No pain, no gain? Effort and productivity in professional soccer.

Wicker, Pamela ; Prinz, Joachim ; Weimar, Daniel 等

Introduction

The recruitment of skilled personnel is a central role of firms (Lazear, 2000) and can be regarded as a war of talent. Many firms do not (only) advertise positions, they look for skilled people using scouts and head hunters. Potentially new staff is selected based on a set of selection criteria (Spence, 1973). This procedure is similar in professional soccer where potential players are selected by talent scouts. These scouts identify players based on specific selection criteria. Typically, these selection criteria are related to human capital, talent/ability (Bryson, Frick, & Simmons, 2012), leadership skills (Deutscher, 2009), productivity (Franck & Nuesch, 2012), cognitive skills (Deutscher, Frick, & Prinz, 2012), and effort (or synonymously diligence). For example, one club may seek a young player with good scoring performance that fits into the specific system of the club. Yet, players cannot control all factors; human capital and talent can hardly be changed by players and productivity may differ among players of different positions. While this may not be an issue for talented and productive players, less talented players may experience problems in being recruited. Nevertheless, they can control the level of effort they exert within the game. This effort may convince scouts to recruit the players. For example, the players could put forth effort in their endurance and sprint abilities. This could be a way of signaling their quality to scouts. Since a player's quality is typically reflected in his salary or market value, the question arises to what extent a player's market value is determined by a player's effort. If there is a positive relationship between effort and market value, signaling effort could be a marketing strategy especially for less talented players.

Therefore, the purpose of this study is to examine the influence of effort on a player's market value in professional soccer. Two aspects are important with regard to measuring effort. First, the technical equipment must be available. In professional soccer, technical advancements in recording routes and running distances represent an innovative approach of measuring effort. Second, measurement costs have to be low to ensure that pay (or market value) is a function of effort (Lazear & Shaw, 2007). This study uses recent technological innovations to measure player effort and advances the following main research question: What impact does effort have on a player's market value (controlling for human capital and ability)? Based on signaling theory the relationship between effort and market value is conceptualized. Secondary data on player characteristics from the 2011/2012 season and the first half of the 2012/2013 season of the German Bundesliga were collected. Most importantly, this study tries to disentangle ability and effort by providing an empirical discussion of Nicholls's (1976) statement: "Effort is virtuous, but it's better to have ability" (p. 306).

Literature Review

Previous research has identified individual and team-related factors that influence the salary of players (Hakes & Sauer, 2006, 2007; Wallace, 1988; for an overview of soccer studies see Frick, 2007). With regard to team factors, it was documented that they explain 14% of the explained variance in salaries in the National Basketball Association (NBA; Wallace, 1988). In soccer, a player's salary was higher when his team qualified for a European competition (e.g., Huebl & Swieter, 2002) or when he played in a European or World Cup tournament, providing support for a shop window effect (Simmons & Deutscher, 2012). Furthermore, players who were part of their respective national teams received higher salaries (Franck & Nuesch, 2008; Lehmann & Schulze, 2008; Lucifora & Simmons, 2003). Moreover, some teams were found to pay their players a premium salary (Frick, 2008). For example, teams such as Real Madrid or the Los Angeles Lakers tend to pay higher average salaries than other teams and therefore athletes of these teams benefit financially, supporting the need to include team dummies in salary equations (Garcia-del-Barrio & Pujol, 2007; Wallace, 1988).

The individual factors can be further divided into human capital and productivity (e.g., performance, talent). Initiated by seminal work on human capital theory (e.g, Becker, 1962; Mincer 1974; Schultz, 1961) numerous studies attempted to explain salary dispersion using human capital measures. In line with this theory, age and experience were found to have an impact on salary (Franck & Nuesch, 2008, 2012; Lehmann & Schulze, 2008; Lucifora & Simmons, 2003; Wallace, 1988). Rookies tend to earn less than experienced players (Hakes & Turner, 2011) and players who are eligible for arbitration earn more than their counterparts (Hakes & Sauer, 2006). Furthermore, month of birth (Ashworth & Heyndels, 2007), position (Frick, 2007; Garcia-del-Barrio & Pujol, 2007; Lehmann & Schulze, 2008; Wallace, 1988), and nationality (Franck & Nuesch, 2008) were found to influence player salaries. Also, a positive relationship between contract duration and salary could be observed (Krautmann & Oppenheimer, 2002); yet, it must be considered that a player's performance seems to be associated with his contractual situation (Stiroh, 2007). Previous studies found support for shirking because players' performance improved significantly in the year before signing a new contract, but declined afterwards (e.g., Krautmann & Solow, 2009; Stiroh, 2007).

