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Do Soccer Associations Really Spend on a Good Thing?Empirical Evidence on Heterogeneity in the Consumer Response

to Match Uncertainty of Outcome

Franck, E; Brandes, L; Benz, M A

Franck, E; Brandes, L; Benz, M A (2009). Do Soccer Associations Really Spend on a Good Thing? EmpiricalEvidence on Heterogeneity in the Consumer Response to Match Uncertainty of Outcome. Contemporary EconomicPolicy, 27(2):216-235.Postprint available at:http://www.zora.uzh.ch

Posted at the Zurich Open Repository and Archive, University of Zurich.http://www.zora.uzh.ch

Originally published at:Contemporary Economic Policy 2009, 27(2):216-235.

Franck, E; Brandes, L; Benz, M A (2009). Do Soccer Associations Really Spend on a Good Thing? EmpiricalEvidence on Heterogeneity in the Consumer Response to Match Uncertainty of Outcome. Contemporary EconomicPolicy, 27(2):216-235.Postprint available at:http://www.zora.uzh.ch

Posted at the Zurich Open Repository and Archive, University of Zurich.http://www.zora.uzh.ch

Originally published at:Contemporary Economic Policy 2009, 27(2):216-235.

Do Soccer Associations Really Spend on a Good Thing?Empirical Evidence on Heterogeneity in the Consumer Response

to Match Uncertainty of Outcome

Abstract

The purpose of this study is to analyze whether previous results describing the effect of uncertainty ofoutcome on match attendance in team sports have been driven by heterogeneity in fan demand. Weapply censored quantile regression methods and place particular emphasis on the relationship betweenmatch uncertainty and attendance demand, as previous results are highly ambiguous. This is moresurprising, as each season association and league officials continue to spend millions on enhancing thisuncertainty. We also control for season ticket holders, who are unlikely to be influenced by matchspecificities. Based on data from German soccer, our results indicate that fan demand showsheterogeneity across quantiles and that increasing match uncertainty of outcome exclusively benefitsteams who already face strong attendance demand.

DO SOCCER ASSOCIATIONS REALLY SPEND ON A GOOD THING?EMPIRICAL EVIDENCE ON HETEROGENEITY IN THE CONSUMER

RESPONSE TO MATCH UNCERTAINTY OF OUTCOME

MEN-ANDRI BENZ, LEIF BRANDES and EGON FRANCK*

The purpose of this study is to analyze whether previous results describing the effectof uncertainty of outcome on match attendance in team sports have been driven by het-erogeneity in fan demand. We apply censored quantile regression methods and placeparticular emphasis on the relationship between match uncertainty and attendancedemand, as previous results are highly ambiguous.This ismore surprising, as each seasonassociation and league officials continue to spendmillions on enhancing this uncertainty.Wealsocontrol forseasonticketholders,whoareunlikelytobeinfluencedbymatchspeci-ficities. Based on data from German soccer, our results indicate that fan demandshows heterogeneity across quantiles and that increasing match uncertainty of out-come exclusively benefits teams who already face strong attendance demand. (JELD12, C14, C24, L83)

I. INTRODUCTION

Analyzing the demand for sport has been ofmajor interest to many researchers in the fieldof sports economics. The sports examined rangefromcricket over rugby to, perhapsmost impor-tant in Europe, football (or soccer). Whereassome factors can consistently be found to affectthe demand for sport, the role played by un-

certainty of outcome variables still remainsunclear.1 This is perhaps surprising for two rea-sons. First, the underlying idea, introduced byRottenberg (1956), is rather appealing: Ceterisparibus, consumers of sport matches value ahigheruncertaintyabouttheoutcomeofamatch;that is, they prefer matches exhibiting teams of(almost) equal playing strength within a specificsituation.2

*We are grateful to BoHonore, Rob Simmons, RainerWinkelmann, Jaume Garcıa, Stefan Boes, Gabi Ruoff,Stephan Veen, Johannes Mure, and seminar participantsat the University of Zurich, participants at the Interna-tional Association of Sports Economists (IASE) Confer-ence 2006 and at the 81st meeting of the WesternEconomic Association (WEA) in 2006 for helpful com-ments. We would also like to thank three anonymous ref-erees for their helpful comments and suggestions. ErwinVerbeek provided helpful research assistance. Financialsupport from the Swiss National Fund is gratefullyacknowledged. All errors remain our own.

