Maximising the Set-Piece Return: Optimising Football Corner Tactics with Graph Reinforcement Learning

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/.

Curling is often referred to as "Chess on Ice", owing to the tactical complexity of its decision-making process. Yet unlike chess, curling remains largely underexplored from a machine learning perspective, with prior work confined mainly to statistical approaches. We propose a reinforcement learning framework capable of quantitatively evaluating and comparing tactical options in curling. The game poses several modeling challenges: continuous state and action spaces, stochastic action outcomes reflecting player skill variability, and state transitions that are highly sensitive to small perturbations in the executed action. To address them, we employ the Deep Deterministic Policy Gradient actor-critic algorithm, adapted to exploit the finite-horizon structure of the game. Our experiments show that effective curling strategies can be acquired in a fully self-supervised manner, without any human-annotated data: on a reduced four-rock variant, the learned agent matches a hand-crafted expert heuristic in a regime where that heuristic is close to optimal, a parity we quantify against the intrinsic hammer advantage of the variant. Beyond the resulting policy, the learned critic provides a dense value estimate over the entire continuous action space, enabling the quantitative comparison of tactical alternatives for applications such as post-game performance analysis and decision support during athlete preparation.

Vision-language models (VLMs) can describe a scene, but can they act well within one? We study whether VLMs can make sound strategic decisions, using soccer as an objective testbed with quantifiably-valued actions. We introduce SportD, a dataset and evaluation consisting of 1421 decision scenarios across professional men's and women's soccer games, where a VLM must decide what action to take next. Models on average select the optimal action around 27% of the time, less often than the professional players, and capture markedly less of the value at stake. Furthermore, they exhibit a clear preference for safer actions, favoring lower-variance, lower-value choices that also make less physical progress toward goal. Frontier VLMs are better at estimating whether an action will succeed, placing the highest-success-probability action among their top choices in 72-85% of cases. Yet VLMs systematically conflate likelihood with value, assigning higher value to actions that are more likely to succeed ($ρ=+0.30$ to $+0.52$), despite no such relationship in the ground truth ($ρ=-0.08$). Modifying the deliberation instructions to encourage risk-taking brings the frontier models closer to the players' skill levels. SportD opens a new direction for rigorously evaluating physical strategic decision-making in VLMs, showing that careful decomposition of their choices can reveal the mechanisms underlying systematic biases such as risk aversion.