Choking under pressure – Evidence of the causal effect of audience size on performance

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Journal of Economic Behavior and Organization journal homepage: www.elsevier.com/locate/jebo

Choking under pressure – Evidence of the causal effect of audience size on performanceR René Böheim a, Dominik Grübl b, Mario Lackner b,c,∗ a

Department of Economics, Johannes Kepler University Linz, Austrian Institute of Economic Research, IZA Bonn, CESifo Munich (Germony) Department of Economics, Johannes Kepler University Linz (Austria) c Christian Doppler Laboratory “Aging, Health and the Labor Market” Linz (Austria) b

a r t i c l e

i n f o

Article history: Received 18 October 2018 Revised 30 September 2019 Accepted 7 October 2019 Available online xxx JEL classification: D03 J24 M54 Keywords: Performance under pressure Choking Paradoxical performance effects on incentives Social pressure

a b s t r a c t We analyze performance under pressure and estimate the causal effect of audience size on the success of free throws in top-level professional basketball. We use data from the National Basketball Association (NBA) for the seasons 2007/08 through 2015/16. We exploit the exogenous variation in weather conditions on game day to establish a causal link between attendance size and performance. Our results confirm a sizeable and strong negative effect of the number of spectators on performance. Home teams in (non-critical) situations at the beginning of games perform worse when the audience is larger. This result is consistent with the theory of a home choke rather than a home field advantage. Our results have potentially large implications for general questions of workplace design and help to further understand how the social environment affects performance. We demonstrate that positive feedback from a friendly audience does affect performance negatively. © 2019 Elsevier B.V. All rights reserved.

1. Introduction Theory and empirical evidence indicate that greater incentives increase effort and thus improve output Lazear and Rosen, 1981; Ehrenberg and Bognanno, 1990; Dechenaux et al., 2015. The greater the potential reward, the larger the expected improvement in performance and productivity. However, when pressure to perform increases, performance is often found to decrease (Dohmen, 2008b; Harb-Wu and Krumer, 2017). This unexpected negative consequence has been termed “choking under pressure” (Hill et al., 2010; Baumeister, 1984). The literature identifies multiple sources of pressure to perform that deteriorate performance. For example, pressure is found to arise from the disadvantage of being the second mover in a particular contest (e.g., Jose and PalaciosHuerta, 2010 or Kocher et al., 2012). Another source of pressure is identified in intermediate standings in contests (Dohmen, 2008a; Cohen-Zada et al., 2017) or the imminent importance of a certain situation (González-Díaz et al., 2012). Increased monetary incentives may create pressure to perform (Hickman and Metz, 2015). In public events, pressure to perform could R The authors are grateful for funding by the Austrian National Bank, project number 16242. Thanks to Alex Krumer, Bernd Frick, Martina Zweimüller, Rudolf Winter-Ebmer, Jochen Güntner, Alexander Ahammer, participants at the 2018 SESM in Vienna, as well as two anonymous referees for highly valuable comments. ∗ Corresponding author. E-mail address: [email protected] (M. Lackner).

https://doi.org/10.1016/j.jebo.2019.10.001 0167-2681/© 2019 Elsevier B.V. All rights reserved.

Please cite this article as: R. Böheim, D. Grübl and M. Lackner, Choking under pressure – Evidence of the causal effect of audience size on performance, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.10.001

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be affected by the presence and size of a supportive or hostile audience (Butler and Baumeister, 1998; Wallace et al., 2005; Harb-Wu and Krumer, 2017). Although an audience is generally believed to have an effect on performance, little is known about the causal effect of audience size on performance. Results depend on the assumptions made. A supportive home audience is frequently considered to raise expectations and thus increase pressure to perform well (Epting et al., 2011). It seems plausible that a supportive audience provides emotional ease and reduces pressure, however, Taylor et al. (2010) show that a supportive audience increases stress as measured by biological stress indicators. This is in contrast to the well-described “home field advantage” and the use of audience size to explain it (Boudreaux et al., 2017). In general, professional sports provide an excellent opportunity to study choking under pressure. The rules limit available strategies and provide a clearly defined environment, which allows to distinguish among the effects of timing, intermediate scores, and variation in prizes or audience size on players’ performance. We estimate the causal effect of audience size on the performance of players. Our measure for performance is the success of free throws in professional basketball games in the National Basketball Association (NBA), a well-established indicator of performance (Cao et al., 2011; Toma, 2017). Free throws are penalties that are awarded after rule infractions and are ideally suited to study choking under pressure. They are a particular type of scoring attempt, which is isolated from interactions with other players. Consequently, unobserved disturbances— which might originate from interactions between the teams (offense versus defense)— are eliminated. Further, a team typically cannot choose the player who attempts the free throw; only the player who has been fouled may attempt it.1 This limits the potential danger of the impact of endogenous selection on performance. In addition, free throws are classical skill-based tasks, similar to penalty kicks in soccer (Dohmen, 2008a) or shooting in biathlon (Harb-Wu and Krumer, 2017), which are thought to be affected primarily by the pressure to perform (Wallace et al., 2005). In our empirical analysis, we use play-by-play data from top-level professional basketball games (NBA) from all regularseason games in 9 seasons from 2007/08 through 2015/16. Play-by-play data identify all actions in a game, in particular, free throws and their outcomes. They allow us to control for different circumstances that could potentially influence performance, such as the score difference or time of the game. We use an instrumental variable approach to identify the causal effect of performance pressure on performance as the size of the audience is endogenous. In particular, we use weather conditions to instrument for attendance. Our instrumental variable is a binary variable equal to 1 if the game was on a day with unfavorable weather, and 0 otherwise. The underlying assumption is that bad weather induces lower attendance as travel costs increase. As all NBA games are staged inside domes with controlled climate conditions, there is no direct effect of the weather on the performance of the players on the court. The empirical literature demonstrates that the performance of (semi-) professional basketball players is correlated with in-game characteristics (Worthy et al., 2009; Cao et al., 2011; Toma, 2017). While the size of the audience could affect the overall performance in a game, it is also necessary to control for within-game dynamics that will affect performance.2 It is essential to control for intermediate score differences, as well as the timing of free throws, to identify the causal effect of attendance size on performance. Moreover, as the growing literature on choking under pressure illustrates, we expect the effect of the audience size to vary with the time of game and intermediate score. If the pressure to perform increases in crucial moments of a game (Cao et al., 2011; Toma, 2017), we expect to find a pronounced causal effect of the audience for attempts during such moments. We find a negative causal effect of audience size on the probability of a successful free throw for players of the home team. The effect is driven by attempts during the first half of a game. We estimate a 6.9 percentage point (ppt) decrease in the probability of a successful free throw if attendance increases by 10 ppts. At the sample mean, this corresponds to a 9% lower success rate. Additionally, the effects are estimated for attempts when the home team is trailing, which amplifies our results. We do not find any significant effects for the players of the away team. The results imply causal evidence for a home choke or home disadvantage (Wallace et al., 2005). In addition, our results suggest that the home choke is present during the early phases of games.