Benz: Simon Kucher & Partners, Strategy & MarketingConsultants, Financial Services and Consumer GoodsDivision, Imbisbuhlstrasse 149, 8049 Zurich, Switzer-land. Phone +41 44 226 50 40, Fax +41 44 226 50 50,E-mail [email protected]

Brandes: Faculty of Economics, Business Administrationand Information Technology, Institute for Strategyand Business Economics, University of Zurich, CH-8032 Zurich, Switzerland. Phone +41 44 634 2962,Fax +41 44 634 4348, E-mail [email protected]

Franck: Faculty of Economics, Business Administrationand Information Technology, Institute for Strategyand Business Economics, University of Zurich, CH-8032 Zurich, Switzerland. Phone + 41 44 634 2845,Fax + 41 44 634 4348, E-mail [email protected]

ABBREVIATIONS

CQR: Censored Quantile Regression

ICE: InterCity Express

ILPA: Iterative Linear Programming Algorithm

OLS: Ordinary Least Squares

UOO: Uncertainty of Outcome

UEFA: Union of European Football Associations

VIF: Variance Inflation Factors

1. Following Szymanski (2003), depending on the rele-vant time span of interest, it is possible to distinguishbetween three different types of uncertainty of outcome,namely seasonal uncertainty (close championship race),championship uncertainty (absence of long-run domina-tion), and individual match uncertainty. Throughout thispaper, we are exclusively interested in the last of these.

2. Forrest and Simmons (2002) have argued thatmatch uncertainty also depends on factors such ashome-field advantage. Thus, it could be that uncertaintyis actually highest when a strong visiting team playsa ‘‘mediocre’’ team that is particularly strong at home.

Contemporary Economic Policy (ISSN 1074-3529)Vol. 27, No. 2, April 2009, 216–235 doi:10.1111/j.1465-7287.2008.00127.xOnline Early publication November 24, 2008 � 2008 Western Economic Association International

216

Second, the success of Rottenberg’s idea isbeyond doubt3 as, nowadays, the concept ofcompetitive balance is omnipresent when itcomes to organizational issues in professionalteam sport leagues. In some European leagues(including Germany), this concept has beenput forward as a justification for centralizedTV rights selling4 combined with revenue shar-ing. Besides, the Union of European FootballAssociations (UEFA) is redistributing signifi-cant shares of their revenues from the Cham-pions League to non-participating clubs inorder to close the financial gap between partic-ipants and non-participants. This in turn shouldresult in a more equal distribution of financialpower for the clubs within a league, which ishoped to maintain a certain degree of com-petitive balance.5 In other words, based onRottenberg’s idea, millions of Euro are spenteach year.6

However, Borland and Macdonald (2003)and Szymanski (2003) in their extensive liter-ature reviews state that the empirical resultsare far from being unambiguous.7 In thispaper we argue that these results might bedriven by the existence of heterogeneity inthe demand for sport, which has not beenaddressed in previous studies: To the best ofour knowledge, all previous studies analyzingthe demand for sport used ordinary leastsquares (OLS) or censored normal (Tobit) re-gression.Whereas these methods differ in theirtreatment of censored observations,8 bothexclusively model changes in the conditionalmean. In other words, all previous studies have(implicitly) assumed that regressors affectthe location of the conditional mean only.The shape of the distribution, however, wouldthen not be altered by different values for

the regressors (with the notable exception ofheteroskedasticity).

We are skeptical about this approach. Inparticular, we are concerned that an exclusivefocus on average effects might misguide policymakers in the presence of heterogeneity in con-sumer demand.9 By heterogeneity, we refer toa situation in which the group of (statistically)relevant factors for match attendance demandvaries across different quantiles in the distri-bution of this demand. More precisely, wewant to allow for the case that the level ofexpected demand influences the importanceof influence factors; for instance, it might bethe case that a consumer’s utility from cele-brating the home team’s victory is increasingin the number of spectators (whose majoritywill also be home team supporters). Thiswould induce a greater influence from thehome team’s winning probability on atten-dance demand for large quantiles.

