Faculty of economics and business
‘The belief that success breeds success and failure breeds failure’
Hot-hand theory - penalty kicks in soccer.
Author: Sjoerd Hochstenbach
Student number: 11060751
Amsterdam, 21-6-2020
Business Administration: Management in the
digital age
University of Amsterdam
Supervisor: Rob van Hemert
Abstract
The belief that success breeds success and failure breeds failure is referred to as the hot hand theory in sports. Casual observers of sports, as well as athletes themselves, believe in the existence of hot hand. However, especially in the case of team sports, not much evidence is found that supports the hot hand belief. Therefore, a quantitative analysis of 239 penalty shootouts in soccer could be subject to interesting insights. Six hypotheses were set up to estimate the influence of hot hand on individual performance, team performance, and
allocation to important penalty kicks. No evidence was found for increased individual or team performance as a result of hot hand. However, the results showed that more players were assigned to the important first kick of the shootout if they were ‘feeling hot’. This study helps with understanding the human decision-making process and provides suggestions for
Introduction
The interest from behavioral economists in the role of misperceptions of randomness in the human decision-making process has risen. Parsons and Rohde (2015) state that falsely connecting causal explanations to low probability events can result in inaccurate resource allocations and inefficiencies. Examples range from overreaction to perceived trends in financial markets (Kahneman & Riepe, 1998) (Rabin & Vayanos, 2010) to the exploitation of consumers in marketing (Camerer, 1989) (Johnson & Tellis, 2005). Because of this, hot hand theory in sporting competitions and the possible connection with misperceptions of
randomness could be subject to interesting findings. A large amount of survey evidence suggests that both casual observers of sports, as well as athletes themselves, believe in the existence of going on a ‘hot-hand’ streak (Gilovich, Vallone & Tversky, 1985) (Burns, 2004).
The hot hand theory refers to the common assumption in sports that success breeds success and failure breeds failure (Bar-Eli, Avugos & Raab, 2006). This term indicates that successive attempts of an individual player are positively related. Leading to the belief that a player's performance during a particular period is significantly better than could be expected based on the player’s overall record (Gilovich et al., 1985).
The phenomenon of the hot hand is well known to everyone who either plays or watches basketball regularly. After a player successfully has a run of baskets, the expectation is that he has higher odds of having success with the next shot as well (Bar-Eli et al., 2006). As Hales (1999) states, this has a plausible causal relationship. When a player is feeling ‘hot’ the confidence in his abilities will rise. Therefore, the player becomes more relaxed and focused, causing more likelihood of success in his next attempts.
One might wonder, however, whether the observed superior (or inferior) performance genuinely differs from what could be expected by mere chance. Studies from Koehler and Conley (2003), Gilovich et al. (1985), and Vergin (2000) failed to reveal evidence of hot hands in basketball. Similarly, no evidence was found for hot hand in baseball (Siwoff, Hirdt & Hirdt, 1988) (Albright, 1993) (Frohlich, 1994) (Albert and Bennett, 2001).
Contrary, some researchers challenged these views and did find evidence for the existence of hot hand in sports. Examples range from horseshoe pitching, where Smith (2003) demonstrated that pitchers do have modest spells, to rolling strikes in bowling
(Dorsey-Palmateer & Smith, 2004).
Considering the lack of evidence for hot hands in team-sports, it is worth investigating the case of team sports such as soccer where the hot hand belief has been less extensively analyzed.
Research about hot hand in soccer on the team-level is limited. One of the few studies about soccer and hot hand on a team-level by Parsons & Rohde (2015) found mixed evidence for the existence of streaks of wins, draws, or losses in the English Premier League. While soccer players themselves stated the belief that the cohesiveness of a team can increase team-level performance (Redwood-Brown et al., 2018) and setting an example is seen as a
psychological factor that can influence follow up actions of the team (Van Hemert, 2020), this belief has not been statistically proved yet.
The same applies to studies about hot hand on the individual level in soccer since these studies are mainly about the perceptions of soccer players themselves. Soccer players stated the belief that past performance can increase confidence and, in turn, affect
performance positively (Redwood-Brown, Sunderland, Minniti & O’Donoghue, 2018) (Jones & Harwood, 2008).
From the evidence so far presented, it is not possible to either reject or accept hot hand as a real phenomenon in soccer. A drawback of using soccer to test hot hand is that scoring does not happen frequently. Therefore, fluctuations in performance are measured with a lot of statistical noise (Parsons & Rohde, 2015). A big data set is needed to find reliable results about hot hand in soccer without statistical noise.