2. Related literature It is plausible that individual performance is affected by pressure, e.g. other people who are observing. The relationship between pressure to perform and audience has been studied mostly in laboratory experiments. Otten (2009) finds that some athletes perform better when their performance is videotaped. He attributes this to the athletes’ reported perceived control which enhances self-confidence and, consequently, performance. Georganas et al. (2015) show that subjects perform better when being observed by a peer. Uziel (2007) conclude from a meta-analysis of experimental studies that the effect of pressure on performance is generally positive if the agent is an extrovert and has high self-esteem.

1 This is the case for personal fouls. In the comparatively rare case of a technical foul (i.e. a breach of the rules that does not involve physical contact or is a foul by a non-player), the team can decide who will attempt the free throw. During the final 2 min. of a game, in case of an off-the-ball foul, the team can assign a player to go to the free throw line. As a robustness check, we drop all free throws from the final 3 min. All main results are confirmed. 2 Earlier work by La (2014) indicates a significant negative effect of relative audience size on performance for the away team. This, however, is based on the implausible assumption of a random scheduling of games over weekdays.

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In psychology, there is no consensus on the mechanisms that cause choking under pressure (Beilock and Gray, 2012). Drive theories postulate that performance depends on the drive or level of arousal. Zajonc (1965) suggests that the dominant response will be revealed under high arousal, leading to better performance of experts and poorer performance of novices in a task. Failure avoidance is another explanation for choking under pressure. Wallace et al. (2005) argue that an audience communicates expectations to the performer, which may raise the performer’s will to succeed. It could also trigger choking under pressure, if the fear of disappointing these expectations becomes dominant. Attentional theories, in contrast, focus on the cognitive demand of a task. For example, the self-focus theory assumes that pressure increases anxiety about losing. This, in turn, increases self-consciousness and proceduralized skills are more poorly executed due to an attentional shift to task-irrelevant cues (Baumeister, 1984; Wallace, Baumeister, and Vohs, 2005). Analyzing biathlon competitions, Lindner (2017) finds that athletes who take more time to shoot the decisive and final shot miss more often. He states that this might be due to an athlete’s possible over-thinking of the task and potential outcomes. Similarly, the explicit monitoring theory explains choking through cognitive processes that are detrimental to performance. The mechanisms of choking are found to operate on “proceduralized task control structures” (Beilock and Carr, 2001), i.e., sensorimotor skills such as putting in golf or converting a free throw in basketball. Free throws combine gross motor and fine motor activities (Wang et al., 2004) to form a particular motor skill. The primary determinant for success is the quality of movement (Schmidt and Wrisberg, 2008). A basketball free throw is a fully standardized task, which is practiced extensively by professional athletes throughout their careers. Wallace et al. (2005) argue that it takes extensive practice to master initially difficult skill tasks. They point out that “performers practise the same routines repeatedly until they can reliably perform many aspects of their task automatically without having to think about” (Wallace et al., 2005, p. 431). Consequently, if the player performs the well-practiced throwing motion, the attempt will typically succeed. Beilock and Carr (2001) argue that highly practiced tasks are “automated” in the sense that they are controlled by procedural knowledge. Performers should take little attention when performing these tasks, as extra attention to perform a free throw might be detrimental for success. They also point out that skill tasks are especially susceptible to attention-induced disturbances as described by the explicit monitoring theory. Performance in motor skills improves over time through practice (Wallace et al., 2005). NBA players have undergone extensive practice and are top performers in converting a free throw. We argue that they are likely at their personal (physical) limit for this specific task, such that sizeable changes in performance through changes in effort are not likely. The free throw is proceduralized and automatic to a degree where the act of consciously trying to increase effort may actually decrease performance. Gray (2004) uses a similar sport task — baseball batting — in multiple experiments and shows that highly skilled players base their performance on automated procedures and they suffer in performance when put under pressure. This is consistent with the theory of experts choking under pressure when performing a proceduralized task (Langer and Imber, 1979; Baumeister, 1984; Lewis and Linder, 1997). We assume that free throws are skill tasks (motor skill) rather than effort tasks, but we cannot entirely rule out that effort may also play a secondary and minor role for successful free throws. To provide empirical evidence for the validity of our assumption, we collect team-level data from season 2007/08 through 2015/16 for three distinct phases of the season: (1) the regular season before the all star game break3 , (2) the regular season after the all star break, and (3) the NBA playoff tournament. Incentives and the importance to perform varies in these phases. Players and coaches often mention that the games after the all star break are crucial for reaching the playoffs and to compete for the NBA title. Most important, however, are playoff games, as playoff performance is the ultimate measure of a team’s success in a particular season. We assume that — on average — all members of a team will increase effort after the all star break and especially in the playoffs. Thus, if free throws were (primarily) an effort task, we should see the free throw conversion rate to be greatest in the playoffs. Fig. 5 in the Appendix illustrates average free throw percentages, by season phase. There is no difference between the average free throw percentage before and after the all star break. Teams do not improve their free throw performance in the more critical phase of the regular season. For the playoffs, the average free throw percentage is even lower than for the two regular season periods. This pattern is not consistent with free throws being an effort task, as we should expect highest effort in the playoffs. It is, however, consistent with choking under pressure, as the success rate is lower in playoff games when pressure to perform is greatest. The career free throw performances of Shaquille O’Neal, one of the best players in NBA history, serve as an illustration. O’Neal is known for his bad free throw success rate at a subpar 52.7% (illustrated in Fig. 6 in the Appendix). Despite arguing that he usually performed better when it mattered most, he was almost never able to improve his free throw percentage for playoff games. He performed significantly above his career average due to being coached by Ed Palubinskas, who was hired especially to train the free throw.4 As this collaboration ended, O’Neal had an extended period of bad free throw performances. We consider this anecdote to be evidence in favor of free throws being a skill task. Empirical evidence on choking under pressure for skill tasks by type or size of the audience is scarce. Analyzing target shooting as a skill task in biathlon competitions, Harb-Wu and Krumer (2017) find evidence of athletes choking at home

3 The NBA All Star Game is an exhibition game of most popular players, taking place every February. Since there are no games in days before and following the game, all teams have a break they can use to regroup and adjust strategies for the remainder of the regular season and the playoffs. 4 See https://en.wikipedia.org/wiki/Ed_Palubinskas for details.