Thus, the purpose of this paper is to in-troduce quantile regression analysis to thedemand for sport, as we believe that thismethod provides a fuller picture of the con-ditional distribution of match attendancefigures. Furthermore, we are able to overcomethe major weakness of the Tobit estimator,namely the explicit assumption of normallydistributed error terms. However, to allowfor a comparison, results from a Tobit modelare also given within this paper.

Throughout this paper we will analyzematch attendance data from the first divisionof professional German Football (soccer) todetermine the effect of match uncertainty ofoutcome variables on match attendance.The focus on match attendance demand stemsfrom the economic significance of ticket salesfor overall team revenues. This point is furtherstrengthened by the existence of a positive cor-relation between a club’s attendance demandand advertising revenues in subsequent sea-sons:10 For the seasons 2001/02, 2002/03,and 2003/04 the combined revenue shares ofticket sales and advertising in the GermanBundesliga accounted for 39.88%, 45.71%and 49.53%, respectively.11

Our data contain information onmore than1,200 matches in the seasons 1999/2000 until2003/04. For each team we have information

3. Recently, the 50th anniversary of Rottenberg’spaper was celebrated in the Journal of Political Economyby Sanderson and Siegfried (2006).

4. See, for example, Forrest, Simmons, and Buraimo(2005) for the UK.

5. Theoretical support for this procedure has comefrom, for example,Marburger (1997), who shows how rev-enue sharing may improve competitive balance.

6. Over the last 6 yr, approximately 215 million Eurohave been redistributed from Champions League revenuesto non-participating clubs from the national leagues; seeArnaut (2006, p. 145). Moreover, ‘‘enhancing competitivebalance’’ is explicitly mentioned as one of the main directbenefits to European Football.

7. See Subsection II.A.8. Due to stadium capacity constraints, censored

observations are regularly encountered in studies aboutthe demand for sport.

9. See Brandes (2007) for a very preliminary discus-sion of this aspect.

10. See Czarnitzki and Stadtmann (2002).11. Source:Deutsche Fussball Liga, own calculations.

BENZ, BRANDES & FRANCK: DO SOCCER ASSOCIATIONS REALLY SPEND ON A GOOD THING? 217

about the number of season ticket holders.Thus, we are able to focus on the ‘‘true’’ matchdemand by subtracting season tickets from theobserved number of spectators.12 We will referto this variable as adjusted ticket demand.

Our empirical results clearly support theadoption of quantile regression methods tothe demand for sport. Most interesting, we findstrong evidence that match uncertainty of out-come (UOO) almost exclusively affects matchesexhibiting a strong degree of attendancedemand. Moreover, we are able to obtain thetheoretically predicted signs on all significantUOOmeasures. In our opinion, this has impor-tant consequences for league and associationofficials, alike; revenue redistribution is intendedto close the financial gap between ‘‘low-demand’’ teams and ‘‘high-demand’’ teams.13

Based on our empirical findings, however, theeffect from this revenue redistribution on theleague as a whole is twofold: On the one hand,weak teams are able to spend more money onplayer talent. However, the extent to which thiswill increase their playing strength (which wouldincrease attendance demand for home matches)depends crucially on the efficiency of their talentinvestments. If such teams would be able to suc-ceed in improving their playing strengths, thereward would also be shared by ‘‘high-demand’’teams: These teams would profit from a positiveexternality—given by a higher degree of matchuncertainty of outcome—as UOO exclusivelyaffects the high quantiles of match attendancedemand. We conclude that in order to avoida wider gap in financial power across teams,league and association officials should comple-ment revenue redistribution schemes by appro-priate governance standards. This should alsoincrease the need for managerial efficiency withrespect to existing financial resources of teams.

