PERFORMANCE MEASUREMENT & MATCHING

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PERFORMANCE MEASUREMENT &

MATCHING

Evidence from the Market for German Football Coaches

November 13, 2008

MASTER’S THESIS

Author Dirk Möllers S1705164 Wagnersingel 12A, 9722 CX Groningen, The Netherlands D.Mollers@student.rug.nl

Research Supervisor Dr. P. Rao Sahib Faculty of Economics Landleven 5, 9747 AD Groningen, The Netherlands P.Rao.Sahib@rug.nl

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ABSTRACT

This piece of research analyses the matching-effects as a parameter of performance and mobility in the market of German football coaches within the “Bundesliga” between 1971 and 2002. Using a large dataset of football coaches of the German Premier league, the author performs two different tests of the matching-effect. The author investigates direct evidence of a coach-team match-effect on team performance. A good match between coach and team is found to improve team-performance for approximately 5 percent. Furthermore, the author finds no evidence for a confirmation of the matching hypothesis by analyzing hazard rates of coaches within this time period. The hazard-rates of coaches show no initially increasing and then decreasing probability of separation over years of coach-tenure or –experience, like what theories of worker mobility predict. Contrary to previous findings, the examined hazard-rates seem not to be influenced by coach-tenure or -experience.

An implication of this research is that teams are able to significantly improve their performance by finding the right match.

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D. Möllers PERFORMANCE MEASUREMENT & MATCHING Master’s Thesis

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PREFACE

This thesis was written in order to finish my studies in the field of International Economics and Business at the University of Groningen. The topic of “Performance Measurement” and the theory and estimation of matching models gained my interest through the encouragement of Prof. Sahib. Especially conducting research on the market of German football coaches - “Die Deutsche Bundesliga” attracted my attention.

The main point of research on performance measurement and matching was to find out if matching effects between coaches and team in the German “Bundesliga” are existent and, how these effects influence team-performance. I have tried to add a new perspective to the actual stand of literature about testing the matching effect. The course ‘Research

Methodology’ by Prof. Sahib accompanied the thesis and helped me with the methodology of

the thesis and with obtaining analyses with the statistical program Eviews 5.1.

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INTRODUCTION ... 7

1. THEORETICAL BACKGROUND ... 9

1.1 OBJECTIVES ... 12 1.2 FOCUS ... 12 1.3 RESEARCH QUESTIONS ... 13

2. THE DIRECT MANAGER-TEAM MATCH-EFFECT ON PERFORMANCE ... 13

2.1 LITERATURE REVIEW ... 13

2.2 HYPOTHESES... 22

2.3 MEASURING MATCH QUALITY ... 23

2.3.1 A DIRECT TEST OF THE COACH-TEAM MATCH-EFFECT ... 24

2.3.2 MATCH-DUMMIES – PROXIES FOR TEAM-SPECIFIC EFFECTS? ... 29

2.3.3 INVESTIGATION OF THE MATCH-EFFECTS CONTRIBUTION TO PERFORMANCE ... 32

2.4 VARIABLE DEFINITIONS & SOURCES ... 34

2.5 METHODOLOGIES IN RELEVANT LITERATURE ... 36

3. DESCRIPTION OF THE DATASET ... 37

3.1 ANALYZING PANEL DATA ... 38

3.1.1 CONSTANT COEFFICIENTS MODEL (POOLED OLS) ... 39

3.1.2 FIXED EFFECTS MODEL ... 39

3.1.3 RANDOM EFFECTS MODEL ... 40

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4.3 WALD TEST OF SIGNIFICANCE ... 53

4.4 MODEL ESTIMATION ... 54

4.5 TESTS OF MATCH-SPECIFIC EFFECTS ON TEAM-PERFORMANCE ... 55

4.5.1 DIRECT TEST OF THE COACH-TEAM MATCH-EFFECT ... 57

4.5.2 MATCH-DUMMIES – PROXIES FOR TEAM-SPECIFIC EFFECTS? ... 57

4.5.3 TEST FOR A BIAS IN THE REGRESSION ANALYSIS ... 58

4.5.4 INVESTIGATION OF THE MATCH-EFFECT’S CONTRIBUTION TO PERFORMANCE ... 61

4.6 EXAMINATION OF COACH-TEAM SEPARATIONS ... 62

4.6.1 THE PROBABLITY OF SEPARATION & THE COACH-TEAM MATCH-EFFECT ... 62

4.6.2 THE PROBABLITY OF SEPARATION, TENURE & EXPERIENCE ... 66

5. CONCLUSIONS ... 69

6. FUTURE RESEARCH EXPANSIONS ... 72

REFERENCES ... 73

SOURCES ... 74

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LIST OF TABLES & FIGURES

TABLE 1: OVERVIEW OF FINDINGS ... 21

TABLE 2: THE COACH-DUMMY EXAMPLE ... 25

TABLE 3: THE MATCH-DUMMY EXAMPLE ... 27

TABLE 4: THE TEAM-DUMMY EXAMPLE ... 30

TABLE 5: EXAMPLE – ALL DUMMY VARIABLES ... 31

TABLE 6: VARIABLE DEFINITIONS & THEIR SOURCES ... 34

TABLE 7: SAMPLE DESCRIPTIVE INFORMATION ... 42

TABLE 8: AVERAGE ANNUAL SEPARATIONS PER TEAM ... 43

TABLE 9: CORRELATION MATRIX OF INDEPENDENT VARIABLES; EXCLUDING DUMMIES ... 49

TABLE 10: SUMMARY OF OLS PERFORMANCE REGRESSIONS ... 56

TABLE 11: ANNUAL OLS PREFORMANCE REGRESSIONS: ALL COACHES WITH MULTIPLE SPELLS ... 59

TABLE 12a: SUMMARY OF WALD TESTS OF SIGNIFICANCE OF MATCH-EFFECTS & TEAM-EFFECTS ... 60

TABLE 12b: WALD TEST OF TEAM RESTRICTION ON MATCH-EFFECTS ... 60

TABLE 13: REGRESSION ON WINNING PERCENTAGE WHILE CONTROLLING FOR A GOOD MATCH ... 61

TABLE 14: PROBABILITY OF SEPARATION/FIRING LEAVING OF THE COACH BY ADJUSTED WINNING PERCENTAGE IN PREVIOUS SEASONS (FOR SPELL 1) ... 63

TABLE 15: PROBABILITY OF SEPARATION/FIRING LEAVING OF THE COACH BY ADJUSTED WINNING PERCENTAGE IN PREVIOUS SEASONS (FOR SPELL 2+) ... 64

TABLE 16: PROBABILITY OF SEPARATION/FIRING LEAVING OF THE COACH BY ADJUSTED WINNING PERCENTAGE IN PREVIOUS SEASONS (FOR ALL SPELLS) ... 64

TABLE 17: PROBABILITY OF SEPARATION/FIRING LEAVING OF THE COACH BY AVERAGE ADJUSTED WINNING PERCENTAGE IN SPELL ... 65

FIGURE 1: AVERAGE COACH DURATION PER SEASON & SPELL ... 44

FIGURE 2: AVERAGE EXPERIENCE OF ALL/INITIAL/MULTIPLE SPELL COACHES ... 44

FIGURE 3: AVERAGE TENURE OF ALL/INITIAL/MULTIPLE SPELL COACHES ... 46

FIGURE 4: SCATTER-PLOT OF THE RESIDUALS (EQ.1) AND THE DEPENDENT NON-DUMMY VARIABLE. .... 50

FIGURE 5: SCATTER-PLOT OF THE RESIDUALS (EQ.2) AND THE DEPENDENT NON-DUMMY VARIABLE ... 51

FIGURE 8: HAZARD RATE BY TENURE – ALL SPELLS ... 67

FIGURE 9: HAZARD RATE BY TENURE: COACHES WITH MULTIPLE SPELLS – INITIAL & REPEAT ... 67

FIGURE 10: HAZARD RATE BY TENURE: COACHES WITH INITIAL SPELLS – SINGLE & MULTIPLE ... 68

FIGURE 11: HAZARD RATE BY EXPERIENCE - SEPARATIONS ... 68

FIGURE 12: HAZARD RATE BY EXPERIENCE – COACHES FIRED ... 68

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7 __________________________________________________________________________ lllllh lthough the job-matching hypothesis and its deduced predictions about worker-firm separations received most attention among worker-mobility theories, testing this approach in traditional labor markets is difficult. It requires knowledge of unobservable firm-, worker- and match characteristics. These difficulties hamper isolating the effect of job-matching from other effects which increase worker-firm performance and make examinations problematic. Within the last two decades, scholars tried to overcome these difficulties by analyzing examples of diverse sports markets from different countries. The results vary depending on the specific sport or country that these scholars focus on. For example, Chapman and Southwick (1991) find evidence for the matching hypothesis by examining managers in major-league baseball in the USA. However, other investigations like the one done by Ohtake and Ohkusa (1993), who conducted the same test with data of professional baseball in Japan, find no evidence.

