Academic journal article International Journal of Sport Finance

The Hot Hand vs. Cold Hand on the PGA Tour

Academic journal article International Journal of Sport Finance

The Hot Hand vs. Cold Hand on the PGA Tour

Article excerpt

(ProQuest: ... denotes formulae omitted.)

Introduction

There has been much research devoted to the "hot hand" in sports. The hot hand is a period of elevated performance for an individual player. The most studied sport for the hot hand-and the one that has had the greatest recent transformation in the results-has been basketball. Starting with Gilovich et al. (1985), a series of articles over 25 years had found no evidence for the hot hand in basketball and claimed that the hot hand was a myth. That is, when players or fans believe a player has the hot hand, the argument goes, they are just misperceiving natural statistical variation as having patterns.

In the last five years, however, new research has cast doubt on this conclusion. Arkes (2010) developed a player-fixed-effects model that allowed all players to be included in one model (in contrast with prior studies that examined one player at a time), thus allowing for a much larger sample. Using free throw data, he found that making the first of two free throws leads to a 3-percentage-point increase in the probability of making the second free throw. This is not a large effect, but it was the first evidence for the hot hand in basketball. Recent studies using similar methods also found evidence for hot-hand effects in basketball (Bocskocsky et al., 2014; Miller & Sanjuro, 2014). Further studies by Stone (2012) and Arkes (2013) demonstrated that the methods used in prior studies-which includes, by extrapolation, the more recent articles with evidence for the hot hand-were subject to a downward bias, largely from measurement error. The prior studies, they found, would have had a low probability of detecting the hot hand (i.e., statistical significance) even if there were a strong and relatively frequent hot hand effect.

The main problem with the studies, Stone (2012) argues, is equivalent to measurement error. That is, the typical measure for whether a player is hot is whether the player hit the prior shot. But, the hot hand means that a player is shooting at an elevated level, not hitting every shot. Thus, due to natural variation, a player could be hot and miss the shot, and a person could be in a normal state and make the shot. Measurement error would then bias the estimated hot-hand effect towards zero. This problem with the basketball hot-hand studies would apply to models on the hot hand for any sport, given the large role of randomness in sports outcomes and the inevitable measurement error. And, there does not appear to be any solution to this inherent bias other than increase the sample size to generate enough power to detect a hot-hand effect, if one indeed were to exist.

Further problems in the hot-hand studies were recently discovered by Miller and Sanjurjo (2015). They argued that there is selection bias in the studies in that the common practice of comparing performance after streaks of made shots to performance after streaks of missed shots takes out of the sample part of the hot-hand period. They then corrected for the selection bias with data from the initial hot-hand study (Gilovich, 1985) and find a fairly large and significant hot-hand effect.

One other problem with some of the literature on the basketball hot hand is the possibility of endogenous responses. That is, if a player is hot, the defense may adjust by various methods, such as shifting the best defender on the hot player or double-teaming the player. This would make it more difficult to detect the hot hand.

Addressing the issue of endogenous responses, some studies have studied the hot hand in sports that have no defense, such as horseshoes (Smith, 2003) and bowling (Dorsey-Palmateer & Smith, 2004), although these studies had weak power. Baseball is a sport with some defense, but limited endogenous responses of just pitching around a hitter. Most of the research has found no evidence for a hot hand in baseball (Albert & Bennett, 2003; Albright, 1993; Vergin, 2000); but, a recent study with two million observations found strong evidence for the hot hand using a variety of offensive measures (Zwiebell & Green, 2014). …

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