Abstract Continuous-time assessments of game outcomes in sports have become increasingly common in the last decade. In American football, only discrete-time estimates of play value were possible, since the most advanced public football datasets were recorded at the play-by-play level. While measures such as expected points and win probability are useful for evaluating football plays and game situations, there has been no research into how these values change throughout the course of a play. In this work, we make two main contributions: First, we introduce a general framework for continuous-time within-play valuation in the National Football League using player-tracking data. Our modular framework incorporates several modular sub-models, to easily incorporate recent work involving player tracking data in football. Second, we use a long short-term memory recurrent neural network to construct a ball-carrier model to estimate how many yards the ball-carrier is expected to gain from their current position, conditional on the locations and trajectories of the ball-carrier, their teammates and opponents. Additionally, we demonstrate an extension with conditional density estimation so that the expectation of any measure of play value can be calculated in continuous-time, which was never before possible at such a granular level.

中文翻译：

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深入：具有跟踪数据的美式足球比赛结果的连续时间场内价值评估模型

摘要在过去的十年中，对运动比赛结果进行连续时间评估变得越来越普遍。在美式足球中，仅可能对比赛价值进行离散时间估计，因为最先进的公共足球数据集是逐项进行记录的。尽管诸如预期点和获胜概率之类的度量对于评估足球比赛和比赛情况很有用，但尚未研究这些价值在整个比赛过程中如何变化。在这项工作中，我们做出了两个主要贡献：首先，我们介绍了使用球员跟踪数据在国家足球联赛中进行连续时间内比赛进行评估的通用框架。我们的模块化框架整合了多个模块化子模型，可以轻松地整合涉及足球运动员追踪数据的最新工作。第二，我们使用一个长期的短期记忆递归神经网络来构建一个运球车模型，以估计运球车从当前位置获得的码数，条件是运球车的位置和轨迹及其队友和对手。此外，我们演示了使用条件密度估计的扩展，以便可以连续时间计算对任何游戏值度量的期望，而在这种粒度级别上这是前所未有的。