Performance under pressure: preliminary evidence from the National Hockey League.

Depken, Craig A., II ; Sonora, Robert J. ; Wilson, Dennis P. 等

Introduction

Apesteguia and Palacios-Huerta (2010) (hereafter APH) investigate an interesting stylized fact from international football (soccer). In knock-out games in which a shootout is used to determine the end of a match (which ended in a draw during regulation and extra-time play), the team that shoots first wins approximately 61% of the time and the team that shoots second consistently underperforms the team that shoots first in terms of odds of a successful shot. APH's test of failure-to-performunder-pressure (failure-to-perform) hypothesis is facilitated by the random nature by which the first shooting team is determined in soccer: the team that shoots first is determined by the toss of a coin. To motivate their empirical analysis, they present a behavior model in which the shooter will have a lower success rate when forced to respond to pressure. Those players who react more negatively to pressure are more likely to miss their opportunity during the shootout. Their empirical evidence suggests that the second shooter fails to score more often than first shooters even after controlling for match characteristics and goalkeeper fixed effects. The persistent lower probability of second shooters scoring is attributed to the increased pressure felt by the second shooters.

In this paper we ask whether the failure to perform under pressure extends beyond soccer shootouts. Specifically, we replicate APH's analysis and test whether the APH hypothesis extends to the game-outcome determining shootout in the National Hockey League (NHL). Since 2005-06, regular season NHL matches that end in a tie after three 20-minute periods and a single five-minute overtime period are settled with a shootout structured similar to the shootout employed in soccer. Initially, the visiting team was designated the team to shoot first; however, beginning in 2006-07, the home team was given the decision of who shoots first. Teams alternate shots for up to three rounds. If at any point during the first three rounds one team is down more goals than they can score in the remaining first three rounds the shootout ends. If the teams are tied after the first three rounds the shootout moves to sudden-death rounds where the shootout continues until one team scores and the other team does not during the same round. The team that wins the shootout earns two points toward its season total and the losing team is awarded one point.

Generally the empirical evidence suggests that, unlike in soccer shootouts, the second shooter has a slight advantage in NHL shootouts, specifically in the first two rounds. This result provides evidence for the home field disadvantage first discussed in the psychology literature by Baumeister and Steinhilber (1984) and updated in Wallace, Baumeister, and Voh (2005). However, the second-shooter advantage disappears during the sudden death rounds when the first shooter obtains a slight advantage. Notwithstanding the persistence of the second shooter advantage in the early rounds, the home team, which decides which team shoots first, overwhelmingly chooses to shoot first and actually wins less than 50% of the time.

Literature Associated with Performance Under Pressure

Behavioral economics blends the rationality principles established in most economic models with psychological motives that have traditionally been omitted. (1) Much of the empirical support of theoretical behavioral economics has been generated through the observation of carefully constructed laboratory experiments. Such experiments help control for many dynamic and endogenous factors that may influence a subject's behavior. Behavioral economics has found that under various levels of psychological influences, including pressure, strict rationality can be compromised. Since these laboratory experiments are often open to the criticism of a contrived outcome, natural experiments are of significant usefulness in testing the validity of laboratory experiments or behavioral theory in general.

Some of the first empirical tests of sports performance under pressure--coined "performance anxiety" or "choking"--appeared in the psychology literature and were conducted by Baumeister and various co-authors. In these articles they examined how athletes performed under various "stressors" such as playing at home championships (e.g., Baumeister and Steinhilber, 1984) and show that in basketball and baseball home fields become a disadvantage to better performance. This conclusion was supported by Wallace, Baumeister, and Voh (2005), who find that home audience may increase choking. Baumeister (1984) shows that when athletes concentrate on activities that had become second nature, they underperform. Clearly this is immediately applicable to the current research where shootouts require that players make more conscious efforts to score rather than more instinctive behavior found in normal play.

Baumeister, Hamilton, and Tice (1985) show that players experience a greater degree of anxiety when public expectations rise, which, in turn, hurts performance. Interestingly, they also showed that underperformance in a public arena can be overcome if sufficient private confidence is held by the athlete. In a review of the existent literature, Baumeister and Showers (1986) conclude that performance anxiety is enhanced by distraction, "overthinking" instinctive behavior, audience behavior, performance contingent incentives, ego relevance to the task, and player idiosyncratic endowments.

The method by which an NHL shootout is conducted is in the form of a sequential tournament. Such tournaments are not uncommon in labor markets, corporate competition, political elections, patent races, and various other forums. The economics of tournaments has investigated many theoretical and empirical elements of competition, and incentive schemes. (2) The subject of analysis used here is one of a tournament with increasing pressure on its participants. This pressure is found by APH to cause an underperformance of the second shooter in each round of a soccer shootout tournament. The influence of motivations and pressure on performance is a familiar strand of literature in social psychology (Ericsson et al., 2006; Beilock, 2007; Beilock & Gray, 2007; Ariely et al., 2009; Hill et al., 2010; Mesagno et al., 2012).

Natural experiments in which the psychological effects are clearly measurable are difficult to find. Various elements such as the difficulty of the task, the ability of the subject, selectivity bias, the importance to outcome, risk, and the clarity of a conclusion can make many circumstances unsuitable for scientific evaluation. However, the subject of this paper, NHL shootouts, provides a means of limiting the influence of these elements and help to provide a natural circumstance for evaluating the effects of mounting pressure on professionals performing a relatively simple task (at least relatively simple for them).

