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EBS BUSINESS SCHOOL
EBS UNIVERSITÄT FÜR WIRTSCHAFT UND RECHT
Thesis
Spring Term 2020
to obtain the academic degree
Master of Science
Strategic Behavior in Sport Contests: Application to
Middle-Distance Races From the 2010-2019 Decade
Name: Nicolas Herbin
Addresse: 42, rue des Ardoisières
50000 Saint-Lô France
Submitted to: Dr Elena Jarocinska
Submission Date: April
21st 2020
Strategic Behavior in Sport Contests i
Table of Content
List of Abbreviations iii
List of Figures iv
List of Tables v
1 Introduction 1
1.1 Problem Definition and Objectives 1
1.2 Course of the Investigation 4
2 Theoretical Background 6
2.1 Why sport is a good field to study economics? 6
2.1.1 Tournament Theory 6
2.1.2 Equilibria in Mixed Strategies 8
2.1.3 Contract Theory 13
2.1.4 Behavioral economics 13
2.1.4.1 Social pressure and favouritism 14
2.1.4.2 The role of emotions 14
2.2 Theory of Contests 17
2.2.1 Contests Modelling Framework 17
2.2.1.1 All-pay Auctions 18
2.2.1.2 Rank-Order Tournaments With Additive Noise 18
2.2.1.3 Contests With Ratio-Form Success Function 19
2.2.2 Contests Models in Various Framework 20
2.2.2.1 Sequential Moves in Contests 20
2.2.2.2 Contests With Budget Constraints 21
2.2.2.3 Contests With Non-Risk-Neutral Players 21
2.2.2.4 Asymmetric Contests 22
2.3 Strategic Behavior in Contests 23
2.3.1 Theoretical Background 23
2.3.2 Empirical Studies 27
2.3.3 Application to the Field Events of 1992 Olympic Games 29
2.3.3.1 Context and Presentation of the Experiment 29
Strategic Behavior in Sport Contests ii
2.3.3.2 Empirical Model 30
2.3.3.3 Results... 31
2.3.3.4 Observations on this Experiment 34
3 Methodology 36
3.1 Delimitation of the Frame of the Study 37
3.2 Underdog-Favorite Variable Implementation 40
3.3 Empirical Model 45
4 Results 47
4.1 Validation of the Favorite Index 47
4.2 800m Races Results 48
4.3 1500m Races Results 50
4.4 5000m Races Results 51
4.5 Aggregated Results 52
4.6 Analysis of Strategic Behavior in Middle-Distance Races 53
4.6.1 Impact of Gender on Strategic Behavior in Contests 54
4.6.2 Impact of Gender on Strategic Behavior in Contests 54
4.6.3 Impact of Gender on Strategic Behavior in Contests 56
5 Discussion 57
5.1 General Implications for Management 57
5.2 What the Analysis on Gender, Culture and Density Implies?
58
5.3 Why is 800m Still Not Working? 61
5.4 What Could Have Been Improved in This Study? 62
6 Conclusion 63
References 66
Strategic Behavior in Sport Contests iii
List of Abbreviations
AME America
AMO Africa and Middle Orient
APA American Psychological Association
ASO Asia and Oceania
EUR Europe
HDR High-Density Races
HRM Human Resources Management
LDR Low-Density Races
PB Personal Best
PGA Professional Golfers Association
NBA National Basketball Association
R&D Research and Development
SB Season Best
SME Small and Medium Enterprises
Strategic Behavior in Sport Contests iv
List of Figures
Figure 1. Return and marginal return for
player 1 24
Figure 2. Reaction functions in a two-player
case 25
Figure 3. Reaction functions when the player
1 is the favorite 26
Figure 4. Hypothesized relative race
positions over time 29
Strategic Behavior in Sport Contests v
List of Tables
Table 1. Results of Walker and Wooders 9
Table 2. Gain Distribution 11
Table 3. Observation Versus Theoretical
Predictions 11
Table 4. Regression Results for Men's and
Women's running events 32
Table 5. Regression Results for Men's and
Women's Distance Field Events 33
Table 6. Comparison Between Position and
Ranking Over the Lap 35
Table 7. Available Level of Detail for Data
for Each Event 39
Table 8. Rules for Estimation of the Missing
Data 41
Table 9. Honors Multiplier Settings 43
Table 10. Results of Underdog-Favorite
Parameter Regression 48
Table 11. Results of the 800m Races 49
Table 12. Results of the 1500m Races 50
Table 13. Results of the 5000m Races 51
Table 14. Aggregated Results 52
Table 15. Gender and Strategic Behavior 54
Table 16. Culture and Strategic Behavior
55
Table 17. Density of Competition and
Strategic Behavior 56
Strategic Behavior in Sport Contests 1
1 Introduction
1.1 Problem Definition and Objectives