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competitions in the presence of a supportive crowd. In contrast, Braga and Guillén (2012) use data from the Brazilian Soccer Championships 2006 and find no effect of pressure on performance. Epting et al. (2011) suggest that undergraduate basketball players, who lack the financial incentives of professional players, do perform differently at free throws when exposed to supportive, discouraging or neutral audiences. In their experiment, however, the audiences consisted of ten spectators, while NBA audiences typically number up to 20,0 0 0 spectators. Studying the performance of professional soccer players at the penalty kick, Dohmen (2008a) identifies intermediate standings as a source of choking under pressure. However, he finds no significant correlation between attendance size and performance. Cao et al. (2011) argue that the performance of free throws is only moderately affected by attendance size (1 ppt decrease as attendance increases by 10,0 0 0 spectators).

3. Data and empirical strategy We use data on free throws from professional basketball games (NBA) to analyze how audience size impacts the performance of basketball players. We combine play-by-play data from regular season games with attendance data and detailed weather information for seasons from 2007/08 through 2015/16.5 The NBA consists of 30 operational franchises, competing against each other in a two stage contest format. Each team plays a total of 82 regular season games, starting in October and culminating in April.6 The data provide information on 10,758 individual games and we observe 502,133 free throws, with 51.21 percent of all free throws attempted by the home teams. We do not use data from playoff games as playoff games are typically always sold out. Consequently, attendance at these games is censored. Following Otten (2009), we measure success by the probability of a successful attempt. Each free throw is awarded after a rule infraction (e.g., a personal foul) and is typically granted to the fouled player. He has ten seconds to throw the ball from a distance of 4.6 meters. Play-by-play data allow controlling for circumstances that could potentially influence performance. In particular, in our analyses, we control for players’ characteristics, the time of the attempt, and the intermediate score. In our data, attendance is not accurately measured, due to a divergence between reported ticket sales and actual attendance, as well as non-reported standing places. In addition, different sources report slightly varying arena capacities.7 We use maximum capacity for each arena and account for changes in seating capacity over time. To ease comparison, we use attendance as percent of an arena’s maximum capacity. It is plausible that that there is a considerable amount of measurement error in the attendance measure we use for our empirical analysis. However, this measure is the only one which is available. The NBA has a strict policy to publish ticket sales (including give-away tickets for players and public relations purpose) instead of actual attendance evaluated by turnstile counts. However, intensive research allowed us to obtain a few data points for actual attendance for some teams in a single season.8 Our data perfectly predicts the bottom 5 teams in actual attendance as reported by this alternative data, while the top 5 are also ranked high in our data. Looking at correlations, we see that these actual attendance numbers are correlated at 0.952 with the measure we employ. Any correlation between attendance and performance could be due to reverse causality. More successful teams (or teams who perform better under pressure) could attract more spectators. Better teams are more satisfying to watch and the number of spectators is larger because of better performance. We exploit random variations in weather conditions, which were measured close to the arena, to identify the causal effect of attendance on performance. As distances to an arena can be large and road conditions depend on the weather, we argue that bad weather will lead to lower attendance because of worse driving conditions. Weather conditions do not influence performance and risk taking behavior in the arena directly since all NBA games are indoors in air conditioned and heated facilities.9 After controlling for location (home-team) fixed effects, weather conditions can be considered perfectly random exogenous shocks. We use an instrument that is a binary variable equal to 1 if the game, t, was on a day with bad weather, and 0 otherwise. We categorize weather as bad if the average temperature on the day was below 0 ◦ C, or if it snowed, there was a thunderstorm or it rained heavily. The instrument is then defined as:

 bad weatheri,t =

1 if average temperature on game day < 0 ◦ C, 1 thunderstorm, snow, rain, fog, or any combination, 0 else.

(1)

5 Play-by-play data on free throw attempts for seasons 2007/08 through 2015/16 are available at https://www.basketball- reference.com/play- index/event_ finder.cgi. Daily local weather information for each arena was obtained from http://wunderground.com. 6 Due to a lock-out in the 2011/12 season, each team played only 66 games. 7 Recent capacities were drawn from the arenas’ websites and http://espn.go.com/nba/. Historical data are available on www.wikipedia.org. 8 Available at http://www.cbssports.com. 9 This makes the existence of defiers unlikely. Defiers would be arenas which have less attendance in better weather than in bad weather. Better weather conditions make it easier to visit the arena.

Please cite this article as: R. Böheim, D. Grübl and M. Lackner, Choking under pressure – Evidence of the causal effect of audience size on performance, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.10.001

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Fig. 1. Attendance by weather condition by season. Notes: Bad weather (1) is defined as an average temperature below 0 ◦ C, thunderstorm, snow, rain, fog, or any combination; 0 otherwise. Mean adjusted relative attendance is specified as the number of spectators in an arena relative to the maximum capacity, averaged over the season, capped at 100%. N = 10,758.

Table 1 Summary statistics. Home

Attendance (%) Team score Win ratio Attempts before (player) Travel effort Minutes left

Away

mean

(sd)

mean

(sd)

90.4 57.1 0.5 2.5 2.5 20.6

(12.4) (29.9) (0.2) (2.7) (1.2) (13.8)

90.3 55.5 0.5 2.4 2.5 20.5

(12.5) (29.2) (0.2) (2.7) (1.2) (13.8)

Notes: N = 256,817 attempts by the home, 245,316 attempts by the away team. Team score is the score before the observed attempt. Win ratio is the ratio of the running sums of previously won and lost games by the team during a season. Attempts before are the number of free throw attempts by player within the game. Travel effort is measured in hours. Minutes left is the number of minutes left in the game.