Natural experiments in the economics literature include Cao et al. (2011), who analyze NBA free throw data and demonstrate that key determinants of player performance under pressure are the score differential at the time of the foul, whether or not the player's team is winning at the time, and the amount of time remaining in the game. They find evidence that attendance, playoff status, or game location impact performance. It should be noted that the Cao et al. (2011) analysis using free throws is not strictly applicable to the NHL shootouts examined here as free throws can occur at any time during a game and do not depend on the score at the end of regulation, whereas shootouts are conducted when teams are tied at the end of regulation and at the end of a five-minute extra period.

In contrast, Dohmen (2008) analyzes German Bundesliga soccer shootout data and finds that home players face increased pressure, which makes them more likely to "choke." Dohmen defines choking not as a non-score, which could either be saved or the goal as missed altogether, but as missing the goal (i.e., a non-save no-goal). Choking on the home field, where the home field is generally considered an advantage, is interpreted as cognitive anxiety in a "friendly" social environment. Like Cao et al. (2011), Dohmen's results dispel the notion that professionals choke under high stakes or properly designed incentives.

APH's (2010) use of soccer shootouts provides two levels of empirical analysis. They first investigate game level data and find that the team that kicks first wins more often, all else equal. They control for various game-level characteristics including the type of match and where the match was played. Their original sample of 262 matches is reduced to 129 usable observations included in their analysis. Their second level of investigation is at the shot level. APH employ data describing 2,731 soccer shootout shots and find that when a shooter is one shot down they have a significantly (both statistically and materially) lower probability of success, all else equal. In this analysis, APH control for goalkeeper fixed effects but unfortunately do not know the identity of the various kickers and therefore are unable to control for kicker-specific effects. Moreover, the sample of soccer shootout shots used in their analysis is not universal.

Notwithstanding the interesting and persistent findings in APH, there are at least three other papers that test the robustness of the performance-under-pressure hypothesis. Feri, Innocenti, and Pin (2011) create an experimental framework in which highquality basketball players are matched against each other and compete in a free-throw shooting contest. The experiment randomly assigns first shooters and shows no firstshooter advantage. However, the stakes and pressure involved in the free-throw shooting contest are low relative to the international stage on which the soccer shootouts occur and the rote act of the free-throw would seem to offer no substantial advantage to either shooter.

A more substantial criticism of APH is offered by Kocher, Lenz, and Sutter (2010), who argue that APH use only a subset of a larger universe of soccer shootouts. They employ an expanded data set which includes 540 shootouts rather than the 126 used in APH. Using the expanded number of shootouts, Kocher, Lenz, and Sutter are unable to replicate the performance-under-pressure results in the APH study. They argue that the (undocumented) sample selection process used by APH contributes to their finding that the performance-under-pressure result might not be as robust as initially thought. While there are some concerns with the data employed by APH, it is possible that the expanded data set pools disparate soccer shootouts, in particular that many of the additional shootouts come from lower-level leagues and lower-pressure tournaments where there might not be as much of an advantage to one shooter over another.

Kolev, Pina, and Todeschini (2010) are closest in spirit to the empirical analysis presented herein and investigate NHL shootouts and document the same stylized fact acknowledged herein: home teams tend to shoot first more often than not and home teams that shoot first tend to lose more often than not. However, their empirical analysis does not focus on more than documenting the unconditional statistical "facts" and they conjecture that these stylized facts are caused by "over confidence" on the part of home teams. We argue below that there are other possible reasons for home teams to shoot first "too often" that do not necessarily involve over confidence. Nevertheless, it is clear that the performance-under-pressure analysis by APH has initiated a wide ranging number of subsequent studies.

Soccer and National Hockey League Shootouts

The NHL shootout was introduced as a new way to determine the outcome of a tied match beginning in 2005-06. Following a labor lockout that canceled the 2003-04 season, it was believed that determining a winner of every game, in a timely fashion, would (re)attract consumers to professional hockey. If regulation ends in a tie score, a single five-minute sudden-death overtime period is played. If a winner is still not determined, the shootout immediately follows. Moreover, the introduction of the shootout required an alteration to the way season aggregated performance points were awarded. Before the shootout, teams were awarded two points for a win, one point to each team for a tie, and no points for a loss. Since the new overtime/shootout rules were introduced, the winning team continues to receive two points but the team losing in overtime or in the shootout receives one point (see Appendix A for the text of the NHL rules governing the shootout).

Variations on the shootout have been introduced in international hockey, association football, and cricket in order to provide an orderly determination of the winner of an otherwise tied match. In soccer the use of the shootout is generally reserved for special matches and is not used during regular season matches and "friendlies," matches that do not contribute points to a competition (e.g., World Cup qualifying games). Various structures of shootouts have been introduced, even within the same sport (not league) and the differences provide an interesting point of departure when thinking about how the performance-under-pressure hypothesis would apply in various contexts.

In a soccer shootout there are five rounds of shots. Each round consists of a single shot from each team. For each successful shot a team is awarded a single point. If, at any point during the first five rounds it is not possible for one team to score enough goals to at least tie the other team, the shootout is over. If the two teams are tied after the first five rounds the shootout moves to a sudden-death scenario where the loser is the first team to miss in round r when the other team scores in round r. The shooting order of the teams in soccer shootouts is determined by a coin flip. The ball is set 12 yards from the goal line and the shooter must directly strike the ball at the goal. The goalkeeper must stay on the goal line until the ball is struck. A soccer goal is 24 feet by 8 feet or 192 square feet. Soccer shots can regularly approach 75-80 miles per hour, that is, the ball will reach the goal line is approximately 0.3 seconds. During the 2010-11 season, the average English Premier League goalkeeper was 74.85 inches tall and 183 pounds (EPL, 2011).

