Transcript Psychological Pressure in Competitive Environments

Psychological Pressure in
Competitive Environments
Ignacio Palacios-Huerta
LSE
Rationality, Heuristics and Motivation in
Decision Making
Centro di Ricerca Matematica Ennio De Giorgi
Scuola Normale Superiore
Pisa, November 2010
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.
2
• 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.
3
• 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)
4
1. “Psychological Pressure in Competitive
Environments: Evidence from a
Randomized Natural Experiment”
(with Jose Apesteguia, U Pompeu Fabra)
American Economic Review forthcoming
5
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.
A B A B A B A B A B
– 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.
6
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).
7
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.
8
• 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.
9
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).
10
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.
11
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.
12
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
13
14
No difference in pre-treatment characteristics:
15
The Main Result
Since this is a perfect Randomized Experiment
the Average Treatment Effect is: 60.5 – 39.5: 21%
16
Result prevalent across characteristics
17
18
19
Using Probit and Logit regressions:
20
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 Analysis
ii. Kicker vs goalkeeper effects
• Policy Implications
21
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.”
22
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
23
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?”
24
Answer: 96% say “in order to put pressure on the kicker”
25
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.”
26
2.1. The Mechanism: Descriptive Evidence
27
28
29
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.
30
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.
31
32
33
Marginal Effects: Transition Across States
34
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.
35
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.
36
Evidence from a subsample
37
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
38
Appendix: Theoretical Model
• A simple two parameter model:
p > 0 probability of scoring if a team is ahead or tied
q > 0 probability of scoring if a team is behind
p>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
39
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.
40
2. “Pawns of the Emotions:
Psychological Elements in
Cognitively Sophisticated Humans”
(joint with Julio González-Díaz
U Santiago de Compostela)
41
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.
42
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)
43
Beginning with Whites Gives a Significant Advantage
44
The Effect is Greater at the Top: Elite and WC matches
45
Effect Only When Players Are Very Similar
46
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.
47
Addendum
Psychological Pressure
in Competitive Environments
From the Field to the Laboratory
48
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 Sequential2006, 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.
49
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.
50
Winning Frequencies
8
6
7
5
5
4
4
3
2
2
2
0
1
Sequential
2006
1
1
Simultaneous
2
First team
Second team
Sequential
3 2007
Tied
51
Scoring Prob by Round
SEQUENTIAL TREATMENTS
1,0
0,9 0,9
0,9 0,9
0,8
0,8
0,9
0,9
0,8
0,5
0,5
0,6
0,4
0,2
0,0
1
2
3
First team
4
5
Second team
Scoring Prob by Round
SIMULTANEOUS TREATMENT
1
0,9
0,8
0,8
0,9
0,7
0,8
0,8 0,8
0,7 0,7
0,8
0,6
0,4
0,2
0
1
2
3
First team
4
Second team
5
52
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?
53
There is an easy solution
Take 2 contestants: A and B
First two penalties or games of a chess match:
1º
2º
A B
…
…
54
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 ? ?
…
55
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
…
56
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 ? ?
…
57
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
…
58
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.
59
How should the next 4 penalties be?
1º
2º
3º
4º
5º
6º
A B B A ? ?
7º
8º
? ?
60
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 AB
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.
61
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!
62
• 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?
63
ABBAABBAABBAABBA
64
This is exactly how services are assigned
in tie-breaks in tennis:
ABBAABBAABBAABB
……
65
And if you want just 10 penalties (5 per team):
ABBAABBAAB
66
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.
67
• 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.
68
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 noncognitive performance in humans in dynamic
competitive environments.
69