篮球中热手效应的连续时间状态空间建模

Modelling basketball players' performance and interactions between teammates with a regime switching approach

Basketball players' performance measurement is of critical importance for a broad spectrum of decisions related to training and game strategy. Despite this recognized central role, the main part of the studies on this topic focus on performance level measurement, neglecting other important characteristics, such as variability. In this paper, shooting performance variability is modeled with a Markov Switching dynamic, assuming the existence of two alternating performance regimes. Then, the relationships between each player's variability and the lineup composition is modeled as an ARIMA process …

热手现象能否建模？一种贝叶斯隐马尔可夫方法

Can the hot hand phenomenon be modelled? A Bayesian hidden Markov approach

本文提出一种贝叶斯隐马尔可夫模型，用于分析篮球比赛中热手现象，通过考虑隐藏状态和投篮距离建模成功概率，以量化球队连续命中势头。

The Hot Hand and Its Effect on the NBA

This paper aims to revisit and expand upon previous work on the "hot hand" phenomenon in basketball, specifically in the NBA. Using larger, modern data sets, we test streakiness of shooting patterns and the presence of hot hand behavior in free throw shooting, while going further by examining league-wide hot hand trends and the changes in individual player behavior. Additionally, we perform simulations in order to assess their power. While we find no evidence of the hot hand in game-play and only weak evidence in free throw trials, we find that some NBA players exhibit behavioral changes based…

Uncertainty in the Hot Hand Fallacy: Detecting Streaky Alternatives to Random Bernoulli Sequences

We study a class of permutation tests of the randomness of a collection of Bernoulli sequences and their application to analyses of the human tendency to perceive streaks of consecutive successes as overly representative of positive dependence - the hot hand fallacy. In particular, we study permutation tests of the null hypothesis of randomness (i.e., that trials are i.i.d.) based on test statistics that compare the proportion of successes that directly follow k consecutive successes with either the overall proportion of successes or the proportion of successes that directly follow k consecuti…

A regularized hidden Markov model for analyzing the 'hot shoe' in football

Although academic research on the 'hot hand' effect (in particular, in sports, especially in basketball) has been going on for more than 30 years, it still remains a central question in different areas of research whether such an effect exists. In this contribution, we investigate the potential occurrence of a 'hot shoe' effect for the performance of penalty takers in football based on data from the German Bundesliga. For this purpose, we consider hidden Markov models (HMMs) to model the (latent) forms of players. To further account for individual heterogeneity of the penalty taker as well as …

Heating Up in NBA Free Throw Shooting

I demonstrate that repetition heats players up, while interruption cools players down in NBA free throw shooting. My analysis also suggests that fatigue and stress come into play. If, as seems likely, all four of these effects have comparable impact on field goal shooting, they would justify strategic choices throughout a basketball game that take into account the hot hand. More generally my analysis motivates approaching causal investigation of the variation in the quality of all types of human performance by seeking to operationalize and measure these effects. Viewing the hot hand as a dynam…