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TALENT AND/OR POPULARITY: WHAT DOES IT TAKETO BE A SUPERSTAR?

EGON FRANCK and STEPHAN NUESCH∗

We show that both talent and popularity significantly contribute to stars’ marketvalues in German soccer. The talent-versus-popularity controversy on the sourcesof stardom goes back to Rosen (1981) and Adler (1985). All attempts to resolvethe controversy empirically face the difficulty of accurately identifying talent. Inprofessional sports, rank-order tournaments help in ascertaining talent. Analyzinga team setting, we use 20 different performance indicators to estimate a player’stalent according to his ability to increase the team’s winning probability. (JEL J31,J44, L83)

The phenomenon of Superstars, wherein small num-bers of people earn enormous amounts of money anddominate the activities in which they engage, seemsto be increasingly important in the modern world(Rosen 1981, 845).

I. INTRODUCTION

This, the opening sentence of SherwinRosen’s seminal paper “The Economics ofSuperstars,” applies today more than ever. Tech-nological change has increased the scope and theintensity of the so-called winner-takes-all mar-kets in the last decades. The central questionaddressed in this article is: What does it take tobe a superstar? Why do some artists, media stars,professional athletes, or executives earn dispro-portionately high salaries while others receivecomparatively low remuneration? In the liter-ature, there are basically two competing—butnot mutually exclusive—theories of superstarformation proposed by Rosen (1981) and Adler

*We are grateful to Leif Brandes, Stefan Szymanski,Rainer Winkelmann, two anonymous referees, and to theseminar participants at the Western Economic Associationconference 2007 in Seattle, the Workshop of Commissionof Organization 2008 in Munich, and the Annual Meetingof the German Academic Association for Business Research2008 in Berlin for helpful comments. Remaining errors are,of course, our own.

Franck: Full Professor, Institute for Strategy and Busi-ness Economics, University of Zurich, Plattenstrasse 14,Zurich 8032, Switzerland. Phone 0041-44-634-2845, Fax0041-44-634-4348, E-mail [email protected]

Nuesch: Senior Teaching and Research Associate, Insti-tute for Strategy and Business Economics, Universityof Zurich, Plattenstrasse 14, Zurich 8032, Switzer-land. Phone 0041-44-634-2914, Fax 0041-44-634-4348,E-mail [email protected]

(1985).1 Although Sherwin Rosen explains howsmall differences in talent translate into largedifferences in earnings, Moshe Adler argues thatsuperstars might even emerge among equallytalented performers due to the positive networkexternalities of popularity.

Empirical tests of the different driving forcesof superstar salaries have proved to be very dif-ficult because an objective measure of a star’stalent is often hard to find and even harderto quantify (Krueger 2005). For example, whatcharacterizes the talent of a pop music star? Theliterature offers different approaches. Hamlen(1991, 1994) uses the physical concept of “voicequality,” which measures the frequency of har-monic content that singers use when they singthe word “love” in one of their songs—butis such a “high-quality” voice really a decid-ing factor for success in pop music? Krueger(2005) measures star quality by the number ofmillimeters of print columns devoted to eachartist in The Rolling Stone Encyclopedia of Rock& Roll. Nevertheless, as he admits, this mea-sure reflects the subjective importance the edi-tors of the Encyclopedia implicitly devote toeach artist, which may correlate both with theartist’s talent and with his/her popularity. In

1. There are, of course, other superstar theories as well(e.g., Borghans and Groot 1998; Frank and Cook 1995;Kremer 1993; MacDonald 1988). The basic principles ofRosen (1981) and Adler (1985) have remained presentthroughout, however.

ABBREVIATIONOLS: Ordinary Least Squares

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Economic Inquiry(ISSN 0095-2583)Vol. 50, No. 1, January 2012, 202–216

doi:10.1111/j.1465-7295.2010.00360.xOnline Early publication December 22, 2010© 2010 Western Economic Association International

FRANCK & NUESCH: TALENT AND/OR POPULARITY 203

team settings, the difficulty of accurately mea-suring star talent is even greater, as individualcontributions to team output are mostly unclear.However, the empirical relevance of stars withinteams is undoubted. Star CEOs in top manage-ment teams, lead singers of rock bands, and starathletes on sports teams are just a few examplesof superstars embedded in teams.

This article argues that rank-order tourna-ments in professional sports allow a more accu-rate determination of talent than in the arts.Even though each athlete’s performance is alsoaffected by random events (luck) or other factorslike weak fitness, in individual sports it can typ-ically be assumed that the most talented athleteenjoys the highest probability of winning. Aswe examine superstars in a team setting, namelyin professional soccer, we first estimate a teamproduction function to identify the playing char-acteristics that significantly influence the proba-bility of a team winning. To do so, we use thedetailed statistics of the Opta Sports Data Com-pany, which counts and classifies every touchof the ball during the game by each player. In asecond step, we use the individual performancestatistics of all variables that have proved to becritical for winning as indicators of the player’stalent. We estimate the impact of talent, popular-ity, and various controls on the player’s marketvalue, employing individual panel data from thehighest German soccer league. A player’s pop-ularity is measured by the annual press public-ity he receives in over 20 different newspapersand magazines, purged of the positive influencesof on-field performance so that our popularityindicator captures the nonperformance-relatedcelebrity status of a player.

We find empirical evidence that both talentand nonperformance-related popularity increasethe market values of soccer stars. The marginalinfluence of talent is magnified near the top endof the scale, as postulated by Rosen’s star the-ory. Although one additional goal scored perseason increases a player’s market value by¤0.06 million at the mean, the impact increasesto ¤0.25 million at the 95% quantile. Usingteam revenue data, we find that the magnitudeof the talent effect is plausible given the largereturns to scale in German soccer.

The remainder of the article is organized asfollows. Section II illustrates the two alterna-tive theories of superstar formation and theirhypotheses. Section III presents the relevantempirical literature. In Section IV, we explainthe difficulty of adequately measuring talent and

the advantages the sports industry offers. Thepopularity measure is described in Section V.Section VI includes the main empirical analy-sis that relates the stars’ market values to theircharacteristics before we conduct two sensitivityanalyses in Section VII. Section VIII discussesthe results and their possible implications.