The remainder of this paper is structured asfollows: The next section reviews previousstudies of the relationship between matchattendance and the degree of outcome uncer-tainty. In Section III we present our data anddiscuss our chosen measures of competitivebalance. Section IV contains our empiricalresults and Section V concludes.

II. COMPETITIVE BALANCE AND THE DEMANDFOR SPORT

A. Related Literature

Over the last decade, there has been a hugevarietyof academic research14 about thedemandfor sports ingeneralandtherelationshipbetweenuncertaintyofoutcomevariablesandattendancefigures in particular. Perhaps this has beenmoti-vated by the fact that, as already mentioned,league officials refer to this connection as anexcuse for adopting institutional devices like sal-ary caps, reserve clauses, draft systems or collec-tive selling, which would usually be subject toantitrust laws. However, the results on the rela-tionshipbetween(match)uncertaintyofoutcomeand attendance are mixed.15

Borland and Macdonald (2003) summarizeresults from 18 empirical studies based onmatch level attendance. Only four of thesestudies find a clear positive influence of greateruncertainty on attendance, five studies presentstatistically significant mixed effects and ninestudies come up with negative or statisticallyinsignificant effects.

As we base our analysis on data for Ger-man football, those results treating footballmatches are of special interest to us. Out ofthe 18 studies covered by the survey, sevenwere conducted on football data. Out of these,four studies find statistically negative or insig-nificant effects, two show a concave relation-ship, and only one presents a statisticallysignificant positive influence of greater uncer-tainty on attendance.

Since the publication of the review byBorland and MacDonald, several new studieshave been done on match attendance, some ofthem proposing newmeasures of match uncer-tainty of outcome. Since we will rely on aslightly adjusted version of their proposedmeasure, we would like to name Forrest andSimmons (2006) as a prominent example. Theauthors analyze demand for match attendance

12. See Section III for further details.13. Usually, low-demand (high-demand) teams will

also be the weaker (stronger) teams within a league. How-ever, within this paper, we will distinguish between teamson an attendance demand basis.

14. See, for example, Simmons (1996), Dobson andGoddard (1992), Wilson and Sim (1995) and the recentwork by Owen and Weatherston (2004). Excellent reviewsmay be found in Borland and Macdonald (2003) andSzymanski (2003).

15. As already mentioned in the Introduction, weplace exclusive emphasis on the relationship betweenmatch uncertainty of outcome and match attendancedemand. Therefore, we focus on this relationship withinour literature review. For the effect from seasonal and/or championship uncertainty on attendance demand,see also Borland and Macdonald (2003) and Szymanski(2003).

218 CONTEMPORARY ECONOMIC POLICY

in the English Football League. They use an un-certainty measure, which incorporates homeadvantage of home teams.16 However, they donot find any significant relationship betweenmatchattendanceanduncertaintyofoutcome.17

Unfortunately, the authors lack information onseason ticket holders, which might result inbiased estimates.

Although not covered by the survey, thereis previous work analyzing individual matchattendance for German football. Czarnitzkiand Stadtmann (2002) analyze match atten-dance for all teams in the seasons 1996/97and 1997/98 and provide results from Tobitestimation. Basically, they find that neitherthe short-term nor the medium-term measuresof uncertainty have a significant influence onmatch attendance. Their results point at thedominating influence of a team’s reputationand its fans’ loyalty on ticket demand.

Roy (2004) analyzes home match attendancedata for six teams in the German Bundesligain the period 1998/99–2001/02. Estimatingfeasible generalized least squares models forteam revenues from standing and seatingaccommodation separately, he finds a positiveinfluence of the home team’s winning proba-bility on revenues from standing accommoda-tion. However, he does not use a quadraticspecification for this measure. Furthermore,the question of representativeness and survi-vor bias of these six teams18 arises. Basedon these results, we believe that further anal-ysis of the German Bundesliga is required.

