Psychological Pressure in Competitive EnvironmentsPsychological Pressure in

Competitive Environments

Ignacio Palacios-HuertaLSE

Rationality, Heuristics and Motivation in Decision Making

Centro di Ricerca Matematica Ennio De GiorgiScuola Normale Superiore

Pisa, November 2010

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Motivation

• How important are psychological elements:- as constituents of human nature?- as determinants of human behavior and human performance (behavior and skills)?- as determinants of human behavior in competitive environments?

• Evidence from laboratory experiments and real life.

» See Falk and Heckman, Science 2009.

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• Ideal: Study human behavior in real life settings

• But unfortunately... Nature rarely creates the circumstances that allow a clear view and a precise measurement of the psychological elements at work.

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• Today, two papers:1. “Psychological Pressure in Competitive Environments: Evidence from a Randomized Natural Experiment”(joint with Jose Apesteguia, U Pompeu Fabra) American Economic Review forthcoming.

2. “Pawns of the Emotions: Psychological Elements in Cognitively Sophisticated Humans” (joint with Julio González-Díaz, U Santiago de Compostela)

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1. “Psychological Pressure in Competitive Environments: Evidence from a Randomized Natural Experiment”

(with Jose Apesteguia, U Pompeu Fabra) American Economic Review forthcoming

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Penalty Shoot-outs in Soccer

• Shoot-outs are a method to determine the winning team when a soccer match ends in a draw.

• Basic FIFA rules (1970-2003):– The referee tosses a coin and the team whose captain wins the toss takes the

first kick (there is no choice).– The kicks are taken alternately by the teams.– A kick has only two possible outcomes: score or no score.– Both teams take five kicks.

– If, after both teams have taken five kicks, both have scored the same number of goals, kicks continue to be taken in the same order until one team has scored a goal more than the other from the same number of kicks.

A B A B B B BA A A

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Main Characteristics

• Randomized experiment: the treatment and control groups are determined via explicit randomization.

Plus:• Natural setting.• Subjects are professionals.• Stakes are high.• The task is simple and well-defined.• The task is effortless.• Risk plays no role (two outcomes, Bernoulli trials)• The outcome is determined immediately (no subsequent play).

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Preview of Main Results

• Intuitively, there is no rational reason in this setting why winning probabilities should be different from 50-50.

• And yet, we find a greater winning probability for the team that kicks first, about 60-40.

• Further, professionals:– are aware of psychological effects;– rationally respond to them: when a change in 2003 in the FIFA

rules gives them the chance to choose the kicking order, they systematically choose to go first;

– when surveyed, professionals identify a specific psychological mechanism for their choices.

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• The mechanism that professionals identify is the one for which we find support in a discrete dynamic panel data analysis with lagged endogenous variables:

– Idea: Kicking first means a greater chance to lead in the partial score, and kicking second a greater chance to lag in the score and at most, get even.

– “Lagging Aversion:” lagging in the score, and thus having a worse “local” prospect than the opponent, appears to hinder the performance of the subjects.

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Related Literature I

• Behavioral Economics:

– Reference points (e.g., preferences with gain-loss asymmetries).– Pessimism and Anxiety– Evidence from changes in mood and arousal (media violence,

weather, etc)– No evidence from dynamic and strictly competitive settings

(leading vs lagging asymmetry as oppossed to gains vs losses asymmetry).

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Related Literature II

• Labor Economics: Tournaments– Tournaments are pervasive in organizations.

– Extensive theoretical and empirical literature.

– No evidence that psychological elements may be a relevant determinant of performance in tournament settings (zero-sum or strictly competitive settings).

– Risk, effort and other variables are often important, but play no role in this setting.

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Related Literature III

• Social Psychology Literature– Expert performance

– Performance under pressure from high stakes, audience, etc

but not psychological pressure from the “state” of the competition

• Ex Post Fairness of Coins Flips in Sports– Is a coin fair? E.g., in NFL sudden death extra time a coin

gives more chances to a team.

– But here both teams have the same chances, and yet human nature makes a coin flip ex post unfair.

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Dataset

• Fully comprehensive– All shoot-outs in the major international competitions (at national and

club levels), e.g., World Cup, European Cup, Champions League, etc.

– Finals of main national Cups

– Others

• All relevant variables: – Outcomes for each penalty kick: score, no score.

– Team information: rankings, category, position, experience.

– Location of the match (home, away, neutral)

– Competition type

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No difference in pre-treatment characteristics:

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The Main Result

Since this is a perfect Randomized Experimentthe Average Treatment Effect is: 60.5 – 39.5: 21%

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Result prevalent across characteristics

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Using Probit and Logit regressions:

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Next

• i. Are subjects aware of any psychological effects on performance?ii. If so, how do they react when they are given the chance to choose the kicking order? iii. Why they react the way they do?

• Where does the effect come from?i. Dynamic Performance: Dynamic Panel Data Analysisii. Kicker vs goalkeeper effects

• Policy Implications

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1. Awareness of the Effects and Players’ Reaction

FIFA changed the rule in July 2003,

from:

“The referee tosses a coin and the team whose

captain wins the toss takes the first kick”

to:

“The referee tosses a coin and the team whose

captain wins the toss chooses whether to take the

first kick or the second kick.”