One relevant study in the field of testing the job-matching hypothesis was performed by Borland and Lye (1996). They carried out a study, which directly focused on testing the job-matching hypothesis. Their study examined the job-matching-effect as a determinant of mobility. For their analysis, they looked at the market of Australian Rules football coaches between the years 1931 and 1994. Borland and Lye (1996) found direct evidence of a specific coach-team match effect on coach-team performance. Their results suggest that two coach-teams might considerably improve their performance by changing the coaches – depending on the specific coach and team characteristics.

Following the study of Borland and Lye (1996), I will perform a direct test of the job-matching hypothesis on a sports market, in which the limitation of data on managerial personnel and inputs is not significant – Premiership football. In my master’s thesis, I will use Borland and Lye’s (1996) analysis of matching and mobility in the market of Australian Rules football coaches as a base, and I will replicate their methods on data from the German “Bundesliga”. In addition, Borland’s and Lye’s (1996) study will be extended, by:

1) Including new variables in their models;

2) Making a distinction between coaches, who were fired from a team and coaches, who left a team on their own free will. Then the probability of coach-team separations is analyzed;

3) Measuring the contribution of a good coach-team match to team performance.

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8 By applying this method, the effect of the coach-team match on performance will be identified. In more detail, this study will investigate, how

a) A good coach, b) A good team, and

c) The synergy between a coach and a team,

make their contributions to team performance. Furthermore, this piece of research will examine the mobility of German football coaches by analyzing probabilities of coach-team separation.

Unlike Borland and Lye (1996), I will examine the job-matching hypothesis with applying data of the “Bundesliga” in Germany. German football is the sport with the highest number of spectators in Germany; in the season 2007/2008, there were more than 12 million people following the games. Since there is a large sample, examining this market will make a contribution to identify the match-effect. The market of football coaches particularly suits the examination of the job-matching hypothesis as a parameter for mobility within the labor market (Brown et al.; 2007).

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1. THEORETICAL BACKGROUND

Nowadays the mobility between employees and companies is a main characteristic of today’s labor market. In the USA, a typical worker traverses an employment within 11 different firms during his entire career. For a company, the personnel management and recruitment is an important time- and monetary-consuming task. Acquiring qualified managers not only secures the existence of a company, but also helps to improve its growth and performance. However, for employers, finding a person that best fits the job is not as simple as selecting the person with the best qualifications, but selecting the person that best fits the company. So excellent past performance or an outstanding university grade does not cut it.

I. The Job-Matching Hypothesis

According to Jovanovic’s matching hypothesis (1979), the better an individual “fits” a firm, the more productive he or she will be. Consequently, not only the overall best qualified person, but also the individual with the greatest person-to-firm match should be offered a particular job. The matching hypothesis states that a key-component of performance is defined by an exogenous, normally distributed random variable. “This variable is observable prior to the employment, is specific to a particular worker-job combination, and is independently drawn each time the worker changes jobs” (Chapman & Southwick; 1991; p.1352). Worker-performance varies between different firms and mobility of workers across jobs will occur to respond to these differences. Both workers and firms share symmetric imperfect information of the worker’s performance at the firm.

Information about the uncertain value of the worker-firm match may be obtained through: 1) worker search – the value of the worker’s current match with a firm is known, but the value of available alternative matches with different firms is unknown and has to be discovered by active search through the worker; 2) experience of a worker in a match – initially, the value of a worker’s current match is uncertain, but learned over time, while the value of alternative matches has a constant expected value.

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10 firms offer compensation packages including payment, health and retirement benefits. Also non-pecuniary aspects like prestige or advancement in the company determine the job attractiveness.

The alternative hypothesis to Jovanovic’s matching hypothesis (1979), adopted by most other theories of worker mobility, follows the standard neoclassical postulate of equal worker-performance at any firm (Simmons; 1997). It is possible to identify different groups of such theories: 1) Sectoral-shift theories, which suggest that the occurrence of worker mobility responds to changes in labor demand, as the composition of product technology or product demand varies inter-temporal across industries (Lilien; 1982); 2) Theories of internal labor markets, which suggest that mobility occurs through up-or-out employment rules, that are designed to improve worker incentives (Hubermann & Kahn; 1988); 3) Theories of career mobility, which suggest that workers move between jobs that provide different learning opportunities (Rosen; 1972); and 4) Theories of asymmetric information, which suggest that a worker’s current employer obtains private information about the worker’s performance. The market concludes that retained workers at a firm are the high-productive type and bid up the wages of these workers. This leads to the condition that low-productive workers for a firm are unprofitable and therefore, worker mobility occurs (Gibbons & Katz; 1991).

II. The Matching Hypothesis & Worker Mobility

As worker-performance levels differ across firms and imperfect information concerning these differences is given, worker mobility may arise due to learning about the worth of a particular worker/firm match (Borland & Lye; 1996). The quality of service, which an employee provides to his employer, is difficult to be concluded during observations made in advance by the firm. However, it can be ascertained upon consumption (of the “good” worker by the firm). In economics, this is called an “experience-good”, as both employer and employee experience the performance-level on the job.

Furthermore, Jovanovic’s matching hypothesis (1979) has been employed by matching theories of worker mobility to predict:

A) The relationship between a worker/firm match and the probability of worker/firm separations;

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11 C) The relationship between worker experience (later in this context, the number of

seasons over the coach’s career) and the probability of worker/firm separations. The better a worker/firm match is, the longer the time to separation from a specific company will be. Here, a separation is defined as the critical point in time, at which an employee is getting fired or leaves the company out of his own free will. A worker who matches with a specific company delivers superior working quality for this company than most other potential employees. Therefore, with a rising worker/firm match, the company will be less likely to initiate a separation. Furthermore, increasing compensation packages with a rising value of the worker/firm match will lower the probability of a separation initiated by the employee. The relationship between the probability of separation and a worker’s years of tenure is highly dependent on the “interaction between mobility costs and the increasing precision of the signal of future output in the worker’s current match” (Borland & Lye; 1996; p.145). Within the first period of a worker’s employment, newly-obtained information about the value of a worker/firm match is not able to change its expected worker/firm match output in a way, that a worker-change would compensate mobility costs. It will be more expensive to switch to a different worker/firm match, than to keep the current one. Therefore, in the initial period of employment, the rate of separation will be low. As time passes by, the output of an expected worker/firm match may decline to a special point. At this point, an expected gain in wage payment to an alternative match outweighs higher mobility costs. Therefore shifting to another match will be favorable. A higher rate of separation will arise. Eventually, the years of worker tenure increase even more. With this increase, the precision, at which a firm is able to measure the expected worker/firm match output, improves. If this occurs, an expected decrease of future output of the current worker/firm match is not sufficient to induce a separation. At this point, it is unlikely that a firm’s information about the future worker/firm match output will ever be adequate to revise the expected output in a way that induces separation. Consequently, the rate of separation will decline.(Borland & Lye; 1996)

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1.1 OBJECTIVES

The key objective of this paper will be to test whether the match between a coach and a particular team – the so-called “coach-team match” - influences the respective team’s performance. Obtained results of this analysis can be applied to the business level to conclude, whether a team’s performance depends on the right manager-team match.

