Measurement Error and the Hot Hand

A Cold Shower for the Hot Hand Fallacy

“…The difference between these two conditional hit rates provides a conservative estimate of the hot hand effect, in that the true magnitude of the effect, should it exist, will be larger than the estimated effect because not every shot taken immediately following three or more hits in a row occurs while a player is in a hot state (see Appendix B.2; also see Arkes 2013, Green and Zwiebel 2013, and Stone 2012 for a discussion in relation to previous work). 50 The issue of power limitations in GVT's original study has been pointed out by other authors (Albert 1993;Albert and Williamson 2001;Dorsey-Palmateer and Smith 2004;Hooke 1989;Korb and Stillwell 2003;Miyoshi 2000;Stern and Morris 1993;Stone 2012;Swartz 1990;Wardrop 1999), with only one attempt to address the issue (see Footnote 14).…”

“…For pooling across players we average across these player averages, permuting shots within all strata defined by each player and session. As an example, Stone (2012) has demonstrated that a player can simultaneously have a large serial correlation in shooting ability and a sample serial correlation that is, asymptotically, orders of magnitudes smaller (e.g. .4 and .06, respectively).…”

A Cold Shower for the Hot Hand Fallacy: Robust Evidence that Belief in the Hot Hand is Justified

“…See Appendix B for a power analysis of GVT's statistics vs. ours. The issue of power limitations in GVT's original study has been pointed out by other authors(Albert 1993;Albert and Williamson 2001;Dorsey-Palmateer and Smith 2004;Hooke 1989;Korb and Stillwell 2003;Miyoshi 2000;Stern and Morris 1993;Stone 2012;Swartz 1990; Wardrop 1999), withWardrop (1999) being the only attempt to address it (see Footnote 11) 9 The bias discovered in Miller and Sanjurjo (2018) is a separate issue that leads to the underestimation of performance when a shooter is on a streak of makes and the overestimation of performance when a shooter is on a streak of misses.…”

“…We can pool all of a player's shooting data, compute the hit streak statistic for each session, standardize it by subtracting the mean and dividing by the standard deviation for that session, then calculate the average of the standardized statistics across sessions, and then generate the distribution of this average by permuting shots within session strata, to assure that the results are not being driven by good day/bad day effects. For pooling across players we average across these player averages, permuting shots within all strata defined by each player and session.43 As an example,Stone [2012] has demonstrated that a player can simultaneously have a large serial correlation in shooting ability and a sample serial correlation that is, asymptotically, orders of magnitudes smaller (e.g. .4 and .06, respectively).…”

Do (Australian) jockeys have hot hands?

“…3 This definition implicitly assumes that players are always in a (latent) 'hot' state which is triggered into action by a 'success'. An alternative view is that players are only sometimes in the 'hot' state and that a success in a 'cold' state would have no effect on the future probability of success (Stone 2012, Arkes 2013. Arkes (2013) notes that tests may fail to detect hot hands even where they are present because the sample size is low and hot hands events are infrequent.…”