II. THEORIES OF SUPERSTAR FORMATION

Marshall (1947) has already pointed out thatinnovations in technology and mass productionwill lower the per-unit price of quality goods andultimately allow higher-quality goods to obtaina greater market share. In 1981, Sherwin Rosennamed this effect the “superstar phenomenon.”Extraordinary salaries earned by superstars aredriven by a market equilibrium that rewards tal-ented people with increasing returns to ability.The key to the high earnings of superstars lies inthe vast audience they are able to reach becauseof scale economies. Superstars arise in mar-kets in which the production technology allowsfor joint consumption. For example, if one per-son watches a tennis game on television, thisdoes not diminish someone else’s opportunityto watch it as well. In superstar industries, pro-duction costs do not rise in proportion to thesize of the seller’s market. This enables a fewor just one supplier to serve the whole market.

However, large economies of scale do notguarantee high salaries for a small numberof stars unless the market demand becomeshighly concentrated on their services. In thesuperstar literature, the demand for superstarservices is basically driven by two distinctbut not mutually exclusive factors: superiortalent, according to Rosen (1981), and networkexternalities of popularity, according to Adler(1985).

First, market demand may be concentratedon superstars because of their superior talent.Rosen (1981) argues that poorer quality is onlyan imperfect substitute for higher quality. Thus,people prefer consuming fewer high-quality ser-vices to more of the same service at moderatequality levels: “(. . .) hearing a succession ofmediocre singers does not add up to a single out-standing performance” (Rosen 1981, 846). Mostpeople tend not to be satisfied with the perfor-mance of a less talented but cheaper artist whenthey are able to enjoy a top performance, evenif the costs are somewhat higher (Frey 1998).This sort of imperfect substitutability applies inparticular to status goods or gifts: To celebrate a

204 ECONOMIC INQUIRY

special occasion, people search not for an aver-age restaurant meal or bottle of wine, but forthe best (Frank and Cook 1995). According toRosen (1981), small differences in talent amongperformers are magnified into large earnings dif-ferentials. Rosen stars are simply better thantheir rivals. In professional sports, they attractfans with their outstanding performances.

Network externalities of popularity offer asecond explanation of why demand may behighly focused on the services of a few super-stars. In contrast to the network externalities inthe typical standardization literature,2 the net-work externalities of superstars are not confinedto issues of technological compatibility or alarger variety of complements. Moshe Adler,rather, suggests a cognitive and social form ofnetwork externalities. Adler (1985) argues thatthe marginal utility of consuming a superstarservice increases with the ability to appreci-ate it, which depends not only on the star’stalent, but also on the amount of star-specificknowledge the consumer has acquired. Thisspecific knowledge—called consumption capi-tal—is accumulated through past consumptionactivities or by discussing the star’s performancewith likewise knowledgeable individuals. Thelatter effect gives rise to positive network exter-nalities. The more popular the artist is, the easierit becomes to find other fans. Economies ofsearching costs imply that consumers are betteroff patronizing the most popular star as long asothers are not perceived to be clearly superior.

Stardom is a market device to economize on learn-ing costs in activities where “the more you know themore you enjoy.” Thus stardom may be independentof the existence of a hierarchy of talent (Adler 1985,208–09).

Adler (1985) considered the emergence ofa superstar from a group of equally talentedartists to be simply because of luck, for example,initially being known by slightly more peo-ple. Adler (2006), however, recognizes that luckcannot be the only mechanism. Aspiring super-stars do not usually entrust selection ahead oftheir peers to pure chance. Instead, they con-sciously use publicity, such as appearances ontalk shows, and coverage in tabloids, maga-zines, newspapers, and the Internet to signaland strengthen their popularity. Adler (2006)

2. See, for example, Katz and Shapiro (1985) or Farrelland Saloner (1985).

emphasizes that consumption capital is acquirednot only through past consumption activitiesand discussions, but also by reading about thestar’s performance in newspapers, in magazines,and on the Internet. On the one hand, publicitydirectly reduces the costs of learning about starservices and on the other hand, it is also a goodindicator of the star’s popularity in society.

Both Rosen (1981) and Adler (1985) agreethat superstars provide services of superior per-ceived quality. But according to Rosen (1981),the star’s talent alone determines the perceivedquality. Adler (1985) argues that factors otherthan talent, like popularity, matter too. Thus,Adler’s superstar theory does not contradictRosen’s star model, but rather supplements it. Inteam sports, for example, superstars may havepersonal appeal or charisma, an element thatattracts fan interest even after controlling fortheir contribution to the team’s (increased) play-ing quality.

III. RELEVANT EMPIRICAL LITERATURE

In this section, we give a brief introduction tothe empirical literature on superstar emergence.A first body of literature (Hamlen 1991, 1994;Krueger 2005; Lucifora and Simmons 2003)relates star remuneration to talent proxies butdoes not include separate explanatory variablesdistinguishing the Adler effect. A second strandof literature (Chung and Cox 1994; Giles 2006;Spierdijk and Voorneveld 2009) tests whethersuperstar market outcomes could be merely theresult of a probability mechanism determiningthat “outputs will be concentrated among a fewlucky individuals” (Chung and Cox 1994, 771,emphasis in original), regardless of talent. Thisconcept is, in its spirit, similar to the ideas ofAdler (1985), although the question regardingthe underlying reason for the consumer’s deci-sion to buy a star’s service remains unanswered(Schulze 2003).

A third body of related literature uses bothtalent and popularity proxies in its empiricalframework. Lehmann and Schulze (2008), aswell as Franck and Nuesch (2008), test the influ-ence of on-field performance and media public-ity on the emergence of superstars in Germansoccer. Regressing salary proxies of 359 playerson three performance measures (goals, assists,and tackles) and the number of citations in theonline version of the soccer magazine Kicker,Lehmann and Schulze (2008) discover that nei-ther performance nor publicity can explain the


salaries of superstars at the 95% quantile. Franckand Nuesch (2008) find contrary evidence: bothtalent, as measured by expert opinions, and pop-ularity increase the demand for star players.Both Lehmann and Schulze (2008) and Franckand Nuesch (2008) use cross-sectional samplesand consider the talent indicators as exogenouslygiven without proving their relevance for a soc-cer game.

Salganik, Dodds, and Watts (2006) use anexperimental study to investigate the talent andpopularity hypotheses in an artificial culturalmarket. The participants (14,341) downloadedpreviously unknown songs either (a) with or(b) without knowledge of the previous partic-ipants’ choices, the participants having beenrandomly assigned to one of these two exper-imental conditions. In this experiment, know-ing the choices of other customers contributedto both the inequality and the unpredictabil-ity of the artificial music market. Social influ-ence increases the skewness of the marketdistribution and the unpredictability of success.The latter is analyzed as the extent to whichtwo “worlds” with identical songs, identicalinitial conditions, and indistinguishable popula-tions generate different outcomes. As the out-come is unpredictable even when consumers hadno knowledge about download statistics, theyconclude that no measure of a song’s qualitycan reliably predict success.

