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Strategic behavior in sport contests : application to middle-distance races from the 2010-2019 decade

par Nicolas Herbin
EBS Universität für Wirtschaft und Recht - Master of Science in Management 2020

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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 Social pressure and favouritism 14 The role of emotions 14

2.2 Theory of Contests 17

2.2.1 Contests Modelling Framework 17 All-pay Auctions 18 Rank-Order Tournaments With Additive Noise 18 Contests With Ratio-Form Success Function 19

2.2.2 Contests Models in Various Framework 20 Sequential Moves in Contests 20 Contests With Budget Constraints 21 Contests With Non-Risk-Neutral Players 21 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 Context and Presentation of the Experiment 29

Strategic Behavior in Sport Contests ii Empirical Model 30 Results... 31 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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