In this article quantitative data about shootouts in soccer, game field goals, and in-game penalties will be collected from multiple websites to answer the research question: Can evidence be found in penalty shootouts for the existence of hot-hand in soccer? Hot hand will be tested both on the team-level (can team factors such as scoring the equalizing goal in normal time increase the chances for the team to win the shootout) and individual-level (can scoring an in-game field goal increase the chances for an individual to score a penalty kick during the shootout). After the collecting of data multivariate associations will be analyzed by using binary regressions in SPSS.
This article adds to the body of empirical literature by analyzing the hot hand phenomenon in a not yet investigated environment, namely penalty kicks in soccer. Data about penalty kicks are readily available and are being continually generated. Moreover, by combining different researchers on the data collection a big data set is obtained. After the data collection, the results will be interpreted to provide insight into the relationship between hot
hand, soccer, and misperceptions of randomness, and thereby help to understand the human decision-making process.
This paper proceeds with a theoretical framework in which hot hand theory definitions and previous literature about this topic will be discussed. Next, in the method section, there will be described how data is collected, which variables were included, and how the analysis of this data is performed. Finally, the results and a discussion of these results will be
Theoretical Framework
History of hot hand research in sports
Initially, the hot hand research started with a paper of Gilovich et al. (1985), where an attempt was made to find empirical support for hot hand shooting in statistical data of basketball games. No evidence of the hot hand phenomenon for individuals was found in any of the data sets. Actually, contrary to the hot hand belief it appeared that the probability of making a shot usually decreased after making a shot compared to having missed shots.
Gilovich and his fellow researchers (1985) suggested that the belief in the hot hand is merely an illusion, based on biases and heuristics. For example, according to the memory bias, streaks of hits are more memorable than combinations of streaks and misses. Therefore, the observer overestimates the frequency of positive streaks. The research of Gilovich et al. (1985) generated a considerable number of follow-up studies and extended to other sports as well.
A more recent study by Koehler and Conley (2003) also failed to reveal evidence of hot hands for individuals in basketball. They suggested that the NBA Long Distance Shootout contest is a more appropriate setting to detect hotness. However, they did not encounter unusual streaks of success and no sequential dependency in performances of 23 different participants spread around four annual contests.
Vergin (2000) extended the hot hand research in basketball to the team-level, by investigating momentum over the length of a season. He collected winning and losing streaks of 29 NBA teams. These streaks were compared to streaks that would have occurred under the assumption of independence of previous game outcomes. The results of the research showed a very close fit of observed streaks to expected streaks. This suggested that the probability of winning or losing is not related to team performances in previous games.
Moreover, evidence against the hot hand for individuals was found in baseball by various researchers (Siwoff, Hirdt & Hirdt, 1988) (Albright, 1993) (Frohlich, 1994) (Albert and Bennett, 2001). For example, Albright (1993) investigated streakiness in batting by analyzing records of professional baseball players throughout four seasons. Although some batters exhibited streakiness in some seasons, this happened more occasionally than
consistently, and the number of streaks in the dataset did not significantly deviate from randomness.
Additionally, Albert and Bennett (2001) used a computer simulation to find existence of hot hand in baseball. This simulation replicated the game performances of Todd Zeile
during the first half of the 1999 season. The results illustrated that the peaks and valleys of the player’s batting average occurred due to chance. Therefore, again not providing a hot hand effect on individual performance.
While these former studies did not detect evidence for the hot hand theory, other studies found different results. The first example of this is a study conducted by Smith (2003). He suggested that the most famous study about hot hand by Gilovich et al. (1985) did not control for several confounding influences. Therefore, an analysis of horseshoe pitching - which unlike basketball does not have these defects - can provide new insights. The results indicated that horseshoe pitchers do have modest hot and cold spells.
Secondly, support for the hot hand is found in bowling (Dorsey-Palmateer & Smith, 2004). The analysis of professional bowlers argued that, for many players, the probability of rolling a strike is dependent on previous outcomes. Because the number of strikes rolled variates more throughout games than can be the sole consequence of chance.
Thirdly, Klaassen and Magnus (2001) used 481 games at Wimbledon spread across multiple years to demonstrate that winning the previous point in tennis had a positive effect on winning the current point, therefore providing evidence for the hot hand. However, the effect was small, and the sample size was big, suggesting that this significant result may not have occurred with a smaller sample. Moreover, they found that if the previous point was lost the chances of winning a point lowered, providing the existence of a cold hand.