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How Do Players Behave?

• Small sample of videos (around 20):- Difficult to observe the coin toss moment;- In every case except one (Italy vs Spain, European Championship, June 2008) the winner chose to go first.

http://www.youtube.com/watch?v=k8xRMqCA9y4

● Better with a survey

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Survey of 240 Players and Coaches

• Q1: “Assume you are playing a penalty shoot-out. You win the coin toss and have to choose whether to kick first or second. What would you choose: first; second; either one, I am indifferent; or, it depends?”

• Q2: “Please explain your decision: why would you do what you just said?”

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Answer: 96% say “in order to put pressure on the kicker”

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Hence:

• Subjects are aware of the result;• They react rationally to these psychological effects by

systematically choosing to kick first;• They attribute the result to a specific psychological

mechanism: “to put pressure on the kicker of the opposing team.”

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2.1. The Mechanism: Descriptive Evidence

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Descriptive Patterns

Scoring rate: Typically lower and drops over the rounds for the second team.

PK Importance: Greater for the second team.

Scoring and Importance negatively correlated along the two most frequent paths of observations.

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2.2 The Mechanism: Dynamic Performance

• We need to estimate a dynamic discrete choice panel data model with lagged endogenous variables (e.g., lagged outcomes, partial score) and unobserved heterogeneity.

• The estimation of these models involves a great deal of difficulties (Arellano and Honore, 2002).

• Ignoring state dependence (lagged outcomes) and unobserved heterogeneity yields biased and inconsistent estimates.

• We implement the model by Arellano and Carrasco (2003):It is a semi-parametric, random effects model with lagged endogenous variables and unobserved heterogeneity that yields consistent estimates.

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Marginal Effects: Transition Across States

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The evidence is consistent with the survey results:

• Lagging in the partial score has a detrimental effect on performance:

- The second team is more likely to find itself with a partial score of -1, and hence has significantly greater chances of losing the tournament.

• No evidence that leading in the score has a positive effect on scoring.

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2.3. Additional Evidence: Kicker or Goalkeeper?

• A penalty kick involves 2 players, not one. Why should all the psychological effects come from the kicker?

• Survey: – “Pressure only on the kicker”– Not a single player says “in order to enhance the performance

of my goalkeeper”• Intuition why it may come mostly from the kicker:

- Since most penalties are scored, the upside for the goalkeeper is always greater but less likely than the downside. The opposite is the case for the kicker: his upside is smaller but more likely than the downside. - Hence, a greater pressure on the kicker may reflect some form of probabilistic loss aversion, that is if losses are perceived disproportionally larger than gains.

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Evidence from a subsample

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3. Policy Implications

• Performance information available or released during a competition may affect performance exclusively for psychological reasons.

• Timing of tasks and release of information in contests.

• Examples:- Student competitions in schools (e.g., release of interim student scores both own and others)- Competitions for promotion in organizations- R&D races, political competitions (e.g., release of voting tendencies)- Sequential ordering of tasks

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Appendix: Theoretical Model

• A simple two parameter model:p > 0 probability of scoring if a team is ahead or tiedq > 0 probability of scoring if a team is behindp > q > 0

• This p-q model always generates a first team advantage

• Other models (e.g., p-q are team specific or players are heterogeneous in quality) do not.

• No implications with respect to location of players even in simplest version

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Conclusions

• Randomized natural experiment with unusually useful characteristics.

• For Behavioral Economics: We find a novel psychological effect not documented previously.- This effect has an impact on human performance.- Applicability: Competitive environments.

• For Rational choice theory: Individuals are aware and rationally respond to it.

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2. “Pawns of the Emotions: Psychological Elements in

Cognitively Sophisticated Humans”

(joint with Julio González-DíazU Santiago de Compostela)

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A “Chess Match”

Similarities with a penalty shoot-out:

● A chess match is a tournament between 2 players with an even number of chess games (typically 8 to 12)● Colors of the pieces (white/black) alternate from game to game. ● Both players play the same amount of times with each color.● Whites are better, and who begins in the first game with the white pieces is randomly decided.

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Differences with a penalty shoot-out:

1. Task: A cognitive task (kicking a ball is non-cognitive) 2. Subjects: Chess players are extremely smart humans (soccer players not at the same cognitive level)3. Time: One game per day, with plenty of time and a team of analysts (not just a few seconds, in the “heat of the moment”).4. Chance to lead: Minimal. In soccer: very large.

Beginning the first game with white pieces gives a minimal advantage to lead 28%(win)-17%(lose)-55%(draw), whereas in a penalty shoot-out penalties are scored around 80% of the time)

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Beginning with Whites Gives a Significant Advantage

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The Effect is Greater at the Top: Elite and WC matches

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Effect Only When Players Are Very Similar

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Notes on the potential role of risk:

• Three outcomes are possible in a game: win, lose and draw.• Players may adapt the risk they take.• If risk is taken into consideration, then the effects we have

documented are a lower bound on the actual size of the psychological effect.