Given the physical structure of the soccer shootout it is not surprising that soccer penalty shots are approximately 78% successful. In other words, there seems to be a significant built-in advantage to the shooter; obviously the goalkeeper can influence the outcome of the shootout to some extent but it is a relatively rare occurrence.

Unlike the selective use of soccer shootouts, the NHL shootout is used throughout the regular season and abandoned for unlimited sudden-death overtime during the post-season and Stanley Cup Finals. (3) Beginning in the 2005-06 season, the hockey shootout consists of three initial rounds with the home team choosing which team shoots first; if after three rounds the teams are still tied the shootout goes to sudden death. Unlike in soccer, where the ball must be directly struck and can only be struck once by the shooter, in the NHL the puck is set at center ice (89 feet from the goal) and must be carried in a continuous forward motion until the shot is taken (NHL rules book, 2010). The goalie must stay in his crease until the puck is touched and then may move freely in defense of the shot. The hockey goal is 4 feet by 6 feet (or 24 square feet) and during the 2010-11 season the average NHL goalie was 73.67 inches tall and 197.7 pounds (NHL.com, 2011).

In contrast to soccer penalty/shootout shots where success is overwhelmingly in favor of the shooter, in the NHL only about 33% of all shootout shots result in a goal; the unconditional evidence suggests that there is a substantial built-in advantage for the hockey goalie. A practical implication of these different success rates is that it might be difficult to isolate when a soccer goalkeeper fails to perform because their success rate is so low. On the other hand, it should be easier to measure and find significant differences between shooters who perform well and those who do not because of the high success rate afforded shooters in the context of a soccer shootout. In the case of the NHL shootout, the roles would seem reversed. Instead of a first-shooter or secondshooter advantage one might think of the performance-under-pressure hypothesis to more clearly fall on the goalie rather than the shooter. Instead of a first-shooter advantage/disadvantage it might prove useful to cast the question in terms of first-goalie advantage/disadvantage. In other words, in a hockey shootout a first-shooter advantage would not necessarily point to a failure of the second shooter to perform but might point to the first goalie failing to perform relative to the second goalie.

This subtle but arguably important distinction between the NHL and soccer shootouts allows for an interesting test of the failure-to-perform hypothesis. If, after controlling for goalie and shooter characteristics to the extent possible, there exists an advantage for one team over the other, it would suggest that the failure-to-perform hypothesis is applicable to shootouts in regular season hockey matches.

National Hockey League Shootouts: Data and Empirical Strategy

Data

The data employed in this study reflect every shootout from the 2004-05 through the end of the 2010-11 season. Data describing a total of 956 hockey shootouts were gathered from the NHL and include whether the home team won (yes/no), whether the home team shot first (yes/no), statistics describing the play of both teams during regulation, including the number of penalty minutes, power play opportunities, power play goals, and the number of shots on goal. We also identify whether the game is between two teams in different conferences or within the same division, whether the game is between two traditional rivals, the day of the week and month of the season on which the match was played, and the home team and visiting team divisions. These data are used to test whether there is a systematic advantage for the home team winning a shootout and whether any advantage has shifted from the initial year of NHL shootouts, 2005-06, during which the visiting team shot first by rule. As described below, there is an inherent endogeneity problem with the game-level data since the initial season of the shootout. Unlike soccer shootouts, the choice of who shoots first is not random but is determined by the home team. To accommodate the endogeneity a Heckman-like estimator is employed with several instruments used to model the choice of who shoots first.

Again following APH, additional analysis focuses on what contributes to a successful shootout shot. However, unlike APH, the shot-level data used here represent the entire universe of the 6,760 NHL shootout shots through the 2010-2011 season. The data record whether the shot was a goal or not, the net score between the first-shooting team and second-shooting team going into the shot, a dummy variable that indicates whether the shot is a potential winner (if shot is made then shooter's team wins) or a potential loser (if shot is missed then shooter's team loses), the importance of the shot, and the previous shot's outcome (success or failure).

Table 1 reports descriptive statistics for the two data sets employed in this paper; the upper panel reports on game-level data and the bottom panel reports on shot-level data. For the entire sample period, which includes the entire period of time during which the NHL has used shootouts to determine the winner of regular season games, the home team has won 47.8% of all matches. The team that shoots first has won 48.6% of shootouts, indicating that there may be a slight advantage in NHL shootouts to shooting second. However, over the history of the NHL shootout the home team has shot first 63.2% of the time, and that includes the 145 shootouts that occurred in the 2005-06 season during which the visiting team shot first by rule. Indeed, since the home team began choosing who shoots first in the 2006-07 season, the home team has chosen to shoot first 76% of the time even though it seems to have a deleterious impact on their chances of winning. The trend is for the home team to shoot first, despite the lower frequency of success when doing so. Since 2005-06, the rate at which the home team has selected to shoot first has increased annually from 64% in 2006-07 to 82% in 2010-11. (4)

The average number of rounds for a shootout is 3.40 and 67% of all shootouts never enter the sudden-death stage beyond three rounds. The longest shootout was 15 rounds (Washington at New York Rangers, November 26, 2005) and shortest shootouts are only two rounds. Among those games that went to a shootout, approximately 18% were between teams in different conferences, 35% were between teams in the same division, and only 3% were between teams considered historical rivals. (5)

The upper panel of Table 1 also reports the percentage of time that the home team had more penalty minutes during regulation play (48%), that the home team had more power play opportunities than the visiting team (49%), that the home team had more power play goals scored during regulation (30%), that the home team had more shots on goal during regulation play (54%), and that the home team had participated in more shootouts coming into the match (45%). However, much like APH, we find little statistical evidence that there is a systematic difference between home team and visiting team characteristics when a shootout occurs. That is, the occurrence of a shootout appears to be essentially random with respect to team performance statistics.

