用路径签名建模足球进攻，更准且更快。
The path to a goal: Understanding soccer possessions via path signatures
- 用数学上严谨的路径签名捕捉传球序列的时空结构
- 在多个指标上优于Transformer模型，计算成本更低
- 新评估指标结合动作类型和位置，更可靠
我们提出一种新框架，通过路径签名编码足球进攻中的复杂时空结构来预测下一步动作。与现有方法不同，该框架不依赖固定历史窗口或人工设计特征，而是编码整个近期进攻过程，避免引入无关或误导性信息。路径签名天然捕捉事件的顺序与交互关系，为长度可变、采样不规则的时间序列提供数学基础的特征表示，无需手动特征工程。所提方法在多个损失指标上超越基于Transformer的基准模型，且显著降低计算开销。基于此，我们构建了一种新的进攻评估指标，融合了动作类型概率和位置信息，该指标在领域内对比中表现出更高可靠性。最后，我们通过2017/18英超赛季的详细分析验证了该方法的有效性，并讨论了未来扩展方向。
原文摘要 · Abstract (English)
We present a novel framework for predicting next actions in soccer possessions by leveraging path signatures to encode their complex spatio-temporal structure. Unlike existing approaches, we do not rely on fixed historical windows and handcrafted features, but rather encode the entire recent possession, thereby avoiding the inclusion of potentially irrelevant or misleading historical information. Path signatures naturally capture the order and interaction of events, providing a mathematically grounded feature encoding for variable-length time series of irregular sampling frequencies without the necessity for manual feature engineering. Our proposed approach outperforms a transformer-based benchmark across various loss metrics and considerably reduces computational cost. Building on these results, we introduce a new possession evaluation metric based on well-established frameworks in soccer analytics, incorporating both predicted action type probabilities and action location. Our metric shows greater reliability than existing metrics in domain-specific comparisons. Finally, we validate our approach through a detailed analysis of the 2017/18 Premier League season and discuss further applications and future extensions.
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