1.2 FOCUS

In my research, I focus on a large sample of German football coaches from 1971 to 2002, to apply a direct test of the matching hypothesis. I expect matching effects between coaches and teams to be significant in influencing a team’s performance.

Moreover, I will focus on the theoretical predictions derived from the matching hypothesis concerning:

A) The relationship between the value of a coach/team match and the probability of coach/team separations;

B) The relationship between the years of a coach’s tenure and the probability of coach/team separations;

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1.3 RESEARCH QUESTIONS

Referring to the two different focuses of this study, the following research questions and investigative questions will be addressed:

1.1) Does team-performance depend on the quality of the match between the team and coach?

1.2) If team-performance depends on the quality of the match between team and coach, for how much improvement of performance does it account?

2.1) Does the probability of coach/team separation decrease with a high-value of the match between team and coach?

2.2) Does the probability of a coach-team separation initially increase and then decrease, with the years of a coach’s tenure (number of seasons with a particular team)?

2.3) Does the probability of a coach/team separation initially increase and then decrease, with the years of a coach’s experience (cumulative experience over multiple jobs; number of seasons over the coach’s career)?

In order to address these research questions, I will follow a well-defined structure. First of all, an overview about the hypotheses that I want to test will be elaborated. Secondly, the models resulted from the hypotheses will be explained. Thirdly, a brief summary of the methodologies in the relevant literature will be given. Fourthly, the dataset and empirical analysis, which will be applied, will be discussed. Furthermore, the results of analyzing the dataset of the German “Bundesliga” will be presented. Finally, in the conclusion, I will give the final remarks, contributions and possible extensions for future research.

2. THE DIRECT MANAGER-TEAM MATCH-EFFECT ON PERFORMANCE

2.1 LITERATURE REVIEW

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14 matching hypothesis received high attention, most empirical studies tested its implications rather than its assumptions.

One major example of testing an implication of the matching hypothesis is to test its prediction that wages and job-tenure are positively related to each other. Workers that match a company well will consequently receive higher wages and stay in their jobs for longer periods. Tests of this implication were carried out by inter alia Altonji and Shakotko (1987) and by Abraham and Farber (1987) by analyzing panel data. These authors explored in their studies that most of cross-sectional variation between wages and tenure results from matching.

One study that tried to isolate the worker-firm match, while using data from an ordinary labor market, was conducted by Hersch and Reagan (1990). By analyzing

I. the positive relationship between the strength of a match and received compensations in appearance of payments and

II. the positive relationship between the strength of a match and worker-tenure,

Hersch and Reagan (1990) indirectly tested the worker-firm match-effect. In order to obtain their test, the authors used a dataset which consisted of a matched sample of workers and firms and included measures for match quality. Applying their dataset, Hersch and Reagan (1990) estimated an original two-equation structural model for wages and tenure. The authors chose the specific two-equation wage-tenure structure to receive unbiased estimates of returns to tenure and wages. Their model incorporated not only standard human capital variables, but also direct measures of the quality of a job-match. Furthermore, their model included factors which were able to reflect a varying demand structure across firms regarding to their output over time.

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15 However, Hersch and Reagan’s (1990) results have to be handled with care, as their study relied on a small dataset of only 18 companies in Oregon with few firm-change observations on employees. Therefore, due to data-limitation problems of the study, the informational value and robustness of their obtained results are restricted.

Most of the data used in studies, which try to test the matching hypothesis indirectly, are fragmentary, as there are lacks of observations related to multiple workers for the same firm, job or industry. Moreover, only a few job-changes are observable. These limitations hamper separating the match-effect from other effects and cause problems if indirect tests of the matching hypothesis are obtained.

In order to avoid those difficulties and to be able to directly test the matching hypothesis, recent literature used sports data to substitute for companies, as this kind of data provides relatively homogenous samples of employees and companies within a large time-horizon. Hence, within the last two decades, a limited amount of studies directly tested the matching hypothesis by examining data on professional sports. The five studies of capital importance, which are continuously referred to in this field, will be summarized in the following paragraphs.

For testing the effect of coach-team matches on team performance, the studies by Chapman and Southwick (1991) and by Othake and Ohkusa (1994), following Chapman’s and Southwick’s (1991) examination, analyzed data on professional baseball in the USA and Japan. These authors justified their choice of datasets by the fact that in this kind of industry, no data limitations and lacks of information about managerial personnel are existent. As data of major-league baseball was examined, complete and extremely disaggregated data concerning firm in- and output were available.

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16 Squares regression (OLS) and a Generalized Least Squares (GLS) regression. Furthermore, they examined the match-effect by comparing the sum of squared residuals of different OLS regression models – including only coach dummy variables, including coach- and match-dummies, and including coach and team dummy variables – and of different GLS regression models – including only coach dummy variables, including coach- and match-dummies, and including coach and team dummy variables. With this methodology, both studies were able to isolate the coach-team match-effect. After their regression analysis, Chapman and Southwick (1991) found evidence for a significant matching-effect, while Ohtake and Ohkusa (1994) found no evidence for it.

Furthermore, both studies addressed another implication of the matching model. Namely they examined the theoretical prediction that the probability of a job-separation should initially increase and then decrease as tenure increases. The authors tested this prediction by analyzing the hazard-rates of coaches.

Chapman and Southwick (1991) explored that based on their dataset, the hazard-rate of coaches rose for the first three years of tenure and then declined for the next three years of tenure. Their finding strongly supports the matching hypothesis.

Ohtake and Ohkusa (1994) found an increasing and then decreasing probability of job-separations by analyzing hazard-rates of coaches according to their dataset. Their results showed that the observed hazard-rate of coaches increased for the first three years tenure and then decreased with trend except within the fifth and sixth year. Also they found that, when they made a distinction between the hazard-rates of veteran managers and rookie managers, the hazard rate for veteran managers was flatter than that for rookie managers. Furthermore, Ohtake and Ohkusa (1994) investigated that the probability of job separation with rising years of tenure only for rookie managers first increased and then declined, but not for veteran managers.

Ohtake and Ohkusa (1994) conducted an additional test of the matching hypothesis by examining the wage of individual managers on their tenure. They found that only the variance of rookie manager’s wages declined as tenure increases, not the variance of veteran manager’s wages. All these findings lead to a rejection of the matching hypothesis by Ohtake and Ohkusa (1994) for Japan.

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17 Borland and Lye (1996) examined the labor market for Australian Rules football coaches, a single and narrowly delimited labor market. They legitimized their choice of dataset with the reason that other theories of mobility are likely to be irrelevant for the examined labor market of football-coaches. The performance and activities of coaches were observable for their own and other teams. Therefore, theories that characterized worker mobility with information asymmetries were not having explanatory power for a football-coach’s mobility. Also this choice of dataset provided the authors with long-time-period observations and exact team-performance measures.

Borland and Lye (1996) directly tested the matching hypothesis by the examination whether an individual’s productivity showed a variation between different matches. To do so, the authors followed the example of Chapman and Southwick (1991) and Ohtake and Ohkusa (1994) and examined the effect of the coach-team match-effect by the comparison of regression equations – this time using an OLS regression with White’s heteroskedastic-constistent covariance standard errors. For the purpose of improving the match variable, they monitored on-the-job learning by taking player quality and coaching experience into account. Their results showed a significant influence of the coach-team match-effect on team-performance. Furthermore, the authors investigated that their estimated match effects not simply proxy for fixed team effects. They addressed a possible selection-effects bias in their sample of coaches by estimating their regression equations again, this time on subsamples of coaches. Also after this analysis, their results showed presence of the coach-team match-effect.

Moreover, Borland and Lye (1996) addressed the predictions of matching theories of worker mobility, regarding the relationship between the probability of worker-firm separation and the years of worker experience, worker tenure, or the value of the coach-team match. They did so, by examining non-parametric Kaplan-Meier hazard rates by years of tenure and experience aggregated between different subgroups of coaches. Their results showed for years of tenure and experience, an initially increasing and then decreasing probability of separation, confirming the predictions of the matching hypothesis.