The lower panel of Table 1 reports descriptive statistics for the 6,670 individual shootout shots from the 2005-06 through the 2010-11 seasons. The shooter is successful approximately 32% of the time (which is in stark contrast to the success rate in soccer of approximately 75%). Figure 1 provides a representation of the unconditional probability of each shooter being successful in each of the first five rounds of a shootout. While the second shooter in the first two rounds tends to be successful at a higher rate, this advantage flips in later rounds (the higher success rate of the first shooter continues into later rounds not shown in Figure 1).

The dummy variable Second Shooter takes a value of one if the shooter is the second shooter in the round; slightly less than half of the observations are of second shooter, which occurs because a second shooter might not be necessary if a shootout's results are determined after the first shooter in the third round. Approximately 19% of all shootout shots are a potential winner in the sense that if the shot is successful the shooter's team wins. On the other hand 12% of all shootout shots are potential losers in the sense that if the shot is not successful the shooter's team will lose. Approximately 3% of all shootout shots take place during a rivalry game (as defined here), 17% take place during an inter-conference game, and 36% take place during an intra-division game.

Empirical Methodology

Our empirical methodology aims to replicate, as much as possible, that used by APH. This is done in order to be able to compare the results from NHL shootouts with those from international soccer, thus we mimic their explanatory variables and empirical methodology as much as possible. We first look at unconditional tests to determine if there are systematic reasons that one team might win a shootout , including whether performance statistics from regulation play of the game in question influence the outcome of the shootout and whether the number of shootouts in which a team has participated influences the odds of winning the shootout. In other words, it might be the case that two teams happen to end up tied at the end of regulation but one team has out-performed the other in ways not reflected in the score. If this imbalance of on-ice performance influences the outcome of the shootout then this might obviate any failure-to-perform under pressure that might appear to describe the data. Our unconditional analysis is very much in the spirit of APH.

The next step in our analysis also replicates that of APH. While the unconditional analysis shows whether specific characteristics of regulation play or team experience influence the outcome of a shootout, a conditional analysis is undertaken in which the dependent variable takes a value of one if the home team wins and zero otherwise. The explanatory variables include the game's characteristics during regulation play, characteristics of the game that attempt to capture the importance or pressure the players might feel during the game, e.g., is the game a rivalry game, is the game an intra-division game, which might be more important and hence carry more pressure, and whether the game is an inter-conference game, which should carry the least amount of pressure, all else equal. The most important variable in this model is whether the home team shoots first. However, unlike the international soccer shootouts, in the NHL the decision of whether to shoot first is not random: since the 2005-06 season the home team chooses which team shoots first. This suggests that the decision for the home team to shoot first is an endogenous variable that requires at least one instrument. We first estimate models that treat the decision of home team shooting first as exogenous and then expand our analysis to accommodate the endogeneity of which team shoots first.

If we consider the probability that the home team wins as p and the probability that the home team loses as 1-p, then the likelihood function that the home team wins over N can be modeled as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [y.sub.i] equals one if the home team wins and zero otherwise. Various specifications of p exist; here we choose the standard Normal distribution such that:

[phi]{Homewins = 1|[x.sub.i]) = 0([x.sub.i][beta]),

where [x.sub.i][beta] is a linear combination of explanatory variables, x, and parameters to be estimated, [beta], and i = 1 ... 957 where i = 1 corresponds with the first shootout in NHL history. Estimation entails maximizing the log-likelihood function over b using the standard probit estimator.

The regressors include the following dichotomous variables: HOMESHOTFIRST takes a value of one if the home team shoots first (as mentioned the decision on what team shoots first is not random and the endogeneity issue is addressed in the next section); INTERCONFERENCE equals one if the game is between two teams in separate conferences; INTRADIVISION takes a value of one if the two teams are in the same division; RIVALRY takes a value of one if the game is a rivalry game; HOMEPIM takes a value of one if the home team had more penalties in minutes than the visiting team during regulation play; HOMEPPOPP is one if the home team had more power play opportunities than the visiting team during regulation play; HOMEPPGF takes a value of one if the home team had more power play goals scored than the visiting team during regulation; HOMESHOTS is one if the home team had more shots on goal than the visiting team during regulation; and HOMEEXP takes a value of one if the home team had participated in more shootouts than the visiting team (in the current season) coming into the game. The remaining regressors are vectors of exogenous dummy variables: HOMEDIVISION takes the value of one for the home team's division; DAYOFWEEK represents the day of the week during which the match was played; MONTHOFSEASON controls for month of the season during which the match was played; and YEAR represents the year the match was played.

A comparison of the in-game characteristics based on which team shoots first or second in the shootout is presented in Table 2. There is no statistical difference between the first and second shooting team in the shootout in regards to who had the most penalty minutes, power play opportunities, power play goals during regulation play, or shootout experience. However, teams that have taken more shots during the course of play also tend to shoot first slightly more often in the shootout.

After analyzing game-level data, APH also investigate shot-level data for soccer shootouts. They find that, after controlling for the setting in which the shot takes place, ostensibly to control for the shot's importance and relative pressure, the second shooter consistently underperforms. We replicate their analysis after creating analogous explanatory variables in the hockey data.