III. EMPIRICAL FRAMEWORK

A. Playing Schedule and Institutional Designof the Bundesliga

The professional German soccer leagueconsists of two divisions, namely 1. Bundesliga(top division) and 2. Bundesliga. Within eachseason, 18 teams in the top division competewith each other for winning the German cham-pionship, qualifying for international compet-itions, such as UEFA Champions League

(teams ranked first to third), UEFACup (teamsranked fourth and fifth) and for avoiding rel-egation. This latter aspect distinguishes theleague critically from most American sportsleagues, which are referred to in the literatureas closed leagues: In the Bundesliga, at the endof each season, the three worst performingteams in the 1. Bundesliga are demoted to the2. Bundesliga and replaced by the three bestperforming teams from the latter.

The playing schedule in the 1. Bundesligaconsists of each team playing each other teamtwice within the season, where one match isplayed at the team’s home field and the otherat the competitor’s home field. Most of thematches are played on Saturdays and Sun-days, starting at 3:30 p.m. (Saturday) or5.30 p.m. (Sunday). Moreover, a team thatplayed at home on the previous weekend willusually have to play ‘‘on the road’’ on the sub-sequent weekend. Based on this scheduling,at the end of the season, each team will haveplayed 34 matches, among them 17 being homematches.

B. The Data

Our data contains information on over1,200 individual matches in the first divisionof professional German football within theperiod 1999–2004. Thus, we are able to studydemand for football over five consecutiveseasons. Besides different measures of match-specific UOO, we also have detailed informa-tion on a variety of influence factors, such asentertainment and team quality proxies (shortand long term), economic factors, and weatherconditions.

Throughout our empirical analysis, we willuse logarithmic adjusted match attendance asthe dependent variable, which has been ob-tained by subtracting the number of seasonticket holders for the home team from itsobserved home match attendance figures withina particular season. Of course, this is equiv-alent to the assumption that all season ticketholders attend each match within a certainseason. Although this assumption may be crit-icized,19 it seems justified for our analysis

16. See Section III for details.17. Interestingly, applying the same measure to tele-

vision demand, the authors find a positive influencefrom higher uncertainty to demand, whereas anotherstudy onmatch attendance also fails to derive the expectedinfluence. See Forrest, Simmons, and Buraimo (2005) andBuraimo and Simmons (2006).

18. The choice was based on permanent participationin the league over the period and an average attendance ofless than 80% of the stadium capacity.

19. We thank Bernd Frick for pointing out to us thatseason tickets may allow preferential access to ChampionsLeague (CL) tickets, which might induce consumers toensure CL match participation through purchase of sea-son tickets. It would then be possible that at least someseason-ticket holders would not attend each single match.


as season ticket holders show a strong habitpersistence independent of match-specificcharacteristics.20

Based on these arguments, we can write ourestimation equation as

logðD*it Þ 5 UOOitbþ x#itfþ z#itcþ e#itn

þ w#itkþ eitt 5 1; . . . ; T ; i 5 1; . . . ; 25:

ð1Þ

where D*it denotes adjusted ticket demand fora home match21 of team i at time t. Further-more, xit contains entertainment proxies, zitdenotes team quality variables, eit refers toeconomic factors, wit corresponds to weathervariables, and eit denotes the unobserved influ-ence on attendance.

From Equation (1), it is revealed that weadopt the standard approach in the sports eco-nomics literature with respect to the functionalform for the match uncertainty measures(UOO): At first glance, it might seem as ifwe explicitly ruled out the possibility thatthe influence from UOO on match attendancedemand varies with the quality of the teamsinvolved as there is no interaction effectincluding team quality and UOO in Equation(1).22 The reader should note, however, thatthe use of quantile regression allows for thepossibility that the extent of the effect ofUOO on attendance demand is still affectedby the quality of teams involved if, as seemslikely, high-quality teams occupy a differentpart of the distribution of attendance demandcompared to low-quality teams.

The elements of the other regressor groupscan be found in Table 1. However, through-out the empirical analysis of this paper, bfrom Equation (1) will be our main concern.It should be clear that—whereas several

measures of UOO are applied across differentspecifications (see also below)—the variablesfrom the other regressor groups alwaysremain the same.