IV. TALENT DETERMINATION

One of the main obstacles to testing superstartheories is the “inherent difficulty of objectivitymeasuring talent or quality in a meaningful met-ric apart from economic success” (Connolly andKrueger 2006, 696). Throsby (1994, 19) writes:

While it is quite plausible to take estimated earningsfunctions and to attribute at least some of the (oftenlarge) unexplained residual to differences in talent,such a hypothesis remains untestable when no inde-pendent measure of talent is forthcoming.

Hamlen (1994, 405) calls a “sour grapes con-clusion” any conclusion drawn when scholarsbelieve they have found empirical evidence ofthe superstar phenomenon by examining onlymeasures of success and failing to compare theseto some objective and external measure of qual-ity or ability. “A proper test of the superstarphenomenon requires that the measure of ‘qual-ity’ (‘ability’) be an external measure” (Hamlen

1994, 399). As innate talent is unobservable,Rosen (1981) argues that any cardinal measureof talent must rely on measurements of actualoutcomes.

The first issue in talent determination is itsvalidity. Although some pop fans love the musicof Madonna, others may hate it. In the pop-ular music industry, talent is hard to define.Some music appeals to a subset of listeners butnot to others because, in the arts, there is “anintrinsically subjective component to quality”(Connolly and Krueger 2006, 697). Both Rosen(1981) and Adler (1985), however, assume iden-tical consumers who demand the same unspeci-fied artistic activity. They argue that a diversityof tastes does not change the basic mechanismsof superstar formation, but simply confines aseller’s market. Consumers of similar taste con-stitute a market with its own stars. As statedpreviously, Hamlen (1991) uses the harmoniccontent of the voice as a singer’s talent indicator.Harmonic content is a clearly quantifiable vari-able that measures the “richness” and “depth” ofthe singer’s voice. Still, does harmonic contentof the voice really matter? In classical musicor opera, presumably yes. In the case of popor rock music, however, we have strong doubtsabout the relevance of the harmonic content ofthe voice. More important factors for the successof such singers are probably charm, sex appeal,or the show on stage. Hence, one possibility fordealing with heterogeneous tastes is to use spe-cific talent indicators only within a genre; oth-erwise, how is it possible to compare a chamberorchestra with a heavy metal band? Neverthe-less, quality perceptions often differ even withina particular genre.

A second obstacle in empirical superstarstudies is the measurement of talent. Theabsence of “natural units” for measuring talent isa major limitation of empirical superstar studiesin the arts (Connolly and Krueger 2006). Evenif all pop fans agreed that charisma on stage isthe most important ability of a pop star, schol-ars would still face the difficulty of capturingcharisma on a metrical scale. Talent is inherentand thus hard to quantify.

In professional sports, the empirical problemsdescribed above are less serious because validtalent measures are easier to find than in otherfields like the arts or entertainment activities(Schulze 2003). In professional sports, the win-ners are determined by a set of well-establishedtournaments relying either on objective qual-ity indicators and/or on institutionalized voting


procedures by proven expert judges. Althoughdifferent effort levels and uncontrollable factorslike incorrect refereeing decisions or pure luckmight also affect the final result, the competitionis generally won by the most talented athlete.In individual sports, the winning probability is,therefore, a valid and measurable indicator of theathlete’s talent. Even though a high likelihoodof winning marks great sporting success, it doesnot necessarily imply enormous salaries as well.Or inversely, even less talented and thus lesssuccessful athletes might earn superstar wages.3

So, there is no danger of a tautological Rosenstar definition.

In team settings, talent determination ismore complex. It requires a proper evalua-tion of the team production technology becauseteams—and not individuals—compete in rank-order tournaments. In this article, the (Rosen)talent of a soccer star is considered the player’sability to increase the winning chances of histeam. This definition of talent represents pureon-the-field prowess. Other facets of a star thatattract fans, such as his celebrity or pop iconstatus, are as Adler (1985, 211) writes, “factorsother than talent.”

Using team-level data for all games in thehighest German soccer league during five sea-sons (2001/2002–2005/2006), we empiricallyestimate a team production function in order toidentify all playing elements that significantlyincrease (or reduce) the team’s winning proba-bility. To do so, we make use of a large seriesof performance categories, namely shots on tar-get; shots off target; shots hitting the frame ofthe goal; clearances, blocks, and interceptions;saves to shots ratio of the goalkeeper; numberof times the ball was caught by the goalkeeper;number of times the ball was dropped by thegoalkeeper; number of red and yellow cards;number of fouls, number of “dangerous” fouls(conceded in the own third of the playing area),penalties, and handballs conceded, as well as thesuccess rate of passes, flicks, crosses, dribbles,

3. The Russian tennis player Anna Kournikova servesas a good illustration here. She did not achieve anysignificant success in single tournaments and her overallsingles ranking was never better than eight. Nevertheless,in 2002 she was the second highest earner in femaletennis behind Venus Williams, the number one at the time.In Kournikova’s case, sponsorships and other lucrativecommercial opportunities have arisen not from a consistentrecord of successful performances on the tennis court, butinstead as a consequence of an image of sexual attractivenessand an associated media profile.

and tackles, respectively. These data are pro-vided by the Opta Sports Data Company, whichcounts and classifies every touch of the ball byeach player during the game based on live andoff-tape analysis of every match by a team ofspecialist analysts.

We find evidence that team success is pos-itively affected by the number of goals andassists; the number of clearances, blocks, andinterceptions; the number of shots on target; thesaves to shots ratio of the goalkeeper; and the(average) success rate of crosses. The numberof shots off target, the number of red and yel-low cards, and the number of penalties concededreduce the winning likelihood of a team. Allother performance indicators do not significantlyinfluence the game’s result. For a more detaileddescription of the team production estimation aswell as a table showing the results, we refer toa previous working paper version of this article(Franck and Nuesch 2009).

We consider all field plays that significantlyaffect the team’s winning chances as charac-teristics of the unobserved (good or bad) tal-ent of a player. The descriptive statistics ofthe individual talent variables are illustrated inTable 1. In the following section, we explainhow we measure the nonperformance-relatedpopularity of a player, before both talent andpopularity are related to the player’s marketvalue.