Estimation Results

The outcomes of soccer shootouts, as presented in APH, and outcomes of hockey shootouts tend to be significantly different from one another. The first team is found to win approximately 60% of soccer shootouts, even though the team that shoots first is randomly determined. Meanwhile, the unconditional results suggest that teams that shoot second in a NHL shootout win slightly more frequently than teams that shoot first. At the same time, home teams increasingly select to shoot first. In the 2005-06 season, when the visiting team shot first by rule, the first shooting team won 48.3% of all shootouts. In the following seasons, when the home team was given the choice of shooting first or second, the first shooting team won 48.6% of all shootouts and the home team selected to shoot first 76% of the time. These unconditional results might mask more nuanced influences on who wins a shootout and when the home team decides to shoot first. The results from various probit models are presented in Table 3.

The first two models presented in Table 3 are standard probit estimations of the home team's success in winning the shootout. The first model is estimated using only data from the 2005-06 season, when the visiting team shot first by rule. The only game characteristic that is a significant determinant of whether the home team is victorious in the shootout is whether the home team had more shots on goal during regulation and overtime play: home teams that have shot more than their opponents in the course of play do tend to win shootouts less frequently. The second model estimates a similar probit for the entire data set, treating whether the home team shot first in the shootout as exogenous to the outcome of the shootout. Once again, game characteristics provide little insight into whether the home team wins the shootout. The lone exception is that home teams that score more power play goals during regulation lose more often in the shootout. In this specification the the home team shooting first has a positive but insignificant influence on home team winning.

Endogeneity of Who Shoots First

While in international soccer shootouts the first-shooting team is determined by a coin toss, since 2006 the home team chooses which team shoots first in a NHL shootout. Thus, since 2006 shooting first is not a strictly exogenous factor in the outcome of the hockey shootout. To highlight the potential problem with failing to account for the endogeneity, consider Model (1) and Model (2) in Table 3. Model (1) uses only the 145 shootouts from the 2005-06 season whereas Model (2) uses all 957 shootouts from the sample period. In Model (1) home teams that have shot more than their opponents during regulation tend to win shootouts less frequently. This is the only significant determinant of whether the home team wins a shootout. In Model (2) home teams with more power play goals tend to win shootouts less frequently. This is the only significant determinant of whether the home team wins a shootout; the home team shooting first carries a positive parameter estimate that is statistically insignificant.

However, in a probit model it is not possible to sign the endogeneity bias as is often possible in the linear regression model. Therefore, it is not possible to say with certainty whether the impact of the home team shooting first is actually positive or negative on the odds of winning. Thus, it is necessary to move to an instrumental variables approach. To accommodate the endogeneity of the home team shooting first, a bivariate probit model is estimated which entails estimates of two probit models simultaneously, the first describing whether the home team wins the shootout and the second whether the home team shoots first.

Identifying the choice of shooting first requires at least one variable that is correlated with the probability of the home team shooting first that is not correlated with the odds that the home team would win a particular shootout. Among possible instruments we considered the number of shootouts which the home team and the visiting team have lost during the current season and the attendance to the game. Intuitively, the more overtime losses the home team has suffered, the home team coach might feel pressure to elect to shoot first to show confidence in his players and to the home team fans. On the other hand, the more overtime losses the visiting team has suffered, the home team might choose to let the visiting team shoot first. Finally, the more people in attendance at the game the greater the pressure the home team coach might feel to elect to shoot first. These variables are also considered candidate instruments because it is not clear how these variables would directly influence the odds of the home team winning or losing. (6)

In Table 3, Model (3a) and Model (3b) report the results of the bi-variate probit estimation for each equation; Model (3a) reports the results of the model describing whether the home team shoots first and Model (3b) the results of the model describing whether the home team wins.

Model (3a) presents the marginal effects from the probit equation describing whether the home team elects to shoot first. The greater the number of overtime losses the home team has incurred prior to the relevant game, the more likely they are to choose to shoot first. There is evidence that home teams choose to shoot first to please home fans: greater attendance is correlated with an increase probability of the home team shooting first. Meanwhile, the number of overtime losses by the visiting team has no statistically meaningful impact on whether the home team elects to shoot first.

In Model (3b) the odds of the home team winning the shootout falls when the home team shoots first. This result is in contrast to that obtained with standard probit estimation, reported as Model (2) in Table 3, which ignored the endogeneity of which team shoots first. Consistent with Model (2) when the home team has scored more power play goals during regulation play, it tends to win a shootout less frequently. Despite the fact that the home team can choose to shoot second in the shootout and shooting first reduces the odds of winning the shootout, home teams overwhelmingly continue to select to go first. Why?

One possible explanation is that the decision maker, usually the head coach, might be responding to the demands of fans and other stakeholders. If "conventional wisdom" is that shooting first has an advantage, the coach of a lower quality team might opt to go first in an attempt to avoid blame for a loss. Even though shooting first leads to a greater likelihood of losing, the coach is unlikely to be questioned about his decision if it is the accepted norm. On the other hand, if a coach elects to shoot second and his team loses, it might be he, and not the players, who will be questioned about the result. (7)

Individual Shot Analysis

The outcome of an individual shot in an NHL shootout, goal or no goal, may depend upon various characteristics of the team, the game, and the current circumstances of the shootout tournament. In Table 4, we replicate the models of APH (2010) to evaluate the determinants of shot success based on the various conditions within the shootout under which the shot is taken and controlling through various fixed effects for when the game is played, the round of the shot, and various characteristics of the game. Model (1) is a baseline model that includes only whether the previous shot was a goal, and whether the current shooter's team is ahead by one, whether the two teams are tied, and whether the current shooter's team is behind by one; none of these variables are statistically meaningful. Models (2), (3), and (4) in Table 4 include more explanatory variables including a dummy variable that takes a value of one if the shot is the second shot in a round, whether the shot is a potential loser for the shooter, whether the shot is a potential winner for the shooter, and the importance of the shot. (8) The models differ in the other control variables included: Model (2) includes month and year fixed effects but no round fixed effects or game characteristics; Model (3) includes month, year, and round fixed effects but no game characteristics; Model (4) includes month and year fixed effects and game characteristics but not round fixed effects.