Therefore, Borland and Lye (1996) found in both main tests – the regression analysis and the examination of coach-team separations - they applied for testing the matching hypothesis, confirmation for the hypothesis and its predictions concerning worker mobility.

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18 the help of taking manager’s winning percentage as dependent variable, not the winning percentage of a team per season, he was able to analyze the manager directly. Also his player-input variables measured more correctly the effect of player ability on performance. Moreover, his match quality variable assigned a value to the manager-team match effect instead of including coach-team match dummy variables. Using this variable to detect the match-effect was only possible for Prisinzano (2000), as he had access to the complete dataset of the baseball league, which had already included the proxy for the match effect, namely the measure of quality of team performance relative to the team talent. The presence of this variable allowed him to directly test the matching hypothesis in this way.

For his analysis of the matching hypothesis, Prisinzano (2000) first conducted an OLS estimation and then compared the outcome of this regression with the outcome of a fixed-effects model and random-fixed-effects model which he additionally estimated to eliminate the problem of omitted variables. By obtaining a Hausman test, he was able to identify that the fixed-effects model fit best for his case. By following this method, he found the coach-team match to be an important determinant for a team’s performance.

Furthermore, to check the robustness of his results, he replicated the regression models of Chapman and Southwick (1991) and Ohtake and Ohkusa (1994) with his modified match variable. A test of the match effect in this way led to the same outcome and therefore confirmed his results. Obtaining the fixed-effects model to produce more efficient estimates and using alternative measures for the match effect and player input made his study to be a good extension of Chapman’s and Southwick’s (1991) and Ohtake’s and Ohkusa’s (1994) work.

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19 authors were able to make use of a large sample of coaches. This sample of coaches provided information about a labor market, where performance of managers can be measured relatively easily.

Applying this dataset for their study, Brown et al (2007) were able to identify the coach-team match effect as a significant factor of determining a team’s performance. Also Brown et al (2007) investigated that a good match between coach and team accounted for around a five percent improvement in team-performance. In addition, they found that the hazard rate of college football coaches increased for the first five years of coach-tenure and then systematically declined after this first five years of coach-tenure. Their findings strongly support the matching-hypothesis.

In order to obtain their results, Brown et al (2007) used a college draft instead of player statistics as a proxy for the player-talent level. The authors therefore ignored player talent in their examination of the matching hypothesis, as talent in college-sports is strongly influenced by the coaching abilities of the coach. Players at the top of the draft receive exceptionally higher payments indicating their skill level, compared to players at the bottom of the draft. Hence, the authors assumed the talent level of players within the draft to be nonlinear due to a greater estimation error at later positions of the draft. Moreover, Brown et al (2007) specified a strength-of-schedule variable, which measured the difficulty-level of opponent teams, as the strength of an opponent team had significant influence on team performance.

Following Chapman and Southwick (1991), Brown et al (2007) measured the coach-team match effect by comparing two regression equations. These regression equations were similar to the ones Chapman and Southwick (1991) used, except of the different measures for the strength of opponents and player-talent. Brown et al (2007) used team performance as dependent variable and measured a team’s performance by average winning percentage of that team. Therefore, cross-sectional errors of the teams were correlated. As this correlation could lead to upward biased estimates of the variance of different teams, the authors re-estimated their equations using the GLS method. Both estimations of the models detected a match-effect on team-performance and therefore confirmed the matching hypothesis.

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20 interpreted the findings in the way that if a coach’s tenure lasted five years, the match between coach and team was a good one.

Applying this result, Brown et al (2007) measured the contribution of a good match between coach and team on team performance. For this, they defined a dummy variable, which was 1 if the tenure of a coach was more than five years within a college and 0 if the tenure of a coach was five years or less than five years within a college. Then, they replaced their match-dummy variables with the good match variable and ran both an OLS and a GLS regression on this model. Their results suggested a 5 percent improvement of a team’s performance in the presence of a good coach-team match.

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STUDY MAIN QUESTION THEORETICAL FOCUS TYPE OF STUDY DATASET USED RESULTS OF THE STUDY

Hersch & Reagan (1990)

Is there a positive relationship between the strength of a match and wages?

Is there positive relationship between the strength of a match and tenure?

Test of predictions of Jovanovic’s (1979) matchings hypothesis.

Empirical study

Method:

Estimation of an original two-equation structural model.

Sample from employees of 18 firms in the Eugene, Oregon area.

• The job-match is important for determining wages, but not for determining tenure.

• There is a positive relationship between wages and the worker-firm match quality, but no direct influence of the worker-firm match quality on tenure. • Worker-tenure is primarily determined by wage, age

and firm demand characteristics.

Chapman & Southwick (1991)

Is there a coach-team match effect on team performance at professional baseball in the USA?

Test of Jovanovic’s (1979) matching hypothesis.

Empirical study

Method:

Estimation of OLS &GLS regression models.

Survival analysis.

Sample from the Major Baseball League of the USA between 1930 and 1988.

• Presence of a significant coach-team match-effect. • The hazard-rate of coaches rose for the first three

years of tenure and then declined for the next three years of tenure.

Ohtake & Ohkusa (1994)

Is there a coach-team match effect on team performance at professional baseball in Japan?

Application of Chapman’s and Southwick’s (1991) analysis to Japan.

Empirical study

Method: Estimation of OLS &GLS

regression models. Survival analysis.

Sample from the Major Baseball League of Japan between 1950 and 1991.

• No evidence for a significant coach-team match-effect.

• The probability of job separation with rising years of tenure managers first increases and then declines only for rookie, not for veteran managers.

• The variance of rookie manager’s wages declines as tenure increases, not the variance of veteran manager’s wages.

Borland & Lye (1996)

Is there a coach-team match effect on team performance in Australian Rules football?

Aapplication of Chapman’s and Southwick’s (1991) analysis to a different sports and labor market – Australian Rules football.

Empirical study

Method: Estimation of OLS regression

models with White’s heteroskedastic-consistent covariance standard errors.

Survival analysis.

Sample from the Major League of Australian Rules football between 1931 and 1994.

• Significant influence of the coach-team match-effect on team-performance.

• With rising years of a coach’s tenure and experience, there is an initially increasing and then decreasing probability of coach-team separation.

Prisinzano (2000)

Is there a coach-team match effect on team performance at professional baseball in the USA?

Improvement of Chapman’s and Southwick’s (1991) analysis.

Empirical study

Method: Estimation of OLS regression, random & fixed effects models.

Work histories of Major League Baseball managers in the USA from 1901 to 1992.

• The coach-team match is an important determinant for a team’s performance.

Brown et al (2007)

Is there a coach-team match effect on team performance at college football in the USA, and if so, for how much improvement of performance does it account?

Empirical study

Method: Estimation of OLS &GLS

regression models. Survival Analysis. Estimation of “Good match”

model.

Data on college football coaches and their teams from 1968 to 2003 of the Division 1A-football schools.

• Detection of a match-effect on team-performance and therefore confirmation the matching hypothesis. • The hazard rate of coaches over coach tenure

increased for the first five years and then continuously decreased.

• There is a 5 percent improvement of a team’s performance in the presence of a good coach-team match.

Table 1: Overview of Findings.

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22

2.2 HYPOTHESES

All in all, evidence shows that a good manager-team match increases the performance of a team on a significant level. Therefore, the first hypothesis to be stated is:

Hypothesis 1

The coach-team match-effect will positively influence a team’s performance.

Besides identifying that the coach-team match is an important factor of a team’s performance, Brown et al. (2007) found that a good coach-match considerably increases the performance of a team. Therefore, the second hypothesis to be stated is:

Hypothesis 2

A team’s performance will rise in presence of a good coach-team match.

