用贝叶斯网络解析足球经理游戏的隐藏机制，首次公开完整模型。
Decoding the mechanisms of the Hattrick football manager game using Bayesian network structure learning
- 结合专家知识与数据，用结构学习构建贝叶斯网络模拟游戏机制。
- 模型性能媲美社区顶尖预测工具，且可解释性更强。
- 适合对游戏机制建模、因果推理或行为分析的研究者参考。
Hattrick 是一款自1997年在瑞典启动的免费网页式概率性足球经理游戏，拥有超过20万用户，在国家和国际层面竞争冠军。其缓慢的游戏节奏培育了忠诚的长期活跃社区。游戏引擎机制部分隐藏，多年来玩家通过规则、统计和机器学习方法逐步破解，但这些方法尚未在科学文献中被正式评估。本研究首次采用结构学习技术与贝叶斯网络，整合专家知识与真实数据，构建可模拟和解释游戏机制的模型。我们评估了结构学习算法相对于基于知识的结构的有效性，并公开发布了一个完全指定的贝叶斯网络模型，其性能与社区顶尖模型相当。进一步展示了分析不仅限于预测，还提供特征间依赖关系的可视化，并可用于游戏内决策优化。为支持未来研究，所有数据、图结构和模型均在线公开。
原文摘要 · Abstract (English)
Hattrick is a free web-based probabilistic football manager game with over 200,000 users competing for titles at national and international levels. Launched in Sweden in 1997 as part of an MSc project, the game's slow-paced design has fostered a loyal community, with users remaining active for decades. Hattrick's game-engine mechanics are partially hidden, and users have attempted to decode them with incremental success over the years. Rule-based, statistical and machine learning models have been developed to aid this effort and are widely used by the community, but have not been formally evaluated in the scientific literature. This study is the first to explore Hattrick using structure learning techniques and Bayesian networks, integrating expert knowledge with data to develop models that simulate and explain the game-engine. We assess the effectiveness of structure learning algorithms in relation to knowledge-based structures, and publicly share a fully specified Bayesian network model that matches the performance of top models used by the Hattrick community. We further demonstrate how analysis extends beyond prediction by providing a visual representation of dependencies between features, and using the optimal model for in-game decision-making. To support future research, we make all data, graphical structures, and models publicly available online.
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