The belief in the cold hand is, just like the belief in hot hand, a belief in streaks. However, players begin in a neutral state and are pushed into negative momentum chains by negative precipitating events (Livingston, 2012). So far, not much research is done on cold hand in sports, also called negative hot hands. Studies that prove the existence of cold hands could extend research on the hot hand by reviewing behaviors in situations in which is focused on unlucky streaks, such as when a player should be substituted (Köppen & Raab, 2012).
Hot hand in soccer
Everyone has to deal with unavoidable decisions daily. While some of these decisions have minor consequences, others may be more critical. Many of these decisions are based on probability beliefs of uncertain events. An example comes from the game of basketball. Sometimes players decide to pass the ball to the team's best shooter, who is closely guarded by the opposing team. This might be a non-optimal decision if other players have a better
unavoidable decisions also occur in soccer. An example is deciding on the allocation of penalty takers in a penalty shootout.
Penalty shootouts have some unique characteristics (Chiappori, Levitt & Groseclose, 2002). First, the shootouts have the structure of "matching pennies," meaning that there is a unique mixed-strategy equilibrium. The kicker and the goalie play a zero-sum game where both of their strategies are identified. Namely, the kicker can shoot at the left, middle, or right side of the goal and the keeper can jump to either of those sides or stay in the middle. Second, the preferences of the players are well known: the kicker wants to maximize the probability of a score and the goalie wants to minimize scoring. Third, there is a lot at stake. The teams of the players can lose or win an enormous amount of money and the players’ egotism is threatened which can result in face loss (Baumeister, 1997). Fourth, data is continually generated and available. Finally, at least in professional soccer, there is a lot of information available on the history of the kicker and goalie. Teams routinely track information about shootouts by other teams.
The ‘penalty shootout’ in knock-out-phases is one of the most dramatic events in international soccer (Jordet, Hartman, Visscher & Lemmink, 2007). The outcome of this kick is dependent on factors such as skill, physiology, chance, and psychology (Jordet et al., 2007). The main aim of this study was to estimate if the outcome of the penalty kick is dependent on one of these psychological factors, the hot hand. A lot of people in the soccer community see the outcome of a penalty shootout as a lottery. In this study, there will be tested if feeling ‘hot’ can influence the outcome on the individual and team-level
Parsons & Rohde (2015) used data from the English Premier League to examine hot hand on a team-level within games and across games in soccer. Hot hand across games was measured by comparing the actual number of runs in each season with the expected number under the assumption of randomness. Overall, the results indicated that there is little
difference between the actual and expected number of streaks in the EPL. Suggesting that there is some, but not much evidence found for the existence of hot hand across games. Furthermore, the study demonstrated that negative momentum occurred more than positive momentum across games.
As named before, Parsons & Rohde (2015) also examined hot hand within games. Within games momentum was measured with a Poisson regression where the independent variable was goals scored in the first half and the dependent variable goals in the second half. As a consequence, they tested if scoring in the first half of a game (going on a hot hand) increases the likelihood of scoring in the second half. While the results indicated that scoring
a goal in the first half increases the ratio of scoring in the second half, the effect was not significant.
Participants of two different studies described confidence as a factor that can increase performance. Jones and Harwood (2008) identified and examined the perceptions of
university soccer players about psychological momentum. One player stated: ‘When you are feeling good about yourself you have got a good chance of performing to a high standard”, indicating the belief of the player of the importance of a hot hand. Redwood-Brown et all. (2018) also contributed to this topic. They studied the perceptions of elite players and found that scoring is the most frequently named variable associated with positive momentum in soccer. Besides, they established that “being cohesive as a team” is an important aspect of positive momentum. Indicating that hot hand is also believed to play a factor on the team-level.
Athletes can have different psychological states at a neutral score, depending on how the score came about (Briki, Den Hartigh, Markman & Gernigon, 2014). By scoring or conceding an equalizing goal, a team can move to a more positive or negative mindset. Den Hartigh, Van Yperen and Gernigon (2019) found that positive psychological momentum was higher when the team itself scored the equalizer than when the opponent tied the score.
Setting a good or bad example is a psychological factor that can influence follow up actions (Van Hemert, 2020). Thus, in the case of penalty kicks, a player can set a good example by scoring in the normal game which will reduce the pressure for the players that have to take a penalty kick in the shootout. Contrary, a player who sets a bad example by missing the in-game penalty kick will likely increase the pressure for the players in the shootout.
Lastly, Jordet and Hartman (2008) studied shot valence and described positive shot valence and negative shot valence. Positive shot valence is classified as a kick which, when scored, immediately leads to a victory. Contrary, a negative valence shot is a kick where a miss instantly leads to a loss. Valence shots are referred to as high-pressure situations for athletes (Jordet, 2009).