As aforementioned, via Jovanovic’s matching hypothesis (1979), it is also possible to predict the relationship between the fit-level of a manager-team match and the probability of a manager-team separation. If a match between a manager and a team is in the high fit-level, due to the matching hypothesis, the output of this match will be high. Furthermore, the company will suppose that the future expected output of the match will be high as well. The higher the expected output of an existing match is, the lower the probability that a firm will initiate a separation. Moreover, the better the output of a worker-firm match and the higher its expected future output are, the higher compensation packages for the manager will be (as they are rewarded to him for high performance). Therefore, the manager will be less likely to leave the team. Following this argumentation and applying this to the level of football coaches, the third hypothesis to be stated is:

Hypothesis 3

A good coach-team match decreases the probability of separation.

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23 coaches should follow the same paradigm. Following this argumentation, the fourth and fifth hypotheses are:

Hypothesis 4

The number of coach-team separations initially increases and then decreases with the years of coach tenure.

Hypothesis 5

The number of coach-team separations initially increases and then decreases with the years of coach experience.

2.3 MEASURING MATCH-QUALITY

In this study, two main tests to identify the role of matching effects in the market of German football coaches will be conducted:

1) The first test is a direct test on the influence of the coach-team match on team performance. For the first test, I will use the models which will be explained later in this chapter.

2) The second test examines the predicted relationship between the probability of coach-team separations and a coach’s years of experience or a coach’s years of tenure. For the second test, I will not use the models which will be explained later, but conduct a survival analysis, namely by analyzing the Kaplan Meier Hazard rates of coaches (see Chapter 1.2).

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24

𝑐𝑐 ∈ 𝐶𝐶

2.3.1 A DIRECT TEST OF THE COACH-TEAM MATCH EFFECT

In the first equation, I state that the performance of a team depends on its coach’s identity (due to the assumption that some coaches might be more talented for their job than others), the specific coach’s experience, the performance of players within that team, and the presence of the Bosman ruling in the examined period of time:

1) 𝑃𝑃_{𝑗𝑗𝑗𝑗} = ∑ β_c 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶_{𝑐𝑐𝑗𝑗} + 𝛿𝛿𝑃𝑃𝑃𝑃_{𝑗𝑗𝑗𝑗} + 𝜃𝜃𝐵𝐵𝐶𝐶𝐵𝐵𝐵𝐵𝐶𝐶𝐵𝐵_{𝑗𝑗𝑗𝑗} + 𝜗𝜗𝐸𝐸𝐸𝐸𝑃𝑃_{𝑐𝑐𝑗𝑗𝑗𝑗} + 𝜇𝜇(𝐸𝐸𝐸𝐸𝑃𝑃_{𝑐𝑐𝑗𝑗𝑗𝑗})2+ 𝜀𝜀_{𝑗𝑗𝑗𝑗}.

Before defining the meaning of the different variables, I will focus on their indices. All variables in this equation are indexed by j in order to identify the employment spells of coaches (one spell is equal to the amount of seasons that coaches were employed in a specific team without interruption) which were examined. The total number of employment spells of all coaches examined in the sample is 475. Therefore j can be numbered from 1 to 475 (later, when I structure the data as a dated panel, these spells will be used as the cross-sectional unit).

The entire set of variables, which is directly influenced by the identity of a coach, is indexed by c, in order to identify the coach’s identity in the spell that is examined. The whole sample of coaching spells is divided by 241 coaches. Therefore, c can adopt numbers from 1 to 241. Of these coaches, 130 had a single spell of employment, while 111 coaches had multiple spells.

The variables which are changing over time are indexed by t, in order to identify the season that is currently examined. As the period of examination focuses on the seasons from 1971/72 to 2002/2003, t can adopt values from 1971 to 2002 (later, when I structure the data as a dated panel, these seasons will be used for the time periods).

Now I will focus on the variables, mentioned in the equation:

The dependent variable 𝑃𝑃_{𝑗𝑗𝑗𝑗} is equivalent with team performance in season 𝑗𝑗 (𝑗𝑗 =1971,…,2002) of spell 𝑗𝑗 (𝑗𝑗 =1,…,475).

The independent variables 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶_{𝑐𝑐𝑗𝑗} are the set of dummy variables, that measure the fixed value of the influence of coach c (𝑐𝑐 =1,…,241) on the team performance in spell 𝑗𝑗 (𝑗𝑗 =1,…,475). The dummy variable adopts the value 1 if the particular coach is coaching in this current spell, 0 otherwise. Its coefficient β is indexed with c, because it will vary from coach to coach.

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25 Within his career, Lattek was inter alia coach of Bayern Munich, Borussia Dortmund and Borussia Mönchengladbach in the German “Bundesliga”. His career ended in season 1999/2000, as the coach of Borussia Dortmund. This coach was the first coach being observed in the dataset. Therefore, his spell-numbering begins with 1. Also Cramer was an active coach in the German “Bundesliga”, coaching Bayern Munich, Bayer Leverkusen and Eintracht Frankfurt. He is the second coach being observed in the dataset. Therefore, the spell-numbering starts with 8 (as the first 7 spells were used for Lattek). His career ended in season 1984/1985 as coach of Bayer Leverkusen. Therefore, the coach-dummy variables for the coach Lattek and Cramer look like in Table 2.

Table 2: The Coach-Dummy Example.

Season Spell Coach Team Coach-Dummy Lettek Coach-Dummy Cramer

1971/1972 1 Lattek Bayern 1 0 1972/1973 1 Lattek Bayern 1 0 1973/1974 1 Lattek Bayern 1 0 1974/1975 1 Lattek Bayern 1 0 1975/1976 2 Lattek M’Gladbach 1 0 1976/1977 2 Lattek M’Gladbach 1 0 1977/1978 2 Lattek M’Gladbach 1 0 1978/1979 2 Lattek M’Gladbach 1 0 … … Lattek … 1 0 1999/2000 7 Lattek Dortmund 1 0 1974/1975 8 Cramer Bayern 0 1 1975/1976 8 Cramer Bayern 0 1 1976/1977 8 Cramer Bayern 0 1 1977/1978 8 Cramer Bayern 0 1 1978/1979 9 Cramer Frankfurt 0 1 1982/1983 10 Cramer Leverkusen 0 1 1983/1984 10 Cramer Leverkusen 0 1 1984/1985 10 Cramer Leverkusen 0 1

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26

𝑐𝑐 ∈ 𝐶𝐶 𝑚𝑚 𝜖𝜖 𝐵𝐵

The independent variable 𝑃𝑃𝑃𝑃_{𝑗𝑗𝑗𝑗} is a dummy variable to measure player performance, defined as the performance of all players combined together within a specific team, in season 𝑗𝑗 of spell 𝑗𝑗. It is 1 if a team participated in the UEFA Cup or Champions League, 0 otherwise. The independent variable 𝐵𝐵𝐶𝐶𝐵𝐵𝐵𝐵𝐶𝐶𝐵𝐵_{𝑗𝑗𝑗𝑗} is a dummy variable to control for the event of the Bosman ruling in season 𝑗𝑗 of spell 𝑗𝑗. It adopts the value 1 in the presence of the event, 0 otherwise.

The independent variable 𝐸𝐸𝐸𝐸𝑃𝑃_{𝑐𝑐𝑗𝑗𝑗𝑗} identifies the years of experience of a coach 𝑐𝑐 in season 𝑗𝑗 of spell 𝑗𝑗.

The independent variable (𝐸𝐸𝐸𝐸𝑃𝑃_{𝑐𝑐𝑗𝑗𝑗𝑗})P

2_{is the squared term of the years of experience of a coach} 𝑐𝑐 in season 𝑗𝑗 of spell 𝑗𝑗. A quadratic term is used, as learning is frequently modeled as increasing in a decreasing rate.