Lots of economic and social interactions consists in a
competition where the players expend their effort in order to increase their
probability to win a prize. These situation can be research and development
(R&D) rivalry between firms or countries to get a lucrative or strategic
innovation, bribery to assure a profitable license, patent or contract from the
government, the war for a new global market that has been created by a new
innovative product, a political election where candidates fight during long
campaigns in order to get elected, or candidates who compete for a job, or to
win a promotion.
Example of contests can also be found in sport competition.
These competitions can take shape in three different forms. Championships,
where each player plays against each other and the ranking of the competition
is determined by the results of the players against all the players of the
championship. Famous examples of championships are the English Premier League
or the Bundesliga in football, the Six Nations Tournament in Rugby. Another
type of competition is the tournament. Tournaments is a form of competition
which takes the shape of a direct elimination competition. The competitors
compete pair by pair and the winner can play against the winner of another pair
until only one winner remains and win the prize. Famous examples of tournaments
are Grand Slam Tournaments in Tennis, or the play-offs of the National
Basketball Association (NBA). Eventually, another type of sport competition
takes the form of a race. A race is a competition where the prize is given to
the first competitor to cross the finish line. This type of competition is
different from a tournament or a championship since in a race, the competitors
are competing against one another at the same time. They are not challenging
each other by pairs like in a game of football or tennis. Therefore, they are
the most interesting competition in order to analyze the behavior of agents in
a situation where they are faced to many competitors. Races are therefore in
regard of their nature more interesting to analyze agents' behaviors in order
to find beginning of answers on the behavior of agents in a R&D rivalry
between firms or country because a lot of countries or firms are involved at
the same time to develop the same technology and the first one to be able to
create it will gain an economic or strategic advantage upon the others that can
be seen as the prize.
Strategic Behavior in Sport Contests 2
Some models of the tournament theory take an interest in the
strategic behaviors of the players in a case where the intrinsic capacities of
the agents are heterogenous, which means in a case where there is a favorite
and an underdog. Dixit (1987), shows with a model of game theory that if he
plays first, the favorite has always an interest to engage a high level of
effort, while the underdog has the opposite incentive. Baik and Shogren (1992)
extended Dixit's model considering an endogenous choice for the order of
intervention of the agents. They show that the underdog has always an interest
to play first while the favorite's best interest is to wait and play in
second.
The theoretical models on the strategic behaviors of the
favorite and the underdog haven't been much studied empirically. The reason why
is quite obvious, it is very difficult to find economic situations where the
status of favorite and underdog is clearly established and defined and the
strategies of the favorites and underdogs are directly observable, especially
the order in which they are engaging their effort. This is particularly true in
the economic context used by Dixit (1987) and Baik and Shogren (1992) which is
the race to innovation.
Boyd and Boyd (1995) avoid this difficulty by analyzing the
strategic behaviors of the athletes during athletics competitions (from 800
meters (m) to 10 000 m) at the Olympic Games of 1992. As part of an athletics
race, the model of Baik and Shogren (1992) predicts clearly the following
course: underdogs tend to start the fastest, then are caught back before being
usually passed by the favorite.