Penalty kicks and hot hand: hypotheses
If feeling ‘hot’ influences kick outcome, different outcomes for individual kickers are expected based on their feeling of hotness. Therefore, the first hypotheses will be about the
baskets a player is more likely to score with the next shot (Bar-Eli et al., 2006). Since scoring is the most frequently named variable associated with positive momentum in soccer
(Redwood-Brown et al, 2018), and confidence is a factor that can increase performance (Redwood-Brown et al, 2018) (Jones & Harwood, 2008), the first hypothesis is about this effect. The assumption is that, if a player scores a field goal in the game his confidence will increase, the player will feel ‘hot’ in his abilities and he will be more likely to score in the shootout.
H1: Scoring a field goal during the game will lead to higher odds of scoring a penalty kick in the shootout
This effect is also expected if a player already scored an in-game penalty kick.
H2: Scoring a penalty kick during the game will lead to higher odds of scoring a penalty kick in the shootout
Furthermore, the expectation is that penalty takers can reduce the pressure for follow-up players by setting a good example by scoring their penalty kick (Van Hemert, 2020). When a player of a team scores a penalty kick the next player of the team will feel ‘hot’ and will be more likely to score the penalty kick. Thus, since the effect of a fellow teammate kick on the current shot is estimated this relationship measures the hot hand effect on a team-level.
H3: When the previous player of the team scored his penalty the penalty taker of the current penalty kick is more likely to score.
Moreover, Redwood-Brown et all. (2018) found that “being cohesive as a team” can enhance positive momentum. Moreover, Briki et all. (2014) found that players can differ in
psychological momentum in a neutral, dependent on which team scored the equalizer. When the team itself scored the equalizing goal instead of the opponent team momentum was more positive (Den Hartigh et al., 2019). Therefore, the expectation is that the team that scored the equalizing goal is more likely to win the shootout.
Finally, the prediction is made that players who feel confident because they scored a goal during the normal game are more likely to engage in high-pressure penalty kicks. Jordet (2009) described shots with negative or positive valence as high-pressure situations. Since valence shots are most of the time the fifth kick of the shootout, they are identified as the most decisive kicks. The expectation is therefore that players who already scored a field goal are more likely to take these types of kicks.
H5: Players who already scored a field goal during the game are more likely to take the fifth penalty kick of the shootout.
The same is expected for the allocation to the first penalty kick in the shootout. Jordet et all. (2007) found that coaches often select skilled players for the first kick with the purpose of securing a good start. Possibly, coaches will select players that feel hot because they scored a field goal to the first kick to secure a good start.
H6: Players who already scored a field goal during the game are more likely to take the first penalty kick of the shootout.
Methods Data
Data were collected for penalty kicks in 17 league cup tournaments, the Champions League, the Europe League, the European Cup, and the World Cup. To get information on the kicks and the kickers, an internet-based game record analysis was performed on the websites soccerway.com and transfermarket.com. However, some information on less known players or older tournaments was not registered. Therefore, additional information was obtained from other sources using google.com. A total of 2566 penalty kicks from 11 seasons (2007/2008-2018/2019) was collected. The average age of the players in the sample was 27.41 years with a standard deviation of 4.53 years. Of these players, 762 were left-footed and 1737 were right-footed. The position of the players on the field was: 761 defenders, 907 midfielders, and 852 attackers. Player or penalty kick information that could not be found on the websites or the additional sources was given the value -99. These values were later indicated as ‘missing’ and therefore not included in the analysis.
Variables
First, there is aimed to explain the individual hot hand effect by analyzing the relationship between two independent variables and one dependent variable. The dependent variable to measure this effect, score, had two primary values – goal (=1) or miss (=0). The first
independent variable was field goal which measures if the player already scored a field goal during the normal game. If the player did score a field goal a value of one is assigned, if the player did not a value of zero is assigned. The second independent variable, scorePK, measures the performance of players’ in-game penalty kicks. Three dummies were made for this variable. Namely, a dummy for penalty taken and scored, a dummy for penalty taken but missed, and a dummy for no in-game penalty taken.
Second, the effect of hot hand on team performance was investigated. To examine this effect, two independent variables and two dependent variables were included. The first independent variable to measure the team effect was PreviousTakerTeam. This variable indicates if the previous penalty taker of the team scored or missed the penalty kick. If the player scored, value one is assigned, if he missed, value zero is assigned. The dependent variable was again score. The second independent variable to measure the team effect was equalizer. This variable gives value one to teams that scored the equalizing goal in normal playing time and value zero to teams that were equalized against. The dependent variable,
winner, had two primary values – win (=1) and lose (=0), which indicated if a team won or lost the shootout at the end of the series.
