TacSIm: A Dataset and Benchmark for Football Tactical Style Imitation

Modeling open-play soccer tactics is a formidable challenge due to the stochastic, multi-agent nature of the game. Existing computational approaches typically produce single, deterministic trajectory forecasts or focus on highly structured set-pieces, fundamentally failing to capture the inherent variance and branching possibilities of real-world match evolution. Here, we introduce GenTac, a diffusion-based generative framework that conceptualizes soccer tactics as a stochastic process over continuous multi-player trajectories and discrete semantic events. By learning the underlying distribution of player movements from historical tracking data, GenTac samples diverse, plausible, long-horizon future trajectories. The framework supports rich contextual conditioning, including opponent behavior, specific team or league playing styles, and strategic objectives, while grounding continuous spatial dynamics into a 15-class tactical event space. Extensive evaluations on our proposed benchmark, TacBench, demonstrate four key capabilities: (1) GenTac achieves high geometric accuracy while strictly preserving the collective structural consistency of the team; (2) it accurately simulates stylistic nuances, distinguishing between specific teams (e.g., Auckland FC) and leagues (e.g., A-League versus German leagues); (3) it enables controllable counterfactual simulations, demonstrably altering spatial control and expected threat metrics based on offensive or defensive guidance; and (4) it reliably anticipates future tactical outcomes directly from generated rollouts. Finally, we demonstrate that GenTac can be successfully trained to generalize to other dynamic team sports, including basketball, American football, and ice hockey.

Success in association football relies on both individual skill and coordinated tactics. While recent advancements in spatio-temporal data and deep learning have enabled predictive analyses like trajectory forecasting, the development of tactical design remains limited. Bridging this gap is essential, as prediction reveals what is likely to occur, whereas tactic generation determines what should occur to achieve strategic objectives. In this work, we present TacticGen, a generative model for adaptable and scalable tactic generation. TacticGen formulates tactics as sequences of multi-agent movements and interactions conditioned on the game context. It employs a multi-agent diffusion transformer with agent-wise self-attention and context-aware cross-attention to capture cooperative and competitive dynamics among players and the ball. Trained with over 3.3 million events and 100 million tracking frames from top-tier leagues, TacticGen achieves state-of-the-art precision in predicting player trajectories. Building on it, TacticGen enables adaptable tactic generation tailored to diverse inference-time objectives through classifier guidance mechanism, specified via rules, natural language, or neural models. Its modeling performance is also inherently scalable. A case study with football experts confirms that TacticGen generates realistic, strategically valuable tactics, demonstrating its practical utility for tactical planning in professional football. The project page is available at: https://shengxu.net/TacticGen/.

Humans imitate at the level of intent: given a demonstration, we infer its goal and carry it out with whatever tools, objects, and layouts are at hand. Current robot policies instead learn observation-to-action mappings from visual inputs and language instructions, without explicitly inferring the demonstrated task. Learning from human video thus remains largely trajectory-level: models can replay motions in near-identical scenes, but still struggle to imitate what the demonstrator intends rather than merely what they do. We introduce The Imitator Game, a four-level benchmark (L0-L3) that progressively widens the gap between the human demonstration and the robot's own scene, isolating where trajectory replay ceases to suffice and task understanding becomes necessary. We pair it with IG-10K, the largest environment-aligned paired human-robot dataset to date and the only one instantiated across all four levels in both real and simulated settings (20,000+ paired episodes, 50+ tasks, 6 domains), and Imitator Arena, an open platform for blind A/B human evaluation. Across nine state-of-the-art models, performance is stable from L0 to L2 but collapses at L3, identifying functional substitution - achieving the same intent through a different object affordance - as the decisive barrier to intent-level imitation. Human-video-conditioned models outperform caption-conditioned ones, yet every model falls below 13% zero-shot success on unseen tasks; fine-tuning IG-10K-pretrained models with only $10$ paired human-robot demonstrations yields large gains that grow with pretraining scale. The project website and access to Imitator Arena are available at https://imitator-game.github.io.