Performance under pressure in skill tasks: An analysis of professional darts

Marius Ötting; Christian Deutscher; Sandra Schneemann; Roland Langrock; Sebastian Gehrmann; Hendrik Scholten

doi:10.1371/journal.pone.0228870

. 2020 Feb 21;15(2):e0228870. doi: 10.1371/journal.pone.0228870

Performance under pressure in skill tasks: An analysis of professional darts

Marius Ötting ^1,^2,^*, Christian Deutscher ², Sandra Schneemann ², Roland Langrock ¹, Sebastian Gehrmann ², Hendrik Scholten ²

Editor: Darrell A Worthy³

PMCID: PMC7034807 PMID: 32084161

Abstract

Understanding and predicting how individuals perform in high-pressure situations is of importance in designing and managing workplaces. We investigate performance under pressure in professional darts as a near-ideal setting with no direct interaction between players and a high number of observations per subject. Analyzing almost one year of tournament data covering 32,274 dart throws, we find no evidence in favor of either choking or excelling under pressure.

Introduction

The effect of pressure on human performance is relevant in various areas of the society, including sports competitions [1], political crises [2], and performance-based payment in workplaces [3], to name but a few. A broad distinction differentiates between effort and skill tasks. Success in effort tasks is dependent on motivation to perform while skill task outcomes underlie precision of (often automatic) execution. For effort tasks, such as counting digits [4] or filling envelopes [5], individuals will typically respond to increased pressure (e.g. resulting from performance-related payment schemes) by investing more effort, which given the nature of such tasks will improve their performance [6; 7; 8; 9]. However, the literature on the impact of pressure on performance in skill tasks, e.g. juggling a soccer ball [10], is inconsistent and effectively divided into two different strands of research.

On the one hand, the existing literature related to potential “choking under pressure” indicates broad agreement that performance in skill tasks declines in high-pressure or decisive situations. An individual is said to be choking under pressure when their performance is worse than expected given their capabilities and past performances [11]. While there may also be random fluctuations in skill levels, choking under pressure refers to systematic suboptimal performance in high-pressure situations. The associated empirical findings—both such that are based on experimental data but also those using field data—consistently confirm a negative impact of pressure on skill tasks. On the other hand, and to some extent in contrast to the literature related to choking under pressure, the literature related to the concept of “social facilitation” refers to potential negative but also potential positive effects of (social) pressure on performance—depending on circumstances associated with the performance. The social facilitation literature explicitly incorporates characteristics of the task and individuals’ level of expertise into their analyses, and generally states that the circumstances surrounding performance play an important role regarding the impact of pressure on performance. Existing contributions focusing on potential choking have largely neglected the corresponding more comprehensive picture drawn by the social facilitation literature, by simply relating performance decrements to changes in the execution of actions, or simply distraction, generated either by rewards in case of success [12; 3] or potential penalties in case of failure [13].

Our empirical investigation of individual’s performance in pressure situations is based on a large data set from a skill task, namely professional darts, comprising 32,274 individual dart throws, for a comprehensive empirical test of performance under pressure. For the professional darts players analyzed in this study, playing darts is a full time job. The top players regularly earn prize money exceeding one million Euro per year. In professional darts, highly skilled players repeatedly throw at the dartboard from the exact same position effectively without any interaction between competitors, making the task highly standardized. The amount of data available on throwing performances not only allows for comprehensive inference on the existence and the magnitude of any potential effect of pressure on performance, but also enables to track the variability of the effect across players. The literature on choking would suggest that performance of professional darts players declines in high-pressure situations. However, when considering the highly standardized task to be performed and players’ high level of expertise, we do not expect dart players to choke under pressure.

The paper is structured as follows: Section 2 reviews the literature on performance under pressure, and in particular details what we consider to be advantages of the darts setting with respect to investigating performance under pressure. In Section 3, we explain the rules of darts and define what constitutes pressure situations in darts. Section 4 presents the empirical approach and results.

Performance under pressure

Terminology

Pressure results from individuals’ ambitions to perform in an optimal way in situations where high-level performance is in demand [12]. Performance under pressure could in principle go either way, i.e. high expectations towards (the own) performance could impact performance in a negative (choking) or a positive (clutch) way—or not at all. To measure the impact of pressure, performance in pressure situations is compared to performance in non-pressure situations. Choking under pressure refers specifically to a negative impact of high performance expectations [14; 15] while clutch performance is described as “any performance increment or superior performance that occurs under pressure circumstances” (see p. 584 in [16]).

Potential effects of pressure

The impact of pressure on performance crucially depends on the type of task to be performed. Tasks can be such that performance is determined mostly by effort, or alternatively tasks can be such that the skill level is the key factor for success. For effort tasks, pressure situations result in increased effort and hence improved performance [17]. For skill tasks, performance has been demonstrated to be both impaired (choking) and increased (clutching) by pressure—or not affected at all. While the effect of pressure on effort tasks is obvious and well documented, in skill tasks the potential psychological factors at play are likely more complex, such that we focus on these tasks in the following.

Choking

Choking under pressure in skill tasks may be related to various drivers. In particular, different skills may make use of different memory functions, namely explicit and procedural memory, respectively [18]. Explicit memory enables the intentional recollection of factual information, while procedural memory works without conscious awareness and helps at performing tasks. Two classes of attentional theories capture choking under pressure, distraction theories and explicit monitoring theories [19; 1]. Some authors argue that distraction and explicit monitoring theories are not necessarily mutually exclusive, but rather complementary (see, e.g., [20; 21]). Distraction theories claim high-pressure situations to harm performance by putting individuals’ attention to task irrelevant thoughts [20; 22]. Put in a nutshell, individuals concern about two tasks at once, since the situation-related thoughts add to the task to be performed. Given the restricted working memory individuals performance declines as focus is drawn away from the main task [23].

On the other hand, self-focus or explicit monitoring theories explicitly predict that pressure increases self-consciousness to a point where it harms performance (overattention). It can cause the skilled performer to deviate from routine actions [24]. Instead, closer attention is paid to the single processes of performance and their step-by-step control. This ties in with the concept of skill acquisition: when initially learning a skill, performance is controlled consciously by explicit knowledge as actions are executed step-by-step [25]. Over time and through practice, skills become internalized and usage of conscious control decreases. Pressure can interfere with this now automated control processes of skilled performers [26]. Under pressure, actions are no longer executed automatically as attention is redirected to task execution [19]. The overall sequence of actions is broken down into step-by-step control as in early stages of learning, resulting in impaired performance [27]. Consequently, individuals consciously monitor and control a skill they would perform automatically in non-pressure situations [28; 19].

Other potential effects

An alternative strand of literature suggests that ‘pressure’ situations do not inevitably affect performance in a negative way but may also have a positive impact on task performance—or no effect at all. The corresponding notion of social facilitation is one of the oldest paradigms within experimental social psychology (see, e.g., [29; 30]): “Generally, social facilitation refers to performance enhancement and impairment effects engendered by the presence of others either as coactors or, more typically, as observers or an audience” (see p. 75 in [31]). A potential theoretical explanation for the opposing effects of audience is that social presence facilitates dominant behavior [29]. Dominant behavior refers to the kind of response which is more likely: correct or incorrect. In case of, e.g., simple tasks it is more likely to perform the task correctly while individuals tend to make more mistakes when executing more complex tasks [32]. Hence, whether audience facilitates [+] or impairs [−] performance depends on the type of task (simple [+] vs. complex [−]) and/or individuals’ level of expertise (expert [+] vs. beginner [−]) [33]. The presence of others increases the individuals’ (physiological) arousal or drive level which in turn impairs or enhances task performance, respectively [29]. A review of 12 years of research following the drive theory suggests that their propositions are still valid [30]. Nonetheless, alternatives to drive theory have evolved in the following decades. While some non-drive theories relate audience effects to self-awareness [32], others refer to (cognitive) attention focus [34]. Though experimental research uniformly confirms that social presence affects individuals’ performance, it remains unclear which mechanism mainly drives behavior. As the presence of others represents a particular case of pressure, it hence seems perfectly possible that pressure enhances performance—depending on the type of task and the individuals’ level of expertise.

Empirical findings for performance under pressure in skill tasks

As this paper analyses performance under pressure in a sport-related skill task, this section is devoted to previous findings from sports. There are also early non-sport studies [12; 35]. Golf putting performance is investigated in an experimental setting, suggesting performance to be worse when subjects are put under pressure [22]. However, in high-pressure situations participants who are distracted by a secondary task (counting down from 100) outperform subjects who solely concentrate on the putting task. The latter result is explained by too much focus on the task execution induced by the additional motivation to perform well in high-pressure conditions. The additional focus disturbs task execution which normally is performed automatically. There is also further evidence for diminishing golf putting performance under pressure provided by asking 108 undergraduate students with little or no golf experience to putt a golf ball as close to a target as possible [36]. Considering different kinds of intervention methods, pressure-like situations using monetary incentives are created. Results generally confirm decreasing performance for high-pressure situations. However, the authors show putting accuracy to slightly increase under pressure when subjects had made their practice putts under self-consciousness-raising conditions.

Based on the assumption that pressure increases left-hemispheric activation which in turn is related to the controlled execution of a task and thereby to performance decrements, participants of a previous study performed a sport-related motor skill task in three blocks (in soccer, tea kwon do, or badminton) [37]. While the first two trials serve as for the introduction of pressure, the third trial is performed after participants have squeezed a softball for 30 seconds. Thereby, half of the participants activated their right hemisphere by squeezing the ball in their left hand, before again performing the task under pressure. Overall, the findings indicate performance deterioration when pressure is introduced but that the activation of the right hemisphere can eliminate this effect, thus preventing choking under pressure. However, they find no evidence for increased performance under pressure.

In a further study, a throwing task had to be performed by the participants to analyze novices’ performances [38]. During the experiment, the performance expectancy within the experimental group regarding the ability to perform under pressure is manipulated. The results show a significant performance increase of the experimental group when pressure is applied, while the performance of the participants in the control group does not alter before and during pressure situations.