In all three models shooting second increases the odds of a successful shot. (9) And the more important the shot the more likely the shot is a success. These results seem to contradict those of APH, who find that going second lowers a shooter's success rate. However, there is a potential reconciliation between these two seemingly different results. In a soccer shootout the advantage lies with the shooter; approximately 75% of all shots are successful. In hockey the advantage lies with the goalie; only 33% of all shots are successful. Therefore, the two results are consistent with the player with the greater inherent advantage in the shootout failing to perform in the second half of a shootout round. In soccer the shooter performs worse, in hockey the goalie performs worse. (10)

Conclusions

APH have an interesting and compelling empirical finding that suggests performance is negatively affected by pressure. We replicate their analysis with a similar data set from a different sport: while APH use international soccer shootouts, we use all NHL shootouts from the 2005-2006 through the 2010-2011 seasons. Following APH's methodology we find that the team that shoots second tends to win more often. Unlike in the case of international soccer, wherein the team that shoots first is determined by coin toss, in the NHL the home team chooses who shoots first, introducing endogeneity. We estimate a bivariate probit model which suggests that greater attendance corresponds with a higher probability that the home team shoots first and that lower quality home teams also are more likely to shoot first. However, even after controlling for the endogeneity of which team shoots first, the second shooting team tends to win more often. This leads to a natural question: why do home teams continue to choose to shoot first when they are more likely to lose? We suggest that coaches might be risk-averse and therefore choose to go first to satisfy home fans' desire to see their team go first (regardless of its effect on winning) or to avoid blame if the team loses the shootout as the second shooting team.

To evaluate the direct effects of pressure on individual shots, we also estimate APH-like models for 6,760 shootout shots. Consistent with the game-level results, the evidence suggests that second shooters tend to perform better during hockey shootouts even after controlling for goalie-shooter combination fixed effects. Because the natural advantage in the hockey shootout lies with the goalie, we interpret this evidence as suggestive that second goalies underperform due to pressure. While this seems to counter APH's finding, it actually offers support to their intuition because in soccer shootouts the overwhelming advantage lies with the shooter. When the second shooter underperforms, APH interpret that as failure to perform under pressure; similarly, when the second goalie underperforms in hockey, we interpret that as failure to perform under pressure.

Future research in this area will focus on modeling whether a particular hockey shot was a goal, corresponding with clear success by the shooter and clear failure by the goalie; a save, corresponding with clear failure by the shooter and clear success by the goalie; or a miss, corresponding with clear failure by the shooter and ambiguous success by the goalie. The latter category should allow for a clear identification of which player in the shootout is failing to perform under pressure.

Appendix A: NHL Rule 84.4 Concerning the Shootout and NHL Rule 24 Concerning the Penalty Shot

The following is the direct text of NHL rule 84.4, which describes the rules pertaining to the shootout as of February 2012:

84.4 Shootout-During regular-season games, if the game remains tied at the end of the five (5) minute overtime period, the teams will proceed to a shootout. The rules governing the shootout shall be the same as those listed under Rule 24 - Penalty Shot.

The teams will not change ends for the shootout. The home team shall have the choice of shooting first or second. The teams shall alternate shots.

Three (3) players from each team shall participate in the shootout and they shall proceed in such order as the coach selects. All players are eligible to participate in the shootout unless they are serving a ten-minute misconduct or have been assessed a game misconduct or match penalty.

Guidelines related to stick measurement requests during the shootout are outlined in 10.7-Stick Measurements-Prior to Shootout Attempt.

Once the shootout begins, the goalkeeper cannot be replaced unless he is injured. No warm up shall be permitted for a substitute goalkeeper.

Each team will be given three shots, unless the outcome is determined earlier in the shootout. After each team has taken three shots, if the score remains tied, the shootout will proceed to a "sudden death" format. No player may shoot twice until everyone who is eligible has shot. If, however, because of injury or penalty, one team has fewer players eligible for the shootout than its opponent, both teams may select from among the players who have already shot. This procedure would continue until the team with fewer players has again used all eligible shooters.

Regardless of the number of goals scored during the shootout portion of overtime, the final score recorded for the game will give the winning team one more goal than its opponent, based on the score at the end of overtime.

The losing goalkeeper will not be charged with the extra goal against. The player scoring the game-winning goal in the shootout will not be credited with a goal scored in his personal statistics.

If a team declines to participate in the shootout procedure, the game will be declared as a shootout loss for that Team. If a team declines to take a shot it will be declared as "no goal."

The following is the direct text of NHL Rule 24.1 and NHL Rule 24.2 which describe the rules pertaining to the penalty shot as of February 2012:

24.1 Penalty Shot--A penalty shot is designed to restore a scoring opportunity which was lost as a result of a foul being committed by the offending team, based on the parameters set out in these rules.

24.2 Procedure--The referee shall ask to have announced over the public address system the name of the player designated by him or selected by the team entitled to take the shot (as appropriate). He shall then place the puck on the center face-off spot and the player taking the shot will, on the instruction of the referee (by blowing his whistle), play the puck from there and shall attempt to score on the goalkeeper. The puck must be kept in motion towards the opponent's goal line and once it is shot, the play shall be considered complete. No goal can be scored on a rebound of any kind (an exception being the puck off the goal post or crossbar, then the goalkeeper and then directly into the goal), and any time the puck crosses the goal line or comes to a complete stop, the shot shall be considered complete.