The pay-productivity relationship has been extensively investigated in previous research supporting a positive relationship (e.g., Miceli & Huber, 2009). In detail, playing time (Hakes & Sauer, 2006) and offensive performance (Frick, 2008; Lehmann & Schulze, 2008; Wallace, 1988) were found to have a positive impact on salary. Previous research also showed that the number of appearances on the field per season, games played for the team, and years employed by the club were positively associated with a player's income (Franck & Nuesch, 2008, 2012; Frick, 2008; Garcia-del-Barrio & Pujol, 2007; Lucifora & Simmons, 2003; Vincent & Eastman, 2009; Wallace, 1988). The draft position, used as an indicator for a player's talent in North American professional sports leagues, also contributed to the explanation of salaries. The draft number has the expected negative influence on player salaries: The earlier a player is selected in the amateur draft by an NBA team, the higher his income (Vincent & Eastman, 2009; Wallace, 1988).

The value of different player skills was also examined, particularly in baseball. For example, Bradbury (2007) showed that the value of pitchers is determined by individual run prevention, while the defensive output of team production does not play a role. The pay-performance relationship has received further attention after Michael Lewis's (2003) controversially discussed publication Moneyball suggesting that some skills of baseball players are undervalued by the baseball labor market. His Moneyball hypothesis has been tested empirically suggesting that some skills such as on-base percentage, hitting for average, hitting for power, and plate discipline have been undervalued in several seasons before the Moneyball publication (Hakes & Sauer, 2006, 2007). While different skills are critical in soccer, the finding that specific skills were undervalued may also inform the present research.

In addition to the above mentioned factors, a player's effort may influence his salary. General labor market research suggested that individual effort was associated with salary. For example, theoretical work by Lazear and Shaw (2007) supported an effect of effort on pay: "Very large pay spreads induce high effort [...] If individuals are working at a very high level of intensity [...] it will be necessary to compensate those employees at a very high level" (p. 95). Moreover, empirical studies document that effort (measured by e.g., absenteeism, unpaid overtime work, and working more than others) was associated with wages and the contractual situation (Engellandt & Riphahn, 2005; Givord & Wilner, 2009; Riphahn, 2004; Treble, 2001). However, evidence of the impact of effort on salary was rare. One reason for this scarcity could be the difficulty to disentangle ability and effort. While sound measures of ability have already been provided in previous research, it was difficult to quantify an individual's effort. These difficulties also apply to the professional sports sector. Independent of the sport under investigation, the impact of effort on income has been largely neglected in previous research. This study tries to address these shortcomings by including effort in the income equation and by using innovative effort measures. Moreover, it provides a theoretical explanation as to why effort can be critical to the market value of soccer players. In fact, effort could serve as a signaling device which could be particularly relevant to less talented, less productive, and less experienced players to compensate missing talent (Hau & Salili, 1996).

Effort as a Potential Signaling Device

Although the professional team sport industry is characterized by high performance visibility and trackability (Kahn, 2000; Rosen & Sanderson 2000), it is unclear from the outset of the employer-employee relationship whether the partnership becomes profitable. From the firm's (principal) point of view it is risky to employ a new player (agent); hence the firm might face an adverse selection problem. Typically, the firm initializes some screening mechanism in order to reveal a potential player's true productivity to make sure that the individual is worth his potential salary. On the other hand, the player faces the risk of being mismatched with the potential firm since his expectations might not be met by the employer. As in many other (labor) markets with imperfect information, an individual may seek the highest wage among possible firms depending on given talent. Opposite to the firm's point of view, the agent wants to maximize his income, while the firm tries to motivate the agent to put forth more effort. As outlined above, an agent's wage is presumably driven by his stock of knowledge and abilities (Becker, 1962).

Signaling theory (Spence, 1973) offers an alternative explanation as to why a player's income may depend to some extent on effort. Individual effort forms the signal in the following argument which is based on two main assumptions. First, there is some degree of imperfect information among a football club and a potential agent offering his service to the team. Second, the soccer club has good knowledge about an incoming player's abilities from watching his past productivity in a rival team. Yet, it is still questionable whether the (talented) player finally fits into an existing team, that is, into the team's production function. For example, it is highly uncertain whether a player who performs excellent with team A is of similar value to team B.

