • Eigenvector Centrality and PageRank: World Cup data showed more even PageRank distributions for the Netherlands and Uruguay than for Spain and Germany.

4.2 Clustering Coefficients

Clustering coefficients are used to represent cooperation among players, but their connection to team performance remains uncertain. The survey identifies systematic evaluation of these measures as an open research need.

  • Higher player clustering coefficients are interpreted as indicating greater cooperation with teammates.
  • Cotta et al. associated Spain’s high clustering coefficient with its elaborate playing style and the number of passes made.
  • The relationship between clustering coefficients and team performance is unclear, with one study reporting no reasonable results.
  • A large-scale systematic comparison of centrality and clustering measures against predefined criteria remains a useful research direction.

4.3 Density and Heterogeneity

Passing-network density and heterogeneity are proposed as measures related to collaboration and team performance. Observations that density falls while heterogeneity rises during second halves motivate further scientific testing of the density-performance hypothesis.

  • The density-performance hypothesis proposes that stronger collaboration, reflected in more passes, makes a team stronger.
  • Passing-network density is calculated from the number of edges relative to the total number of possible edges.
  • High passing heterogeneity indicates that a team coalesces into sub-communities with lower cooperation between players.
  • Density usually decreased in the second half while passing heterogeneity increased.
  • Whether the density-performance hypothesis can be tested scientifically remains an open question.

4.4 Entropy, Topological Depth, Price-of-Anarchy and Power Law Distributions

The survey describes entropy and network-structure analyses that represent uncertainty, strategic trade-offs, and the organization of passing interactions. These approaches include the possibility that locally preferred decisions or highly used players may not maximize overall team outcomes.

  • Entropy: Team entropy estimates uncertainty in ball transitions from aggregated player entropies, emphasizing the number of options available to an opposing team.
  • Price-of-Anarchy: The Price of Anarchy frames a possible difference between the best network outcome and the community optimum, so the highest-percentage shot need not always be selected.
  • Topological Depth and Price-of-Anarchy: Low flow centrality for basketball’s most-used position suggests that controlling the ball more often may negatively affect key-player contribution.
  • Price-of-Anarchy: Removing a key player may improve team performance in a passing network, a phenomenon described as Braess’ paradox.

5 Data Mining

Data-mining approaches use spatio-temporal representations to label events, predict possession, identify formations and plays, and segment matches into phases. The surveyed studies report promising task-specific results, while also highlighting open questions such as measuring match intensity.

  • Spatio-temporal representations can serve as inputs to more complex algorithmic and probabilistic analyses of team sports.
  • Automated event labelling targets qualitative attributes such as shot riskiness or pass quality that are otherwise obtained manually.
  • Labelling Events: 85.8 % accuracy was achieved when classifying football passes as good, OK or bad from spatial match-state features.
  • Predicting Future Event Types and Locations: An aHCRF predicted which football player would possess the ball after 2 s with 99.25 % accuracy.
  • Identifying Formations: Role assignment supported phase segmentation, while role-swaps preceding three-point shots affected the probability that the shooter was open.
  • Identifying Formations: Formation clustering produced six formations and achieved 75.33 % accuracy against expert-assigned formation labels.
  • Identifying Formations: Teams were observed to defend more deeply when playing away from home.
  • Identifying Plays and Tactical Group Movement: Models and rules were developed to identify passing tactics and offensive plays, including five predefined American-football plays and frequent football interaction sequences.

6 Performance Metrics

Performance metrics increasingly incorporate spatial context to evaluate offensive and defensive play, especially in basketball, while football remains comparatively underdeveloped. Surveyed approaches model shot quality, possession value, defensive impact, and rebounding from player and event locations.

  • 6.1 Offensive Performance: Spatial factors such as shot location and defender proximity expose limitations in conventional basketball shooting metrics.Effective field goal percentage confounds shooter efficiency with shot difficulty.
  • 6.1 Offensive Performance: Expected possession value estimates the expected points from a possession using macro-events, player movement, and a Markov-chain model.Non-negative matrix factorization provides a compact spatial representation within the transition framework.
  • 6.1 Offensive Performance: Expected Goal Value uses shot location, defensive proximity, and defensive formation to estimate football scoring probability.Its analyses found expected goals better predicted outcomes when winners produced fewer shots, indicating fewer but better-quality chances.
  • 6.2 Defensive Performance: Basketball defensive metrics use spatial shooting splits and defender assignments to assess how defenses affect shot frequency and efficiency.These approaches distinguish close-range, mid-range, and 3-point-range outcomes and model man-to-man coverage across court regions.
  • 6.2 Defensive Performance: Football defensive analysis remains less developed because scoring chances are less frequent, leaving spatially informed football metrics as an open research question.The survey notes that comparable basketball-style defensive analyses had not been attempted for football.

7 Visualisation

Visualization systems help analysts explore real-time events, football phases, and evolving game situations, but the field still lacks large user studies linking expert needs to understandable analytical tools.

  • 7 Visualisation: Football phase exploration combines timelines, small multiples, and linked action-specific views to examine sequences bounded by changes in possession.Selected phases can include passing networks, timelines, and detailed sidebars for actions such as long balls or corners.
  • 7 Visualisation: Interactive football pattern systems couple visualizations such as parallel coordinates and scalable bar charts with data-mining classifiers.They show feature rankings over time and changes in game-play situations to support interpretation of complex events.
  • 7 Visualisation: Large user studies are needed to identify the analytical questions experts need supported and the visual tools they can understand.This is presented as a crucial gap in team-sports visual analytics.

8 Conclusion

The growth of tracking systems has produced abundant trajectory data and diverse analytical research, but the field lacks consensus on key questions and techniques. This survey organizes those efforts into a framework and offers a concise introduction to the area.

  • 8 Conclusion: Tracking systems have generated large volumes of player and ball trajectory data, stimulating research across diverse communities and techniques.The surveyed communities include fields such as machine learning, network science, computer vision, statistics, and sports science.
  • 8 Conclusion: The survey categorizes recent spatio-temporal team-sports research within a structured framework for research questions and techniques.It is intended to provide a concise introduction for researchers new to the field.
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