εcjt

2) 𝑃𝑃_{𝑗𝑗𝑗𝑗} = ∑ β_c𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶_{𝑐𝑐𝑗𝑗} + ∑ 𝛾𝛾 _𝑚𝑚𝐵𝐵𝐶𝐶𝑀𝑀𝐶𝐶𝐶𝐶_{𝑚𝑚𝑐𝑐𝑗𝑗} + 𝛿𝛿𝑃𝑃𝑃𝑃_{𝑗𝑗𝑗𝑗} + 𝜃𝜃𝐵𝐵𝐶𝐶𝐵𝐵𝐵𝐵𝐶𝐶𝐵𝐵_{𝑗𝑗𝑗𝑗} + 𝜗𝜗𝐸𝐸𝐸𝐸𝑃𝑃_{𝑐𝑐𝑗𝑗𝑗𝑗} + 𝜇𝜇(𝐸𝐸𝐸𝐸𝑃𝑃𝑐𝑐𝑗𝑗𝑗𝑗)2+ 𝜀𝜀𝑗𝑗𝑗𝑗

is the error term at the identity of a coach 𝑐𝑐 in season 𝑗𝑗 of spell 𝑗𝑗.

The second equation is:

This equation, as well as the explanations of the different variables, does not differ from the first equation, except of the inclusion of the set of coach-team match variables 𝐵𝐵𝐶𝐶𝑀𝑀𝐶𝐶𝐶𝐶_{𝑚𝑚𝑐𝑐𝑗𝑗}. The variables itself are dummy variables, which measure all possible coach-team combinations. They adopt the value 1 if a coach c (𝑐𝑐 =1,…,241) was managing a specific team within the seasons of spell j (𝑗𝑗 =1,…,475), 0 otherwise. Also here, the coefficient is indexed, as it will vary with different coach-team matches. The index m identifies the current coach-team match of a specific coach and team at the spell. As the dataset includes 256 possible coach-team match combinations (normally it would be more, but the combinations in which the coach-team match-dummies are only adopting the value of 0 were left out) within the examination period, m can apply values from 1 to 256. Borland and Lye (1996) used the same measure for their match variables. They call this variables “interaction variables”, as the interaction of all coaches with all teams is captured by these dummy variables.

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27 I will again focus on the coach named Lattek, from the example above. Within his career, Lattek was inter alia coach of Bayern Munich and Borussia Dortmund in the German “Bundesliga”. Until now, he was never a trainer for Werder Bremen in the German “Bundesliga”. Then the coach-team match-dummy variables for the coach Lattek look like in the following Table.

Table 3: The Match-Dummy Example.

Season Team Match-Dummy 1 Lattek – Werder Bremen Match-Dummy 2 Lattek – Dortmund Match-Dummy 3 Lattek – Bayern Munich 1977/1978 Bremen 0 0 0 1978/1979 Bremen 0 0 0 1979/1980 Dortmund 0 1 0 1980/1981 Dortmund 0 1 0 … 1984/1985 Bayern 0 0 1 1985/1986 Bayern 0 0 1

Source: Author’s own table.

Lattek has matches with the teams Borussia Dortmund and Bayern Munich, but no match with the team Werder Bremen.

The first regression equation states that team performance depends on different factors, without paying further attention to and not including the influence of coach-team combinations. Coach-team combinations as an influencing factor of team performance are considered in the second regression equation. A direct test of the coach-team match-effect can be obtained through the comparison of these two regression equations. First, if a significant effect of these coach-team combinations on team performance exists, the goodness of fit of the model should increase. Second, “if the coach’s value differs between matches, the coefficients on the match-dummy variables in equation (2) should be statistically significant” (Borland & Lye; 1996; p.149). Also by conducting an F-test, the so-called Wald-test, I will examine its null hypothesis that the match-dummy variables do not explain variation in the winning percentage.

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28 model. However, it should be noted that, contrary to Borland and Lye (1996), I used a different measure for player performance 𝑃𝑃𝑃𝑃_{𝑗𝑗𝑗𝑗} to proxy for player quality. Borland and Lye (1996) used the total number of Brownlow medals awarded to players in the team, but this award is not existent in the German “Bundesliga”. An equivalent measure would have been to use the number of top scorers awarded per season, but these are only a handful of players each season. Therefore, I determine player performance through a dummy variable that measures the participation of a team in the UEFA Cup or Champions league, as this measure reflects total player performance in a team better than the number of top scorers per season. Hence, I suggest that the independent variable 𝑃𝑃𝑃𝑃_{𝑗𝑗𝑗𝑗} has a significantly positive effect on the dependent variable 𝑃𝑃_{𝑗𝑗𝑗𝑗}.

Following Borland and Lye (1996), the independent variable 𝑃𝑃_{𝑗𝑗𝑗𝑗} is measured by the winning percentage of a team per season. However, this variable is a proportion (p), namely a percentage between 0 and 100 and therefore can only adopt values between 0 and 1. This problem has to be addressed, either by choosing a special functional form of the model – the fractional logit, or by making it linear. I chose the alternative to make the dependent variable a linear one, since the results of applying the fractional logit method are more difficult to be interpreted than the results of applying an OLS regression. In order to linear it, I will calculate ln (p/1-p) (where p is the proportion – the winning percentage of a team per season). Then I will use ln (p/1-p) as my dependent variable and run the regressions on it. It should be noted that, since I take ln (p/1-p) as my transformed dependent variable, it can not only obtain values between 0 and 1 but any value. Like Borland and Lye (1996), I also include the dummy variable 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶_{𝑐𝑐𝑗𝑗}, which measures the fixed value a coach brings to performance, and 𝐵𝐵𝐶𝐶𝑀𝑀𝐶𝐶𝐶𝐶_{𝑚𝑚𝑐𝑐𝑗𝑗}, which is the coach-team match “interaction variables” that allows to directly test the coach-team match-effect. As I directly test the matching hypothesis with the variable 𝐵𝐵𝐶𝐶𝑀𝑀𝐶𝐶𝐶𝐶𝑚𝑚𝑐𝑐𝑗𝑗, I expect this variables to have a significantly positive effect on the dependent

variable 𝑃𝑃_{𝑗𝑗𝑗𝑗}.

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29

𝑐𝑐 𝜖𝜖 𝐶𝐶 𝑧𝑧 𝜖𝜖 𝑍𝑍

Prior the season of 1995/1996, transfer fees for football players had to be paid, even if the player had reached a contract ending and wanted to change a club. Also the number of foreign-born players, who could appear on the field within a match, was restricted. In 1995, a Belgian football player, Bosman, sued his old team, which did not want to let him leave, for restraint of trade. In December 1995, the European Court of Justice ruled that this compensation payment is incompatible with the law of “freedom of labor”. Also restrictions to the numbers of foreign players that could appear within a match were found guilty for violating this law. This legal decision opened the market of football players and coaches within Europe and led to a rising player and coach circulation within Europe (Simmons; 1997). As this ruling could bias the coach-team match-effect or change a team’s performance, this event has to be included in the regression model.

The Bosman ruling enabled clubs a better supply with high quality coaches and players. Hence, I assume that the variable 𝐵𝐵𝐶𝐶𝐵𝐵𝐵𝐵𝐶𝐶𝐵𝐵_{𝑗𝑗𝑗𝑗} will have a significantly positive effect on the dependent variable 𝑃𝑃_{𝑗𝑗𝑗𝑗}.

2.3.2 MATCH-DUMMIES – PROXIES FOR TEAM-SPECIFIC EFFECTS?

As stated by Borland and Lye (1996), systematic variations of performance between individual teams may be possible. Therefore, whether the coach-team match-dummies simply proxy for team-specific effects has to be tested. Out of this reason, I state the third equation:

3) 𝑃𝑃_{𝑗𝑗𝑗𝑗} = ∑ 𝛽𝛽 _𝑐𝑐𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶_{𝑐𝑐𝑗𝑗} + ∑ 𝜋𝜋_𝑧𝑧𝑀𝑀𝐸𝐸𝐶𝐶𝐵𝐵_{𝑧𝑧𝑗𝑗} + 𝛿𝛿𝑃𝑃𝑃𝑃_{𝑗𝑗𝑗𝑗} + 𝜃𝜃𝐵𝐵𝐶𝐶𝐵𝐵𝐵𝐵𝐶𝐶𝐵𝐵_{𝑗𝑗𝑗𝑗} + 𝜗𝜗𝐸𝐸𝐸𝐸𝑃𝑃_{𝑐𝑐𝑗𝑗𝑗𝑗} + 𝜇𝜇(𝐸𝐸𝐸𝐸𝑃𝑃_{𝑐𝑐𝑗𝑗𝑗𝑗})2+ 𝜀𝜀𝑗𝑗𝑗𝑗

All variables are defined like in equation (1). Additionally, a set of team-dummy variables 𝑀𝑀𝐸𝐸𝐶𝐶𝐵𝐵𝑧𝑧𝑗𝑗 was added. This set of dummy variables is the measure to identify a team in spell j.