Boyd and Boyd used data coming from the races of the 1992
Olympic Games in Barcelona to test this theory. They only looked at the races
for which distance were superior or equal to 800 m, which are the distances for
which the tactics have a real role to play and where runners run inside a
peloton (and not in lanes). For each distance, they visualized the video
recordings of the semi-finals and the final. For the short distances (such as
800 m or 1500 m, they recorded the positions of the runners every 200 m while
for the longer distances (3000 m women, 5000 m men and 10 000 m), they recorded
the position of the runner every 400 m. At the end, their database contains
more than 2300 observations spread over 14 races. Concerning the key variable
of the study, which is the measure of the runner status before the race,
favorite or underdog, Boyd and Boyd used as a proxy the ranking of the runner
in the previous race, which means in the semi-finals if the race studied is a
final, or the heats if the race studied is a semi-final.
Strategic Behavior in Sport Contests 3
From a general perspective, the results of Boyd and Boyd are
clear and coherent with the theory of Baik and Shogren: the course of races see
the relative position of the underdog decline during the race. On the contrary,
the favorites improve progressively and end up winning most of the time. Boyd
and Boyd also notice that the results are clearer for the men than for the
women since for men, all races (semi-finals and finals) confirm the theory,
except the 800m final.
However, when I read the article of Boyd and Boyd, I noticed
some details that was posing me some problems regarding the model's
veracity.
First, the proxy that Boyd and Boyd used to determine who was
favorite before the race and who was not, which is the ranking of the runner in
the previous round, do not seem to me the best way to measure a runner's
chances to win a race. I am myself a French athlete running 800 m at the
national level since 10 years, I participated to 12 French National
Championships, and I never looked at the ranking of a rival in the previous
round in order to determine if his chances where greater than mine to win.
Indeed, heats or semi-finals are an unreliable information since they runners
who are in my race do not come from the same race. I usually make a complex
calculation based on his personal best (PB), his ability to finish quickly his
races, his recent shape, the races he has won before, his weather preferences,
etc. This way I am able to assess what are the odds for me to beat him and what
is the best strategy to apply, or at least try to apply, in order to beat him.
One of the goals of this thesis is therefore to create a calculated index based
on the different data that can be gathered today for a runner. This way the
proxy will be calculated the same way for all runners of all races and will
give homogeneity to the analyzed races.
My second observation is about the use of the position of the
runner as the parameter which determines the level of effort of the runner over
the lap. I do not think it is the most accurate measure we can have today of
the level of effort for a runner. Indeed, with the race reports that have been
given for the last four World Championships races, we are able to determine who
has run the fastest and the slowest on each lap because we have the split times
for each runner from every kilometers to every hundred meters. This way if a
runner did his first interval much faster than others, then his second interval
slower but he had taken such an advantage over the first interval that he has
not be caught up by others, he will not be any more considered as the one who
has given the greatest effort on the interval. This change is, in my opinion
very important if the purpose of the study is to
Strategic Behavior in Sport Contests 4
measure correctly when runners put their highest level of
effort in regard of the pre-race status.
The third observation is that they only try to verify if there
is a difference in the strategic behavior of men and women. Not only do I
believe there should not be a big difference in the strategic behavior of men
and women, but I also believe that there are other parameters about the runners
or the race that could explain a different behavior, such as the culture of the
runner, or the density of the race. These parameters would be, in my opinion,
very interesting to test in order to see if one of them changes the strategies
of the runners.
The objective of this thesis is to replicate the experiment of
Boyd and Boyd with the data of the last world championships and to apply all
the modifications that I mentioned above. Moreover, I will be studying the
other potential factors of strategic behavioral change in order to see if Baik
and Shogren results are still coherent with this new methodology. Therefore, we
will be trying to give an answer to the question: how effort is expended
over time by a runner in athletics events depending on the pre-race status of
the same runner and what other parameters may affect the runner behavior?
This question is almost the same that the one Boyd and Boyd asked
themselves and the purpose of this study will be to see if we can find similar
results when applying a more efficient methodology.
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