Research map / Multi-agent systems and games / Human-AI and goal-conditioned
Optimising Spatial Teamwork Under Uncertainty
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Models spatial teamwork in football defence as a multi-agent MDP and combines MCTS with linear programming to pick individual or subteam actions, reducing opponent threat by about 21% over real-world play.
Problem
Optimising coordinated spatial positioning of agents to maximise team dominance over an area against adversaries under uncertainty about teammate and opponent actions, with a focus on football defence.
Approach
Defines spatial teamwork where proximity-based K-means subteams act jointly; MCTS (with a learned transition model) optimises individual and subteam actions, and a linear program selects which individuals and subteams form the team's joint action to maximise long-term defensive utility.
Key results
- Teamwork optimiser reduces threat by 20.8% versus 15.1% for the individual optimiser and 11.3% for the pair-based optimiser (Table 1).
- In high-threat situations the teamwork optimiser reduces threat by 14.1% versus 8.5% for individual optimiser.
- Subteam metrics give lower log-loss than individual metrics for predicting pass zones (0.147 vs 0.156).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use spatial subteam coordination instead of individual-only optimisation | Defensive football decision-making · Simulated play sequences | average reward: Individual Optimiser: -0.045 ± 0.001; Teamwork Optimiser: -0.042 ± 0.001; 5.7% more reduction | Helped |
| Use teamwork optimisation instead of real-world decisions | Defensive football decision-making · Simulated play sequences | average reward: Real-World: -0.053 ± 0.001; Teamwork Optimiser: -0.042 ± 0.001; 20.8% | Helped |
| Use individual optimisation instead of real-world decisions | Defensive football decision-making · Simulated play sequences | average reward: Real-World: -0.053 ± 0.001; Individual Optimiser: -0.045 ± 0.001 | Helped |
| Use pair-based optimisation instead of real-world decisions | Defensive football decision-making · Simulated play sequences | average reward: Real-World: -0.053 ± 0.001; Pair-Based Optimiser: -0.047 ± 0.001 | Helped |
| Use teamwork optimisation instead of individual-only optimisation | Defensive football decision-making · High-threat simulated play sequences (≥1% goal probability) | average reward: Individual Optimiser: -0.065 ± 0.001; Teamwork Optimiser: -0.061 ± 0.001; 14.1% vs 8.5% | Helped |
| Use teamwork optimisation instead of real-world decisions | Defensive football decision-making · High-threat simulated play sequences (≥1% goal probability) | average reward: Real-World: -0.071 ± 0.001; Teamwork Optimiser: -0.061 ± 0.001; 14.1% | Helped |
| Use subteam contribution metrics instead of individual contribution metrics | Attack-location prediction · Passes | log-loss: 0.156 ± 0.003 -> 0.147 ± 0.001 | Helped |
| Use subteam contribution metrics instead of individual contribution metrics | Attack-location prediction · Shots | log-loss: 0.0100 ± 0.0004 -> 0.0093 ± 0.0002 | Helped |
| Vary the number of subteams, using five subteams or the optimal k-means silhouette score (ablation) | Teamwork Optimiser · Real-world football scenarios | threat reduction | Helped |
Surprising findings
- Pair-based optimiser improves on real-world performance but is less effective than individual optimisation at reducing threat, suggesting spatial context matters for pairing.
- Five subteams or the silhouette-optimal k most effective, with clusters often forming pairs.
Limitations
- Evaluated only on a single 34-game dataset from one league
- Optimises average threat rather than worst-case outcomes
- Player actions are simplified to discretised directional biases
Experimental setup
Datasets: 34-game K League 1 football dataset (BePro Group Ltd)
Benchmarks: 34-game K League 1 football dataset simulations
Metrics: average reward / accumulated threat (goal concession probabi log-loss for attack zone prediction Pearson correlation with goals conceded
Baselines: Random Real-world Simulated real-world Individual optimiser Pair-Based optimiser
Builds on: Monte Carlo Tree Search UCB1 Expected Threat Beal et al. 2020 team-centred pair model Everett et al. 2023 player location prediction
Closest papers by meaning
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- Sports-Traj: A Unified Trajectory Generation Model for Multi-Agent Movement in Sports (ICLR 2025 · similarity 0.82)
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- Ad Hoc Teamwork via Offline Goal-Based Decision Transformers (ICML 2025 · similarity 0.82)
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