V. NONPERFORMANCE-RELATED POPULARITY

In line with Adler (2006), we proxy a player’spopularity based on press publicity. Usingthe LexisNexis database, which contains morethan 20 different quality nationwide newspa-pers (including Frankfurter Allgemeine Zeitung,Suddeutsche Zeitung, Stuttgarter Zeitung, Ham-burger Abendblatt, Die Welt, taz, Berliner Mor-genpost, Financial Times Deutschland ) as wellas weekly magazines (including Der Spiegel,Stern, Bunte), we count the number of articles inwhich a player is mentioned at least once. Thesearch string included the first and last names ofthe player, as well as the name of the club hewas engaged by during the corresponding sea-son, starting from July 1 at the beginning of theseason and lasting until June 30 at the end ofthe season.

If talent is measured by the player’s on-fieldperformance and popularity by the player’s presspublicity, the concepts of talent and popularityare likely to be positively correlated because of


TABLE 1Variables and Descriptive Statistics

Variable Description M SD

Dependent variableMarket value Logarithm of a player’s market value at the end of the

season according to the Kicker soccer magazine14.28 0.73

Independent variablesTalent variables

Goals Goals 2.52 3.77Assists Assists 1.79 2.25Shots on target Number of shots on target 8.41 10.08Shots off target Number of shots off target 10.37 10.07Clearances, blocks, interceptions Clearances, blocks and interceptions 66.96 76.08Saves to shots ratio Save to shots ratio of the goalkeeper 0.06 0.19Cross success rate % successful crossings 0.21 0.17Red cards Number of red cards 0.18 0.43Yellow cards Number of yellow cards 3.29 2.61Penalty conceded Number of fouls conceded in penalty area 0.19 0.48

Popularity variableNonperformance-related press citations Residuals of a regression of the logarithm of citations

in over 20 German newspapers and weeklymagazines on individual talent measures

0.00 1.24

Control variablesAge Player’s age 25.93 4.06Age squared Squared term of age 688.76 215.48Appearances Appearances in the considered season 20.94 9.24Previous appearances Accumulated appearances before the considered season 70.75 79.61Relegation Club was relegated at the end of the season 0.03Number of players 605Observations 1,370

Notes: The model also includes an intercept as well as position and team fixed effects.

the performance-related publicity. To clearly dif-ferentiate between Rosen’s and Adler’s super-star theory, we need a popularity measure thatis unrelated to the performance of the player.Thus, we proxy a player’s nonperformance-related star attraction by the residuals εit of thefollowing equation:

ln(Press citationsit ) = α + βx ′it + εit ,(1)

where the logarithm of the number of articlesmentioning the player’s name is regressed onthe critical individual on-field performance mea-sures x ′

it according to the previous section.4 Theordinary least squares (OLS) estimation resultsof Equation (1) are illustrated in Table A1 inthe appendix of this article. Most on-field per-formance measures significantly increase presscoverage, with the highest magnitudes for goals,the saves to shots ratio of the goalkeeper, and

4. We are grateful to an anonymous referee for propos-ing this procedure.

assists. The residuals of Equation (1) character-ize a player’s publicity that cannot be explainedby his sporting performance on the pitch; forexample, media publicity that is a result of thestar having an affair or consciously presentinghimself not only as a soccer star but as a popicon as well.5

5. The ceteris paribus condition in multiple regressionanalysis is technically the same as if one were to introducethe residuals of a regression of the considered explana-tory variable on all other explanatory variables (Wooldridge2003, 78–79). The estimated popularity effect would there-fore be the same if we directly introduced the logarithmof press citations into the model. The size of the talenteffect would be comparably lower, however, as the posi-tive correlation with performance-related popularity wouldbe partialed out. By introducing the nonperformance-relatedpublicity of a player that—per construction—does not cor-relate with a player’s performance, we are able to estimateunrestricted talent effects. In other words, we use the resid-uals of Equation (1) as a measure of a player’s popularity,because we want to net out the influence of performance onpublicity, but not the other way around.


VI. SUPERSTAR DETERMINANTS

A. Data Sample and Dependent Variable

The different theories of superstar formationare tested using panel data for players appearingin the highest German soccer league during fiveseasons (2001/2002 until 2005/2006). Althoughmany detailed statistics on individual produc-tivity are available for players in top Europeanleagues, individual salary data are (unlike for theUS Major Leagues) unfortunately not available.German soccer clubs are not required to publishplayer salaries. In 1995, the well-respected soc-cer magazine Kicker, however, began to publishestimates of the market values of the playersappearing in the highest German soccer league.As the market value proxies have been estimatedin a systematic manner for several years by analmost unchanged, qualified editorial board, theyare likely to be consistent and have, therefore,been used in several empirical studies so far(e.g., Franck and Nuesch forthcoming; Haas,Kocher, and Sutter 2004; Kern and Sussmuth2005; Torgler and Schmidt 2007). In line withmost of the previous studies,6 we also use themarket value proxies provided by the Kickersoccer magazine. Kicker is the only source thatprovides systematic panel data and its reliabil-ity is judged to be high in the review articles ofTorgler and Schmidt (2007) and Frick (2007).We additionally test the reliability of the marketvalue data by comparing a Kicker subsamplewith a cross section of market values providedby a second independent source, the webpagewww.transfermarkt.de. The market value prox-ies of the two sources are highly correlated(correlation is 0.89) and the estimation resultsare very similar if the Transfermarkt data areemployed, as we show in our first sensitivityanalysis in Section VII. The fact that separateregressions using different data sources lead tothe same results increases confidence in the reli-ability of our results.

Citing the examples of full-time comedi-ans and soloists, Rosen (1981) considered starsas individual service providers with enormousearnings. The earnings of painters, authors, orathletes in individual sports are directly deter-mined by the market potential of their ser-vices. So, market value and remuneration are,

6. Other studies use cross-sectional samples of remu-neration estimates of players published in Welt am Sonntag(Lehmann and Weigand 1999), in Sportbild (Lehmann andSchulze 2008), or on the webpage www.transfermarkt.de(Franck and Nuesch 2008).

generally speaking, the same. In our case, super-stars cannot provide the service alone. Soc-cer stars are part of teams and receive certainsalary payments, bonuses, or signing fees thatdo not necessarily correspond to their marketpotential. The predetermined (base) salary, forexample, does not increase if the player per-forms exceptionally well. Bonus payments aretypically contingent on a large set of confi-dential terms and conditions. Signing fees ortransfer values depend on (among other factors)the bargaining power of the buying and sellingclubs. Thus, market values should better reflectthe value generation potential of a player thanpure salaries. The Kicker market value prox-ies incorporate not only salaries but also sign-ing fees, bonuses, transfer fees, and possiblyeven a remaining producer surplus. However,the market value proxies do not include individ-ual endorsement fees.