Third, the relationship between hot hand on the individual level and the allocation of penalty kicks is determined. In order to analyze this relationship, the effect of one
independent variable on two different dependent variables was determined. The dependent variables were kick5 and kick1. The variable kick5 consisted of value one when it was indeed the fifth kick of the shootout, and value zero when it was not the fifth kick of the shootout. The same was true for kick1, but now for the first kick. The independent variable was again field goal which was measured in the same manner as described before.
Finally, some control variables were taken into account. Firstly, to control for the effect of the independent variables on the dependent variable score for hypotheses 1,2, and 3 the position and age of the players were included as control variables. This because an improved shot performance can also be the result of a player’s experience (age) or familiarity with the situation (attackers are more familiar with shooting). Secondly, to control for the relationship between equalizer and winner in hypothesis 4, the highest average market value of teams is included as control variable in the regression. Teams that have a higher average market value often have more quality and are therefore more likely to win the shootout. Finally, to control for the effect in hypotheses 5 and 6 of the independent variable on the allocation of the penalty kicks age and position were again included as control variables. An experienced player is more often assigned to important kicks. The same goes for an attacker.
Data analysis
For this study, six different hypotheses are examined. The relation between the dependent variables and the independent variables was investigated with binary logistic regression analyses. In this type of regression, the dependent variable is a dummy variable (Midi, Sarkar & Rana, 2010). A quantitative analysis was performed on the dataset. A quantitative analysis has certain benefits compared to qualitative analysis. Examples range from cost effectiveness to high representativeness (Queirós, Faria & Almeida, 2017). To examine the association between the variables included in the analysis Pearson correlation coefficients were calculated. A distinction was made between weak (0.10-0.30), moderate (0.30-0.50), and strong (>0.50) correlations. The statistical analysis was performed with SPSS version 24. The level of significance was set at 0.05.
Results
Data has been collected on penalty shootouts across eleven years, the total number of penalty kicks consisted of 2566. Of these 2566 penalty kicks, 1871 were scored, leading to a
conversion rate of 72.9%. Furthermore, descriptive information included average age (27.44, SD = 4.349) and position (defender = 761, midfielder = 907 and attacker = 852) of the players (Table 1).
Table 1. Descriptive statistics about penalty kicks, age, foot and position
Variables N Sum Mean SD
Penalty kicks (1=score, 0=miss) 2566 1871 0.73 0.444 Age 2525 - 27.44 4.349 Position (defender) 2526 761 0.30 0.459 Position (midfielder) 2526 907 0.36 0.480 Position (attacker) 2526 852 0.34 0.473
Next, the relationships between the dependent and independent variables for the six hypotheses are identified with correlation tables. Table 2 shows a positive but weak
relationship between the dependent variable score and the independent variable field goal in hypothesis 1. The relationship is not significant. Table 2 also indicates the relationship between the variables score (PK) and score for hypothesis 2, which is a weak, negative, and not significant relationship. Furthermore, the relationships between independent variable field goal and dependent variables kick1 and kick5 are tested. Table 2 shows no relationship
between independent variable field goal and dependent variable kick 5 for hypothesis 5. The relationship between variables field goal and kick 1 for hypothesis 6 is positive and significant (Table 2). Table 3 is about the third hypothesis. The relationship between PreviousTakerTeam and score is weakly positive, but again, not significant. Finally, for the fourth hypothesis, Table 4 shows a weak negative relationship between dependent variable winner and
Table 2 Mean 1. 2. 3. 4. 1. Score 0.73 - 2. Kick1 0.19 0.015 - 3. Kick5 0.12 0.017 -0.177* - 4. Field goal 0.10 0.007 0.062** -0.001 - 5. Score (PK) 0.01 -0.015 0.088** 0.05 0.137** N=2554 * = significant at 0.05, ** = significant at 0.01 Table 3. Mean 1. 1. Score 0.73 - 2. PreviousTakerTeam 0.75 0.09 N= 2087 Table 4. Mean 1. 1. Winner 0.51 - 2. Equalizer 0.49 -0.07** N=1892 ** = significant at 0.01
The first hypothesis is about the individual hot hand effect. Namely if scoring an in-game field goal can increase the chances of scoring a penalty kick during the shootout. The conversion rate of penalty kicks was, as expected, a bit higher for players who scored a field goal (73.9%, n = 245) than for players who had not scored a field goal (72.8%, n = 2300). However, unlike the hypothesis, there is no evidence for an individual hot hand effect of field goals (exp(B) = 1.063, P = 0.698) (Table 5).