Fig. 1 depicts the attendance averaged over all game days per season by weather condition. Attendance was significantly lower when the weather was bad, as defined by our IV. Fig. 2 shows the share of days with bad weather. The top panel of Fig. 7 in the Appendix illustrates the distribution of games by bad weather, over all states with an NBA team. The bottom panel shows the mean adjusted relative attendance. The correlation between weather and attendance is evident. Table 1 provides a descriptive analysis of all main variables, stratified by the location of the game. We measure attendance relative to arena capacity and limit it at a maximum of 100%. Indeed, we observe a significant number of sellouts. Fig. 8 in the Appendix tabulates the share of sellout games by team. There are no systematic differences for our control variables between home and away teams. The players’ mean conversion rate before the attempt is the same for both teams at 0.75. As expected, we see that the home team’s score before each free throw attempt is, on average, greater than the score of the away team. Each player has attempted an average of 2.5 attempts in the particular game before the observed attempt. We do not see a difference in free throw performances by location. We assume that the audience at each game is predominantly supporting the home team. This is a realistic assumption, as all NBA teams have a significant share of season ticket holders. To account for arenas which attract very high or low numbers of visiting fans, we use home and away team-season fixed effects. In addition, we control for the travel effort away Please cite this article as: R. Böheim, D. Grübl and M. Lackner, Choking under pressure – Evidence of the causal effect of audience size on performance, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.10.001

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Fig. 2. Share of bad weather days by NBA regular season games. Notes: Share of bad weather days as defined in Eq. (1), averaged per game-day in a season (seasons 1 to 9). N = 82.

fans have to make if they attended a particular game. Travel effort is measured as the time between relevant airports in hours.10 We expect that a higher win ratio is correlated with a better performance at the free throw line. For travel effort, we do not expect any significant correlation with free throw performance. This should be the case if, as we assume, away fans are a minority in the audience. The more attempts a player had before, the better should be the performance at a particular free throw attempt. To estimate the causal effect of attendance on success we use the following econometric specification

Yi,t = α + Xi,t β + γ Attendancei,t + δh + ξa + i,t ,

(2)

where Yi,t is the dependent variable which equals 1 if the observed free throw i in game t is a successful attempt, zero otherwise. The vector Xi,t includes as control variables the minutes remaining in the game at the time of the attempt, the score difference before the attempt in score difference interval dummies, and the winning ratio before the observed game. To control for the amount of potential away fans, we include a variable travel effort. Intra-week variation in game attendance is captured by including day-of-the-week indicators. Attendancei,t is the number of spectators relative to arena capacity, capped at 100%. In all specifications, we control for team-season fixed effects, δ h , and opponent-season fixed effects, ξ a . In some iid

specifications, we also include the salary of player p in game t. i,t ∼ N (0, σ 2 ) is a well-behaved error term.11 We instrument attendance and the first stage is specified as

Attendancei,t = π0 + π1 Zi,t + Xi,t φ + δh + ξa + νi,t ,

(3) iid

where Zi,t is the instrumental variable as defined above, and νi,t ∼ N (0, σ 2 ) is a well-behaved error term. 4. Results Table 2 tabulates in columns (1) and (3) the results from estimating Eq. (2) for home and away teams, using OLS. We do not find a statistically significant correlation between performance and attendance for home teams. For away teams, however, we estimate a significantly negative coefficient of −0.0 0 04. This can be interpreted as a 0.4 ppt decrease in the probability of a successful throw if attendance increases by 10 ppt. 10

Travel time is taken from the away team’s closest airport to the airport where the game is held, using http://www.flighttime-calculator.com. We do not include player fixed effects in our main estimation model. This would be contrary to the logic of our first stage, where game-level attendance requires controlling for team- as well as opponent-season fixed effects as important factors. To capture the players’ abilities, we use their free throw conversion rates in t − 1. We do, however, provide estimates, including the player fixed effects, in the robustness section. 11

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Table 2 Estimated effects of attendance on performance. Home teams OLS Attendance

b

Effect at the mean [%] Winning percentage Travel effort Attempts before (player) Team × Season FE Opponent × Season FE 1st stage coefficientc F-stat.d N Mean dep. var.

Away teams IV

−0.0001 (0.0001) [−0.011] 0.0108 (0.0080) 0.0011 (0.0008) 0.0063∗ ∗ ∗ (0.0004) yes yes

256,817 0.76

a

IVa

OLS ∗∗

−0.0049 (0.0024) [−0.649] 0.0077 (0.0089) −0.0004 (0.0011) 0.0063∗ ∗ ∗ (0.0004) yes yes −1.0260∗ ∗ ∗ (0.1986) 42.8 256,817 0.76

∗∗∗

−0.0004 (0.0001) [−0.048] 0.0147∗ (0.0079) 0.0000 (0.0009) 0.0072∗ ∗ ∗ (0.0004) yes yes

245,316 0.76

0.0006 (0.0022) [0.080] 0.0171∗ (0.0096) 0.0003 (0.0010) 0.0072∗ ∗ ∗ (0.0004) yes yes −1.0932∗ ∗ ∗ (0.1982) 52.1 245,316 0.76

Notes: The dependent variable is a binary variable equal to 1 if the observed free throw was successful, 0 if not. All estimations include minutes left, weekday dummies, and score difference interval dummies. Game-level clustered standard errors in parentheses, ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. a Instrumental variable is a binary variable as defined in Eq. (1). b Attendance is adjusted relative attendance in percent of arena capacity (capped at maximum of 100). c Estimated coefficients of the first stage. d Kleibergen and Paap (2006) statistics on the instrument in the first stage. Table 3 Instrumental variablea — 1st and 2nd half. Home teams Half 1 Attendance

b

Effect at the mean [%] Additional controls Team × Season FE Opponent × Season FE 1st stage coefficientc F-stat.d N Mean dep. var.

∗∗

−0.0069 (0.0034) [−0.909] yes yes yes −1.1045∗ ∗ ∗ (0.2087) 28.0 114,271 0.7571

Away teams Half 2

Half 1

Half 2

−0.0036 (0.0033) [−0.470] yes yes yes −0.9574∗ ∗ ∗ (0.2021) 22.4 142,546 0.7596

0.0027 (0.0031) [0.359] yes yes yes −1.1274∗ ∗ ∗ (0.2056) 30.1 108,885 0.7536

−0.0006 (0.0030) [−0.082] yes yes yes −1.0735∗ ∗ ∗ (0.2048) 27.5 136,431 0.7585

Notes: The dependent variable is a binary variable equal to 1 if the observed free throw was successful, 0 if not. All estimations include minutes left, weekday dummies, and score difference interval dummies. Game-level clustered standard errors in parentheses, ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. a Instrumental variable is a binary variable as defined in Eq. (1). b Attendance is adjusted relative attendance in percent of arena capacity (capped at maximum of 100). c Estimated coefficients of the first stage. d Kleibergen and Paap (2006) statistics on the instrument in the first stage.