Given this uncertainty, teams as well as agents have incentives to reduce information deficits by searching for and sending additional signals that are independent of teammates' quality. It is posited that players' effort statistics, providing information about running distance and sprints per match, serve as an independent and simultaneously credible indicator. These indicators are of high interest since a player's endurance level on the pitch is much more a function of effort and discipline than talent/ability. Moreover, improving individual physical fitness can be improved in training sessions and again this is principally influenced by hours of running input. Overall, it is believed that physical fitness is strongly correlated with training hours (effort) and is consequently a costly signal that provides inherent information about a player's intrinsic motivation, which then improves quality.

In this context, the question arises if effort substitutes or complements ability. It could be that players have the possibility to compensate talent by putting forth over proportional effort. This may be specifically the case for less talented players. For example, players who are not able to read the game have to run more. This way they can compensate missing talent by putting forth more (running) effort. Conversely, any given level of performance can neither be reached solely by talent nor effort supporting a complementary relationship of effort and productivity. Both inputs (i.e., skill and hard work) are necessary to produce reasonable outputs. Particularly in professional sports, it might be argued that productivity itself is a necessary, but not sufficient condition. A certain ability level is needed to play for a Bundesliga team. Yet, once players play in the Bundesliga, effort may complement their productivity on the field. Some athletes put a lot of effort in reaching their full potential, while equally talented players are not able (or willing) to retrieve their utmost potential because they do not put sufficient effort into training. Yet, this is needed to be in a position to put forth effort on the field. For example, if players do not make intensive runs, they are not in the position to strike the ball at the goal or to properly defend a counterattack supporting the notion that effort complements productivity.

In summary, under the assumption of imperfect information and the fact that individual productivity depends on teammates' productivity (Idson & Kahane, 2000) effort should be a valid signal to the team in order to select agents of different and unknown future productive efficiency. Hence, this study assumes that team managers observe the performance of players imperfectly, but view effort measures as proxies for the potential willingness of players to put forth extraordinary effort. In a world of imperfect information, players may have an incentive to invest in painful effort parameters in an attempt to signal their true ability. Importantly, these parameters are mostly independent of teammates' quality. Consequently, putting forth more (running) effort can be interpreted as signaling device for higher productivity, which should in turn increase a player's market value (Cahuc & Zylberberg, 2004).

Method

Data collection

The database contains information of players from the 2011/2012 season and the first half of the 2012/2013 season of the German Bundesliga (round-robin competition). The panel unit of analysis is half season (n=3). The data were collected from two different sources: (1) Market values and individual information about players were taken from a German transfer market website (www.transfermarkt.de); and (2) performance and effort data were made available from the website of the German Football League (Deutsche Fufiball Liga [DFL]; www.dfl.de). Including earlier seasons in the sample is not possible since effort data have only been available since the beginning of the 2011/2012 season.

The website www.transfermarkt.de is a German community-based information site that provides performance statistics as well as market values of soccer players. Market values are published at the end of each half season. They are assessed and discussed by community members and experts. Only proven and confident members are allowed to enter the discussion forum about market values. At the end of the discussion the head of the internet forum sets the final market value. While this procedure seems subjective, previous research supports the validity of market values because market values were highly correlated with salaries (which are not disclosed in Germany; e.g., Franck & Nuesch, 2012; Frick, 2007). Therefore, they should represent an adequate proxy of salaries. In an attempt to avoid reverse causality problems between market values and performance data (Angrist & Pischke, 2008), market values were gathered at the end of each half season (February/July), while performance variables represent average values from within each half season, i.e., performance precedes compensation.

For the construction of the dataset, all players who appeared in one club roster were considered (n=1,191). Players who were not listed on the transfer market website or transferred during the running season have not been included. Goal keepers were also excluded because their effort measures are not comparable with players from other positions. Altogether, 304 benchwarmers were excluded from the sample to reduce a potential sample selection bias. Thus, the remaining database contains only players who played in at least one of all possible matches (17 per half season) given a total playing time of 90 minutes. Using only these players is important because effort measures may be biased by fitter players who did not play the full 90 minutes. Also, it is not possible to determine the correct playing time of those players who enter the field at the end of the match because the actual overtime is not added to the playing time in the official statistics. Consequently, the final sample of n=877 observations (equivalent to 446 players) should be adequate to investigate the research question of this study.

