Revisiting the Hot Hand Theory with Free Throw Data in a Multivariate Framework

Abstract

Despite the conventional wisdom among players and fans of the existence of the "hot hand" in basketball, studies have found only no evidence or weak evidence for the hot hand in game situations, although stronger evidence in controlled settings. These studies have considered both free throws and field goals. Given the heterogeneous nature of field goals and several potential sources that could cause a positive or negative correlation between consecutive shots (such as having a weak defender), free throws may provide for a more controlled setting to test for the hot hand. Almost all studies have tested for the hot hand at the individual level in univariate frameworks, and as some have pointed out, the studies may not have had enough power to detect the hot hand. In this study, I use a sample based on every free throw attempted during the 2005-06 NBA season. I used a multivariate framework with individual player fixed effects. I find that hitting the first free throw is associated with a 2-to 3-percentage-points higher probability of hitting the second free throw. Furthermore, the infrequent foul-shooters have more streakiness in their shooting than frequent foul-shooters.

Finally, Evidence for a Momentum Effect in the NBA

“…Whereas previous studies examined momentum in the NBA by just looking at whether a team is more likely to win had they won previous games, or by analyzing if winning streaks were different from what would be expected by chance, we develop a model that takes into account differences in the quality of the opponents a team had in previous games as well as the quality of the opponent for the game of the analysis. This research is similar to the advancement in the "hot hand" literature that Arkes (2010) makes in that it combines teams into one model to provide sufficient power to detect a momentum effect, if one exists. We also account for differences in the number of days of rest before the game of analysis and we consider home-court advantage.…”

“…As these authors show, the majority of studies have not found empirical evidence to support the hot hand belief. However, a recent study improved on the previous studies by incorporating all players into one fixed-effects logit model (Arkes, 2010). With the significantly greater power, Arkes found evidence supporting the existence of the "hot hand" in that making the first free throw is associated with a significantly higher probability of making the second free throw.…”

When do soccer players peak? A note

“…Bradbury (2009) also analyzes baseball but employs a random effects estimator. Other applications of fixed effects estimation in sports include Arkes (2010), who tests the hot hand theory in basketball, and Broadie and Rendleman Jr. (2013), who examine world rankings in golf. across seasons -hence commonly known as withinestimation -except using the entire data set.…”

Misses in “Hot Hand” Research

“…Gilovich et al (1985) and Tversky and Gilovich (1989) used a maximum of 884 observations for any model; Koehler and Conley (2003) used a maximum of 174 observations; and Huizinga and Weil (2009) used a maximum of 2,063 observations. This problem of sample size was addressed in a recent study by Arkes (2010), who developed a player-fixed-effects model to include all players in one model. With over 28,000 observations, he found that players were 3 percentage points more likely to make the second of two free throws had they made the first free throw.…”