Hot hands and equilibrium

Abstract

Past literature suggests that success rates in professional basketball are independent of past performance and this has been interpreted as evidence that the commonly shared belief in Hot Hands (HH) is a cognitive illusion. This is often cited as evidence of biased decision making, even when financial stakes are high. We argue that this interpretation ignores changes in both teams’ behaviour after the detection of an HH player. We derive testable hypotheses that differentiate between HH as a real phenomenon and a cognitive illusion. Analysing an entire NBA season, our results are consistent with HH being a real phenomenon.

Keywords:

• hot hands
• competitive response
• rationality
• equilibrium

JEL Classification::

• D00

Acknowledgements

The authors thank Jacob Boudoukh, Christine Brown, Bruce Grundy, seminar participants at IDC, Tel Aviv University, The University of Melbourne, the University of New South Wales, the Wharton School and participants in the EFA meetings in Zurich, the Australian Finance and Banking meetings in Sydney, and the AFFI in Bordeaux for helpful suggestions and comments. We also thank Gilad Katz and Gilad Shoor for their excellent research assistance.

Notes

¹ To date, GVT paper has been cited in more than 300 papers in various academic fields, including psychology, medicine, statistics and sport. Economics and finance papers that quote GVT include: Barber and Odean (2001), Barberis and Thaler (2002), Bloomfield and Hales (2002), Durham et al. (2005), Hirshleifer (2001), Li (2005), Odean (1998), Rabin (2002) and Romer (2006).

² Various researchers argue that deviations from rationality do not necessary lead to suboptimal decision making (Kyle and Wang, 1997; Bernardo and Welch, 2001).

³ The intuition behind this test is that if HH is a cognitive illusion, then both the offensive and defensive teams err in their strategies. The defending team allocates too much defensive effort to the player erroneously perceived to be HH. The offensive team errs in relying too heavily on the shooting ability of the players perceived to be HH. However, if HH is real, then the improved shooting ability of the HH player should lead to a higher Field Goal Percentage (FG%) for the team.

⁴ See Bar-Eli et al. (2006) for a review of the HH literature.

⁵ Note that unlike field goals and free throws (FT), GVT (and other research) has not documented a widespread belief in HH for practice shots. Furthermore, the results of these tests are mixed. In normal practice shots, GVT find no evidence of strictness. However, once players were asked to call their shots they were able to do so (see Wardrop (1999) for interpretation of this test).

⁶ Several studies examine the existence of HH in other sports and report mixed results. The evidence suggests that HH does not exist or is minimal in baseball (Albright, 1993) and tennis (Klaassen and Magnus, 2001). Evidence supportive of HH is reported in billiards (Adams, 1995), bowling (Dorsey-Palmateer and Smith, 2004), and horseshoe pitching (Smith, 2003).

⁷ Additionally, we required that the Next Shot attempted in the same half as the Identify Shot that the HH player is not replaced until the Next Shot and that the Next Shot will be taken within 180 s of the Identify Shot. These restrictions cause the number of Next Shots to be slightly lower than the number of Identify Shots (4993 to 5009, respectively).

⁸ Consistent with this argument we find no relationship between the ranking of the player in his team (either by salary or by field goal attempted, FGA) and his FG%.

⁹ To be consistent with previous literature, we do not require in this test that the shots of the identified player occur in the same half. As a result, the number of cases in which a player succeeds or misses three consecutive times is much greater than in Table 3.

¹⁰ Additionally, if the foul occurs in the act of shooting and the shot is successful, the shooting player is then awarded an additional FT. Furthermore, each player is limited to six personal fouls per game before he is ejected from the game.

¹¹ Changing the definition of a close game to a 15-point difference has no significant effect on our results.

¹² Table is available upon request.

¹³ For example, it may be that we documented a superstar effect. In periods of the game when the superstar is playing (not playing) the FG% of the team are relatively high (low), leading to both a higher (lower) probability of HH detection and higher (lower) FG% in periods (including Next Shot) when the superstar is playing.

¹⁴ Note that if the HH player attempts the shot, then it must be successful, as it is part of the three consecutive shots by which the player is identified as ‘hot’.

¹⁵ The coefficient of the HH players remains significant when HH in FT is defined by two or three successful consecutive FT.

¹⁶ Similarly, we find no ‘spillover’ effect of being HH in FT on the success rate in regular shots.