The dummy variables adopt the value 1 if the team was involved in that spell, 0 otherwise. The index z identifies the current team of 44 teams within the observation period. Therefore z can adopt the values 1 to 44. Also here, the coefficient is indexed, as it will vary with different teams.

For clarification, I will give an example, in which case these dummy variables adopt the value 1 and in which they adopt 0.

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30 This coach was the first coach being observed in the dataset. Therefore, again the spell-numbering begins with 1. Also Cramer was an active coach in the German “Bundesliga”, coaching Bayern Munich within the 8th spell. Therefore, the spell-numbering obtains the value 8. He was not coaching Borussia Mönchengladbach. Then, the team-dummy variables for this case look like the following Table 4.

Table 4: The Team-Dummy Example.

Season Spell Coach Team Team-Dummy Bayern Team-Dummy M’Gladbach 1971/1972 1 Lattek Bayern 1 0 1972/1973 1 Lattek Bayern 1 0 1973/1974 1 Lattek Bayern 1 0 1974/1975 1 Lattek Bayern 1 0 1975/1976 2 Lattek M’Gladbach 0 1 1976/1977 2 Lattek M’Gladbach 0 1 1977/1978 2 Lattek M’Gladbach 0 1 1974/1975 8 Cramer Bayern 1 0 … 8 Cramer Bayern 1 0 1977/1978 8 Cramer Bayern 1 0

The inclusion of this set of team-dummy variables can provide a limited test on the role of team-specific effects. Via an F-test, namely a Wald test of significance, which compares equation (1) and (3), the hypothesis that “the team-dummy variables do not explain variation in the winning percentage” can be tested.

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31

𝑚𝑚 𝜖𝜖 𝑧𝑧

Again, I will use a coach from the examples above. Within his career, Lattek was inter alia coach of Bayern Munich and Borussia Mönchengladbach in the German “Bundesliga”. This coach was the first coach being observed in the dataset. Therefore, again the spell-numbering begins with 1. Then, the dummy variables look like in Table 5.

Table 5: Example – All Dummy Variables.

Season Spell Coach Team

Coach-Dummy Lattek Team-Dummy Bayern Team-Dummy Gladbach Match-Dummy Lattek - Bayern Match-Dummy Lattek - Gladbach 1971/72 1 Lattek Bayern 1 1 0 1 0 1972/73 1 Lattek Bayern 1 1 0 1 0 1973/74 1 Lattek Bayern 1 1 0 1 0 1974/75 1 Lattek Bayern 1 1 0 1 0 1975/76 2 Lattek M’Gladbach 1 0 1 0 1 1976/77 2 Lattek M’Gladbach 1 0 1 0 1 1977/78 2 Lattek M’Gladbach 1 0 1 0 1 1978/79 2 Lattek M’Gladbach 1 0 1 0 1

As I investigated during my analysis, 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶_{𝑐𝑐𝑗𝑗}, the set of coach-dummy variables, and 𝐵𝐵𝐶𝐶𝑀𝑀𝐶𝐶𝐶𝐶𝑚𝑚𝑐𝑐𝑗𝑗, the set of coach-team match-dummy variables, are highly correlated with the

team-dummy variables. Therefore, it was not possible for me to completely include a set of team-dummies in one equation with a set of coach-dummy variables and a set of match-dummy variables. However, it is possible to construct a regression equation, which includes a complete set of coach-dummies and a limited set of team-dummies. Consequently, equation (3) was derived.

Borland and Lye (1996) argued that it is possible to exploit the relationship between team and match-dummies even more. In order to get more information about the explanatory power of these dummy variables, and “since each match-dummy is associated with some individual team” (Borland & Lye; 1996; p.150), the following equation can be stated:

4) ∑ 𝐵𝐵𝐶𝐶𝑀𝑀𝐶𝐶𝐶𝐶_{𝑚𝑚𝑐𝑐𝑗𝑗} = 𝑀𝑀𝐸𝐸𝐶𝐶𝐵𝐵_{𝑧𝑧𝑗𝑗}

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32

𝑐𝑐 ϵ 𝐶𝐶

They investigated that match-effects did not simply proxy for fixed team effects, by using a Wald test. Therefore, I test this statement by using the same method.

2.3.3 INVESTIGATION OF THE MATCH EFFECT’S CONTRIBUTION TO PERFORMANCE

Finally, I will identify how much a good match between a coach and team increases its performance. Therefore, I will use the following equation:

5) 𝑃𝑃_{𝑗𝑗𝑗𝑗} = ∑ 𝛽𝛽 _𝑐𝑐 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶_{𝑐𝑐𝑗𝑗} + 𝛿𝛿 𝑃𝑃𝑃𝑃_{𝑗𝑗𝑗𝑗} + 𝜃𝜃 𝐵𝐵𝐶𝐶𝐵𝐵𝐵𝐵𝐶𝐶𝐵𝐵_{𝑗𝑗𝑗𝑗} + 𝜗𝜗 𝐸𝐸𝐸𝐸𝑃𝑃_{𝑐𝑐𝑗𝑗𝑗𝑗} + 𝜇𝜇 (𝐸𝐸𝐸𝐸𝑃𝑃_{𝑐𝑐𝑗𝑗𝑗𝑗})2+ 𝜌𝜌 𝐺𝐺𝐶𝐶𝐶𝐶𝐺𝐺𝐵𝐵𝐶𝐶𝑀𝑀𝐶𝐶𝐶𝐶𝑗𝑗𝑗𝑗 + 𝜀𝜀𝑗𝑗𝑗𝑗

, where 𝐺𝐺𝐶𝐶𝐶𝐶𝐺𝐺𝐵𝐵𝐶𝐶𝑀𝑀𝐶𝐶𝐶𝐶_{𝑗𝑗𝑗𝑗} is a dummy variable, measuring how good the match of a coach and team in season 𝑗𝑗 of spell 𝑗𝑗 is. All other variables are defined like in the equations above. A good match between a coach and a team is shown by a coach’s tenure in a team. The greater the tenure is, the better is the match between a coach and a team will be.

As mentioned before, it is possible to predict the relationship between the probability of separation and the years of a coach’s tenure. According to diverse scholars (e.g. Borland & Lye (1996); Ohtake & Ohkusa (1993); Chapman & Southwick (1991); Brown et al. (2007)), coach/team separations will initially increase and then decrease at rising years of coach tenure. These studies investigated that on average after 5 years of a coach’s tenure, the turning point of separations is reached. After this point, the probability of separation will constantly decrease. Therefore, the dummy variable is defined equal to one, if the tenure of a coach is equal to or greater than five years, 0 otherwise. Based on Brown et al. (2007), I expect the GOODMATCH variable to influence team performance in a positive and significant way.

After this first analysis, the direct test on the influence of the coach-team match on team performance, I will conduct my second analysis to test the predicted relationship between the probability of coach-team separations and:

A) A coach-team match;

B) A coach’s years of experience; C) A coach’s years of tenure.

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33 theory predicts, the hazard rates should decline with rising years of work tenure or experience. It is expected that the better a coach-team match is, the longer a coach stays in the team.

Furthermore, I will examine this relationship by analyzing both:

- The connection between the team’s inner-season winning percentage and the probability of coaches A) separating from, B) getting fired of, or C) leaving the team. - The connection between a coach’s average winning percentage during a current spell

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2.4 VARIABLE DEFINITIONS AND THEIR SOURCES

For clarification, the table below (see Table 6) shows all variables that were used in this chapter, their definitions and source of data.

Table 6: Variable Definitions and their Sources.