Measures and variables

Table 1 provides an overview of the variables used in this study. Given the skewed market value distribution, a player's logged market value (Mincer, 1974) is computed (MV_LOG). In addition, the percentage change in market value (MV_DIFF) between a player's market value between the previous and the current half season is calculated in order to investigate the effect of effort on a player's market value development. Based on the arguments provided by signaling theory (Spence, 1973), we assume that players are more interested in future market value increases than in present value. As changes are intuitively lower for higher market values, the VALUE_1 variable is used as a reference point (Kahnemann & Tversky, 1979) that controls for players initial starting value.

Individual human capital is measured by a player's age (AGE), nationality (GERMAN), height (HIGH), and position. Since the standard inverse u-shape age-earnings-profile is expected (Maxcy, 1996), the squared term of age is also included in the study (AGE2). The variable APPEAR captures the number of appearances on the pitch in each observed half season. The player's market value should also be influenced by transfers to a new team since the same performance could result in a lower/higher perceived performance in relation to the players of the new team (Lazear & Shaw, 2007). Therefore, the variable TRANSFER covers whether the player has been transferred after the half season. Team-specific human capital is captured with the number of years the player has played for the current club (CLUB_TIME).

Standard performance measures are used to proxy productivity. Following Harder (1992), a player's scoring performance is calculated (SP), which includes goals and assists divided by minutes. Additionally, a player's efficiency is measured by computing the efficiency of ball contacts (EFFIC). This variable represents the number of passes completed, assists, and shots on goal related to the total number of individual ball touches. Successful tackles are covered by the tackling rate (TACK). Another productivity indicator relates to whether the player is (productive enough to be) a member of his national team (NAT, NAT_TOP). While NAT captures a player's participation in his national team, NAT_TOP shows whether a player is a member of one of the highest ranked national teams (Germany, Italy, France, Spain, England, Netherland, Portugal, Brazil).

A player's effort is measured by his average running distance standardized to the minutes played (DIST) and by the number of intensive runs (i.e., faster than 20km/h) per minute (RUN). Since we expect diminishing returns on effort, the squared terms of the two effort measures are also applied (i.e., RUN2, DIST2). To test whether effort either complements or substitutes productivity, the two effort measures are interacted with the three productivity variables. Finally, team dummies are included to control for unobservable team characteristics such as management skills or team budget (TEAM01 to TEAM21).

Previous labor market research has indicated that it is difficult to find an appropriate measure for effort (Givord & Wilner, 2009). The advantage of this data sample of soccer players is that effort can directly be separated from performance by minimizing the halo effect. This effect was considered problematic since "higher effort led to inferences of higher ability" (Nicholls, 1978, p. 808). This problem can be neglected in the current study because a player can choose the level of intensive runs without touching a ball and being productive. To put it differently, an individual can reach his maximum effort independent of his level of ability. This theoretical assumption can be supported empirically: There is only a small correlation between SP and DIST (r=0.12) as well as between SP and RUN (r=0.26). As can be seen from the descriptive statistics in Table 2, players cover 120m per minute and perform 0.58 intensive runs per minute on average. Among those showing high effort are Tom Trybull (Werder Bremen) with 150m per minute and Florian Trinks (Werder Bremen) with 1.11 intensive runs on average (Table 2).

Data analysis

Regression analyses are run to test the impact of effort on market value by controlling for productivity, human capital, and other variables (Table 1). In analogy to the standard Mincer (1974) income equation, the dependent variable is the natural log of a player's market value (MV_LOG). To check for robustness, three regression specifications are run. While model 1 identifies absolute logged market values (MV_LOG), model 2 tests the robustness of model 1 by analyzing percentage changes in market value (MV_DIFF). Model 1 is a fixed-effects model, while model 2 uses random-effects estimates. The modeling decision was based on the Hausman (1978) test, which was significant for model 1 (p<.1) implying that unobserved player characteristics are present. However, the test was insignificant for model 2 (p>.1) supporting the choice of a random-effects model which allows the inclusion of time-invariant variables (i.e., GERMAN, HIGH).