For a hockey dribbling task with 34 experienced participants, performance is found to be worse in high-pressure situations [28]. Results further show that within high and low-pressure conditions subjects perform better when not concentrating explicitly on the task execution. By analyzing a hockey dribbling setting with experienced hockey players, additional evidence for declining performance in pressure situations is found. However, it is demonstrated that in a high-pressure priming condition, performances are equal to those in a low-pressure situation and better (thus faster) than in a high-pressure non-priming condition [39].

For basketball novices, decreasing free throw success in pressure situations is shown [28]. This result only applies to those subjects who are asked to pay close attention to the execution process during the practicing phase. Analyzing free throw performances of competitive basketball players instead of novices supports the results [40]. Thus, participants suffer a significant decrease in free throw success when performing in a high-pressure situation induced by the introduction of an audience, videotaping and offering financial rewards for improved performance.

A further study analyzes the impact of fear of negative evaluation on performance, investigating success rates of throwing a basketball from a short distance [41]. The shots are taken from five different spots which all are placed at the distance of the free throw line. The authors find decreasing performance (thus choking) only for participants who were anxious about being evaluated negatively. For other subjects no significant differences in success rates are found.

Outside of experiments, field studies take advantage of the wealth of data on actual market participants who repeatedly perform almost identical tasks but under varying degrees of pressure. Pressure in these instances is determined by factors such as the importance of the competition considered, the current score in the competition, and the time left to play in a match.

Penalty kicks in soccer are considered to be a prototype pressure situation, as they critically affect the match outcome and the expectation to score a goal is very high. In line with the hypothesis of individuals tending to choke under pressure at skill tasks, success rates of penalty kicks in professional football are found to decline with increasing importance of success, i.e. as pressure increases [42]. However, contradictory to these results, success rates in penalty shootouts are found to increase with pressure in the German cup competition confirming clutch performance [43]. In addition, several studies focus on the “last-mover disadvantage”, i.e. whether teams that go first in a shootout have an advantage over the other team resulting from higher pressure from trailing [44; 45; 46]. One of these studies finds that that last-mover teams indeed suffer from this kind of pressure [45], the other studies refute this finding and speculate the contradictory results to be a consequence of data issues [44; 46]. Potential reasons for varying success in penalty shootouts between players are that players from high-status countries a) generally perform worse and b) engage more in escapist self-regulation strategies than players from low status-countries [47].

In golf, performance under pressure is analyzed for putting [48; 49]. Analyzing the impact of the current leaderboard situation on performance, the author finds that interim results are irrelevant for performance. In particular players who are in the lead or close to the lead in the final round do not perform worse than those who are further behind. Furthermore, players’ performances are constant across rounds. Between-athlete comparisons may explain this finding, which is not in line with the widely accepted hypothesis of individuals choking under pressure [50]. Considering also within-golfer comparisons, such findings cannot be replicated, and corresponding studies instead do find athletes to choke under pressure [50]. Relating choking under pressure to golfers’ age, an inverted U-shaped relationship on the professionals’ tour with performance under pressure peaking at age 36 is shown [51]. The success rate at the final putt of a golf tournament is found to decrease as the value associated with that shot increases [52]. Finally, golfer currently with the lead are found to underperform at the end of close contests [53].

Basketball free throws constitute another scenario that is often investigated to analyze performance under pressure. Considering data from the National Basketball Association (NBA), and modelling free throw success rates as a function of the current score, players are shown to perform much worse when their team is either trailing by 1 or 2 points, or in the lead with 1 point. Attempts are more successful when the score is tied (which equals less pressure since a miss would end in an overtime and not a loss) [54]. Further evidence for choking under pressure in professional basketball is reported with performance declining with additional pressure [55]. However, the authors show performance to be unaffected by the crowd size, the tournament round, and whether or not it is a home game for the player considered. Examining the determinants of choking under pressure, overall lower free-throw success rates are found for different groups (containing females and males, and amateurs and professionals) in case of high-pressure situations [56]. Analyzing the performance of professional basketball players who had been categorized as “clutch players” by basketball experts is also part of previous research [57]. Results show that clutch players are indeed able to increase their performance (which is measured by points scored and fouls drawn) in high-pressure situations such as the final minutes of close games, while performance of other players is not affected by pressure. Therefore, results provide evidence that clutch performers actually do exist. However, the analysis further shows no differences for clutch players’ field goal percentage between low-pressure and high-pressure situations. It is also reported that professional basketball players who maintain their performance under pressure earn higher salaries [58].

While some contradictory results have been reported, overall there still seems to be fairly evidence that professional athletes do choke under pressure, at least in some scenarios.

Task features of the darts setting

Empirical advantages

Despite the effort that has already gone into studying the impact of pressure of performance, we believe that the setting of professional darts is an important addition to the existing body of literature. While we do not claim the following features to be unique to darts—as they effectively also apply to bowling, archery etc.—they are important to mention as they improve the reliability of any results obtained, compared to other more complex settings which have regularly been analyzed in past research.

First, in darts, players cannot interfere the performance of the opponent directly. In order to precisely measure the impact of pressure, analyses need to focus on such performance that is not affected by others [59]. In many other settings, such as penalty kicks in soccer, opponents can impact each other’s success. As a matter of fact missing a penalty shot can be caused by the kicker’s or the goalkeeper’s performance, respectively, or both. The individualistic nature of darts reduces variance caused by interference of opponents present in other settings.

Second, subjects in our data are highly trained in the task they perform. Such experience is obtained from training and previous competition, the latter may or may not be covered in our sample. Observing experienced professionals vastly reduces the noise to be expected for inexperienced players with large fluctuations in performance. The separation of the impact of pressure on performance is hence much clearer in professional sports settings (compared to lab experience with amateurs).

Third and closely related to the previous point, the task to be performed in a pressure situation is more or less identical to the only task the players perform throughout the contest. The only difference is given by the specific field the player attempt to hit. In comparison, penalty shots only account for a very small fraction of actions a soccer player need to perform [60]. In line with our previous argument, estimating skill levels in pressure situations requires such separation of signal and (potentially very large) noise. If pressure is closely related to the task at hand (e.g. a penalty shot) it is hard to separate between pressure generated by the task and pressure generated by the situation.

Fourth, all players in darts are repeatedly confronted with high pressure situations. For penalty kicks or free throws, team managers may rely on the same set of players when confronted with pressure situations, namely those who they have faith in to deal with the pressure or are very skilled in the specific task. Such sample selection can be detrimental to the quality of the results and occurs especially for very specific tasks.

Overall, we believe that professional darts offers a nearly optimal empirical setting to investigate the impact of pressure on performance. Players repeatedly perform highly standardized actions, with no interference by an opponent or any teammates involved, and hardly any relevant external factors.

Characteristics of task / dart players

As already discussed above, the social facilitation literature suggests that the circumstances surrounding performance affects the consequences of pressure. These circumstances mainly refer to the individuals’ level of expertise and complexity / difficulty of the task. As our data set includes professional dart players who are highly trained in throwing darts, we observe individuals of high expertise.

Throwing darts is a skill task which requires high motor skills in order to perform well [61]. There is a high level of standardization of individual throws as well as many repetitions of almost identical actions, performed by professionals. Even though hitting a specific slice of the dartboard requires a high precision of movements, we assume that throwing a dart at a dartboard is less complex than, e.g., shooting a penalty (soccer), throwing at a basket (basketball), or putting a ball (golf). The more the task relies on simple, well-rehearsed responses, the smaller the chances of performance decrements. Hence, we expect performance of dart players to be unaffected by pressure. In contrast to the literature related to social facilitation, the choking literature would predict that performance in darts declines as pressure increases.

Pressure situations in darts

For readers who may be unfamiliar with the rules of darts, we here provide a short description. The dartboard consists of 20 different slices, which differ with respect to their value (ranging from 1 to 20), and the center of the board, which is composed of two fields, namely the single bull and the bullseye. Each slice is further divided into three different parts: two single, one double and one triple field. The bullseye is the double field of the single bull. Fig 1 shows the layout of a standard dartboard, highlighting the single five segment, the double and triple eight, respectively, and the single bull together with the bullseye. The inside width of the triple and double fields is 8mm, whereas the diameter of the bullseye is 12.7mm. A darts match is typically played by two players. (There are cases of team competitions in darts but these are not considered in our analysis.) Players are standing 2.37m away from the dartboard (at the “oche”), the height of which is 1.73m (from the ground to the center of the bullseye).

While there are many possible games in darts, professional darts commonly follow the 501 up format. In order to win a corresponding match, a player must be the first to win a pre-specified number of legs (typically between 7 and 15). Both players start each leg with 501 points and the opening throws in a new leg alternate between the two players. The first player to reach exactly zero points wins the leg, with the restriction that the dart that ultimately reduces the points to zero must hit a double field. For instance, in case a player throws a dart at the single/double/triple field of segment 20, 20/40/60 points are deducted from the player’s current score. If a player hits a field that reduces his score below zero it is called a bust. The player starts with the number of points he had before he busted at his following turn. The players take turns to throw three darts in quick succession. At the beginning of a leg, players consistently aim at high numbers—usually triple 20 or triple 19—to quickly reduce their points. The maximum score per dart is 60 (triple 20) and hence 180 for a set of three darts.

Once a player has the possibility to finish a leg (i.e. reach exactly zero points) with three darts (or less) during his turn, he is in the finish region. If he takes the opportunity and finishes the leg, this is called a checkout. As the last single dart has to hit a double field, the highest possible checkout is 170: two darts at triple 20 (2 × 60 = 120) followed by a dart into the bullseye (50 points). The highest checkout not requiring a bullseye is 160 (two triple 20 followed by a double 20). For some scores below 170 there are multiple combinations for a checkout while there are none for others (e.g. 159 points as there is no three darts combination that leads to exactly zero points with the last dart hitting a double field. 159 points could be reduced to exactly zero points with three darts if the last dart does not need to hit a double field, e.g. by triple 20—triple 20—triple 13. However, since all tournaments in our data are played as “double out”, 159 points can not be reduced to zero within a players’ turn).