Variable Description Source

𝑃𝑃𝑗𝑗𝑗𝑗

The dependent variable 𝑃𝑃_{𝑗𝑗𝑗𝑗} is equivalent

with team performance in season 𝑗𝑗

(𝑗𝑗 =1971,…,2002) of spell 𝑗𝑗

(𝑗𝑗 =1,…,475). It can take values from 1

to 100 percent, as a winning percentage of more than 100 percent is not possible in this context. Therefore, the data is censored and will be made linear (see explanation above).

The “Kicker” Magazine (This variable was also used by

Borland and Lye (1996))

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑐𝑐𝑗𝑗

The independent variables 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶_{𝑐𝑐𝑗𝑗} are

a set of dummy variable that measure the fixed value of the influence of different coaches on the team

performance in spell 𝑗𝑗 (𝑗𝑗 =1,…,475).

The coach itself is identified by c

(𝑐𝑐 =1,…,241), as in the observation

period 241 different coaches were active. The dummy variables adopt the value 1 if the coach is coaching in this current spell, 0 otherwise.

Author’s calculation using data of “Das Fußballstudio”

(This variable was also used by Borland and Lye (1996))

𝑃𝑃𝑃𝑃𝑗𝑗𝑗𝑗

The independent variable _{𝑃𝑃𝑃𝑃}_{𝑗𝑗𝑗𝑗} is a

dummy variable to measure player performance, defined as the performance of all players combined together within a specific team, in

season 𝑗𝑗 of spell 𝑗𝑗. It is 1 if a team

participated in the UEFA Cup or Champions League, 0 otherwise.

(This variable is a modified variable, of the variable Borland and Lye (1996)

used to control for player quality)

𝐵𝐵𝐶𝐶𝐵𝐵𝐵𝐵𝐶𝐶𝐵𝐵𝑗𝑗𝑗𝑗

The independent variable 𝐵𝐵𝐶𝐶𝐵𝐵𝐵𝐵𝐶𝐶𝐵𝐵_{𝑗𝑗𝑗𝑗} is

a dummy variable to control for the

event of the Bosman ruling in season _𝑗𝑗

of spell _{𝑗𝑗. It adopts the value 1 in the}

presence of the event, 0 otherwise.

(This variable is an additional variable, added to the model of

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35 𝐸𝐸𝐸𝐸𝑃𝑃𝑐𝑐𝑗𝑗𝑗𝑗

The independent variable 𝐸𝐸𝐸𝐸𝑃𝑃_{𝑐𝑐𝑗𝑗𝑗𝑗}

identifies the years of experience of a

coach 𝑐𝑐 in season 𝑗𝑗 of spell 𝑗𝑗.

𝐵𝐵𝐶𝐶𝑀𝑀𝐶𝐶𝐶𝐶𝑚𝑚𝑐𝑐𝑗𝑗

The independent variables 𝐵𝐵𝐶𝐶𝑀𝑀𝐶𝐶𝐶𝐶_{𝑚𝑚𝑐𝑐𝑗𝑗}

are the set of coach-team match variables. The variables themselves are dummy variables, which measure all possible coach-team combinations. They adopt the value 1 if a coach c

(𝑐𝑐 =1,…,241) was managing a specific

team within the seasons of spell j

(_{𝑗𝑗 =1,…,475), 0 otherwise. The index m}

identifies the current coach-team match of a specific coach and team at the spell. As the dataset includes 256

possible coach-team match

combinations, m can obtain values from 1 to 256.

Author’s calculation using data of Hardy Grüne’s book “Geheuert,

gefeiert, Gefeuert” & “Das Fußballstudio”

𝑀𝑀𝐸𝐸𝐶𝐶𝐵𝐵𝑧𝑧𝑗𝑗

The independent variables _{𝑀𝑀𝐸𝐸𝐶𝐶𝐵𝐵}_{𝑧𝑧𝑗𝑗} are

a set of team-dummy variables. This set of dummy variables is the measure to identify a team in spell j. The dummy variables adopt the value 1 if the team was active in that spell, 0 otherwise. The index z identifies the current team of 44 teams within the observation period. Therefore, z can adopt the values 1 to 44.

𝐺𝐺𝐶𝐶𝐶𝐶𝐺𝐺𝐵𝐵𝐶𝐶𝑀𝑀𝐶𝐶𝐶𝐶𝑗𝑗𝑗𝑗

The independent variable

𝐺𝐺𝐶𝐶𝐶𝐶𝐺𝐺𝐵𝐵𝐶𝐶𝑀𝑀𝐶𝐶𝐶𝐶𝑗𝑗𝑗𝑗 is a dummy variable,

measuring how good the match of a

coach and a team in season 𝑗𝑗 of spell 𝑗𝑗

is. This dummy variable is defined equal to one, if the tenure of a coach is equal to or greater than five years, zero otherwise

Author’s calculation using data of Hardy Grüne’s book “Geheuert,

gefeiert, Gefeuert” & “Das Fußballstudio”

(This variable was also used by Brown et al. (2007))

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36

2.5 METHODOLOGIES IN RELEVANT LITERATURE

As stated before, five relevant studies performed a direct test of the match-effect. These studies may make use of data from various sports or sport leagues, sample coverage may differ in the specification of their dependent or independent variables; however the methodology they make use of is somehow similar.

All mentioned studies use sports data to directly test the matching hypothesis. The statistical interference of all mentioned studies consists of: 1) presenting the descriptive statistics and a correlation matrix of the non-dummy variables; 2) estimating the model using the Ordinary Least Squares (OLS) procedure; 3) in the presence of heteroskedasticity correcting for it by using White’s heteroskedastic-consistent covariance standard errors; 4) in the presence of collinerarty correcting for it by using generalized least squares (GLS) and, in most of the studies, 5) examining the probability of separation by calculating the hazard rates of managers or coaches. Therefore, I will, if possible, follow the scholars in this field and use the OLS procedure, which will be modified, to fit my model. After that, I will analyze the probability of separation and its relationships with a coach’s tenure and experience.

The research presented in this thesis is taking its cue from Borland and Lye (1996), not at least out of the reason that they used a relatively similar dataset as the one used in the thesis, and their study was inspired by relevant studies in this field. Therefore, I will provide diagnostic checks carried out by Borland and Lye (1996), but also additional detailed diagnostic checks. Appropriate corrections and modifications of the model and variables will be made.

Contrary to Borland and Lye (1996), my model does not encounter for problems of collinearity and autocorrelation, which will be shown in Chapter 4. Therefore, I will obtain a direct test of the match-effect by using the equations mentioned above and by obtaining an analysis using the Ordinary Least Squares procedure. Why I chose the Ordinary Least Squares procedure will be explained in the next chapter - Chapter 3. Moreover, Borland and Lye (1996) used White’s covariance matrix estimator to control for present heteroskedasticity, which I did not detect in my case. (The different diagnostic checks will be conducted to prove the fit and appropriate form of the model. These diagnostic checks will be explained in detail in Chapter 4.)

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37 coaches. Furthermore, by comparing average winning percentages of a team with the different kinds of coach separation, I will try to get more insights in the reasons, why a coach is fired or leaves the team. Is it because of continuous bad performance, short term bad performance or other reasons?

3. DESCRIPTION OF THE DATASET

Every study examining the direct manager-team match-effect I read made use of existing datasets of sports leagues. Most of them used panel data, which were combined with cross-sectional and time series data. In my research, on the direct effect of matching between coach and team, I also apply a panel dataset, consisting of 32 time periods (season 1971/72-2002/03) and 475 cross-sectional units (spells). The sources of data are the “kicker” magazine, one of the biggest German football magazines, the open source database “Das Fußballstudio”, published by VM Logic and sponsored by the German “Bundesliga”, the book of Hardy Grüne, “Geheuert, gefeiert, gefeuert”, which lists the fired coaches of the German “Bundesliga” till the year 2000 and the database “Fussballdaten.de” for applying information about fired coaches within the years 2001 and 2002.

PERFORMANCE MEASUREMENT & MATCHING