In line with Rosen (1981), we define super-stars as the players at the top end of the marketvalue distribution. Although the median playeris valued at ¤1.25 million, star players at the95% quantile are exchanged for ¤5.5 million.Seventy-five percent of the players in the high-est German soccer league have a market value ofone million Euros and above. Table 2 illustratesthe market values at different quantiles.

For the empirical model, we use the natu-ral logarithm of the market values expressedin Euros and adjusted for inflation. During theconsidered time frame (2001 until 2005), theplayers’ market values have remained rather sta-tionary in German soccer.

B. Control Variables

Besides the indicators of individual talent andpopularity described in Sections IV and V, wealso use several control variables to eliminate

TABLE 2Quantiles of the Market Value Distribution

Quantiles Kicker Market Values (¤)

1% 200,0005% 500,000

10% 750,00025% 1,000,00050% 1,500,00075% 2,500,00090% 4,500,00095% 5,500,00099% 8,000,000


alternative explanations, such as age, experi-ence, tactical position, and team effects. Anoverview of all variables is given in Table 1.As several studies (e.g., Lucifora and Simmons2003; Torgler and Schmidt 2007) show that asoccer player’s age has a positive but diminish-ing impact on his salary, we control for age andage squared. In addition, we hold the numberof present and past appearances in the highestGerman league constant to account for the expe-rience of a player. Furthermore, we incorporateteam dummies, as (unobserved) team hetero-geneity may exert a significant influence on aplayer’s market value (Idson and Kahane 2000).Somebody who is on the squad of the teamthat wins the championship enjoys much greaterpublicity and financial rewards than someone ona team that is relegated to the next lower league.Position dummies are used to control for spe-cific effects resulting from the tactical positionof a player.

As the Kicker soccer magazine publishes theestimated market values at the beginning of anew season, we use the values of the next seasonas dependent variable. This implies that we havemissing observations for the dependent variablewhenever a player leaves the league becauseKicker estimates the market values only for theplayers engaged by a top-division German team.If so-called sample attrition is driven by unob-servable factors that also influence the dependentvariable in the main equation, our estimates maybe distorted by selection bias. Thus, the valid-ity of the results largely depends on whether theattrition status is random after conditioning ona vector of covariates. As in German soccer, theweakest three teams, including most of the squadmembers, are relegated to the next lower leagueand, therefore drop out of the sample, we includea dummy variable Relegation that equals 1 ifthe player’s team is demoted (0 otherwise) asan additional control variable. Controlling fora player’s talent, popularity, and experience, aswell as the team’s relegation status, we can-not reject random attrition status using the testfor sample attrition bias proposed by Fitzgerald,Gottschalk, and Moffitt (1998).7

C. Identification Strategy

OLS estimates tell little about tail behavior,because they lead to an approximation to the

7. A table showing the detailed results of this test isincluded in the working paper version of this article (Franckand Nuesch 2009).

mean of a conditional distribution. The OLSprocedure will therefore not be able to capturethe superstar phenomenon correctly. The quan-tile regression approach (Koenker and Bassett1978), however, allows one to characterize aparticular point in the conditional (asymmet-ric) distribution. It minimizes an asymmetri-cally weighted sum of absolute errors where theweights are functions of the quantile of inter-est (θ):

minβ

1

n

⎧⎨⎩

∑i:yit≥x′

itβ

θ|yit − x ′itβ|(2)

+∑

i:yit≤x′it

β

(1 − θ)|yit − x ′itβ|

⎫⎬⎭ .

The application of quantile methods to paneldata can be problematic (Koenker 2004).Although, in the linear regression model, fixedeffects methods can account for the constantunobserved heterogeneity of a player as a linearintercept, quantile regressions require a constantdistributional individual effect. If the numberof time periods is high and the number ofcross-sectional observations is low, the estima-tion of such a distributional individual effect ispossible by including cross-sectional dummies(Koenker 2004). In our setting, however, theinclusion of player dummies would clearly leadto the incidental parameters problem, becausewe have a large number of cross-sectional obser-vations and only one to five time periods. Thus,we use a pooled regression approach to esti-mate the conditional distribution of the depen-dent variable. As the observations of the sameplayer are unlikely to be independent, thestandard asymptotic-variance formula (Koenkerand Basset 1978) and the standard bootstrapapproach to estimate the standard errors cannotbe applied. Instead, a given bootstrap sampleis created by repeatedly drawing (with replace-ments) the same player from the sample ofplayers. In doing so, we allow for serial errorcorrelation between the observations of the sameplayer. As we run 1,000 bootstrap replications,the estimates of the robust standard errors arerather stable (Koenker and Hallock 2000).

D. Results

Table 3 illustrates the estimation results.Besides the 95% quantile regression, we alsopresent the pooled OLS estimates, as well as


TABLE 3Determinants of a Star’s Market Value

Dependent Variable Logarithm of Individual Market Values According to Kicker

Estimation Approach OLS Fixed Effects 95% Quantile Reg.

β-coef. SE β-coef. SE β-coef. SE

Talent variablesGoals 0.039∗∗ 0.009 0.040∗∗ 0.009 0.045∗∗ 0.016Assists 0.039∗∗ 0.007 0.038∗∗ 0.008 0.020 0.011Shots on target 0.006 0.004 0.002 0.003 0.017∗ 0.008Shots off target (in 10−1) 0.018 0.027 0.001 0.001 −0.087 0.047Clearances, blocks, intercept. (in 10−1) 0.012∗∗ 0.003 0.005 0.005 0.017∗ 0.007Saves to shots ratio 0.366∗∗ 0.136 0.938 0.745 0.488∗ 0.231Cross-completion rate −0.043 0.092 −0.156 0.096 −0.140 0.161Red cards 0.035 0.030 −0.056 0.032 0.117 0.083Yellow cards 0.001 0.006 0.004 0.007 0.003 0.011Penalties conceded 0.018 0.026 0.000 0.030 0.022 0.045