Since the two effort measures are highly correlated (r>.8), separate estimates are necessary in order to avoid multicollinearity issues. Models 1 and 2 present three different specifications in order to disentangle the effects of effort and productivity on a player's market value. The first specification displays the benchmark model, i.e., it presents standard human capital and productivity variables excluding effort. The second and third specification enlarges specification 1 by our innovative effort measures. The second one includes RUN, RUN2, and three interaction terms (RUN*SP, RUN*EFFIC, RUN*TACK). Finally, specification 3 includes the respective distance measures (i.e., DIST, DIST2, DIST*SP, DIST*EFFIC, DIST*TACK). The following market value equation applies to the second specification (including intensive runs as effort measure):

MV_LOG = [[alpha].sub.0] + [[alpha].sub.1] AGE+ [[alpha].sub.2] AGE2 + [[alpha].sub.3] GERMAN+ [[alpha].sub.4] HIGH + [[alpha].sub.5] APPEAR + [[alpha].sub.6] TRANSFER + [[alpha].sub.7] TIME_CLUB + [[alpha].sub.8] SP + [[alpha].sub.9] EFFIC + [[alpha].sub.10] TACK + [[alpha].sub.11] NAT + [[alpha].sub.12] NAT_TOP + [[alpha].sub.13] RUN + [[alpha].sub.14] RUN2 + [[alpha].sub.15] RUN*SP + [[alpha].sub.16] RUN*EEFIC + [[alpha].sub.17] RUN*TACK + [[summation].sup.8.sub.i=1] [[alpha].sub.i]POSITION + [[summation].sup.21.sub.i=1] TEAM + [epsilon] (1)

As in many labor markets that are part of the entertainment industry (Franck, 1996), it is no surprise that some superstars have extraordinarily high market values (Rosen, 1981). These superstars can be regarded as outliers in the current sample and need to be controlled for. One standard mechanism to mitigate the effects of outliers is using logged values which reduce the standard deviation of the variable. Altogether, 22 outliers (i.e., the 1st and 99th percentile of the distribution; Vogel & Wagner, 2011) could be detected for MV_LOG and 9 for MV_DIFF. Models without these outliers were run. Results did materially change supporting the robustness of the models.

Results and Discussion

The fixed-effects models (model 1) for logged market value (MV_LOG) are summarized in Table 3. They show that many, but not all parameters influence players' market values. The [R.sup.2] of model 1 reveals that approximately 20% of the variance in market values is explained by the independent variables. This relatively low percentage of explained variance could be driven by the heterogeneity of the sample, i.e., it includes both players who have played in most of the games and those who appeared only once or twice on the pitch (for 90 minutes). The displayed results of the standard human capital coefficients (FE1) are in accordance with the findings from previous research using Mincer (1974) income equations (e.g., Franck & Nuesch, 2008; Lehmann & Schulze, 2008).

Most relevant for the underlying research question is the sign and statistical significance of the two effort proxies RUN and DIST. The second specification (FE2) shows that RUN is insignificantly related to market values indicating that more diligent players are not able to increase their individual market value by putting forth additional effort. In fact, the squared term (RUN2) has a significant and negative impact on market value. This means that running around like headless chickens decreases the market value. Comparing FE1 and FE2, it can be seen that scoring performance (SP) is now insignificant and negative in the second specification, which is driven by the effort measures. Hence, we may assume that effort substitutes productivity. Yet, the results also suggest that effort may complement productivity given the significant interaction of RUN*TACK. This means that players who perform more intensive runs are more successful in winning tackles. One argument could be that these players are one step quicker than the opponent and, therefore, win the tackle. Independent of position, quicker players are always one step ahead of their counterparts. This, in turn, signals quality and increases a player's market value.

Turning to the third specification (FE3), it can be seen that neither DIST nor its squared term (DIST2) have a significant impact on the dependent variable. Thus, running far distances is not evaluated by the market. Again, the interaction term between DIST*TACK is positively and significantly sloped with market value. Given that RUN and DIST are highly correlated, it seems that those players who perform more intensive runs also run longer distances and win more tackles, which positively affects their market value (Table 3).

The results of the random-effects models for MV_DIFF (model 2) are presented in Table 4. These models are more adequately related to our theoretical arguments with regard to signaling. One key issue of the signaling idea is that usually workers signal their quality in hopes of generating a pay increase in the future. Consequently, not absolute market values, but relative increases in market values should be important to them. Like in the previous set of specifications, we concentrate on the specifications including the effort measures (RE2 and RE3). Similar to the previous results, intensive runs (RUN) are not regarded as a quality signal because those players performing more intensive runs are not rewarded with pay increases in the future.

Consistent with our earlier findings (Table 3), scoring performance (SP) turns insignificant when effort measures are added to the model supporting the assumption that effort may partially substitute productivity. Opposite to the fixed-effects model, the interaction RUN*TACK is statistically not relevant in the random-effects model (RE2). This finding suggests that effort may not be a complement of productivity when looking at changes in market values. Since all coefficients of the alternative effort variable DIST are also insignificant, we assume that market progress cannot be explained by putting forth additional effort.