We determine the likelihood of a player checking out for any given number of points left. To do so, we use information on all attempts for the given score to determine the success rate (see below). The checkout proportions for the individual scores are shown in Fig 2, which in addition indicates whether (at least) 1, 2, or 3 darts are needed for a checkout. It is important to note that there is a strategic element to the game, where players sometimes deliberately attempt to set their score to a certain number for their next turn instead of checking out immediately. If, for example, Player A has a fairly high number of points to check out, say 160 points, but Player B has no finish with his next turn, then Player A could set up an easier checkout for his next turn rather than going straight for a checkout. The occurrence of such strategic behavior is corroborated by Fig 3, which shows the checkout proportions in the data for those situations. For scores above 120 the checkout proportion for Player A is usually higher if Player B has a finish (compared to situations where Player B has no finish). When having a high score left to finish, players tend to set up an easier checkout if their opponents have no chance to finish in the next turn. Such strategic behavior becomes less relevant for lower scores. For scores below 50, many of which can be checked out with one dart only, such that setting up a score is less relevant, the checkout proportions do not differ substantially between situations where the opponent had a finish and those where he had no finish. We explicitly account for such strategic considerations by restricting our sample to those observations where the opponent also has a finish.

Fig 2 — Colors indicate whether for the given score 1, 2, or 3 darts are needed for a checkout.

Fig 3 — Finishes with at least 100 observations in each category are shown.

For any given turn of a player, the level of pressure is a result from the player’s own likelihood of finishing within the current turn as well as that of the opponent finishing within his next turn. Respective probabilities are estimated by the corresponding empirical proportions as described above. Following the literature, the intermediate score of a match can also generate pressure. We hence also analyze a sub-sample of throws, which are performed in situations that are very crucial to the outcome of the match. More specifically, we investigate decider legs, referred to as legs where both players only need one more leg to win the match. Winning such a leg hence results in winning the match, whereas losing such a leg would result in losing the match. For example, in a best-of-19 leg match, a decider match occurs when the score is tied at nine legs apiece and leg number 19 decides the winner of the match. Pressure in decider legs is thus higher.

Empirical analysis

The data—extracted from http://live.dartsdata.com/—covers all professional darts tournaments organized by the Professional Darts Corporation (PDC) between April 2017 and September 2018. Based on the raw data it was possible to reconstruct which player makes a throw, the score before each dart, how many legs have been played in the match, which player had the first throw in any leg considered and, of course, if the player making a throw checks out. In the data we analyze, each row, i.e. observation, corresponds to a player’s turn to throw (at most) three darts. From those rows, i.e. from all sets of three darts played by a player, we consider only those instances where both the player and the opponent have the chance to check out within the given and the next turn, respectively. To ensure reliable inference on player-specific effects, we further reduced the data set to consider only those players who had at least 50 attempts to check out. The final data set comprises information on the checkout performances of m = 122 different players, totaling to n = 32, 274 observations (checkout yes/no).

Descriptive statistics

Our response variable Checkout indicates whether a player managed to check out (coded as “Checkout = 1”) or not (“Checkout = 0”). As detailed above, we measure the degree of pressure on a player by differentiating between his and the opponents’ chances to finish a leg prior to his turn. The chance of a player checking out is quantified by the checkout proportions of all finishes from the player’s current score (CheckoutProportion). For the opponent, the corresponding covariate CheckoutProportionOpp indicates the checkout proportion of the opponent’s current score. In an alternative model specification, we replaced the CheckoutProportionOpp variable by a dummy indicating whether or not the opponent had a chance to check out with his next attempt, restricting the sample to 1-dart finishes for comparable checkout proportions. The corresponding results (not shown) were consistent with the ones presented here. To account for the ex-ante heterogeneity of players’ chances to win the match, the competitive balance (Cb) indicates the absolute difference in the winning probabilities. Based on betting odds taken from http://www.oddsportal.com/, and after correcting for the bookmakers’ margin, Cb can take values between 0 and 1. High values of Cb imply that the match is lopsided, whereas the value 0 means that both players have equal winning probabilities. Finally, as our data contains trained athletes, we are able to further control for the experience of the athlete (Exper), proxied by the number of years the player belongs to a professional darts organization (British Darts Organisation or PDC).

Table 1 summarizes all covariates considered. Overall, about 42% of all checkout attempts are successful. However, the probability to successfully complete a checkout is highly dependent on the number of points required: the more points are needed, the less likely is a checkout (see Fig 2).

Table 1. Descriptive statistics for the covariates.

	obs.	mean	std. dev.	min	max
Checkout	32,274	0.420	–	0	1
CheckoutProportion	32,274	0.419	0.279	0.027	1
CheckoutProportionOpp	32,274	0.486	0.266	0.027	1
Exper	32,274	13.15	7.050	0	36
Cb	32,274	0.363	0.228	0	0.899

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To investigate the impact of pressure on performance, Fig 4 shows the checkout proportions for different levels of pressure, which are indicated by the colors. Due to the potential strategic adjustments discussed above, only those observations where the opponent can also finish are included. For scores above 100, the checkout proportions seem to increase with increasing likelihood of the opponent checking out, i.e. the more a player is under pressure. For lower scores there is no such clear trend.

In addition, the pressure as indicated by decider legs is investigated in Fig 5 by comparing the empirical checkout proportions in decider vs. non-decider legs. Since in only about half of the finishes the checkout proportion is higher in decider legs, there is no clear pattern indicated by these summary statistics.

Modelling checkout performance

The structure of the data considered is longitudinal, as we model the binary response variable Checkout_ij, indicating whether or not the i–th player (i = 1, …, m) checked out (Checkout_ij = 1) on the j–th attempt (j = 1, …, n_i). To cover player-specific effects, and also to account for the fact that each individual player’s observations are likely to be correlated, we apply generalised linear mixed models where the linear predictor η_ij contains a vector of fixed effects β as well as a vector of zero-mean random effects γ_i:

\begin{matrix} η_{i j} = x_{i j}^{'} β + u_{i j}^{'} γ_{i}, i = 1, \dots, m, j = 1, \dots, n_{i}, \end{matrix}

with x_ij = (1, CheckoutProportion_ij, …)′, and $u_{i j}^{'}$ the subvector of $x_{i j}^{'}$ with those covariates for which we assume individual-specific effects. The logit function links the binary response variable, Checkout_ij, to the linear predictor:

\begin{matrix} logit (Pr (C h e c k o u t_{i j} = 1 | γ_{i})) = η_{i j} = x_{i j}^{'} β + u_{i j}^{'} γ_{i} . \end{matrix}

The linear predictor includes all covariates considered as well as a random intercept for each player to account for player-specific effects:

η_{i j} = β_{0} + β_{1} C h e c k o u t P r o p o r t i o n_{i j} + β_{2} C h e c k o u t P r o p o r t i o n O p p_{i j} + β_{3} E x p e r_{i} + β_{4} C b_{i j} + γ_{0 i} .

The random intercept γ_0i displays the player-specific deviation from the average intercept β₀—further individual-specific effects will be considered below. These models are fitted by maximum likelihood estimation using the package lme4 in R [62; 63]. Table 2 displays the results for the corresponding fixed effects.

Table 2. Estimation results for the fixed effects of the turn-level model.

	Response variable:
	Checkout
	all attempts	no deciders	deciders
CheckoutProportion	5.132	5.128	5.715
	(0.058)	(0.058)	(0.536)
	p = 0.000	p = 0.000	p = 0.000
CheckoutProportionOpp	0.014	0.016	−0.108
	(0.053)	(0.054)	(0.423)
	p = 0.798	p = 0.766	p = 0.799
Exp	0.005	0.005	0.007
	(0.003)	(0.003)	(0.018)
	p = 0.099	p = 0.090	p = 0.697
Cb	−0.018	−0.014	0.107
	(0.068)	(0.068)	(0.545)
	p = 0.785	p = 0.842	p = 0.845
Constant	−2.799	−2.797	−3.084
	(0.062)	(0.062)	(0.456)
	p = 0.000	p = 0.000	p = 0.000
Observations	32,274	31,715	559

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The estimated coefficients associated with CheckoutProportionOpp are of main interest here as they display the impact of the opponent’s chance of checking out during his next attempt on the player’s chance to check out during his current attempt. To identify different levels of pressure connected to the intermediate score of the game, we fitted the model to different samples, distinguishing non-decider legs and decider legs. Perhaps somewhat surprisingly, evaluating the effect of CheckoutProportionOpp across the first two models, the more pressure a player is exposed to, i.e. the more likely the checkout of the opponent, the higher is the increase in the corresponding odds for a checkout. However, the corresponding effects are not statistically significant. For the third model, the effect is also statistically insignificant. Hence, pressure apparently does not impact performance. This is also supported by a different model formulation where we pooled all attempts and introduced a dummy variable indicating if the throw occurred in a decider leg. The corresponding coefficient is insignificant, again providing no evidence for an effect of pressure on performance (results not shown). The player-specific random intercepts ${\hat{γ}}_{0 i}$ , i.e. the player-specific deviations from the intercept ${\hat{β}}_{0}$ , range (on the logistic scale) from −0.217 to 0.398.

To conduct a more fine-grained analysis of the throwing performance, we ran a second analysis in which we changed the sampling unit to single throws instead of a complete turn of three throws. When analyzing single throws instead of turns in darts, additional strategic adjustments have to be considered. If players can reduce their score to 0 with a single dart (e.g. if their score is 32), players often throw a “marker dart” with their first dart of a turn just outside of the board, such that the second dart is aimed at the marker and may be deflected into the target. To again account for such strategic adjustments, we only consider the third dart of a turn, since no marker darts are thrown with the third throw. The covariate CheckoutProportion is then built from the score-specific checkout proportion of the third dart of a turn. The results of fitting the model to data of single throws are shown in Table 3. As was done also for the previous analysis based on turns (see Table 2), we fitted the model to data of all attempts, to non-decider legs, and to decider legs separately. The results again indicate that pressure does not impact performance in professional darts.