Results from 2SLS regressions are presented in columns (2) and (4) of Table 2. In contrast to the OLS results, we do not find a significant effect of attendance size on performance for away teams. However, the effect for home teams is significantly negative and sizeable. In particular, a 10 ppt increase in game attendance decreases the probability of a successful attempt by about 5 ppt. Our instrument is strong with a Kleibergen and Paap (2006) F-statistics greater than 40. The firststage results confirm our assumption that good weather conditions increase attendance at NBA games. The literature on choking under pressure illustrates the importance of timing within a contest. Consequently, we split the sample into attempts from the first and second halves of games. The results are tabulated in Table 3. For the first half of the game, we estimate a 7 ppt lower probability of a successful attempt for home teams, if the attendance increases by 10 ppt. We find no evidence of a causal effect for attempts during the second half for home teams. We conclude that the overall effect presented above is driven by the attempts during the first half of a game. Again, irrespective of the timing of the attempt, we do not find any effect of attendance on performance for away teams. Please cite this article as: R. Böheim, D. Grübl and M. Lackner, Choking under pressure – Evidence of the causal effect of audience size on performance, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.10.001

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R. Böheim, D. Grübl and M. Lackner / Journal of Economic Behavior and Organization xxx (xxxx) xxx TAble 4 Instrumental variablea — Score differences. score difference trailing ]-∞,-7]

[-6,-1]

leading

[0,6]

[7,∞[

-0.0066∗ ∗ (0.0027) [-0.876] yes yes yes 27.5 105.484 0.7587

-0.0055 (0.0036) [-0.724] yes yes yes 16.3 51.846 0.7586

-0.0064∗ (0.0035) [-0.837] yes yes yes 29.3 53.638 0.7588

-0.0010 (0.0044) [-0.134] yes yes yes 10.8 128.579 0.7587

-0.0025 (0.0050) [-0.326] yes yes yes 12.0 76.645 0.7611

-0.0011 (0.0059) [-0.147] yes yes yes 8.2 65.865 0.7542

0.0019 (0.0036) [0.255] yes yes yes 17.8 135.104 0.7554

-0.0029 (0.0048) [-0.379] yes yes yes 13.0 78.287 0.7540

0.0066 (0.0051) [0.870] yes yes yes 15.5 56.817 0.7575

-0.0002 (0.0027) [-0.022] yes yes yes 23.2 89.247 0.7588

0.0044 (0.0032) [0.576] yes yes yes 28.4 64.504 0.7573

-0.0086 (0.0055) [-1.139] yes yes yes 9.8 39.225 0.7575

Home teams Attendanceb Effect at the mean[%] Additional controls Team × Season FE Opponent × Season FE F-stat. c N Mean dep. var. Away teams Attendanceb Effect at the mean[%] Additional controls Team × Season FE Opponent × Season FE F-stat. c N Mean dep. var.

Notes: The dependent variable is a binary variable equal to 1 if the observed free throw was successful, 0 if not. All estimations include minutes left, weekday dummies, and score difference interval dummies. Game-level clustered standard errors in parentheses, ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. a Instrumental variable is a binary variable as defined in Eq. (1). b Attendance is adjusted relative attendance in percent of arena capacity (capped at maximum of 100). c Kleibergen and Paap (2006) statistics on the instrument in the first stage.

In addition to timing, the intermediate score could affect the relationship between attendance and performance. To investigate potential effect heterogeneity related to intermediate standings, we split the sample by whether the attempts were made when the score differences were small or large. Large score deficits are in the interval ]−∞, −7] and small deficits are in [−6, −1]. Trailing six points is a significant threshold where pressure is high as the possibility of tying the game can be achieved in two possessions. This is known as a two possession game. Small leads are score differences in the interval [0,6] and large leads range in between [7,∞[. Table 4 presents the estimated effects when we split the sample according to score differences. Again, there are no significant effects for the away team. We estimate a significant negative effect of attendance on performance for home teams when they are trailing in the game. Overall, the results suggest that the negative effects of audience size on performance are relevant, if the home team is trailing. NBA players differ in their abilities to shoot free throws. A better player could be affected differently by attendance size than a worse player. Consequently, we use the conversion rate, measured before the attempt, to stratify the sample. We estimate the specifications separately for players who have a conversion rate in the lower 25th percentile of the conversion rate distribution and for players who have a conversion rate in the upper 25th percentile. Table 5 tabulates the estimated effects for these two subsamples. We estimate a significant negative effect of attendance on performance for worse players on the home teams. The results suggest that a 10 ppt increase in attendance decreases the probability of free throw success by 12.6 ppt. The estimate, however, is significant at the 10 percent level with an F-statistics of around 12. We do not find a significant effect of audience size on performance for players with a top conversion rate. 5. Robustness checks In Section 3, we use a binary instrumental variable which is an indicator of unfavorable weather conditions which have the potential to deter potential visitors from actually attending the game. Since categorizing these bad weather conditions might not be completely obvious, we define an alternative instrumental variable as the average minimum temperature on game day and the three days before:

1  ∗ (min temperaturei,t−s ), 4 3

Zi,t =

(4)

s=0

where temperatures are measured at weather stations closest to arena on game day t, with calendar days s. We assume that low temperatures induce some spectators to stay at home and not visit the arena. Fig. 3 shows the relative and absolute attendances over all regular season games. The 4-day average minimum temperatures over time are plotted in Fig. 4. Please cite this article as: R. Böheim, D. Grübl and M. Lackner, Choking under pressure – Evidence of the causal effect of audience size on performance, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.10.001

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Table 5 Instrumental variablea — Good and bad free throw players. Home teams

Attendanceb Effect at the mean [%] Additional controls Team × Season FE Opponent × Season FE F-stat.c N Mean dep. var.

Away teams

≤ 25th

≥ 75th

≤ 25th

≥ 75th

−0.0126∗ (0.0068) [−2.019] yes yes yes 11.9 64,921 0.6233

−0.0009 (0.0035) [−0.108] yes yes yes 21.4 64,066 0.8601

−0.0025 (0.0051) [−0.405] yes yes yes 19.8 61,058 0.6165

0.0055 (0.0035) [0.648] yes yes yes 22.0 62,076 0.8558

Notes: The dependent variable is a binary variable equal to 1 if the observed free throw was successful, 0 if not. All estimations include minutes left, weekday dummies, and score difference interval dummies. Game-level clustered standard errors in parentheses, ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. a Instrumental variable is a binary variable as defined in Eq. (1). b Attendance is adjusted relative attendance in percent of arena capacity (capped at maximum of 100). c Kleibergen and Paap (2006) statistics on the instrument in the first stage. Columns one and three include all players with a conversion rate below the 25th percentile of all players (bad), columns two and four those above the 75th percentile (good).

Fig. 3. Attendance by NBA regular season games. Notes: Average attendance per game in a season. Attendance is the number of spectators relative to arena capacity, capped at 100% (left axis). Absolute attendance is measured in 1,0 0 0s (right axis). Confidence intervals are at 95% level. N = 10,758 games.