Additionally, there is no evidence for the second hypothesis about the individual hot hand effect. In contradiction with the hypothesis, the conversion rate of penalty kicks in the shootout was the highest for players that did not take an in-game penalty kick (72.9%, n = 2513). This was followed by players that scored their in-game penalty kick (66.7%, n = 30)
and players that missed their in-game penalty kick (63.6%, n = 11). As can be seen in Table 5, the negative effects of a scored in-game penalty kick (exp(B) = 0.715, P = 0.395) and a missed in-game penalty kick (exp(B) = 0.618, P = 0.446) are, however, not significant.
Table 5. Binary Logistic Regression
Variable Score
Exp(B) ratio (p-value)
Field goal 1.063 (0.698) Score (PK) à score Score (PK) à miss 0.715 (0.395) 0.618 (0.446) Attacker 1.101 (0.399) Midfielder 1.031 (0.784) Age 1.002 (0.826) N = 2525
For the third hypothesis, the dependent variable is again score. However, now there is tried to capture the hot hand effect on team performance. As hypothesized, if the former teammate that took a penalty in the shootout scored the kick the conversion rate is higher for the current penalty taker (72.8%, n = 1575) than when the former teammate did not score the previous kick in the shootout (71.9%, n = 512). Although there is almost 1% difference in the conversion rates, this positive effect is not significant (exp(B) = 1.052, P = 0.654) (Table 6).
Table 6. Binary Logistic Regression
Variable Score
Exp(B) ratio (p-value)
Previouskicktaker 1.052 (0.654)
Attacker 1.114 (0.380)
Midfielder 1.049 (0.690)
Age 1.008 (0.474)
Furthermore, the fourth hypothesis was made to estimate the hot hand effect on team performance again. The results show, in contradiction to the hypothesis, that winning the penalty shootout happened less often for teams that equalized in normal time (47%, n = 927) than for teams that were equalized against (53.9%, n =945). The negative difference in winning percentage is significant (exp(B) = 0.756, P = 0.003).
Table 7. Binary Logistic Regression
Variable Winner
Exp(B) ratio (p-value)
Equalizer 0.756 (0.003)
Highest average MV 1.399 (0.000)
N = 1872
The fifth hypothesis, as well as the sixth hypothesis, was made to detect the effect of ‘feeling hot’ on the allocation of penalty kicks. The prediction was that players that already scored a field goal would be more likely to take the fifth kick. However, the allocation of players to the fifth penalty kick is rather similar for players who scored a field goal (11.8%, n = 245) as for players who did not score a field goal (11.9%, n =2300). Therefore, unlike hypothesized, there is no statistical evidence for allocation to the fifth kick based on field goals (exp(B) = 0.875, P = 0.530).
Table 8. Binary Logistic Regression
Variable Kick5
Exp(B) ratio (p-value)
Field goal 0.875 (0.530)
Attacker 1.451 (0.014)
Midfielder 0.844 (0.292)
Age 1.013 (0.348)
Finally, the same positive effect of scoring an in-game field goal on the allocation to kick1 was expected. Relatively, more players were allocated to the first kick of the shootout if they already scored a field goal (26.1%, n = 245) then players that did not score a field goal (17.9%, n = 2280). There is enough statistical evidence to confirm the hypothesis that players who scored a field goal will more likely be assigned to the first penalty kick (exp(B) = 1.479, P = 0.014).
Table 9. Binary Logistic Regression
Variable kick1
Exp(B) ratio (p-value)
Field goal 1.479 (0.014)
Attacker 1.883 (0.000)
Midfielder 1.932 (0.000)
Age 1.072 (0.000)
Discussion
To examine hot hand in soccer, and its possible relationship to misperceptions of randomness a quantitative study was set up. The main aim of this study was to provide an objective assessment of the effect of hot hand on individual performance, team performance, and resource allocation. Summing up all results, the research can be answered. The results of the binary logistic regression provided enough evidence that argues against the existence of a hot hand effect on the individual and team-level. However, the results showed that the allocation of important tasks is, nevertheless, influenced by hot hand factors.
The first two hypotheses were made to detect the hot hand effect on individual performances in penalty shootouts. Hypothesis 1 tried to identify if scoring an in-game field goal could lead to higher odds of scoring a penalty kick during the shootout. No statistical evidence is found in support of this hypothesis. Suggesting that performing a penalty kick for individuals is not dependent on their feeling of ‘hotness’.