Table 3. Estimation results for the fixed effects of the model fitted to data of single throws.

	Response variable:
	Checkout
	all attempts	no deciders	deciders
CheckoutProportion	4.534	4.562	2.749
	(0.308)	(0.310)	(2.586)
	p = 0.000	p = 0.000	p = 0.288
CheckoutProportionOpp	0.076	0.084	−0.327
	(0.066)	(0.067)	(0.508)
	p = 0.253	p = 0.208	p = 0.520
Exp	0.005	0.006	−0.001
	(0.003)	(0.003)	(0.021)
	p = 0.035	p = 0.032	p = 0.962
Cb	0.150	0.148	0.710
	(0.082)	(0.082)	(0.658)
	p = 0.068	p = 0.074	p = 0.281
Constant	−2.394	−2.408	−1.570
	(0.129)	(0.130)	(1.041)
	p = 0.000	p = 0.000	p = 0.132
Observations	14,849	14,590	259

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Since in the current model formulation we only allow for player heterogeneity in the baseline throwing performance, we further consider an extension where potential additional variation in the performance-in-pressure situations across players is investigated. The corresponding (and again insignificant) results are presented in the appendix.

Discussion

We find no evidence that professional darts players are impacted by (high) pressure situations. While player-specific effects for performance under pressure indicate that some professional players in our sample may improve, and some may worsen their performance in pressure situations, the average effect over all players is not statistically significant. Hence, our results do not corroborate studies supporting the choking hypothesis which states that overall performance in skill tasks decreases with increasing pressure.

The difference between our findings and previous studies on performance under pressure may partly be due to the fact that in our study we consider very highly skilled individuals who have to deal with the considered type of pressure situations on a regular basis. Professional darts players are at the very top of their profession and cannot fluke out of pressure situations, which is possible in team settings where tasks can be assigned to different team members. In fact, darts players face pressure situations on a regular basis and hence gain experience in dealing with these. While throwing darts is the one skill required in the setting considered, in other professions the set of tasks is much more diverse, often combing the requirement of both, skill and effort.

The literature on social facilitation offers a possible explanation for the absence of any choking effect. Social facilitation suggests that the type of task and level of expertise greatly affect the consequences of audiences or general pressure. As all players in our data set are professionals, pressure situations should affect performance positively. However, we find positive effects only for some but not all players. Accordingly, results cannot be attributed to the type of task. Since all of the players are of high expertise and execute the same task, the type of task should have the same effect on all players. On the one hand, “ceiling effects by performing a well-learned task” (see p. 75 in [31]) may lead to such insignificant performance effects. Hence, future research on darts players should also observe less experienced subjects in order to circumvent such ceiling effects. On the other hand, players may differ with respect to personal variables, such as self-confidence. Thus, pressure may affect performance differently depending on personal attributes. Further research on performance under pressure would benefit from including more information on personal characteristics.

Investigating semi-professional players (such as youth players) may further be beneficial with respect to a potential selection bias. Our sample may to some extent be the result of selection effects of subjects who can withstand pressure and become professionals, such that only those individuals who do not choke in pressure situations succeeded in the profession at hand and made it to the top (and hence into our sample).

The importance of coping with pressure situations has been investigated by in a qualitative study by interviewing ten international top athletes [64]. In this study, several attributes are stated as important factors for being “mental tough”, such as to be in control under pressure. In a further study, again several former Olympic or world championship winning athletes are interviewed as well as sport psychologists and coaches, finding that mentally tough athletes can not only cope with pressure situations, but even use it to raise their performance [65]. An explanation for this is that individuals are either entering a “competition state” or a “threat state” when forced to pressure situations, where the former helps their performance and the latter does not [66]. Thus, to not choke under pressure is not a conscious decision but rather a state of mind which is reached subconsciously.

Throwing darts arguably is a very specific task, much less complex than other actions required to perform in under pressure situations. Our finding of individuals not choking under pressure may be due to this specific task feature. Thus, future research on performance under pressure should include characteristics of the task and individuals into their considerations as these drive pressure effects. While the setting itself would be ideal to test gender differences in performance under pressure in a specific task, women’s darts does not offer the data necessary to draw comparisons. Empirical comparisons in line with the research by [67] are thus not possible at this time. Given the high number of observations for each player, further research could tackle the question if there is a memory for choking under pressure. More precisely, one could determine if choking under pressure impacts future choking under pressure, similar to a hot hand phenomenon particularly concerning pressure situations [68; 69].

Even though the social facilitation literature helps to understand the inconsistent impact of pressure on individuals’ behavior, it may be the case that pressure resulting from, e.g., competing for large monetary rewards or championship titles differs from pressure due to the presence of others. Whether individuals react to pressure with enhanced or impaired performance may hence also depend on the kind of pressure they experience while performing a certain task. It would be interesting to test whether dart players react differently to pressure situations (due to interim results) when playing before an audience or no spectators, respectively. However, this scenario would only be testable in laboratory settings as there are no contests taking place without spectators.

Appendix

In the appendix, we present the analysis of potential additional variation in the performance in pressure situations across players. This is investigated by analyzing throwing performance based on individual throws. While the model presented here provides some insights regarding player-specific performances under pressure, it should be noted that it does not yield an improvement in the AIC compared to the individual-throw model considered above. To analyze scores which are of about the same difficulty, we consider the scores 2, 8, 16, 22, 32 and 36. The corresponding checkout proportion of these scores with the third dart of a turn vary between 0.408 and 0.476. The checkout proportion for all scores which can be finished with a single dart vary between 0.231 (34 points) and 0.476 (2 points). To make the throws comparable, we restrict our analysis to the above mentioned scores with checkout proportion of at least 0.4. Considering these finishes for third throws where the opponent also had a finish accounts for n = 4, 773 single dart throws. A first comparison of the performance under pressure situation between players is investigated in Fig 6. The colors indicate whether the opponent also has a remaining score of 2, 8, 16, 22, 32 or 36, thus indicating pressure situations for the player (denoted by OppCanFinish below). Remarkably, there are substantial differences between the players. To extend the model formulation considered above, we include additional zero-mean random effects, γ_1i, which represent the player-specific deviations from the fixed effect of OppCanFinish, leading to the following linear predictor:

\begin{matrix} \begin{matrix} η_{i j} & = β_{0} + β_{1} O p p C a n F i n i s h_{i j} + β_{2} E x p e r_{i} + β_{3} C b_{i j} + \\ γ_{0 i} + γ_{1 i} O p p C a n F i n i s h_{i j} . \end{matrix} \end{matrix}

Fig 6 — Colours indicate whether the opponent also had 2, 8, 16, 22, 32 or 36 points left. Checkout proportions are shown for players with at least 10 observations in the corresponding subsample, i.e. third throws of non-decider legs with 2, 8, 16, 22, 32 or 36 points left.

As was done also for the previous analyses (see Tables 2 and 3), we fitted the model to data of all attempts, to non-decider legs, and to decider legs separately. The estimated fixed effects are displayed in Table 4. The particular pressure situation defined above, as indicated by OppCanFinish, i.e. the situations where the opponent also has 2, 8, 16, 22, 32 or 36 points left, does not have a statistically significant effect on the checkout performance. The estimated random effects ${\hat{γ}}_{1 i}$ are further investigated in Table 5, displaying the sum of the estimated fixed effect of CheckoutProportionOpp, ${\hat{β}}_{2}$ , and the corresponding player-specific random effect ${\hat{γ}}_{1 i}$ . As already indicated by Fig 6, the checkout performance in pressure situations varies substantially between players, but the model fit is not improved compared to the models presented above without additional random effects for the performance under pressure.

Table 4. Results of the individual-throw model with random slopes.

	Response variable:
	Checkout
	all attempts	no deciders	deciders
OppCanFinish	0.025	0.037	−1.244
OppCanFinish	(0.092)	(0.092)	(1.161)
Exper	0.002	0.002	−0.034
Exper	(0.004)	(0.004)	(0.032)
Cb	0.426	0.432	0.440
Cb	(0.126)	(0.127)	(1.156)
Constant	−0.473	−0.488	0.202
Constant	(0.074)	(0.075)	(0.553)
Observations	4,773	4,698	75

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Table 5. Estimated fixed effects of OppCanFinish with the added corresponding random slope.

	${\hat{β}}_{2} + {\hat{γ}}_{1 i}$
Player with biggest performance improvement	0.161
Player with 2nd biggest performance improvement	0.147
Player with 3rd biggest performance improvement	0.136
⋮	⋮
Player with 3rd biggest performance decline	-0.128
Player with 2nd biggest performance decline	-0.135
Player with biggest performance decline	-0.139

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Data Availability

All relevant data are within the manuscript and its Supporting Information files. In addition, if the article will be published, we will make the data and the corresponding R-Code available in a GitHub repository. Alternatively, the data and R-Code can also be uploaded at PLOS ONE (if possible) to provide it to the readers, as we submitted data and code together with the manuscript in the submission.

Funding Statement

The author(s) received no specific funding for this work.

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PLoS One. doi: 10.1371/journal.pone.0228870.r001

Decision Letter 0

Darrell A Worthy

20 Sep 2019

PONE-D-19-24035

Very Highly Skilled Individuals Do Not Choke Under Pressure: Evidence from Professional Darts

PLOS ONE

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Reviewer #1: Partly

Reviewer #2: Partly

Reviewer #3: Partly

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Reviewer #1: Yes

Reviewer #2: No

Reviewer #3: Yes

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #1: Note: I previously reviewed this article for a different journal and its content is unchanged from the submission I previously reviewed. Thus, I am providing the exact same review.

This paper has a very interesting topic and a great data set to explore psychological issues of performance. As laid out by the authors, darts appears to be an ideal setting to measure the performance of individuals. The writing and placement of their contribution within the literature is on point. However, I also have several questions and suggestions as it relates to the data and analysis. I hope my comments are helpful.