Finally, the results show that a player's market value is significantly determined by his previous market value (MV_1). Hence, we included this variable to test for path dependence and a specific reference point (Kahnemann & Tversky, 1979). After all, a player will compare his future market value (salary) with his original market value. As expected, those players with low absolute market values will encounter higher relative increases in market value. This finding is in accordance with option value arguments as proposed by Lazear (1998). Since younger players typically have lower market values in comparison to older players, younger players generally are more attractive to teams (Table 4).

Conclusion

This study examined the impact of effort (measured by intensive runs and total distance run per game) on the market value of soccer players controlling for human capital and productivity. Panel regression was used to investigate the influence of effort on logged market values and relative increases in market values. The results of the fixed-effects models displayed mainly insignificant and partially negative effects of effort on logged market values. Only the interaction between intensive runs and tackling rate had a significant positive impact on logged market value. Yet, all effort measures were insignificant in the random-effects models that analyzed changes in market values.

These results seem interesting in the view of the classical economic literature, which assumes that higher effort leads to higher performance and subsequent higher payment (Lazear & Shaw, 2007). The insignificant and negative effects of effort on player values seem surprising, although it has already been found in previous research (Treble, 2001). Moreover, several explanations for these findings can be advanced. First, higher effort does not increase performance in a way that can be perceived by managers. Second, effort is not an adequate compensation for missing talent. It was shown in the literature that managers are not the best personnel when translating individual performance into suitable salary, even if all information is available and visible to the public (Berri, Schmidt, & Brooks, 2007). Third, some players may be able to read the game better, resulting in better positioning and hence less meters to run.

Fourth, the role that was assigned to players by the coach may be critical (although the study controlled for position). For example, players like Mario Gomez of Bayern Munich predominantly have the task to position close to the goal in anticipation of teammates' support to score goals. Oppositely, there are other players who run a lot every match because they fight for lost balls or have the task to prevent counter attacks. These players are important for every team because they sacrifice all their energy for the team and go long distances (like the domestiques in professional cycling; Rebeggiani & Tondani, 2008). It is suggested that these players usually do not score and, thus, their contribution to the team's performance is less obvious (but nevertheless very important).

Fifth, it could be that effort is undervalued by the soccer labor market. This situation would be similar to the baseball labor market where plate discipline was undervalued before the publication of Moneyball (Hakes & Sauer, 2006, 2007; Lewis, 2003). To test this assumption for professional soccer, the contribution of effort on the team's performance must be estimated first. Afterwards, the coefficients of the performance model have to be compared with those from the value model (Hakes & Sauer, 2006) and differences in coefficients would support the assumption that specific factors like effort are undervalued by the labor market. However, estimating the contribution of effort on team performance in soccer is more difficult than the contribution of plate discipline in baseball.

This study was among the first to examine the impact of effort on market values; yet, it has some limitations that also represent avenues for future research. First, it must be taken into account that effort can be influenced by drug cheating, although the effects may be smaller in soccer compared with other sports like track and field or cycling. Second, this study only looked at intensive effort margins; yet, extensive effort margins could also influence players' market values. For example, player's ability to be fit and ready for a game every week of the playing season can also play a role. Future studies may consider measures for extensive effort margins. Third, this study is restricted to the player level. Yet, as noted above, effort may also show up in team performance equations which could be estimated in future research. Fourth, this study is limited to a relatively short period of time in only one sport. Future research should check the robustness of the present findings by using longer observation periods and by looking at effort measures in other sports than soccer.

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Pamela Wicker [1], Joachim Prinz [2], Daniel Weimar [2], Christian Deutscher [3], and Thorsten Upmann [2]

[1] German Sport University Cologne

[2] University of Duisburg-Essen

[3] University of Paderborn

Dr. Pamela Wicker is a senior lecturer in the Department of Sport Economics and Sport Management. Her research interests include economics of sport consumer behavior, sport participation, and financing of non-profit sport clubs.

Prof. Dr. Joachim Prinz is a professor in the Department of Managerial Economics in the Mercator School of Management. His research interests include labor market and team sports economics.

Daniel Weimar is a PhD student in the Department of Managerial Economics in the Mercator School of Management. His research interests include empirical sports and media economics.