Additionally, for the second hypothesis about the individual hot hand effect, there was not an increase in performance of the penalty kick in the shootout if the player already scored an in-game penalty kick. The conversion rate was the highest for players that did not take an in-game penalty kick followed by players that scored an in-game penalty kick and finally for players that missed their in-game penalty kick. It seems that not take an in-game penalty kick is beneficial for players that have to take a kick in the shootout, contrary to what was
hypothesized. However, the negative effect of scoring or missing an in-game penalty kick on penalty kick performance was not statistically confirmed. Meaning that the difference in performance did not genuinely differ from what could be expected by chance alone.
The findings of this study could provide useful insights into the effect of hot hand on individual performance. In keeping with previous findings, there was no statistical evidence for the individual hot hand effect. Next to soccer, former researchers also failed to find statistical evidence for improved individual performance due to feeling hot in basketball (Gilovich et al., 1985), (Koehler & Conley, 2003) and baseball (Siwoff, Hirdt & Hirdt, 1988) (Albright, 1993) (Frohlich, 1994) (Albert and Bennett, 2001).
Still, it should be noted that other researchers did find some statistical evidence for individuals that went on a hot hand streak. For example, Klaassen and Magnus (2001) demonstrated that winning the previous point in tennis had a positive effect on winning the current point. However, there can be noted that the effect of Klaassen and Magnus research’
was small and the sample size was big, suggesting that the effect found would not have been occurred under a different sample.
It seems that the hot hand effect on individual performances is only present in specific circumstances. The question rises why still so many people believe in an individual hot hand effect. Athletes believe in the hot hand because they believe they experienced it themselves. Nonetheless, this belief is often suspect to biases and heuristics. There can be argued that streaks of hits are easier to remember than combinations of streaks of misses. Because of this memory bias, the observer and the performer himself are likely to overestimate the occurrence of positive streaks (Gilovich et al., 1985)
For the third and fourth hypotheses, an attempt was made to detect hot hand effect on performances of teams. Although the third hypothesis found a small positive difference in the dependent variable score as a result of the previous penalty taker of the team, the effect was not significant. The individual performance of a player on a penalty kick did not significantly increase when the previous penalty taker of the team scored his penalty in the shootout. Meaning that the team performance did not increase as a result of the hot hand factor.
Also, the fourth hypothesis did not find an increase in team performance due to hot hand. The prediction was that if a team scored the equalizing goal in normal time, they would be more likely to win the shootouts afterward. Surprisingly, the opposite was found. There was a significant negative effect of independent variable equalizer on dependent variable winner. Teams that made the equalizer perform less in the shootout and are more likely to lose.
One of the few studies about hot hand on a team-level was conducted by Parsons & Rohde (2015), who examined hot hand within games and across games in soccer. They discovered some improvements in team performance due to feeling hot, but there was not much evidence for this and more importantly – the results were not significant. Furthermore, other research found that setting an example can increase team performance (Van Hemert, 2020). Not much analysis is performed on the relationship between hot hand and team performance, however.
Therefore, this study, which conducted quantitative analysis about penalty kicks provided new insights about hot hand theory and team performance. In both the hypothesis there was no statistical evidence for improved team performance due to hot hand factors. Even more, in the hypothesis where the effect of an equalizing goal on winning or losing the shootout was tested, the results showed that confidence increasing factors (scoring the
a result of an increased level of confidence. An exception is the study of Gould, Petlichkoff, Simons & Vevera (1987) where a negative significant effect was revealed between self-confidence and pistol shooting performance. Since this study is rather old, more quantitative research on how confidence factors can decrease (team) performance is needed.
Finally, with the fifth and sixth hypothesis, an attempt had been made to detect how hot hand could affect the allocation of the penalty kicks in the shootout. Hypothesis 5 did not find a significant effect of the independent variable field goal on the allocation to kick 5. Meaning that there was no significant increase in players assigned to the fifth kick if they scored a field goal.
In contradiction to hypothesis 5, the sixth hypothesis did find statistical evidence for the increased allocation of players to the first penalty kick when the specific player already scored a field goal. Meaning that if a player already scored an in-game field goal he is more likely to be assigned to the first penalty kick in the shoot-out.
The sixth hypothesis is particularly interesting. Falsely connecting causal explanations to low probability events can result in inaccurate resource allocations and inefficiencies (Parsons & Rhode, 2015). In this research, there is no statistical evidence found that supports the hot hand effect on individual or team performance. Therefore, the allocation of players on basis of their hotness to the important first kick of the shootout is not an optimal decision.