Fig. 9 in the Appendix illustrates the standard deviations of both instruments. For some states our binary IV has less variation, however, in these cases, the continuous instrument has more variation. Table 6 reports the means of the instrument by NBA team. As a robustness check of our main results, we re-estimated all specifications using the alternative continuous instrument. The results are shown in Tables 7–10. All results support our findings, however, there are slight differences in the magnitude of the estimates. Since both instruments produce comparable results, we are confident that our conclusions are robust to the definition of the exogenous weather shock. One possible concern with our approach is the existence of defiers, which would violate a key assumption of the Local Average Treatment Effect (LATE) interpretation of the IV approach. This would be the case if some people decide to avoid attending a game when the weather is good, perhaps because they expect traffic congestion, for example on weekends. Please cite this article as: R. Böheim, D. Grübl and M. Lackner, Choking under pressure – Evidence of the causal effect of audience size on performance, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.10.001

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Fig. 4. 4-day average minimum temperature by NBA regular season games. Notes: Averages of the lowest temperatures on game day and the three previous days, per game. N = 10,758 games.

This would violate the necessary assumption of no defiers for identifying the causal effect of attendance on choking under pressure. To check the robustness of our results, we omit all games on Saturdays and Sundays. Typically, favorable weather would lead to increased traffic and although traffic in general decreases during weekends, the share of social and recreational trips is higher during clear weather days (Maze and Manish Agarwal, 2006). Table 11 tabulates the results restricting the sample to weekdays. The estimates confirm earlier results. Another potential threat to our identification strategy is the unobserved heterogeneity of players. Our data have no direct measure of the players’ abilities or the susceptibility to choking. We address this by including players’ salaries.12 We also estimate specifications that use player-team-season fixed effects. Using player-team-season fixed effects controls for any unobserved player characteristics, while player salaries should provide a proxy for a player’s ability. The results from these specifications are tabulated in columns (1), (2), (4) and (5) in Table 12 in the Appendix. We estimate that salaries are positively correlated with free throw success. Overall, the results confirm our main results presented above. We estimate that attendance has a negative effect on the performance of players from home teams, but not for players from away teams. Another potential concern is the selection of players according to their contract status. In the NBA, players frequently change teams as free agents or get traded. A coach might select players from the roster based on their contract status (Deutscher, 2011). However, the contract status could systematically affect not only free throw performances, but also the pressure from the audience. Unfortunately, we do not have information on the contract status for most players in this sample. Instead, we estimate player-team-season fixed effects in the specifications to investigate this channel, which control for potential unobserved heterogeneity coming from contract situations (Table 12, col. (2) and (4)). In addition, we estimate an alternative specification of Eq. (2) where we control for the number of games that each player has played as a member of the current team. This is our best proxy for a player’s tenure with a team. The estimation results are presented in columns (3) and (6) of Table 12. Our main result of a negative effect of attendance size on free throw performance is confirmed and robust to unobserved player-team-season characteristics. As additional robustness checks, we also used different specifications including lags of the dependent variable. Again, our results are confirmed qualitatively and quantitatively. As a further robustness check we dropped all attempts from the last 3 min. of a game to account for intentional misses due to strategic considerations, and for player selection after fouls in the last minutes of games with the intention to stop the clock. We also estimate a IV-Probit model to account for the fact that we have a binary dependent variable. All these results confirm our finding of a negative effect of audience size on free throw performance of home teams in the first half of games.

12

Salaries were obtained from http://www.ESPN.com.

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6. Conclusion and discussion We provide evidence of the effect of audience size on performance. We use play-by-play data from top-level professional basketball (NBA) to identify the causal effect of audience size on performance. Our indicator for performance is the success of the skill-based task of shooting a free throw. A free throw is a highly standardized, often-practiced sensorimotor task that is not affected by the performance or style of play of the opposing team. Psychological theory predicts a likely negative effect of audience-induced performance pressure on a player’s performance. To establish the causal link between attendance and performance, we apply an instrumental variable approach using weather conditions to provide an exogenous variation in arena attendance. Weather conditions cannot have a direct effect on performance as all NBA games are held in airconditioned and heated indoor facilities. We do not find any causal effect of attendance on the performance of away teams. This is surprising, as a non-supportive or even hostile crowd could be a major distraction for players of away teams. However, we do find a significant and negative causal effect of attendance on the performance of home team players. The performance of home-team players decreases as the size of the crowd increases. Taking into account that the average audience size in our sample is 17,455, we estimate a total decrease of 10 ppt in the probability of a successful free throw when audience size increases by about 2500 (14.3%) spectators. In addition, we analyze if the choking under pressure that we find for the home teams’ players is affected by the period of play in which the free throw is attempted. We only find a negative effect for free throws in the first half of games, and the negative effect results from attempts that are made when teams are trailing. We construct a proxy for the players’ ability to shoot free throws based on their conversion rates. We find that it is the relatively worse players on their home court, who choke under pressure. This result confirms Wallace et al. (2005), who state that prior experience with an audience that involved a bad performance might lower future performance when the (supportive) audience is larger. All main results are confirmed by several robustness checks. Our results confirm Goldman and Rao (2012) who find that performance is lower when the audience is larger. We extend Harb-Wu and Krumer (2017) and estimate the effect of the size of the audience on performance. We estimate that the negative effect of the presence of a supportive audience increases with the size of the crowd. Our results are also in line with Cao et al. (2011) who find a small and significant negative correlation between attendance size and free throw performance during quarters 1 through 3 of NBA games. The audience effect we find could also explain results by Galily and Morgulev (2018) who find that performance of NBA teams significantly declines when stakes are high. Obviously, important games will draw large attendances. In contrast, Toma (2017) finds no effect of audience type or size on free throw performances for home and away teams. One limitation of our analysis is the omission of playoff games. The overall number of games in the NBA playoffs during our sample period is too small for our identification strategy to provide a sufficiently strong first stage. Consequently, we do not analyze how attendance does affect performance in these particular games. However, it is of potentially great interest to investigate how the attendance size effect quantifies in the relatively more important playoff games. Thus, it leaves room for future research to analyze how the general importance of a game affects the negative effect of a supportive audience. Although we analyze a specific environment, our results have potentially large implications for more general questions related to incentive design and performance evaluation in work places. For example, workers who are monitored and incentivized by supportive and encouraging feedback might actually perform worse due to increased performance pressure. Following our results, this could especially be the case for workers who are behind their target already or have recently performed below average. Our results help to further understand how the social environment affects performance of individuals. We demonstrate that not only a supportive audience (Harb-Wu and Krumer, 2017), but also the amount of support plays a crucial role for success of skill tasks.