Christian Deutscher, PhD, is a scientific assistant in the Faculty of Business Administration and Economics. His research interests include salary determination and effort provision in tournaments.

Dr. Thorsten Upmann is a professor in the Department of Managerial Economics in the Mercator School of Management. His research interests include labor supply decisions, labor market negotiations, tax competition, theory of taxation, as well as environmental and resource economics.

Table 1. Overview of variables

Variable        Description                                   Scale

Market value

MV              Market value at the end of half               Metric
                season (in [euro])
MV_LOG          Logarithm of VALUE                            Metric

MV_DIFF         Percentage change in market value             Metric
                from previous to current half season

MV_1            Market value in previous half                 Metric
                season (in [euro])

Human capital

AGE             Age in years                                  Metric

AGE2            AGE squared                                   Metric

GERMAN          Nationality (1=German)                        Dummy

HIGH            Height of player (in cm)                      Metric

POSITION        Position of the player played in              Dummy
                most of the games of one half season
                (central defense, left wing defense,
                right wing defense, defense midfield,
                right wing midfield, left wing midfield,
                offense midfield, attack)

APPEAR          Number of appearances in half season          Metric

TRANSFER        Transfer at the end of half season (1=yes)    Dummy

TIME_CLUB       Time played for the club (in years)           Metric

Productivity

SP              Scoring Performance (goals+assists)           Metric
                per minute

EFFIC           Efficiency (rate) of ball contacts            Metric
                (=[flanks+ right passes+ shots]/ball
                contacts)

TACK            Tackling rate (=tackles won/all tackles)      Metric

NAT             National player in the player's               Dummy
                home country (2=yes)

NAT_TOP         National player in one of the top             Dummy
                FIFA ranked nations (2=yes)
Effort

RUN             Average number of intensive runs              Metric
                (i.e., >20km/h) per game (per minute)

RUN2            RUN squared                                   Metric

DIST            Average running distance per game
                (km per minute) Metric

DIST2           DIST squared                                  Metric

Controls

TEAM1-TEAM21    Team dummies                                  Dummy

Table 2. Descriptive statistics (n=446 players)

Variable    Obs.   Mean         SD           Min          Max

MV          877    5126739.00   6426055.00   200000.00    42000000.00
MV_LOG      877    14.95        0.97         12.21        17.55
MV_DIFF     867    0.1712654    0.6850334    -0.6428571   9.00
AGE         877    25.90        3.78         17.85        35.89
AGE2        877    684.84       200.74       318.55       1287.89
GERMAN      877    0.44         0.50         0.00         1.00
HIGH        877    183.42       6.26         164          198
APPEAR      877    7.44         4.92         1.00         17.00
TRANSFER    877    0.18         0.38         0.00         1.00
TIME_CLUB   877    2.78         2.79         0.01         14.41
SP          877    0.00         0.00         0.00         0.03
EFFIC       877    0.55         0.10         0.17         0.82
TACK        877    0.12         0.03         0.00         0.23
NAT         877    0.46         0.50         0.00         1.00
NAT_TOP     877    0.11         0.31         0.00         1.00
RUN         877    0.58         0.14         0.23         1.11
RUN2        877    0.36         0.17         0.05         1.23
DIST        877    0.12         0.01         0.06         0.15
DIST2       877    0.01         0.00         0.00         0.02

Table 3. Fixed-effects models for MV_LOG (model 1; n=877;
displayed are the coefficients, t-values in parentheses)

               FE1                  FE2

MV_1           /                    /
AGE            1.479 (9.09) ***     1.427 (8.83) ***
AGE2           -0.029 (-9.87) ***   -0.028 (-9.70) ***
GERMAN         /                    /
HIGH           /                    /
APPEAR         0.021 (6.68) ***     0.021 (6.94) ***
TRANSFER       -0.154 (-5.83) ***   -0.157 (-5.97) ***
POSITION       Incl.                Incl.
TIME_CLUB      0.067 (1.94) *       0.078 (2.64) ***
SP             11.736 (3.55) ***    -5.999 (-0.36)
EFFICIENCY     0.033 (0.17)         -0.105 (-0.16)
TACK           0.750 (1.70) *       -3.805 (-2.38) **
NAT            0.029 (0.19)         0.055 (0.40)
NAT_TOP        0.129 (0.83)         0.086 (0.60)
RUN            /                    0.390 (0.41)
RUN2           /                    -0.985 (-1.75) *
RUN*SP         /                    25.836 (1.02)
RUN*EFFIC      /                    0.256 (0.25)
RUN*TACK       /                    7.559 (2.81) ***
DIST           /                    /
DIST2          /                    /
DIST*SP        /                    /
DIST*EFFIC     /                    /
DIST*TACK      /                    /
TEAM1-TEAM21   Incl.                Incl.
Constant       -4.29 (-1.88) *      -3.37 (-1.47)
R2             0.18                 0.20
F              9.93***              9.20 ***

