Multi-competitor races often feature complicated within-race strategies that are difficult to capture when training data on race outcome level data. Further, models which do not account for such strategic effects may suffer from confounded inferences and predictions. In this work we develop a general generative model for multi-competitor races which allows analysts to explicitly model certain strategic effects such as changing lanes or drafting and separate these impacts from competitor ability. The generative model allows one to simulate full races from any real or created starting position which opens new avenues for attributing value to within-race actions and to perform counter-factual analyses. This methodology is sufficiently general to apply to any track based multi-competitor races where both tracking data is available and competitor movement is well described by simultaneous forward and lateral movements. We apply this methodology to one-mile horse races using data provided by the New York Racing Association (NYRA) and the New York Thoroughbred Horsemen's Association (NYTHA) for the Big Data Derby 2022 Kaggle Competition. This data features granular tracking data for all horses at the frame-level (occurring at approximately 4hz). We demonstrate how this model can yield new inferences, such as the estimation of horse-specific speed profiles which vary over phases of the race, and examples of posterior predictive counterfactual simulations to answer questions of interest such as starting lane impacts on race outcomes.

翻译：多竞争者赛事常包含复杂的赛道内策略，当训练数据仅包含赛事结果层面信息时，这些策略难以被有效捕捉。此外，未考虑此类策略效应的模型可能产生混淆的推断与预测。本研究提出了一种面向多竞争者赛事的通用生成模型，使分析人员能够显式建模换道、跟跑等特定策略效应，并将其与选手能力的影响相分离。该生成模型支持从任意真实或设定的起跑位置模拟完整赛事，为评估赛道内动作价值及开展反事实分析开辟了新途径。该方法具有充分普适性，适用于任何基于赛道的多竞争者场景——既需具备跟踪数据支持，且选手运动可通过同步前进与侧向位移良好描述。我们采用纽约赛马协会（NYRA）与纽约纯血马主协会（NYTHA）为2022年大数据德比Kaggle竞赛提供的数据，将方法应用于一英里赛马赛事。该数据包含所有赛马在帧级（约4Hz采样）的精细跟踪记录。我们展示了该模型如何产生新推断，例如可随比赛阶段变化的赛马特异性速度曲线估计，以及通过后验预测反事实模拟回答起跑赛道位置对赛事结果影响等关键问题的实例。