Please cite this article as: R. Böheim, D. Grübl and M. Lackner, Choking under pressure – Evidence of the causal effect of audience size on performance, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.10.001

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Declaration of Competing Interest None. Appendix A

Fig. 5. Average free throw success by phase of NBA season. Notes: Free throw success in percentage for different phases of NBA seasons 2007/08 through 2015/16. Data was collected from https://www.basketball-reference.com. TAble 6 Mean values of weather condition by team.

continuous IV binary IV

continuous IV binary IV

continuous IV binary IV

ATL

BOS

CHA

CHI

CLE

DAL

DEN

DET

GSW

HOU

0.424 0.119

-0.081 0.399

0.288 0.167

-0.244 0.551

-0.101 0.548

0.731 0.114

-0.487 0.412

-0.459 0.669

0.715 0.038

1.103 0.107

IND

LAC

LAL

MEM

MIA

MIL

MIN

NJN

NOH

NYK

-0.147 0.470

1.081 0.004

1.087 0.016

0.438 0.186

1.876 0.041

-0.408 0.595

-0.804 0.690

0.098 0.333

1.082 0.133

0.132 0.278

OKC

ORL

PHI

PHX

POR

SAC

SAS

TOR

UTA

WAS

0.245 0.216

1.368 0.063

0.099 0.306

1.056 0.014

0.350 0.157

0.530 0.046

0.870 0.109

-0.261 0.554

-0.186 0.381

0.215 0.247

Notes: The alternative (continuous) instrument is measured in 10 ◦ C.

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Fig. 6. Career free throw conversion rate for Shaquille O’Neal by game. Notes: Shaquille O’Neal’s free throw conversion rate in each of his NBA games from 1992 through 2011. In 2001, light grey-shaded area, he was coached by Ed Palubinskas. Data was collected from https://www.basketball-reference.com.

Table 7 Estimated effects of attendance on performance (both instruments). HOME

AWAY

IV-maina Attendance

c

Effect at the mean [%] Winning percentage Attempts before (player) Travel effort Team × Season FE Opponent × Season FE 1st stage coefficientd F-stat.e N Mean dep. var.

∗∗

−0.0049 (0.0024) [−0.649] 0.0077 (0.0089) 0.0063∗ ∗ ∗ (0.0004) −0.0004 (0.0011) yes yes −1.0260∗ ∗ ∗ (0.1986) 26.7 256,817 0.7585

IV-alt.b ∗∗

−0.0040 (0.0016) [−0.524] 0.0083 (0.0085) 0.0063∗ ∗ ∗ (0.0004) −0.0001 (0.0010) yes yes 0.1174∗ ∗ ∗ (0.0158) 54.9 256,817 0.7585

IV-maina

IV-alt.b

0.0006 (0.0022) [0.080] 0.0171∗ (0.0096) 0.0072∗ ∗ ∗ (0.0004) 0.0003 (0.0010) yes yes −1.0932∗ ∗ ∗ (0.1982) 30.4 245,316 0.7563

−0.0010 (0.0015) [−0.132] 0.0131 (0.0086) 0.0072∗ ∗ ∗ (0.0004) −0.0001 (0.0009) yes yes 0.1229∗ ∗ ∗ (0.0157) 61.6 245,316 0.7563

Notes: The dependent variable is a binary variable equal to 1 if the observed free throw was successful, 0 if not. All estimations include minutes left, weekday dummies, and score difference interval dummies. Game-level clustered standard errors in parentheses, ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. a Instrumental variable is a binary variable as defined in Eq. (1). b Alternative instrument is continuous and measures the 4-day average minimum temperature in 10 ◦ C. c Attendance is adjusted relative attendance in percent of arena capacity (capped at maximum of 100). d Estimated coefficients of the first stage. e Kleibergen and Paap (2006) statistics on the instrument in the first stage.

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Fig. 7. Geographical dispersion of NBA games with bad weather and average attendance. Notes: Upper panel depicts the dispersion of games on days with bad weather over US states with an NBA team. Darker areas indicate a higher percentage of bad weather games. Bottom panel plots average attendance by state with an NBA team. Darker areas indicated a higher average attendance. Markers indicate the locations of NBA arenas in our data. US states in white do not have an NBA team. Table 8 Alternative (continuous) IVa - 1st and 2nd half. Home teams Half 1 Attendance

b

Effect at the mean [%] Additional controls Team × Season FE Opponent × Season FE 1st stage coefficientc F-stat.d N Mean dep. var.

∗∗

−0.0060 (0.0024) [−0.794] yes yes yes 0.1202∗ ∗ ∗ (0.0165) 52.9 114,271 0.7571

Away teams Half 2

Half 1

Half 2

−0.0022 (0.0022) [−0.287] yes yes yes 0.1150∗ ∗ ∗ (0.0162) 50.7 142,546 0.7596

−0.0018 (0.0023) [−0.245] yes yes yes 0.1216∗ ∗ ∗ (0.0165) 54.4 108,885 0.7537

−0.0000 (0.0020) [−0.005] yes yes yes 0.1233∗ ∗ ∗ (0.0160) 59.2 136,431 0.7585

Notes: The dependent variable is a binary variable equal to 1 if the observed free throw was successful, 0 if not. All estimations include minutes left, weekday dummies, and score difference interval dummies. Game-level clustered standard errors in parentheses, ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. a Alternative instrument is continuous and measures the 4-day average minimum temperature in 10 ◦ C. b Attendance is adjusted relative attendance in percent of arena capacity (capped at maximum of 100). c Estimated coefficients of the first stage. d Kleibergen and Paap (2006) statistics on the instrument in the first stage.

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Fig. 8. Sellouts by team. Notes: Average ratio of sellouts per team for seasons 2007/08 through 2015/16, N = 10,758 games.

Fig. 9. Standard deviations of weather conditions by team. Notes: 4 day average minimum temperature is measured in 10 ◦ C.

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Table 9 Alternative (continuous) IVa - Score differences. score difference trailing

]-∞,-7]

[-6,-1]

leading

[0,6]

[7,∞[

−0.0080∗ ∗ ∗ (0.0025) [-1.058] yes yes yes 36.5 105.484 0.7587

−0.0075∗ ∗ (0.0035) [-0.989] yes yes yes 20.6 51.846 0.7586

−0.0071∗ ∗ (0.0029) [-0.933] yes yes yes 43.2 53.638 0.7588

0.0006 (0.0023) [0.085] yes yes yes 35.0 128.579 0.7587

−0.0031 (0.0028) [-0.405] yes yes yes 36.0 76.645 0.7611

0.0010 (0.0035) [0.129] yes yes yes 25.0 65.865 0.7542

−0.0020 (0.0023) [-0.270] yes yes yes 45.3 135.104 0.7554

−0.0021 (0.0031) [-0.279] yes yes yes 32.3 78.287 0.7540

−0.0012 (0.0031) [-0.158] yes yes yes 40.0 56.817 0.7575

−0.0000 (0.0021) [-0.001] yes yes yes 35.9 89.247 0.7588

0.0011 (0.0025) [0.140] yes yes yes 45.1 64.504 0.7573

0.0008 (0.0037) [0.108] yes yes yes 15.2 39.225 0.7575

Home teams Attendanceb Effect at the mean[%] Additional controls Team × Season FE Opponent × Season FE F-stat. c N Mean dep. var. Away teams Attendanceb Effect at the mean[%] Additional controls Team × Season FE Opponent × Season FE F-stat.c N Mean dep. var.

