Sports data analytics is a relevant topic in applied statistics that has been growing in importance in recent years. In basketball, a player or team has a hot hand when their performance during a match is better than expected or they are on a streak of making consecutive shots. This phenomenon has generated a great deal of controversy with detractors claiming its non-existence while other authors indicate its evidence. In this work, we present a Bayesian longitudinal hidden Markov model that analyses the hot hand phenomenon in consecutive basketball shots, each of which can be either missed or made. Two possible states (cold or hot) are assumed in the hidden Markov chains of events, and the probability of success for each throw is modelled by considering both the corresponding hidden state and the distance to the basket. This model is applied to a real data set, the Miami Heat team in the season 2005-2006 of the USA National Basketball Association. We show that this model is a powerful tool for assessing the overall performance of a team during a match or a season, and, in particular, for quantifying the magnitude of the team streaks in probabilistic terms.

翻译：体育数据分析是应用统计学中一个与日俱增的重要相关课题。在篮球运动中，当球员或球队在比赛中的表现优于预期，或连续命中投篮时，便称之为“热手”现象。这一现象引发了极大争议：质疑者认为其不存在，而其他学者则指出其证据。本研究提出了一种贝叶斯纵向隐马尔可夫模型，用于分析连续篮球投篮（每次投篮可能命中或未命中）中的“热手”现象。该模型假设隐马尔可夫事件链中存在两种可能状态（冷或热），并通过考虑相应的隐状态和投篮距离来建模每次投篮的成功概率。我们将该模型应用于真实数据集——美国国家篮球协会（NBA）2005-2006赛季的迈阿密热火队。研究表明，该模型是评估球队在单场比赛或整个赛季中整体表现的有力工具，尤其能够以概率形式量化球队连续得分势头的大小。