Joint sig. of talent (F statistic) 17.87∗∗ 11.78∗∗ 7.04∗∗

Popularity variableNonperformance-related press citations 0.135∗∗ 0.017 0.125∗∗ 0.019 0.119∗∗ 0.025

ControlsIntercept 11.313∗∗ 0.584 11.345∗∗ 1.240 14.042∗∗ 1.173Age 0.207∗∗ 0.045 0.386∗∗ 0.089 0.065 0.086Age squared −0.004∗∗ 0.001 −0.011∗∗ 0.002 −0.002 0.002Appearances 0.026∗∗ 0.003 0.014∗∗ 0.004 0.014∗∗ 0.005Previous appearances (in 10−2) −0.018 0.029 0.259∗∗ 0.093 −0.024 0.051Relegation −0.134 0.094 −0.137 0.112 0.395 0.298Position fixed effects Yes Yes YesTeam fixed effects Yes Yes Yes

Pseudo-R2 0.63 0.46 (within) 0.44Number of observations 1,370 1,370 1,370

Notes: The sample includes players who appeared for at least half an hour in the highest German soccer league duringthe seasons 2001/2002 until 2005/2006. As the dependent variable is missing if the player left the league after the season, wetested for potential attrition bias. Attrition probability is, however, not affected by the player’s mean market value, conditionalon the explanatory variables. Standard errors in the OLS and FE procedures are White-robust and clustered at the player level.The standard errors of the quantile specification are clustering adjusted standard errors based on 1,000 bootstrap replications.

Significance levels (two-tailed): ∗5%; ∗∗1%.

the results of a player fixed effects regressionfor the purpose of comparison.

We find clear evidence that both a player’stalent and his nonperformance-related popular-ity increase his market value. This finding isrobust across all specifications. Regarding thetalent indicators, we see that the number ofgoals; the number of shots on target; the num-ber of clearances, blocks, and interceptions; andthe saves to shots ratio of the goalkeeper sig-nificantly increase the star’s market value at the95% quantile.

If a star player at the 95% quantile scores onemore goal per season, his market value increasesby 4.5%. The coefficients in the quantile regres-sions are similar in magnitude to those in the

OLS or fixed effects specification. Thus, the rel-ative marginal effects are more or less constant.The absolute size of the marginal talent effect ismagnified, however, as we move up the marketvalue distribution.8 An additional goal scoredby a superstar at the 95% quantile increaseshis market value by ¤0.25 million (0.045 ×5.5 million), whereas the absolute increase ofan additional goal scored by an average player isworth only ¤0.06 million (0.040 × 1.5 million).

8. The magnification does not apply to the popularityeffect, however, as we measure a player’s popularity withthe logarithm of the nonperformance-related press citations.Hence, the popularity coefficient has to be interpreted aselasticity. Adler (1985) does not necessarily assume aconvex relationship between a star’s salary and popularity.


If a mediocre goalkeeper improves his saves toshots ratio by 1%, his market value increasesby ¤0.006 million (0.01 × 0.37 × 1.5 million).A 1% improvement on the part of a stargoalkeeper, however, leads to an increase of¤0.027 million (0.01 × 0.49 × 5.5 million).9 Atfirst glance, these findings seem counterintuitiveas it should not matter who scores the goalsor prevents the opposition team from scoring.Going back to the superstar theory of Rosen(1981), the magnification effect can be explainedby the imperfect substitutability of higher andlower talent. Thus, from the consumer’s per-spective, one player scoring ten goals is not thesame as ten players scoring one goal each. Thisimplies that additional talent is magnified intolarger earning differences at the top end of thescale than at the bottom end. We have to becautious, however, with generalizations regard-ing the exact magnitudes of the quantile effects:a player who happens to be in a specific quantileof a conditional distribution will not necessarilyfind himself in the same quantile if his indepen-dent variables change (Buchinsky 1998).

Whenever correlational designs are used,concerns about internal validity such as possi-ble reverse causality may be raised. The issueof reverse causality (impact of market valueson talent or popularity) is, however, appeasedby the lag structure of our model. The inde-pendent variables are determined during a givenseason, whereas the dependent variable is esti-mated after the end of that season but prior to thestart of the following season. The market valuesshould therefore be influenced by the player’stalent and popularity and not vice versa. As wehave a typical microeconomic data set with alarge cross-sectional dimension and a small timedimension, adaptions of Granger causality teststo panel data, for example, those formulated byHoltz-Eakin, Newey, and Rosen (1988), are notsuitable in our context. Granger causality is anintrinsically dynamic concept (Attanasio, Picci,and Scorcu 2000).

VII. SENSITIVITY ANALYSES

In this section, we perform two sensitivityanalyses. First, we test the robustness of theresults if the market value proxies of a second

9. The magnitudes of the effects prove plausible whenanalyzing team revenues and revenue performance sensi-tivity in German soccer (see second robustness analysis inSection VII).

independent source are used. Second, we exam-ine the plausibility of the talent coefficients byrelating on-field performance to the team’s win-ning percentage and the winning percentage tothe team’s revenue.

A. Different Data Source of the Players’Market Values

At the end of the 2004/2005 season, we col-lected a cross-sectional sample of market valueestimates of all players who appeared in theseason for at least half an hour (in total, 427players) from www.transfermarkt.de. As Trans-fermarkt does not provide archive data, mar-ket values of players in earlier or later seasonswere unfortunately not available. Similarly tothe Kicker market values, the market valuesfrom Transfermarkt are estimated by industryexperts and include not only salaries but alsosigning fees, bonuses, and transfer fees. Table 4shows that the significantly positive talent andpopularity effects remain robust when takingTransfermarkt as the data source for the depen-dent variable. The coefficients are slightly higherthan in the Kicker panel sample, but the gen-eral empirical findings of the last section areconfirmed throughout. Thus, our results are notdriven by peculiarities of the Kicker proxies.

B. Revenue Performance Sensitivity

The basic unit of competition in our contextis the team. The star’s talent is valuable to theteam because it increases the team’s winningpercentage, which in turn is positively associ-ated with the team’s revenue potential. As wehave access to detailed revenue data for theGerman soccer teams,10 we want to test theplausibility of the returns to talent in the previ-ous section by estimating revenue performancesensitivity at the team level. In doing so, wefollow a procedure outlined by Scully (1974).They suggested first calculating the effect ofdifferent on-field performance measures on theteam’s winning percentage and then consideringthe impact of the team’s winning percentage onteam revenues.11 In line with Scully (1974), wedo not examine the influence of popularity onteam revenues because, unlike with talent, there

10. These data have been provided by courtesy of ReneAlgesheimer, Leif Brandes, and Egon Franck. For a firstempirical analysis of these data, see Algesheimer, Brandes,and Franck (2009).