Notes: The dependent variable is a binary variable equal to 1 if the observed free throw was successful, 0 if not. All estimations include minutes left, weekday dummies, and score difference interval dummies. Game-level clustered standard errors in parentheses, ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. a Alternative instrument is continuous and measures the 4-day average minimum temperature in 10 ◦ C. b Attendance is adjusted relative attendance in percent of arena capacity (capped at maximum of 100). c Kleibergen and Paap (2006) statistics on the instrument in the first stage.

Table 10 Alternative (continuous) IVa - Good and bad players. Home teams

Attendanceb Effect at the mean [%] Additional controls Team × Season FE Opponent × Season FE F-stat.c N Mean dep. var.

Away teams

≤ 25th

≥ 75th

≤ 25th

≥ 75th

−0.0082∗ (0.0044) [−1.319] yes yes yes 22.7 64,921 0.6233

−0.0014 (0.0023) [−0.167] yes yes yes 49.3 64,066 0.8601

−0.0072∗ ∗ (0.0031) [−1.162] yes yes yes 59.7 61,058 0.6165

0.0017 (0.0026) [0.194] yes yes yes 36.1 62,076 0.8558

Notes: The dependent variable is a binary variable equal to 1 if the observed free throw was successful, 0 if not. All estimations include minutes left, weekday dummies, and score difference interval dummies. Game-level clustered standard errors in parentheses, ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. a Alternative instrument is continuous and measures the 4-day average minimum temperature in 10 ◦ C. b Attendance is adjusted relative attendance in percent of arena capacity (capped at maximum of 100). c Kleibergen and Paap (2006) statistics on the instrument in the first stage. The first and third column include all players with a conversion rate below the 25th percentile of all players (bad), columns two and four those above the 75th percentile (good).

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Table 11 IVa - 1st and 2nd half, Monday through Friday. Home teams Half 1 Attendance

∗

b

Effect at mean [%] Additional controls Team × Season FE Opponent × Season FE 1st stage coefficientc F-stat.d N Man dep. var.

−0.0059 (0.0034) [−0.780] yes yes yes −1.2494∗ ∗ ∗ (0.2475) 28.1 83,077 0.7581

Away teams Half 2

Half 1

Half 2

0.0006 (0.0035) [0.079] yes yes yes −1.0217∗ ∗ ∗ (0.2384) 21.2 103,817 0.7585

0.0004 (0.0032) [0.054] yes yes yes −1.2539∗ ∗ ∗ (0.2420) 40.0 79,588 0.7534

−0.0009 (0.0034) [−0.124] yes yes yes −1.1005∗ ∗ ∗ (0.2428) 37.0 99,451 0.7591

Notes: The dependent variable is a binary variable equal to 1 if the observed free throw was successful, 0 if not. All estimations include minutes left, weekday dummies, and score difference interval dummies. Game-level clustered standard errors in parentheses, ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. a Instrumental variable is a binary variable as defined in Eq. (1). b Attendance is adjusted relative attendance in percent of arena capacity (capped at maximum of 100). c Estimated coefficients of the first stage. d Kleibergen and Paap (2006) statistics on the instrument in the first stage.

Table 12 IVa - Alternative specifications. Home teams Attendance

b

Effect at mean [%] Win ratio Attempts before (player) Travel effort log(salary)c Player × Team × Season Team × Season FE Opponent × Season FE Affiliation control 1st stage coefficientd F-stat.e N Mean dep. var.

∗∗

−0.0052 (0.0026) [−0.679] 0.0097 (0.0090) 0.0042∗ ∗ ∗ (0.0004) −0.0005 (0.0011) 0.0149∗ ∗ ∗ (0.0011) no yes yes no −0.9878∗ ∗ ∗ (0.1972) 25.1 237,362 0.7592

Away teams ∗

∗

−0.0039 (0.0024) [−0.515] 0.0078 (0.0086) 0.0052∗ ∗ ∗ (0.0004) −0.0003 (0.0010)

−0.0047 (0.0024) [−0.618] 0.0063 (0.0088) 0.0050∗ ∗ ∗ (0.0004) −0.0002 (0.0011)

yes no no no −1.0151∗ ∗ ∗ (0.1918) 28.0 256,817 0.7585

no yes yes yes −1.0286∗ ∗ ∗ (0.1986) 26.8 256,817 0.7585

0.0000 (0.0024) [0.003] 0.0171∗ (0.0101) 0.0055∗ ∗ ∗ (0.0005) −0.0004 (0.0011) 0.0152∗ ∗ ∗ (0.0011) no yes yes no −1.0510∗ ∗ ∗ (0.2008) 27.4 226,940 0.7563

0.0017 (0.0022) [0.221] 0.0144 (0.0099) 0.0059∗ ∗ ∗ (0.0004) 0.0005 (0.0010)

0.0010 (0.0022) [0.131] 0.0171∗ (0.0096) 0.0063∗ ∗ ∗ (0.0004) 0.0003 (0.0010)

yes no no no −1.0555∗ ∗ ∗ (0.1927) 30.0 245,316 0.7563

no yes yes yes −1.0982∗ ∗ ∗ (0.1982) 30.7 245,316 0.7563

Notes: The dependent variable is a binary variable equal to 1 if the observed free throw was successful, 0 if not. All estimations include minutes left, weekday dummies, and score difference interval dummies. Game-level clustered standard errors in parentheses, ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. a Instrumental variable is a binary variable as defined in Eq. (1). b Attendance is adjusted relative attendance in percent of arena capacity (capped at maximum of 100). c Additional control variables for the player’s yearly salary according to the contract active at the time of the game. d Estimated coefficients of the first stage. e Kleibergen and Paap (2006) statistics on the instrument in the first stage.

Please cite this article as: R. Böheim, D. Grübl and M. Lackner, Choking under pressure – Evidence of the causal effect of audience size on performance, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.10.001

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Please cite this article as: R. Böheim, D. Grübl and M. Lackner, Choking under pressure – Evidence of the causal effect of audience size on performance, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.10.001