The lacrosse-like move whereby the puck is picked up on the blade of the stick and "whipped" into the net shall be permitted provided the puck is not raised above the height of the shoulders at any time and when released, is not carried higher than the crossbar. See also 80.1.

The spin-o-rama type move where the player completes a 360[degrees] turn as he approaches the goal, shall be permitted as this involves continuous motion.

Only a player designated as a goalkeeper or alternate goalkeeper may defend against the penalty shot.

The goalkeeper must remain in his crease until the player taking the penalty shot has touched the puck.

If at the time a penalty shot is awarded, the goalkeeper of the penalized team has been removed from the ice to substitute another player, the goalkeeper shall be permitted to return to the ice before the penalty shot is taken.

The team against whom the penalty shot has been assessed may replace their goalkeeper to defend against the penalty shot, however, the substitute goalkeeper is required to remain in the game until the next stoppage of play. While the penalty shot is being taken, players of both sides shall withdraw to the sides of the rink and in front of their own player's bench

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Endnotes

(1) Rationality principles have incorporated social attitudes, altruism, values, and other elements. Some of the seminal works in this area are from Becker (1976, 1996) and Becker and Murphy (2000).

(2) The initial formal discussion of the economics of tournament was done by Lazear and Rosen (1981). For a review of other tournament related findings see Predergast (1999).

(3) This is in contrast to professional hockey in the Czech Republic, where the shootout is used during all regular season and non-finals post-season matches.

(4) As mentioned by an anonymous referee, the fact that the home team chooses to shoot first may indicate expectation that it puts greater pressure on the second shooter.

(5) The traditional rivalries used here include Detroit vs. Chicago, Boston vs. New York Rangers, Montreal vs. Toronto, Boston vs. Montreal, Calgary vs. Edmonton, and Boston vs. Philadelphia.

(6) Additional instruments were considered, including interacting attendance with home team overtime losses, whether the game was a rivalry game, whether the game was an intra-divisional game, and whether the home team had more points heading into the match. These variables were not correlated with the odds of shooting first and increased the standard error of the impact of the home team shooting first on the odds of winning so that home team shooting first became statistically insignificant. Moreover, the Sargan J-statistic of 3.75 leads one to reject the null of instrument exogeneity.

(7) This is similar in spirit to the experience of Coach Bill Belichick of the New England Patriots. In a controversial move, Belichick decided to go for a fourth-down conversion late in a game against the Indianapolis Colts late in the 2009 season. The conversion failed, which gave Indianapolis a "short field" from which the Colts scored to win the game in the final seconds. Belichick faced considerable second-guessing for his decision to attempt the fourth-down conversion rather than punting, as most people expected him to do.

(8) This measure is borrowed directly from APH (2010). The importance of a shot is measured as the difference in the conditional probabilities of the team winning if the shot is successful and the conditional probability of the team winning if the shot is unsuccessful.

(9) We estimated a model similar to Model (3) but including goalie-shooter fixed effects. When estimating this model the sample size falls to 1,229 observations because the majority of goalieshooter matchups have only one observation or all observations for a particular goalie-shooter combination are goals or all observations for a particular goalie-shooter are non-goals. Nevertheless, the results yield a statistically significant positive marginal effect of being second shooter of 0.377 (standard error of 0.162).

(10) As pointed out by an anonymous referee, it is entirely possible that there is a naturally lower conversion rate in hockey shootouts because the goalie has an inherent advantage because of the smaller square area of the hockey goal and it is still shooters who experience increased pressure in the first round and therefore they perform worse. Future research will focus on newly gathered data that describe the actual outcome of each shootout shot (save, miss, or goal), which will facilitate actually identifying which of the two parties involved in the shootout actually perform worse than expected.

Craig A. Depken, II [1], Robert J. Sonora [2], and Dennis P. Wilson [3]

[1] UNC Charlotte

[2] Fort Lewis College

[3] Western Kentucky University

Craig A. Depken, II, PhD, is a professor in the Department of Economics. His research interests include industrial organization, applied microeconomics, and sport economics. Robert J. Sonora, PhD, is an associate professor of economics and the director of the Office of Business and Economic Research. His research interests include economic transition, monetary economics, international trade, and sport economics. Dennis P. Wilson, PhD, is an associate professor in the Department of Economics. His research interests include applied microeconomics, industrial organization, and sport economics.

Table 1: Descriptive Statistics of the Data

Game Level Data (N=957)

Variable Mean Std. Dev.

Home Victory 0.478 0.499
Home Shot First 0.632 0.482
Number of Rounds 3.40 1.83
Inter-Conference Game 0.177 0.382
Intra-Division Game 0.355 0.478
Rivalry Game 0.030 0.171
Home Team More Penalties in Minutes 0.479 0.199
 During Regulation
Home Team More Power Play Opportunities 0.491 0.500
 During Regulation
Home Team More Power Play Goals Scored 0.304 0.460
 During Regulation
Home Team had More Shots on Goal 0.537 0.498
 During Regulation
Home Team has Participated in More Shootouts 0.446 0.497
Instruments for Home Shooting First
Visitor's Overtime Losses 4.453 3.238
Home's Overtime Losses 4.611 3.318
Home has More Performance Points 0.446 0.497
Attendance (thousands) 17.118 3.164

Shot Level Data (N=6,760)

Goal 0.324 0.468
Shooter's Number of Shootout Shots 12.52 11.963
Goalie's Number of Shootout Shots 50.64 44.494
Number of Shooter-Goalie Matchups 0.25 0.605
Second Shooter 0.481 0.499
Potential Winner 0.185 0.388
Potential Loser 0.120 0.325
Rivalry Game 0.029 0.168
Inter-Conference Game 0.168 0.373
Intra-Division Game 0.356 0.479