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Addendum

Psychological Pressure in Competitive Environments

From the Field to the Laboratory

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Experiments in the Field

In Apesteguia and Palacios-Huerta (2010) we run 3 experiments with professional soccer players:

• Sequential-2006: A sequential penalty shoot-out (as in the natural setting).

• Simultaneous: A simultaneous penalty shoot-out.• Sequential-2007: one year later, same teams as Sequential-

2006, but in reverse order.

Conjectures:(i) First mover advantage in the sequential versions, exactly as in the field.(ii) No diference between the two sequential versions.(iii) No advantage for either team in the simultaneous version.

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Design

• 20 teams of 6 professional soccer players (5 kickers and 1 goalie)

• Each treatment (10 shoot-outs).• Maximum of 5 kicks (ties are allowed).

Payments:- 3 Euros for a score to the kicker

- 3 Euros to the goalie for a failed kick (missed or saved).- 60 Euros for the winning team, 0 to the loser, 20 if tied.

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Winning Frequencies

5

1

5

2 21

3

7

4

0

2

4

6

8

1 2 3

First team Second team Tied

Sequential 2006 Simultaneous Sequential 2007

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Scoring Prob by RoundSEQUENTIAL TREATMENTS

0,9 0,90,8 0,8

0,90,9 0,9 0,9

0,5 0,5

0,0

0,2

0,4

0,6

0,8

1,0

1 2 3 4 5

First team Second team

Scoring Prob by RoundSIMULTANEOUS TREATMENT

0,80,7

0,80,7

0,90,90,8 0,8

0,70,8

0

0,2

0,4

0,6

0,8

1

1 2 3 4 5

First team Second team

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Appendix for World Soccer and Chess Regulations

• The coin gives about a 20% percent advantage to one team or one player in a penalty shoot-out and in a chess match.

• That is, the coin is a CRITICAL player!

• Penalty shoot-outs and chess matches are NOT a 50-50 lottery but a 60-40 lottery.

• How can we solve this problem?

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There is an easy solution

Take 2 contestants: A and B

First two penalties or games of a chess match:

1º 2º …

A B …

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There is an easy solution

Assume that A has an advantage because he kicks first. If we wanted to minimize this advantage, what should be the order in penalties number 3 and 4?

1º 2º 3º 4º …

A B ? ? …

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There is an easy solution

Assume that A has an advantage because he kicks first. If we wanted to minimize this advantage, what should be the order in penalties number 3 and 4?

1º 2º 3º 4º …

A B B A …

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There is an easy solution

What if it is B that has an advantage? If we wanted to minimize this advantage, what should be the order in penalties number 3 and 4?

1º 2º 3º 4º …

A B ? ? …

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There is an easy solution

What if it is B that has an advantage? If we wanted to minimize this advantage, what should be the order in penalties number 3 and 4?

1º 2º 3º 4º …

A B B A …

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There is an easy solution

Hence, regardless of who has an advantage, the order should be reversed:

1º 2º 3º 4º …

A B B A …

And of course if there was no advantage to anyone in the first 2 penalties or games by reversing the order we are not given an advantage or disadvantage to anyone.

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How should the next 4 penalties be?

1º 2º 3º 4º 5º 6º 7º 8º

A B B A ? ? ? ?

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The same logic applies to the next 4 penalties or games:

If having A B B A gives an advantage to anyone, then the order should be reversed in the next 4 penalties or games:

1º 2º 3º 4º 5º 6º 7º 8º …

A B B A B A A B

And if there was no advantage to anyone by reversing the order in the next four we are given no advantage or disadvantage to anyone.

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The same logic applies to the next 8 penalties or games:

That is, we should reverse the order every 2 penalties or games, then every 4, then every 8, etc etc

1º 2º 3º 4º 5º 6º 7º 8º …

ABBABAABBAABABBA

By reversing the order we can only improve!

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• Nice solution (this is called the Thue-Morse sequence in number theory and differential geometry) but perhaps too complicated for the public to understand.

We need a simpler, approximate solution:

How about reversing the order just once and

then repeating the sequence?

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ABBAABBAABBAABBA

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This is exactly how services are assigned in tie-breaks in tennis:

ABBAABBAABBAABB……

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And if you want just 10 penalties (5 per team):

ABBAABBAAB

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Summary

• The random flip of a coin when the order is alternated is NOT NEUTRAL: it gives a 20% advantage to the team or players that begins kicking first or playing first with whites.

• The rules that determine the order of play in soccer or chess MUST BE CHANGED if we want to minimize the impact that a coin has in selecting the World Champion, the European Champion etc etc in soccer or the World Champion etc in chess.

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• FIFA, UEFA, FIDE etc should seriously consider the idea of modifying the order of play in penalty shoot-outs and chess matches to make competition more fair.

• Adopting the order currently used in tie-breaks in tennis is a major improvement over the current system.

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CONCLUSIONS

• Two randomized natural experiments with unnusually useful and clean characteristics.

• We find a novel psychological effect not documented previously in 2 different settings.

• Broad applicability: impact on cognitive and non-cognitive performance in humans in dynamic competitive environments.