Major Comments:

1. Wow, this is really great data! With that being said, the detailed data could allow for a more precise examination of performance than the 1,2,3 dart checkout situations. I agree with the analysis done and its result, but want to know more about the likelihood of checking out from certain scores. I am a little concerned that the 1,2,3 dart finish situations are too broad of a categorization for the difficulty to checkout. From my understanding of darts (playing and watching very little), along with the authors explanation of the rules and situation (great job there), maybe all 2-dart finish situations are not created equal, it could be that 56 is much easier to checkout from than 80. In addition to table 4, I would like to know the probability of checking out from each specific score at the start of a player’s throw of 3 darts. A figure could easily display this information. Also, are there point totals from which a player’s attempt to checkout happen more or less often? I would suspect there are common point totals which players start their checkout attempts from. To address this last point, the authors could add a histogram of the scores at the start of a players turn when they have a chance to check out. In general, my concern is that there is some clumping of scores at a certain spot which make it much easier or harder for a player to checkout and the broad categorization used does not appropriately capture the difficulty.

2. Another issue closely related to #1, is the mention of strategy in not closing out in footnote 6, this brings up some questions as it relates to the data and the strategy of not checking out. At the top of page 14, the description of the data mentions the researchers know “the score before each dart”. All of the analysis in the paper is from the perspective of knowing the score before throwing all 3 darts when it is a player’s turn. Footnote 6 gets more at this idea of having data on each single dart throw as it discusses excluded throws where “the player did not try to check out with his last dart”. Since there is data on each dart throw, then why would you not look at specific dart throws where the player is on an even number and they need to throw the last dart of their turn into a specific double number? You still have the information on the probability for your opponent to check out, and you can more precisely measure performance in this moment of pressure. The 1,2,3 dart checkout scenarios could have many instances of strategies not to checkout when your opponent can’t checkout on their next turn, or situations where there are mistakes made by the player which causes them to land on an odd number and have no ability to check out on their second or last dart.

3. More specifically on footnote 6, it mentions situations when a player has a 1-dart finish, meaning that they have an even numbered score of 50 or less to start their turn. Well, they have 3 chances to make a double, and the footnote is correct that players often times may not go for the checkout on the first dart and instead get their score to an easier position such that a double 8, 16, or 20 would give them a checkout. However, the example in the footnote only discusses two dart throws, when the player would actually have three darts throws in a turn, this makes the example a little confusing. Is the exclusion of 11 observations from the case when a player has a 1-dart finish and decides not to try and checkout on the last dart throw? First, I can see why there would only be 11 excluded in this case as it means that the player had to make a mistake on their two previous throws and then be on a number likely to bust or an odd number for them to decide to not checkout. The main point here, can’t this same type of strategy happen on 2 and 3 dart finish turns? In general, strategy to not checkout may be driving the results in Table 5 as a 3-dart checkout is very difficult, players will often want to land on a good even number (e.g. 40, 32, 16) when their opponent can’t checkout on the next turn.

4. In general, to keep the current analysis in the paper, there needs to be much more discussion of player strategy to checkout and convince the reader that not checking out is a failure in performance and not a strategy decision. A quick google search returns websites with discussions on strategies to closeout (e.g. http://www.sentex.net/~pmartin/patdarts/strategy.htm), meaning the objective can often be to setup an easier closeout next turn when you are in an advantageous position against an opponent.

5. Checking out is an integral part of the game, as mentioned in the paper, matches are won when a player wins somewhere between 7 and 15 legs. This means you will need to checkout at least 7 times in a match to win. I would think checking out in the first leg of a match would have a different level of pressure than checking out for a 7th leg win to take down the match. In this sense, the legs in a match have different levels of importance and pressure as the match progresses. This seems very similar to making putts early vs. late in a round or sinking three throws early in a basketball game vs. the final minute in a close game. Taking the analysis towards a comparison of checking out in pressure vs non-pressure would more closely mirror the situations in other sports research and allow for a result that could be easily compared to other studies. If this type of analysis led to a different result than golf or three throws, it would be very compelling.

6. Section 5 which includes Tables 8 and 9 is a nice addition to tackle the issue of prize money. However, the discussion is incomplete, one sentence on the results from Table 9 in the last paragraph of section 5 is not nearly enough. Also, the discussion of expected results when adding these control variables states, “One would expect a higher Cb to be associated with lower incentives to perform well, hence a negative impact on the probability to check out”. Table 9 results indicate a positive coefficient for the Cb variable, which I understand to mean higher Cb means more likely to checkout, the opposite of the pervious statement. Maybe I am misunderstanding this, but either way this needs some clarification.

Minor Comments:

1. There are several typos, (e.g. ‘in’ instead of ‘is’, ‘price’ instead of ‘prize’).

2. There is a recent paper that could be added to the discussion of golf and performance under pressure (Hickman, Kerr and Metz 2019). The study shows players perform better in 2nd vs 1st. This may fit the story in this paper of performing best in 2 and 3-dart checkout situations (slightly behind) when the opponent has a 1-dart checkout (slightly ahead) on their next turn.

3. My understanding of darts is that there are some nuances about having a number very close to zero and busting (going past zero) which likely deserves some discussion in the paper. There could be a situation where a 1-dart checkout where a single throw will either win you the leg or have you bust; this could be a throw with enormous pressure compared to other situations.

4. While Table 7 is being used to try and indicate better performance under pressure, this result of all 122 players checking out more often when their opponent could checkout next turn vs. not checkout leads me to the strategy conclusion discussed in my previous comments. If all players are checking out less in the “no pressure” situation, then maybe the lower rate of checking out is a strategy decision for the end of leg play.

Reviewer #2: The manuscript depicts results from a large trial field study of dart throwing performance. The authors’ analysis results suggests that among dart throwers performance may improve under pressure. They see this conclusion as interesting because it is at variance with the usual finding from such studies showing that no there is no performance increase under pressure.

I was very interested in the manuscript. My reading suggested that the study was well-conducted and well-analyzed. The use of alternative models and alternative ways of approaching the data (including presenting the data from, an individual-difference perspective) is always a plus for a manuscript, in my opinion. My opinion is that the results are interesting enough to be publishable.

However, I did not think that manuscript itself optimally packaged these findings.

One major source of my concern was rooted in my perception that the manuscript did not fairly reflect the “lay of the land” with respect to the possibility that performance can increase under pressure.

For example, in attempting to describe when performance might increase under pressure, the authors make a broad distinction between effort tasks and skill tasks, and use that as a justification for the study (p. 2). The manuscript is written to imply that darts is more of an effort task, but that status seems be assumed. If my perception is correct, one concern is that the authors do not present any independent evidence validating that assumption.

Moreover, the authors do not link to an especially relevant literature: social facilitation/social impairment. The fact that this literature is often overlooked by researchers who have focused on the absence of evidence for “clutch” performances (e.g., performance enhancement under pressure) has long mystified me, and given the ghosting of this literature, it is not surprising that the authors of this manuscript have also overlooked it.

In my view, that is an important oversight. That social facilitation/social impairment literature is quite relevant to the issue treated in this manuscript. That literature suggests that arousal (which may be conceptually similar to “pressure”) might improve performances on tasks that require the emission of “dominant responses.” Roughly, these are responses that are well-learned in a given context.

In fact, the demonstration of social facilitation effects has been confirmed by meta-analyses (see Bond and Titus, 1983), and has been linked to physiological, cognitive, affective, and self-presentational mechanisms. For examples, see:

1. Blascovich, J., Mendes, W. B., Hunter, S., & Salomon, K. (1999). Social facilitation as challenge and threat. Journal of Personality and Social Psychology, 77, 68-77.

2. Bond, C. F., & Titus, L. J. (1983). Social facilitation: A meta-analysis of 241 studies. Psychological Bulletin, 94, 265-292.

3. Harkins, S. G. (1987). Social loafing and social facilitation. Journal of Experimental Social Psychology, 23, 1-18.

4. Huguet, P., Galvaing, M. P., Monteil, J. M., & Dumas, F. (1999). Social presence effects in the Stroop task: Further evidence for an attentional view of social facilitation. Journal of Personality and Social Psychology, 77,1011-1025.

This body of research is important to the present manuscript because it clearly points to three things: (a) task performance CAN improve under pressure; (b) the idea that whether one gets performance impairment or performance improvement may be moderated by the type of task to be performed, and (c) there are several kinds of psychological variables that may be linked to performance improvements.

Indeed, I raise this literature because it contradicts the authors’ assertion (on p. 2) that “However, there is broad agreement in the literature that performance in skill tasks, e.g. juggling a soccer ball (Ali, 2011), declines in high-pressure or decisive situations.” Prompted by my knowledge of the above literature, my immediate thought was “Oh yeah? WHICH literature?” It is certainly the case that, as is well-documented by the authors, both laboratory studies of sports-like performances and most analyses of real-world sports performances supports the conclusion that players are not “clutch” performers in that they do not improve performances under pressure. However, as I have noted above, there IS ALREADY A LITERATURE suggesting that for some kinds of tasks (maybe dart-throwing is one of them) and for some kinds of people (perhaps dart-throwing experts are those kinds of people), performances MAY improve under pressure (e.g., in high arousal states).

One of my obvious recommendations, then, is that because it suggests that performance improvement under pressure may sometimes occur, the authors need to touch base with the social facilitation literature.

However, it should be noted that other elements of the sports-like task performance literature has recently been more congenial to the performance improvement perspective than has, perhaps, characterized the past.

Examples (not a comprehensive review) of this literature are:

Preventing motor skill failure through hemisphere-specific priming: Cases from choking under pressure.

Beckmann, Jurgen; Gropel, Peter; Ehrlenspiel, Felix.

Journal of Experimental Psychology: General. Vol.142(3), 2013, pp. 679-691.

(see results of Experiment 3).

Choking vs. clutch performance: A study of sport performance under pressure.

Otten, Mark.

Journal of Sport & Exercise Psychology. Vol.31(5), 2009, pp. 583-601.

Do clutch players win the game? Testing the validity of the clutch player's reputation in basketball.