               FE3

MV_1           /
AGE            1.475 (8.97) ***
AGE2           -0.029 (-9.84) ***
GERMAN         /
HIGH           /
APPEAR         0.022 (7.03) ***
TRANSFER       -0.152 (-5.78) ***
POSITION       Incl.
TIME_CLUB      0.075 (2.24) **
SP             11.444 (0.27)
EFFICIENCY     -0.673 (-0.48)
TACK           -7.388 (-1.89) *
NAT            0.052 (0.39)
NAT_TOP        0.136 (1.00)
RUN            /
RUN2           /
RUN*SP         /
RUN*EFFIC      /
RUN*TACK       /
DIST           -8.573 (-0.85)
DIST2          8.554 (0.17)
DIST*SP        -1.625 (0.00)
DIST*EFFIC     5.913 (0.54)
DIST*TACK      66.148 (2.07) **
TEAM1-TEAM21   Incl.
Constant       -3.20 (-1.36)
R2             0.20
F              9.08 ***

Note. * p<.1; ** p<.05; *** p<.01. Robust standard errors
are reported (White, 1980).

Table 4. Random-effects models for MV_DIFF (model 2; n=867;
displayed are the coefficients, t-values in parentheses)

               RE1                  RE2

MV_1           -0.000 (-5.76) ***   -0.000 (-5.77) ***
AGE            -0.619 (-5.38) ***   -0.618 (-5.35) ***
AGE2           0.010 (4.86) ***     0.01 (4.81) ***
GERMAN         0.045 (0.68)         0.044 (0.68)
HIGH           -0.003 (-0.59)       -0.004 (-0.75)
APPEAR         0.028 (5.53) ***     0.027 (5.31) ***
TRANSFER       -0.101 (-2.09) **    -0.101 (-2.12) **
POSITION       Incl.                Incl.
TIME_CLUB      0.002 (0.16)         0.002 (0.18)
SP             14.283 (3.25) ***    -11.666 (-0.65)
EFFICIENCY     -0.034 (-0.11)       0.425 (0.49)
TACK           0.617 (1.04)         0.473 (0.22)
NAT            -0.029 (-0.54)       -0.024 (-0.44)
NAT_TOP        0.277 (3.30) ***     0.278 (3.28) ***
RUN            /                    0.823 (0.72)
RUN2           /                    -0.726 (-0.96)
RUN*SP         /                    40.149 (1.42)
RUN*EFFIC      /                    -0.808 (-0.65)
RUN*TACK       /                    0.39 (0.11)
DIST           /                    /
DIST2          /                    /
DIST*SP        /                    /
DIST*EFFIC     /                    /
DIST*TACK      /                    /
TEAM1-TEAM21   Incl.                Incl.
Constant       -                    -
[R.sup.2]      0.29                 0.30
Wald-Chi       285.36 ***           315.05 ***

               RE3

MV_1           -0.000 (-5.79) ***
AGE            -0.618 (-5.38) ***
AGE2           0.01 (4.86) ***
GERMAN         0.046 (0.70)
HIGH           -0.003 (-0.62)
APPEAR         0.028 (5.39) ***
TRANSFER       -0.101 (-2.10) **
POSITION       Incl.
TIME_CLUB      0.002 (0.14)
SP             67.426 (1.40)
EFFICIENCY     0.906 (0.54)
TACK           1.225 (0.23)
NAT            -0.029 (-0.55)
NAT_TOP        0.280 (3.32) ***
RUN            /
RUN2           /
RUN*SP         /
RUN*EFFIC      /
RUN*TACK       /
DIST           3.985 (0.27)
DIST2          7.935 (0.11)
DIST*SP        -432.552 (-1.12)
DIST*EFFIC     -7.931 (-0.57)
DIST*TACK      -4.618 (-0.11)
TEAM1-TEAM21   Incl.
Constant       9.14 (4.30) ***
[R.sup.2]      0.30
Wald-Chi       -

Note. * p<.1; ** p<.05; *** p<.01. Robust standard errors
are reported (White, 1980).