11. Mullin and Dunn (2002) use a similar approach.


TABLE 4Cross-Sectional Estimates of the Determinants of a Star’s Market Value Using a Second Data

Source

Dependent Variable Logarithm of Individual Market Values According to Transfermarkt

Estimation Approach OLS 95% Quantile Reg.

β-coef. SE β-coef. SE

Talent variablesGoals 0.080∗∗ 0.012 0.095∗∗ 0.022Assists 0.071∗∗ 0.017 0.079∗∗ 0.029Shots on target −0.024 0.023 −0.053 0.137Shots off target 0.023 0.022 0.051 0.135Clearances, blocks, interceptions 0.003∗∗ 0.001 0.002 0.002Saves to shots ratio 0.726∗∗ 0.240 0.067 0.486Cross-completion rate −0.029 0.172 −0.147 0.289Red cards 0.111 0.078 0.268 0.215Yellow cards 0.022 0.016 0.043 0.029Penalties conceded 0.011 0.065 −0.131 0.117

Joint sig. of talent (F statistic) 16.30∗∗ 5.78∗∗

Popularity variableNonperformance-related press citations 0.255∗∗ 0.042 0.300∗∗ 0.059

ControlsIntercept 5.306∗∗ 1.041 9.204∗∗ 2.119Age 0.607∗∗ 0.076 0.418∗∗ 0.157Age squared −0.011∗∗ 0.001 0.008∗∗ 0.003Appearances 0.019∗∗ 0.005 0.007 0.009Previous appearances (in 10−1) −0.015∗∗ 0.005 −0.013 0.010Position fixed effects Yes YesTeam fixed effects Yes Yes

Pseudo-R2 0.70 0.56Number of observations 427 427

Notes: The sample includes all players who played for at least half an hour in the highest German soccer league duringthe season 2004/2005. Standard errors in the OLS are White-robust. The standard errors of the quantile specification are basedon 1,000 bootstrap replications.


is no clear measure of team-level popularity. Itis unclear how individual publicity should beaggregated at the team level.

In our first step, we relate the team’s win-ning percentage to the talent indicators asdescribed in Table 1, but aggregated at the teamlevel. Running a team fixed effects regressionincluding all teams appearing in the highestGerman soccer league between 2001/2002 and2005/2006 (90 observations and 24 differentteams), we find significantly positive coefficientsfor the number of goals scored (coef. = 0.0067,SE = 0.0013) and the saves to shots ratio (coef.= 0.6493, SE = 0.1212). No other performancemeasures have a distinct influence on the team’swinning percentage.12 In a second step, we use

12. A table of detailed regression results is included inthe working paper version of this article (Franck and Nuesch

proprietary team revenue data and relate therevenue to the team’s winning percentage. Theunderlying hypothesis is that fan interest andhence revenue is positively affected by teamwins (Scully 1974). As the clubs usually rene-gotiate sponsoring and broadcasting contractsat the beginning of the season, we use thewinning percentage of the last season as theexplanatory variable. Even match day revenueis largely influenced by the previous season’spercentage of wins because season ticket hold-ers represent around 55% of total match atten-dance (Bundesliga Report 2009). Of course, ateam’s revenue is driven not only by sporting

2009). This regression differs from the team productionestimation in Section IV because it employs seasonal (notmatch-level) data and uses a smaller set of explanatoryvariables.


success, but also by other factors such as thesize of the market, the team’s (nonperformance-related) star attraction, or stadium capacity.By estimating a team fixed effects model, wecontrol for all team aspects that are likely tobe time-constant—for example, the team’s mar-ket potential. Furthermore, we explicitly controlfor the team’s stadium capacity (measured in1,000s) because it may change substantially overtime due to stadium reconstruction. Previousstudies found that stadium capacity significantlyinfluences (gate) revenues (e.g., Berri, Schmidt,and Brook 2004; Brandes, Franck, and Nuesch2008). We run separate models for total rev-enue and for the subcategories of match dayrevenue, sponsoring revenue, broadcasting rev-enue, and the revenue from various sources suchas transfer fees, rental income, and catering andmerchandizing income.

Table 5 reveals that a 1% increase in theteam’s winning percentage increases total rev-enues by 1.18%. The highest revenue perfor-mance sensitivities are found (in decreasingorder) for broadcasting revenue (175%), matchday revenue (163%), and sponsoring revenue(137%). Stadium capacity clearly affects theteam’s match day revenue but has no sig-nificant impact on other revenue categoriessuch as sponsoring or broadcasting revenues.Following Scully (1974), we approximate themarginal revenue product of goal scoring andthe saves to shots ratio by multiplying the coef-ficients of the team production function by thecoefficients of the revenue function. As thecoefficients of the latter are determined in a log-level model, we multiply the product by theaverage revenue of a team. Thus, the averagemarginal revenue product for one additional goalscored is 0.0067 multiplied by 1.18 multipliedby the average team revenue (¤66.2 million),which equals ¤0.52 million. Similarly, we canderive the marginal revenue product if the goal-keeper’s saves to shots ratio improves by 1%. Indoing so, we achieve a marginal revenue prod-uct of ¤0.51 million (0.01 × 0.6493 × 1.18 ×66.2 million). From the market value regres-sions in Section VI, we know that one additionalgoal scored increases the star’s market value by¤0.25 million and that a 1% improvement in thesaves to shots ratio of a star goalkeeper increaseshis market value by ¤0.03 million. Hence, eventhough the marginal effects of the talent vari-ables on the star’s market value seem to berather large, they are still substantially lowerthan the (average) marginal revenue products of

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the same variables. Especially the contributionsof goalkeepers seem to be undervalued, a findingalready shown by Frick (2007). It is dangerous,however, to put much emphasis on the exactmagnitudes of the effects because they react sen-sitively to the chosen estimation strategy andthe explanatory variables included. We know,for example, that not only goal scoring and thesaves to shots ratio matter for winning, but alsothat their strong influence may hide the effectsof other important on-field performance mea-sures such as clearances, blocks, and intercep-tions, and shots on target, to mention just someexamples. Thus, the marginal revenue productsof goal scoring and the saves to shots ratio tendto be overestimated, as they also incorporate thepositive aspects of other important performancecharacteristics that influence winning. Neverthe-less, we can still say that the large impact of aplayer’s talent on his market demand seems tobe justified given the high revenue potential andthe significant revenue performance sensitivityin the highest German soccer league.