TABLE 1

Variable Description

Variable Description

Team quality

Hstand Home: league position beforematch

Astand Away: league position beforematch

Hstand (LS) Home: finishing position previousseason

Astand (LS) Away: finishing position previousseason

HGLM Home: goals last home match

AGLM Away: goals last away match

Hseries3 Dummy 5 1, if home team wonprevious 3 matches

Aseries4 Dummy 5 1, if away team wonprevious 4 matches

Hbudget Home: Budget (in terms of2003 Euro)

Abudget Away: Budget (in terms of2003 Euro)

HREP20 Home: Reputation

AREP20 Away: Reputation

Entertainment proxies

Relegation Dummy 5 1, if Home is inrelegation contention

Championship Dummy 5 1, if Home is inchampionship contention

Home: Promoted Dummy 5 1, if Home has beenpromoted at the end of theprevious season

Away: Promoted Dummy 5 1, if Away has beenpromoted at the end of theprevious season

Economic factors

log(Price) Logarithmic average admissionprice

Hmarket Home team market size

DBtime Travel time by train for awaysupporters

(DBtime)2 Travel time squared

Unemployed Unemployment rate in hometeam area

Midweek Dummy 5 1, if match isMonday-Thursday

Weather variables

Temp Temperature in 0.1°CRain Dummy 5 1, if rain on

match day

Snow Dummy 5 1, if snow onmatch day

Within season trend

Fixture Fixture within season

20. Feehan, Forrest, and Simmons (2003) provide evi-dence from the Premier League that season ticket holdersdo indeed attend almost every match within a season.

21. For reasons of readability, we drop the index ofthe visiting team. Strictly speaking, we would have to writeDijt to denote attendance for a home match of team iagainst team j at time t.

22. We are grateful to an anonymous referee for bring-ing this to our attention. As a result, we also estimateda modified version of Equation (1) in which we incorpo-rated an interaction term including UOO and Hstand.However, the results did not provide empirical supportfor this approach. Therefore, only the results from Equa-tion (1) are given within this paper. The results for themodified equation are available from the authors onrequest.


Measuring team quality can be done on sev-eral time horizons. To control home and awayteams for ‘‘relative’’ performancewithin a givenseason, we rely on Hstand and Astand. Thesevalues are used in virtually every empiricalmatch attendance demand study, for instanceby Garcia and Rodriguez (2002), Roy (2004)and Czarnitzki and Stadtmann (2002). Includ-ing each team’s finishing position in the previ-ous season, Hstand (LS) and Astand (LS),allows us to pick up ‘‘vicious’’ and ‘‘virtuous’’circles of performance as subsequent fan inter-est might vary with previous performance.23

In order to provide a unified treatment forall teams, we applied the ranking 19, 20,and 21 to the best, second and third best pro-moted teams from the second division in theprevious season, respectively.

Including each team’s number of goals in itsprevious home/away match, HGLM andAGLM, seems justified as anecdotal evidencesuggests that celebrating a team’s goals is atthe core of attending a live match. Besides,this approach has also previously been takenby many researchers, such as Garcia andRodriguez (2002).

In controlling for winning streaks of thehome and away team, Hseries3 and Aseries4,we follow Roy (2004), who proposes an asym-metric length of winning streaks for home andaway team for the following reason: As mostspectators will be supporters of the hometeam, these spectators should be expected tobe more responsive to changes in home teamquality aspects than to those of the visitingteam. Thus, they react to winning streaks oftheir home team ‘‘earlier’’ than to the winningstreaks of a visiting team. Although we admitthat the numbers of 3 and 4 consecutive winsmay to some extent be arbitrary, the basic ideaof an asymmetric winning streak measureappealed to us very much.

Including budget information as explana-tory variables we follow the motivation byForrest, Simmons, and Buraimo (2005), whostate that the use of budget informationmay more fully mirror the quality of teamsthan the number of international players,which might significantly differ in quality,dependent on the specific national team. Theirargument is based on the existence of a com-petitive market for player talent.