Solomonov, Yosef; Avugos, Simcha; Bar-Eli, Michael.

Psychology of Sport and Exercise. Vol.16(Part 3), 2015, pp. 130-138.

Changes in putting kinematics associated with choking and excelling under pressure.

Gray, Rob; Allsop, Jonathan; Williams, Sarah E.

International Journal of Sport Psychology. Vol.44(4), 2013, pp. 387-407.

Pitching and clutch hitting in Major League Baseball: What 109 years of statistics reveal.

Otten, Mark P; Barrett, Matthew E.

Psychology of Sport and Exercise. Vol.14(4), 2013, pp. 531-537.

Choking and excelling at the free throw line. [References].

Worthy, Darrell A; Markman, Arthur B; Maddox, W. Todd.

The International Journal of Creativity & Problem Solving. Vol.19(1), 2009, pp. 53-58.

Enhanced expectancies improve performance under pressure. [References].

McKay, Brad; Lewthwaite, Rebecca; Wulf, Gabriele.

Frontiers in Psychology. Vol.3 2012, ArtID 8.

These citations support the notion that even in the “sports performance-like” literature, there have already been reports (especially in recent years) of increases in performance under pressure, as well as articulations of possible mechanisms by which such performances increase. I obviously would recommend that this manuscript touch base with this literature, and as a consequence, tone down (a little) the implication in their manuscript that their data are totally discrepant with the existing literature.

This is especially important when the authors write: “Hence, following the literature, performance in darts would be expected to decline as pressure increases. Against the current state of research on motor tasks, we find (nearly all) professional darts players to excel in pressure situations. We argue that highly skilled individuals are able to digest pressure situations towards a positive outcome, while those who choke under pressure decide towards other professions. This emphasizes the importance of possession of skills for the impact of pressure on performance.” As illustrated by the references I have provided the literature is NOT uniform in supporting choking under pressure.

In this regard, then, I would recommend that the authors add a definition of the term “clutch” to their terminology section, that they review some of the studies suggesting that clutch performances can occur, that they link to some of the conditions under which clutch performances can occur, and that they describe some of the mechanisms that may produce clutch performances. This can all be done, of course, with the caveat that in the literature choking performances tend to be much better documented and seem to be more common than clutch performances.

Note that, in my view, my “packaging concern” does not diminish the interest value of the authors’ findings. Only via the publication of these kinds of data will one gain insight into (what I believe) are the critical questions: (1) on what kinds of tasks will performance increase under pressure and on what kinds of tasks will it decrease, and (2) what are important psychological factors that are at play in such changes (e.g., expertise, attention, etc.).

The authors seem to define choking under pressure as “specifically to a negative impact of high performance expectations (Baumeister and Showers, 1986; Hill et al., 2009).” That definition may be a little restrictive. Choking may also be viewed through a motivational lens in that it may require the desire to do one’s best.

I understand that section 2.4 is intended to try to provide a context for why dart throwing might be a particularly good context to investigate how performances might change under pressure. I agree that the sport of dart throwing has advantages (relatively standardized conditions, outcomes that are not influenced by opponent) that might serve to quiet random variance. However, a counterargument lies in convergent validity: when an outcome (e.g., choking under pressure) is repeatedly observed across very different contexts, one gains extra confidence in the outcome because the confounding variables that are unique to a given context are often not present in other contests. Hence, with convergence it is increasingly unlikely that variables unique to a context caused the result. Thus, although soccer penalty kick outcomes are directly influenced an opponent, golf tournament performances are not. Similarly, while laboratory studies of choking often use non-expert participants, field studies often show the same choking phenomenon in experts. The authors imply that dart thrower expertise is crucial to the clutch performance data that they report (e.g., “The stark difference between our findings and previous studies may partly be due to the fact that in our study we consider very highly skilled individuals who have to deal with 21 the considered type of pressure situations on a regular basis.”). Given results from other field research employing experts, this seems to be an unlikely explanation. To be more specific, as implied by the social facilitation literature, expertise is NOT the only variable that may be important to clutch performances. Studies of many sports (e.g., golf; baseball) have shown that even expert players sometimes choke, or they sometimes do not exhibit either choking or clutch in their performances.

I had concerns about the notion of “pressure” derived from Table 1 and Table 2. I understand that Table 1 is presented to provide a basis for the pressure labels presented in Table 2. However, there is no justification for the Table 2 categorical labels applied to the conjoint probabilities (no, low, moderate, high) depicted in Table 1. The authors’ labels suggest that their view of pressure is determined by how easy both the player’s task is (making one dart is easier than making three darts) and how easy the opponent’s task is. However, this system is not well articulated in the manuscript, and no external validation evidence for the system is presented. Extrapolating from psychophysics research, one needs external validation to determine how much felt pressure changes as the win probability changes, and whether and how felt pressure is related to both the difficulty of one’s own task as well as the difficulty of the opponent’s task. Might it be the case that the two variables do not contribute equally to felt pressure? For example, I can easily see that my task (1 vs. 2 vs. 3 darts needed to win) might contribute more to felt pressure than my knowledge of my opponent’s task.

Moreover, why must these probabilities be translated into categories? Could they not be used as a continuous predictor as a proxy indicator of pressure

In addition, one cannot always expect the change in felt pressure to be linearly related to the change in probability across the probability scale. That is, a change in win probability from.95 to .85 may not produce the same change in felt pressure as a change in win probability from .15 to .05.

I don’t know if these worries are enough to derail the manuscript, but I certainly do think that a thorough discussion of links between pressure and win probability, and the assumptions that the authors made in translating win probability data into pressure categories, is needed.

Given where it is placed, the inclusion of ideas from contest theory (p. 20) seems like an afterthought. If contest theory makes a priori predictions about the patters pf data to be expected, those predictions seem to be better placed in the introduction near to where the effort vs. skill distinction is first raised. Note that this effort vs. skill distinction is not the same as presented in the social facilitation/social inhibition literature. The literature comparable to the “effort” literature would probably lie in the social loafing domain of social psychology. However, I wonder about the relevance of the effort idea. Effort has not generally been posited as an explanation for choking (given the assumption that people choke, even when they are trying to do the best that they can). Hence, I doubted whether this effort-related material added much to the manuscript.

One other very minor point is that I do not know if Frontiers requires articles to be formatted in compliance with the guidelines set forth in the APA publication manual. If that is the cased, then this manuscript exhibits frequent noncompliance. A partial list of noncompliant items includes missing page headers, missing figure captions, misformatting table captions, and the misformatting of references (e.g., issue numbers are no reported only in special cases; no colons before page numbers; use the ampersand instead of the word “and”). If compliance to APA style is required, the authors clearly need to sit down with the manual and alter their manuscript to comply with the manual’s guidelines.

Reviewer #3: I have attached my report, and it can also be found below. Please note that I also served as a reviewer for a submission of this paper to another journal, and as the submission was not changed across these reviews I did not update my report.

Summary: The authors employ throw-level data from professional darts tournaments over the course of one year to examine whether choking under pressure occurs in darts. Higher-pressure situations in this context are defined as those where a player’s opponent is likely to finish on their next turn, conditional on the player himself being within three darts of checking out, compared to situations where a player’s opponent is unlikely to finish. Choking, meanwhile, is defined as a decrease in the likelihood of checking out. By these definitions, the authors find that darts players actually perform better under pressure, i.e. that they are not susceptible to choking under pressure.

Comments:

I had two primary concerns with this paper, both of which are related to how choking under pressure in conceptualized in this context:

1. As noted in my summary above, the authors defined a high-pressure situation as one in which the win probability was lower (because the opponent was doing better), conditional on having a shot to win the leg, or checkout, that turn. However, I am concerned about the aptness of this definition, on which the paper’s conclusion of course relies. While it is difficult to provide an objective definition for a “high-pressure” situation bar, e.g., capturing biometric measures of stress, I would not think that pressure would be increasing in the opponent player’s chance of winning, conditional on having the opportunity to check out yourself. Consider, for instance, a case where a player has a 50% chance of winning compared to a case where a player has a 1% chance of winning; I would say that the first case is higher-pressure because “there’s more on the line to lose” (this could be framed in the context of expectations-based reference dependence, where the loss in utility following a lost opportunity to checkout is not as substantial when a player has a 1% chance of winning because their reference point was that they would fail to do so). In fact, defining a high-pressure situation as one in which a game is “close” is an established approach in the literature (Cao et al, 2011; Toma, 2017). Yet this is different from how the authors define choking in this paper, where the lower the chance a player has of winning, conditional on having a chance that turn, the higher the pressure, even when this means that the game is actually less “close” as in the example above. Since the evidence of choking under pressure presented here is of course contingent on the definition of a high-pressure situation, this naturally substantially affects my perspective on how the results ought to be interpreted.

2. A crucial assumption the authors must make in order to identify choking under pressure in this context is that all else is held constant when comparing play across situations in which the opponent is one dart, two darts, three darts, or more away from checking out. However, my understanding is that players may adjust their strategy according to their opponent’s position. For instance, if their opponent has no chance of checking out during their next turn, a player, especially one who needs either two or three throws to finish, might play more conservatively, throwing in a way that somewhat decreases their chance of checking out this round but positions them better for the following turn. This interpretation is exactly consistent with the results: When a player needs either two or three throws and their opponent cannot checkout their next turn, they are significantly less likely to checkout on the turn in question compared to a case where it is possible for their opponent to checkout; this difference is no longer significant when the player needs just one dart to checkout and thus conceivably has a more narrow strategy set. Thus, the higher probability of checking out on a given turn when the opponent has the chance to check out on their next turn seems quite conceivably due to the differences in optimal strategy across these cases rather than improved performance under pressure.

The ideal analysis would control for these differential strategies across cases (and this is why free throw or soccer penalty kicks are an appealing context in which to study choking – there is just one optimal strategy regardless of the position in the game: try to make the shot/goal). One possible approach would be to compare performance under these different scenarios (the darts required for self vs opponent) when the overall match is close vs not. If we observed that players were more likely to checkout when the overall match was close, conditional on the position they were in in a given lag, this would seem to provide more convincing evidence that darts players indeed excel under pressure. Footnote 7 suggests that no significant results were found using this analysis (which I would think should be highlighted!), though it was unclear whether this specific test was employed.

