We investigate the hot hand phenomenon using data on 110,513 free throws taken in the National Basketball Association. As free throws occur at unevenly spaced time points within a game, we consider a state-space model formulated in continuous time to investigate serial dependence in players’ success probabilities. In particular, the underlying state process can be interpreted as a player’s (latent) varying form and is modelled using the Ornstein-Uhlenbeck process. Our results support the existence of the hot hand, but the magnitude of the estimated effect is rather small as the underlying success probabilities are elevated by only a few percentage points.

我们使用美国国家篮球协会的 110,513 次罚球数据来调查热手现象。由于罚球发生在比赛中不均匀间隔的时间点，我们考虑在连续时间内制定的状态空间模型来研究球员成功概率的连续依赖性。特别是，潜在的状态过程可以解释为玩家的（潜在）变化形式，并使用 Ornstein-Uhlenbeck 过程建模。我们的结果支持热手的存在，但估计影响的幅度相当小，因为潜在的成功概率仅提高了几个百分点。