VIII. DISCUSSION

An empirical validation of the differentsuperstar theories proposed by Rosen (1981)and Adler (1985) requires valid and quantifiabletalent measures. This article argues that tourna-ments in professional sports help to determinethe (relative) talent of an athlete, which is other-wise unobserved and therefore hard to identify.The label of “winner” does not entail a subjec-tive impression, but rather results from a clearlydefined competition in a controlled environment.In team settings, in which teams and not indi-viduals compete against each other, the situa-tion is a little more complicated. In this case, aplayer’s talent is considered his contribution tothe team output. Thus, we first estimated a teamproduction function to detect critical playing ele-ments that affect team success, which are takenas talent indicators in the market value regres-sion. A player’s nonperformance-related popu-larity is defined by the residuals of a regressionof the logarithm of individual press citationsrelating to the player’s performance. Running a95% quantile regression, we find evidence thatboth talent and nonperformance-related popular-ity contribute to the market value differentials inthe highest German soccer league. As the marketvalue proxies we used do not include individualendorsement fees, our estimates may be consid-ered as lower bounds. Endorsement fees usually

react very sensitively to the athlete’s talent andpopularity.

Of course, further work is required to test thegeneralizability of our results. A more in-depthexamination of the factors determining the con-sumer’s decision to buy access to a superstar ser-vice would be very beneficial. In this article, weconsidered (Rosen-style) talent as the individ-ual’s ability to impact the likelihood of winninga sports competition. In contrast, all nonsportingfactors, like celebrity status in the media, wereseen as aspects of (Adler-style) popularity thatalso attract fans with something more to con-sider than the pure quality of the game. Adler(1985) sees star popularity as a way of econo-mizing on the costs of accumulating consump-tion capital, which itself increases the perceivedquality of the star’s service. In this article, wedirectly relate the demand for a star’s servicesto the star’s popularity and neglect consumptioncapital as the theoretical link. But the relevanceof consumption capital definitely deserves thefuture attention of both theorists and empiricists.

Even though the economic concept of super-stars was first developed to describe the enor-mous salaries of individual service providers inthe entertainment industries,13 skewed earningdistributions can be found in many work con-texts, the most prominent of which is the areaof top management compensation. Although wehave not specifically addressed the issue of“management stars” in our article, the set-up andframing of our approach could provide input forthe specific body of literature on the drivers oftop management salaries. Our study analyzes anindividualistic phenomenon (the determinants ofa star player’s remuneration) in an institutionalsetting in which teams, and not individuals, arethe basic unit of competition. This, of course,complicates the identification of an individual’scontribution to the team output. However, thisteam production context captures a basic ele-ment of managerial work, as the superstars inmanagement also emerge from a team produc-tion setting, where firms and not individuals arethe relevant units of competition in markets.

In 1982, Sherwin Rosen expanded his super-star theory to managerial reward distributionsacross ranks in and among hierarchical firms.He argues that the enormous salaries of CEOsare justified if the (superior) abilities of CEOs

13. Rosen (1981) uses examples of full-time comediansand classical musicians, and Alder (1985) mentions singingand painting as artistic activities that generate superstars.


filter through the entire corporation produc-ing improved efficiency at every level. Thus,a small increment in a CEO’s abilities wouldgenerate not an incremental but a multiplica-tive increase in the firm’s overall productiv-ity (Rosen 1982). Empirical studies, however,contest a pure Rosen-type explanation of CEOsalaries: Bertrand and Mullainathan (2001) showthat CEOs are paid not only for their perfor-mance but also based on luck, which meansthat CEOs receive pay premiums associatedwith profit increases that are entirely gener-ated by external factors such as changes inoil prices and exchange rates. Further empiricalstudies find considerable “popularity” effects:Lee (2006) shows that the press coverage ofa CEO increases his/her salary even after con-trolling for the firm’s performance. Malmendierand Tate (2009) and Wade et al. (2006) relatea CEO’s reputation to the CEO’s compensationand subsequent firm performance. Both papersfind that CEOs receive higher remuneration afterwinning a prestigious business award and thatthe ex post consequences for firm performanceare negative. Hence, superstar CEOs tend to bepaid not only for their managerial ability butfor other factors beyond performance as well.Furthermore, the correlations between a starmanager’s talent and popularity and betweenfirm performance and popularity are, unlikein professional sports, not necessarily positivebut indeed often negative. Celebrity CEOs mayindulge in activities that provide little firmvalue, such as writing books, sitting on outsideboards, or playing golf (Malmendier and Tate2009). In addition, CEOs receiving great mediapraise may become overconfident about the effi-ciency of their past actions and about theirfuture abilities (Hayward, Rindova, and Pollock2004). Hayward and Hambrick (1997) show thatCEOs who enjoyed high press publicity paidlarger premiums for acquisitions due to CEOhubris.

Even though both talent and popularityeffects seem highly relevant for top managementcompensation, the specific literature mostly failsto make a clear distinction between the twoeffects, probably because valid and measur-able indicators of managerial ability are hardto find. Our article suggests that future empiri-cal research on top management compensationshould first try to proxy managerial ability byestimating a firm production function beforeother drivers of CEO salaries like popularity canbe properly isolated.

APPENDIX

TABLE A1

Popularity Regressed on On-Field Performance

Dependent Variable Ln(Press Citations)

Estimation Approach Pooled OLS

β t Value

Goals 0.295∗∗ 5.220Assists 0.157∗∗ 4.760Shots on target −0.010 −0.130Shots off target 0.116∗ 2.200Clearances, blocks, and interceptions 0.137∗∗ 3.760Saves to shots ratio of the goalkeeper 0.225∗∗ 5.290% successful crossings 0.021 0.860Number of red cards 0.052∗ 2.160Number of yellow cards 0.070∗ 2.350Penalty conceded −0.010 −0.420Intercept 2.628∗∗ 0.084R2 0.24Number of observations 1,370

Notes: The β coefficients illustrate the change in thedependent variable if the regressor varies by one stan-dard deviation. t values are computed using the White-heteroskedasticity robust standard errors clustered at theplayer level. The sample includes players appearing in thefirst German soccer league for more than half an hour duringthe seasons 2001/2002 until 2004/2005.


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