In addition to these two main concerns, noted below are strengths of the paper as well as some additional concerns and suggestions:

1. I appreciate that the authors took seriously the psychology literature that differentiates, for instance, the theoretical predictions of the impact of choking in effort- vs skill-driven tasks – this is an important literature to understand when exploring performance under pressure and the authors did this justice in the literature review. One suggestion, however, would be to avoid generalizing the findings in this paper to behavior in the labor market in the abstract and conclusion, as this is exactly an instance of crossing from a skill-driven to a (typically in the labor market) effort-driven task, and, as noted, the theory of choking under pressure would predict very different types of behavior across these domains.

2. The paper includes a section on why other studies may not have correctly identified choking under pressure. I indeed believe that this is an important section to include in order to credibly assert that the novel findings in this paper may be true across the board, but I had concerns about a number of the claims made:

a. The authors argued that it’s difficult to disentangle pressure from “nuisance situations” such as weather conditions or the quality of the course. However, I see no reason to believe such nuisance conditions would be correlated with high-pressure situations, and so this should not pose a challenge to the identification of choking under pressure. Similarly, they argue that the small number of e.g. penalty kicks in soccer render the data sufficiently noisy as to make choking difficult to tease apart – I would see this as a specific concern if player fixed effects cannot be netted out (as in Dohmen, 2008) such that you may just have stronger players kicking in high-pressure situations, but otherwise a small number of observations alone should not invalidate results that have been found to be significant.

b. The authors note that fatigue may enter in as high-pressure situations are those in which players are more likely to be fatigued because they have been playing longer or in a more intense game. Toma (2017), however, addresses this using free-throw data by showing (1) that choking only occurs in the final 30 seconds of a close basketball game and not before, when players are presumably similarly fatigued, and (2) that the number of seconds a player has played in a game does not predict choking.

c. The authors argue that coaches may tend to put players best able to handle pressure in high-pressure situations, but this would seemingly work against the finding that players choke under pressure.

d. The remaining points are specific only to certain types of analyses (e.g. soccer or experimental data) and thus cannot explain why findings across the board may not be valid.

3. These data seem like an interesting opportunity to look at heterogeneities in choking across players (once the right definition of choking is nailed down!), and while I appreciate that the authors took a step in this direction I think there’s more that could be done with the analysis:

a. First, just a somewhat picky note that the authors’ claim is not seemingly supported by their evidence given that they do not have any data suggesting others may choke under pressure: “We argue that highly skilled individuals are able to digest pressure situations towards a positive outcome, while those who choke under pressure decide towards other professions.”

b. I like the idea behind Figure 2, but I think I would have found more informative a graph with actual rather than predicted checkout probabilities across opponent scores for players with sufficient data; that way, not only the intercept would change, but we would actually see differences in choking susceptibility (this is seemingly a motive underlying Model 2, which I appreciate!). Perhaps in a new version of Figure 2 bins of different player “types,” by choking propensity, could be created and graphed.

4. The authors work with a great, fine-grained dataset, which is exactly what would be required for this type of analysis!

Some minor additional comments:

1. It took some time for the difference between Table 1 and Table 4 to sink in for me - My interpretation of the difference is that Table 1 looks at the probability of winning the leg overall while Table 4 looks at the probability of checking out that turn. This would be helpful to clarify, especially as the logic behind why the two are differentially relevant for the analysis was not made clear (this gets back to my second point – presumably the probability of winning a leg can’t be considered as a main outcome because this is dependent on opponent play, but even the strategy for the current turn is influenced by the opponent’s standing, so this still seems like a concern when considering checking out for a given turn).

2. For more visually-oriented folks, it may be helpful to plot the degree to which the changes in probabilities of checkouts correspond with the defined pressure in the situation; in other words, create a figure combining the information in Table 1 and Table 2 such that pressure is on the x axis and the probability of checking out is on the y axis.

3. I think there is no question that darts is a skill- rather than effort-driven task, so I did not find the discussion in Section 5 to be necessary. That said, some of the variables included in this analysis, e.g. the prize amount, would seemingly be strong proxies for the pressure in a situation (the higher the prize amount, the higher the pressure) and so could be incorporated in this way. The null effects of the controls alone suggest to me that, consistent with the null effects in the choking literature often found for e.g. more important tournament games, players may internalize more the pressure of making vs breaking a play at a given moment rather than any larger stakes of an overall game that wouldn’t be localized to a particular moment.

4. The statistical analysis tests for significant differences in checking out across opponent position only compared to the reference of the opponent not having the opportunity to check out the next turn; it would be useful to test for significant differences across the different opponent positions as well.

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Reviewer #1: No

Reviewer #2: Yes: JOHN J SKOWRONSKI

Reviewer #3: Yes: Mattie Toma

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PLoS One. 2020 Feb 21;15(2):e0228870. doi: 10.1371/journal.pone.0228870.r002

Author response to Decision Letter 0

5 Nov 2019

The response to the reviewer comments are included in an attached file.

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PLoS One. doi: 10.1371/journal.pone.0228870.r003

Decision Letter 1

Darrell A Worthy

28 Nov 2019

PONE-D-19-24035R1

Performance under pressure in skill tasks: An analysis of professional darts

PLOS ONE

Dear Mr. Ötting,

Two of the reviewers from the first submission evaluated your revision. Although, they noted some improvements, it appears that there is still work to be done in order to make this manuscript suitable for publication. Please try to address their comments in a revision. I will likely send the revised manuscript back to these same reviewers and ask them to evaluate whether all of their comments have been addressed. I hope to make a final decision on publication in the next round, so please do your best to address the comments made by the reviewers.

We would appreciate receiving your revised manuscript by Jan 12 2020 11:59PM. When you are ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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Please include the following items when submitting your revised manuscript:

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An unmarked version of your revised paper without tracked changes. This file should be uploaded as separate file and labeled 'Manuscript'.

We look forward to receiving your revised manuscript.

Kind regards,

Darrell A. Worthy, Ph.D

Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: (No Response)

Reviewer #2: (No Response)

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2. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Yes

Reviewer #2: Partly

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

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4. Have the authors made all data underlying the findings in their manuscript fully available?

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

Reviewer #1: Yes

Reviewer #2: Yes

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6. Review Comments to the Author

Reviewer #1: The approach to examining the data in a more detailed manner is a great improvement. However, I have a few comments and suggestions.

1. The figures in the revised paper are quite cluttered and it is difficult to see exactly what is going on with so many data points and lines. Page 9 of the revision states “the more points are needed, the less likely is a checkout (see Figure 2).” The second figure in the response to reviewers is a viewer friendly manner in which to display this information than the current Figure 2 in the revised paper. While the revision removes analysis using the number of darts to finish, I think a discussion of the 1,2, and 3 dart finish could be helped by using the second figure in the response to reviewers. Along this same general thought, the first figure from the response to reviewers does an excellent job of showing there are a handful of very common point totals from which players start their turn with an opportunity to check out. The first figure in the response to reviewers could be included to help the discussion of strategy and common starting points on pages 7 and 8 of the revision. What if the figures you currently have in the revised paper (Figures 2 thru 4) only displayed point totals to checkout with more than 500 or 1,000 observations? This could help with clarity as the figures are currently quite messy with all the points. This limitation would leave anywhere from 10 to 20 data points, making it visually easier for the reader.

2. As mentioned in the response to reviewers, the first figure with the frequency of different point totals to checkout would seemingly indicate certain point totals for 1-dart finishes are extremely popular and thus there is likely a strategic element to start the next turn with those exact points. The authors take this to mean, lets exclude all the checkout attempts when the opponent can’t checkout on their next turn from the regression. As I might argue, strategy doesn’t exist when we have a 1 dart finish starting at a popular number. For example, 40, which would be double 20 to checkout, has an enormous amount of checkout opportunities. Could you not look at how players perform when an opponent has chance to checkout next turn vs. not at this common number? This information is buried there in Figure 2, but I think there is still an argument to include the inability of the opponent to check out as a part of the regression. What needs to be made sure of is that the player is not choosing to strategically avoid going for the check out. To me, an opponent with a chance to closeout when I am at 40 would represent pressure and opponent without a chance to closeout would be no pressure. Of course, there are varying probabilities for your opponent to checkout, and your regressions are capturing how this may impact the player, but you are also removing many instances when the player is unlikely to be making a strategy choice to not checkout. This comment is a very lengthy way to say, restrict the sample to 1-dart finish situations for the player and report those results as well, but include in the regression throws when the opponent cant checkout on the next turn as well.

3. The “pressure” variable in the revision is the probability of your opponent checking out, but doesn’t pressure depend on a player’s chance to win or lose the leg, the difference in probability to checkout between the players. As the analysis is currently setup, one interprets the CheckoutProportionOpp as the impact the opponent’s chance to check out has on the probability of the player checking out, holding constant the players chance to checkout. This is possibly quite different from a story where the leg is a close competition and I feel pressure, the current “pressure” variable in the revision could include many scenarios when the leg is not a close competition. I suggest using the difference in checkout probability as a measure of pressure, with the argument that greater pressure exists when the difference is very small and less pressure exists when the difference is large.

4. Table 1 in the revision indicates that CheckoutProportion ranges from 0.027 to 1, the second figure in the response to reviewers indicates the probability to checkout from any single number to be at a maximum of approximately 0.8. Is this difference a mistake or is there a part of the sample restriction that makes the probability of 1 occur? You could remove observations where the likelihood of checking out is extremely high (e.g. 1) or extremely low.

Reviewer #2: P1-D19-24035-R1

Performance under pressure in skill tasks: An analysis of professional darts

This is my second viewing of this manuscript. The authors received a considerable amount of feedback on their first draft, and they obviously worked very hard to incorporate that feedback into their revision. The authors’ responsiveness is to be commended. More importantly, in my view the authors have produced a new manuscript that, in my opinion, is better than the first.