There are also some limitations to this research. First, a drawback of using soccer to analyze hot hand theory is that scoring, unlike sports like basketball, is of low frequency. Resulting in that performance fluctuations are measured with a lot of statistical noise (Parsons & Rhode, 2015). By including different researchers on the data collection an attempt has been made to diminish this limitation. For example, independent variable scorePK that tries to measure the individual hot hand effect on dependent variable score only has 41 observations. However, to counter this limitation, the independent variable field goal (with 245
observations) is also included to measure the hot hand effect on individual performance. Second, the failure of detecting hot hand on a team-level in this research could also have been the result of picking the wrong independent variables. Possibly,
PreviousTakerTeam and equalizer are not good indicators of hot hand, and therefore also not appropriate to use as independent variables. More qualitative studies can bring insight into what players think are good estimators of hot hand factors that can influence team
performance.
findings are relevant to other contexts, generalization of the findings has to be done with caution. Future researchers could explore how managers of traditional businesses are influenced by hot hand on a daily business level.
The results of this study bring insights to a variety of markets. In the betting market, for example, Sinkey and Logan (2014) found that soccer betting houses respond to behavioral biases of betters. Another example comes from overreaction to trends in the financial market (Rabin & Vayanos, 2010). If betters and financial managers have more understanding of possible biases, they can develop a more profitable betting or finance strategy.
Additionally, this study could provide useful insights for managers of businesses. To enhance optimal resource allocations, this study suggests that managers should assign employees to specific tasks not just based on recent performances. Rather, managers should take into consideration that recent performances are often random and not always the best predictor of future performance as this study has demonstrated. Therefore, a manager should look at the long-term performance of employees when assessing the allocation of tasks.
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Appendix
Descriptive statistics 1: Score
Descriptive statistics 2: Age
Descriptive Statistics
N Minimu m Maximu m Sum Mean Std. Deviation age 2525 17 48 69293 27,44 4,349 Valid N (listwise) 2525Descriptive statistics 3.1: Position – defender
Descriptive Statistics
N Minimu m Maximu m Sum Mean Std. Deviation defender 2526 0 1 761 ,30 ,459 Valid N (listwise) 2526Descriptive statistics 3.2: Position – midfielder
Descriptive Statistics
N Minimu m Maximu m Sum Mean Std. Deviation midfielder 2526 0 1 907 ,36 ,480 Valid N (listwise) 2526Descriptive Statistics
N Minimu m Maximu m Sum Mean Std. Deviation score 2566 0 1 1871 ,73 ,444 Valid N (listwise) 2566Descriptive statistics 3.3: Position – attacker
Descriptive Statistics
N Minimu m Maximu m Sum Mean Std. Deviation attacker 2526 0 1 852 ,34 ,473 Valid N (listwise) 2526 Correlation table 1Correlations
score kick1 kick5 field goal
score (PK) score Pearson Correlation 1 ,015 ,017 ,007 -,015 Sig. (2-tailed) ,450 ,400 ,708 ,446 N 2554 2554 2554 2543 2554 kick1 Pearson Correlation ,015 1 -,177** ,062** ,088** Sig. (2-tailed) ,450 ,000 ,002 ,000 N 2554 2554 2554 2543 2554 kick5 Pearson Correlation ,017 -,177** 1 -,001 ,005 Sig. (2-tailed) ,400 ,000 ,952 ,819 N 2554 2554 2554 2543 2554
field goal Pearson Correlation ,007 ,062** -,001 1 ,137** Sig. (2-tailed) ,708 ,002 ,952 ,000 N 2543 2543 2543 2543 2543 score (PK) Pearson Correlation -,015 ,088** ,005 ,137** 1 Sig. (2-tailed) ,446 ,000 ,819 ,000 N 2554 2554 2554 2543 2554
Correlation table 2
Crosstable hypothesis 1: Field goal à score
Crosstables hypothesis 2: Score(PK) à score
Crosstable hypothesis 3: PreviousTakerTeam à score
Crosstable hypothesis 4: Equalizer à winner
Crosstable hypothesis 5: Field goal à kick 5
Crosstable hypothesis 6: Field goal à kick1
Binary logistic regression for hypothesis 1 and hypothesis 2: Hypothesis 1: Field goal à Score, Hypothesis 2: ScorePK à Score
Binary logistic regression for hypothesis 3: PreviousTakerTeam à Score
Binary logistic regression for hypothesis 4: Equalizer à Winner
Binary logistic regression for hypothesis 5: Field goal à Kick5
Binary logistic regression for hypothesis 6: Field goal à Kick1