Game Level Data (N=957)

Variable Min Max

Home Victory 0 1
Home Shot First 0 1
Number of Rounds 2 15
Inter-Conference Game 0 1
Intra-Division Game 0 1
Rivalry Game 0 1
Home Team More Penalties in Minutes 0 1
 During Regulation
Home Team More Power Play Opportunities 0 1
 During Regulation
Home Team More Power Play Goals Scored 0 1
 During Regulation
Home Team had More Shots on Goal 0 1
 During Regulation
Home Team has Participated in More Shootouts 0 1
Instruments for Home Shooting First
Visitor's Overtime Losses 0 14
Home's Overtime Losses 0 14
Home has More Performance Points 0 1
Attendance (thousands) 6.495 71.217

Shot Level Data (N=6,760)

Goal 0 1
Shooter's Number of Shootout Shots 0 59
Goalie's Number of Shootout Shots 0 232
Number of Shooter-Goalie Matchups 1 7
Second Shooter 0 1
Potential Winner 0 1
Potential Loser 0 1
Rivalry Game 0 1
Inter-Conference Game 0 1
Intra-Division Game 0 1

Table 2: Unconditional Differences Between First Shooting
and Second Shooting Team

 First Second Equal
Variable Shooter Shooter Means
 Mean Mean (p-value)

More Penalty Minutes During Play 0.485 0.514 0.339

More Power Play Opportunities 0.504 0.495 0.776
During Play

More Power Play Goals During Play 0.515 0.484 0.206

More Shots on Goal During Play 0.526 0.473 0.092

More Shootout Experience 0.496 0.503 0.814

Table 3: Determinants of Home Team Winning Shootout

 (1) (2)
Dependent Variable: Home Home
 Win Win

 Probit Probit
 (2005-06)

Home Shot First 0.025
 (0.044)
Home More Penalty Minutes -0.029 0.037
 (0.110) (0.037)
Home More Power Play Goals -0.045 -0.090 **
 (0.092) (0.036)
Home More Shots on Goal -0.164 * 0.021
 (0.095) (0.043)
Home More Shootout Experience 0.040 0.036
 (0.108) (0.040)
Visitor Overtime Losses
Home Overtime Losses
Attendance
Division Effects YES YES
Month Effects YES YES
Day of Week Effects YES YES
Year Effects NO YES
Observed Prob./Predicted Prob 0.517/0.512 0.477/0.476
[H.sub.0]: Independent Equations
Observations 145 957

 (3a) (3b)
Dependent Variable: Home Team Home
 Shoots First Win

 Bi-variate Bi-variate
 Probit Probit

Home Shot First -0.298 ***
 (0.076)
Home More Penalty Minutes 0.014
 (0.015)
Home More Power Play Goals -0.036 **
 (0.019)
Home More Shots on Goal 0.013
 (0.015)
Home More Shootout Experience 0.020
 (0.015)
Visitor Overtime Losses -0.003
 (0.002)
Home Overtime Losses 0.005 ***
 (0.001)
Attendance 0.003 *
 (0.002)
Division Effects NO NO
Month Effects NO YES
Day of Week Effects NO NO
Year Effects NO YES
Observed Prob./Predicted Prob 0.517/0.512
[H.sub.0]: Independent Equations 3.557 **
Observations 957 957

Notes: Marginal effects reported. Model (1) and Model (2) estimated
using probit estimator with standard errors clustered on home
team/arena. Model (3a) and Model (3b) estimated using bi-variate
probit, which treats as endogenous whether home team shoots first.
Both models have standard errors clustered on home team/arena.
Sargan J statistic is 0.93 (p=0.82), suggesting instruments are
valid. Standard errors reported in parentheses. *** p<0.01, **
p<0.05, * p<0.1

Table 4: Determinants of a Successful Shot

 (1) (2) (3) (4)
VARIABLES Shooter Shooter Shooter Shooter
 Scores Scores Scores Scores

Previous Shot Good -0.019 -0.021 -0.015 -0.021
 (0.015) (0.015) (0.016) (0.015)
Lead by One 0.010 0.064 0.079 0.065
 (0.059) (0.065) (0.073) (0.065)
Tied 0.000 0.064 0.085 0.064
 (0.059) (0.064) (0.072) (0.064)
Trail by One 0.023 0.069 0.075 0.069
 (0.062) (0.067) (0.070) (0.067)
Second Shooter 0.206 *** 0.197 *** 0.205 ***
 (0.047) (0.060) (0.047)
Shot is Potential 0.033 0.058 0.034
 Loser (0.028) (0.042) (0.028)
Shot is Potential 0.013 0.039 0.012
 Winner (0.021) (0.032) (0.021)
Importance of Shot 0.584 *** 0.585 *** 0.582 ***
 (0.150) (0.200) (0.150)
Month Fixed Effects YES YES YES YES
Year Fixed Effects YES YES YES YES
Round Fixed Effects NO NO YES NO
Game Characteristics NO NO NO YES
Observations 6760 6760 6758 (a) 6760

Notes: (a) Two observations are lost because only two shootouts
extended beyond the 13th round. Robust standard errors in parentheses.
*** p<0.01, ** p<0.05, * p<0.1

Figure 1: Unconditional Probability of Scoring by Shooting Order and
by Round (First Five Rounds)

Probability of Scoring by Round

 1 2

1 0.325 0.366
2 0.317 0.348
3 0.328 0.310
4 0.383 0.317
5 0.295 0.271

Note: Table made from bar graph.