It is good enough to rise above the publication threshold? My reading of this document prompted me to have some concerns that would give me some hesitation about seeing this version published.

One concern that I had was expository. While making a substantial effort to incorporate reviewer feedback into their new draft, the authors never quite seemed to be able to abandon some of the approaches now conflict with the new revisions. Thus, the manuscript was not presented in a manner that was as coherent and internally consistent as one might like. If a revision is again called for, I would ask the authors to go through their document carefully to ensure consistency across the document.

For example, in the current draft the authors continue to expound on the “advantages” of the darts setting. This includes that (1) performance is not directly influenced by others, (2) performers are highly trained; (3) task to be performed in a pressure situation is more or less identical to the only task the players perform throughout the contest; and (4) all players in darts are repeatedly confronted with high-pressure situations. In what way(s) are these advantages? One way in which these are an advantage may be statistical: The relatively individualistic nature of the task may work to quell stray variance in analyses (e.g., caused by the interference form the performances of others). However, the rest of the features? These characteristics are certainly not unique to darts: Many such as bowling would seem to present at least one of the characteristics. Indeed, many sports (e.g., bowling) may present them all. Moreover, the fact that darts players are highly trained, while true, is relatively meaningless for those tests of choking that have found evidence of choking in tasks where everyone in a highly trained expert (e.g., top-level professional sports).

Moreover, I do not think that in making this claim the authors have quite abstracted one lesson of the social facilitation/social impairment literature: that the characteristics of the task help to determine the outcome one sees in co-actor performance situations (which presumably are one form of pressure situations). Hence, the nature of the task that is performed will help to determine whether one observes clutchness, choking, or nothing at all in performances. Hence, from the social facilitation/social inhibition view, the things that the authors list are not “advantages” but instead are “task features” that may help to determine the outcome that one observes. Indeed, one of these features (the fact that the motor skill involved (dart throwing) is relatively simple in comparison to many other motor skills needed in sport) would lead me to the prediction that in darts tasks the phenomenon of choking under pressure should be reduced, eliminated, or even reversed (e.g., clutch).

It is this point that, for me, is where the manuscript has its interest. The “choking” literature has focused on choking, but the social facilitation/social impairment literature suggests that choking in pro sports may not be inevitable. Some circumstances may produce evidence of “clutchness,” and some might produce no difference from non-clutch situations. The task is one of the controlling variables, and the facilitation/impairment literature says that the more the task relies on simple, well-rehearsed responses, the smaller the chance of performance decreases (choking).

I would like to see the authors more explicitly and forcefully advocate this position. Why? The authors mention in their cover letter that they did not know about the social facilitation/social impairment stuff because the choking literature never cites it. Thus, in my view the authors can educate the choking researchers about the lessons learned about performance and pressure that have already been documented.

In this regard, the authors need to clean up their language a bit. At one point, they describe social facilitation as a “theory.” That’s wrong. Social facilitation/social impairments are observed performance outcomes. These outcomes supposedly reflect the impact of various arousal-prompted mechanisms (mere presence, evaluation apprehension, cognitive distraction) on tasks, with the outcomes theoretically moderated by individual expertise and task simplicity/difficulty (that’s the theory).

The authors probably over interpret their data. Sure, on a purely descriptive level, some results seem to reflect clutchness, and other results seem to reflect choking. However, in reality, in the authors’ analyses none of these effects is significant. Hence, unless results are so strong that they are “trending,” in my opinion it is probably best practice to simply characterize all the results as non-significant (and some would even use this characterization for “trending” results.

In this regard, stats mavens like me would probably like to know the p-levels of the non-significant choke/clutch tests presented in Tables 2 and 3.

Moreover, I might argue that tests of significant effects have not provided the strongest tests of clutchness/choking. Might not this optimally strong test involve an analysis of the CHANGE in the effect obtained on low-pressure vs. high-pressure situations? In this regard, then, I might have expected to see whether performance changed significantly for the checkout proportion opp variable from the no deciders trials to the deciders trials.

Though non-significant, the fact that the data pattern may have shifted from the no decider trials to the decider trials (an analysis new to this version) again illustrates an important point that I made in my earlier review – that one needs to be careful about (and maybe independently verify) the pressure that accompanies various trial types. One might, for example, expect that decider trials early in a match may not contain as much felt pressure as decider trials that occur late in a match. This idea bears some relation to the Wells. et al. golf idea that pressure is maximized in golf when a player is close to the lead in the final round of a tournament (as opposed to earlier rounds). This suggests that the authors might want to look at the performance during various decider trials in a match – early, middle, late, and final (where, conceivably, one throw can win a match).

The authors presented results across players. I have two thoughts about doing so. The first point concerns the magnitude of the coefficients for the individual players. Are any of them different enough from 0 that they fall out of the range expected from a random distribution? The point is that I wonder if it is necessary to name the players instead of labeling them with a meaningless descriptor. I know that other researchers in the area have explicitly avoided using real names to avoid the use of their results for the purpose of calling some players “chokers.”

One final point linking back to the social facilitation/social impairment issue. The application of that literature to the present task assumes that playing in front of an audience or with/against others applies “pressure”. (The darts task may be seen as an example of the kinds of competitive/social tasks that are featured in that literature). Is that assumption plausible? That is, is that social pressure different from the kind of pressure that can come from non-social sources (e.g., playing for large monetary rewards)? The mechanisms posited for the social facilitation literature would probably suggest that the answer to this is “no” , especially if one considers the mental interference produced by evaluation apprehension to be a special case of broad evaluative concerns. However, I know of colleagues who might try to make a case that there is a different kind of pressure involved if one is playing for a million dollars versus if one is playing to be acknowledged as the champion of one’s city. This latter point leads to the possibility that clutch/choking may also be related to the nature or kind of pressure that is experienced during task performance. The authors, at their discretion, may wish to raise this point in their discussion.

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Reviewer #1: No

Reviewer #2: No

PLoS One. 2020 Feb 21;15(2):e0228870. doi: 10.1371/journal.pone.0228870.r004

Author response to Decision Letter 1

11 Jan 2020

We again would like to thank all referees for their careful reading of our revised manuscript. We made an effort to address all comments that were made. The additional analyses as motivated by the reviewers' comments we believe have improved the level of persuasiveness of our paper, while comments concerning the interpretation of our results have improved the readability.

We also made a number of smaller changes as requested. Detailed point-by-point responses are given in the attached response to reviewers document.

Attachment

Submitted filename: Response_to_reviewers.pdf

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PLoS One. doi: 10.1371/journal.pone.0228870.r005

Decision Letter 2

Darrell A Worthy

27 Jan 2020

Performance under pressure in skill tasks: An analysis of professional darts

PONE-D-19-24035R2

Dear Dr. Ötting,

We are pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it complies with all outstanding technical requirements. I sent your revision back to one of the original referees and they felt that all their comments had been addressed. Thank you for your contribution to the journal and the field, and congratulations on your latest publication.

Within one week, you will receive an e-mail containing information on the amendments required prior to publication. When all required modifications have been addressed, you will receive a formal acceptance letter and your manuscript will proceed to our production department and be scheduled for publication.

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With kind regards,

Darrell A. Worthy, Ph.D

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

Reviewer #1: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: (No Response)

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: (No Response)

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

Reviewer #1: (No Response)

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

Reviewer #1: (No Response)

**********

6. Review Comments to the Author

Reviewer #1: (No Response)

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

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Reviewer #1: No

PLoS One. doi: 10.1371/journal.pone.0228870.r006

Acceptance letter

Darrell A Worthy

6 Feb 2020

PONE-D-19-24035R2

Performance under pressure in skill tasks: An analysis of professional darts

Dear Dr. Ötting:

I am pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

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With kind regards,

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on behalf of

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Academic Editor

PLOS ONE

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

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Submitted filename: Plos One Darts Report.docx

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Attachment

Submitted filename: Response_to_Reviewers.pdf

Click here for additional data file.^{(141.6KB, pdf)}

Attachment

Submitted filename: Response_to_reviewers.pdf

Click here for additional data file.^{(112.9KB, pdf)}

Data Availability Statement

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PERMALINK

Performance under pressure in skill tasks: An analysis of professional darts

Marius Ötting

Christian Deutscher

Sandra Schneemann

Roland Langrock

Sebastian Gehrmann

Hendrik Scholten

Roles

Abstract

Introduction

Performance under pressure

Terminology

Potential effects of pressure

Choking

Other potential effects

Empirical findings for performance under pressure in skill tasks

Task features of the darts setting

Empirical advantages

Characteristics of task / dart players

Pressure situations in darts

Fig 1. Dartboard layout.

Fig 2. Checkout proportions for the individual scores before a player’s turn.

Fig 3. Checkout proportions for situations where the opponent had a finish (blue) and those where the opponent had no finish (yellow).

Empirical analysis

Descriptive statistics

Table 1. Descriptive statistics for the covariates.

Fig 4. Checkout proportions in pressure vs. non-pressure situation.

Fig 5. Checkout proportions in pressure vs. non-pressure situation as indicated by decider legs.

Modelling checkout performance

Table 2. Estimation results for the fixed effects of the turn-level model.

Table 3. Estimation results for the fixed effects of the model fitted to data of single throws.

Discussion

Appendix

Fig 6. Checkout proportions for situations with 2, 8, 16, 22, 32 or 36 points to checkout before the third throw of a turn.

Table 4. Results of the individual-throw model with random slopes.

Table 5. Estimated fixed effects of OppCanFinish with the added corresponding random slope.

Data Availability

Funding Statement

References

Decision Letter 0

Darrell A Worthy

Roles

Author response to Decision Letter 0

Decision Letter 1

Darrell A Worthy

Roles

Author response to Decision Letter 1

Decision Letter 2

Darrell A Worthy

Roles

Acceptance letter

Darrell A Worthy

Roles

Associated Data

Supplementary Materials

Data Availability Statement

ACTIONS

PERMALINK

RESOURCES

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