Based on the empirical results by Czarnitzkiand Stadtmann (2002), who present strongempirical evidence for the importance of ateam’s ‘‘Reputation’’ on match attendance de-mand, we decided to include their ‘‘REP20’’measure for home and visiting team (HREP20and AREP20). The measure REP20 takesinto account the performance of a particularteam over the last 20 yr according to the fol-lowing formula:

REP20 5X20t51

18

xtffiffit

p ;ð2Þ

xt is the team’s final rank in the championshipt yr ago. In the case that the team did notplay in the first German league in season t,the corresponding summand is set equal tozero. By weighting the rankings with thesquare root of the number of years past,the index is constructed to reflect the depre-ciating effect of time.

Relegation and Championship are based onthe following assumptions. First, we followRoy (2004) with respect to the fact that thesemeasures are only feasible for match days29–34. Although we are aware of the fact thatit would be possible to ‘‘cardinalize’’ thesedummy variables, for example, by using ateam’s ‘‘point difference’’ to the league leader(or the team currently ranked 16th), our mea-sure has the advantage that it is easier to inter-pret: The knowledge that a team is currentlylagging 10 points behind the leader does notprovide any information on whether it is stillpossible for this team to win the champion-ship (for instance, if the number of remain-ing matches is larger than four matches).24

We admit, however, that the 29–34 fixture per-iod might be viewed as somewhat arbitrary.On the other hand, starting this measuremuch earlier, for example, around the 20th fix-ture, would heavily increase the number ofteams that are theoretically in Championship/Relegation contention although they wouldnot have necessarily been viewed as such atthe time.

Furthermore, we take the criticism ofForrest, Simmons, and Buraimo (2005) onprevious approaches to this type of variablesinto account. They argue25 that for answering

23. We are grateful to an anonymous referee for sug-gesting this aspect to us.

24. Within our sample period, wins are awarded threepoints, and a draw is awarded one point to each of bothteams.

25. See Forrest, Simmons, and Buraimo (2005, p. 647).


questions as ‘‘could team x still win the cham-pionship if it won y% of available points fromits remaining games and other teams that mightbe champions won z%of available points fromtheir remaining games? y is always chosen tobe a high number and z a low number, butthere is no obvious criterion for choosingthe precise values.’’

Our approach differs with respect to thechosen values on y and z. However, ratherthan choosing fixed values for these variables,we apply a simple rule for our measures: TheChampionship Dummy26 is set to 1, in casethat a team is not more than two pointsbehind the current leader. This would allowa team to win the championship by eithera higher number of points or a higher‘‘goals-scored-minus-goals-received’’ valuein the following way: First, the team wouldhave to win all its own outstanding matchesand the teams that are currently rankedhigher would have to tie at least once in theirremaining matches. This would mean that theteam would end up at least with the samenumber of championship points as the cur-rent leader (or any of the currently betterranked teams). In case that the team wasthe unique end-of-season leader, it wouldimmediately win the championship. In caseof point equality between the team and theend-of-season leader, the team could stillwin the championship by having a highervalue on ‘‘goals scored-minus-goals-received’’than its competitor.27 Based on this approach,depending on the number of remainingmatches, our value for z ranges from 33%to 89%. The underlying dependence on thenumber of remaining matches stems fromthe fact that a ‘‘necessary tie’’ in the lastgame by the leader refers to a ratio of 33%(1 point out of 3), whereas one necessary tiein the last two games refers to 67% (4 pointsout of 6).

With respect to our chosen economic re-gressors, we start by mentioning that the log-arithmic average admission price (log(Price))

is included in Equation (1) to allow for aninterpretation of the corresponding coefficientas the price elasticity of attendance demand.Average admission prices have been calcu-lated as follows: For each category, that is,seating and standing accommodation, weobtained information on the highest and low-est admission prices. Based on these prices, wecalculated the average price for seating andstanding accommodation. The averages ofboth categories were then weighted by theirrelative share in stadium capacity. Afterwards,prices were translated into Euro values (1Euro5 1.95 DM) and deflated by the GermanConsumer Price Index (20045 100). Althoughthis is the only feasible approach within oursample period, this measure suffers from itsinability to incorporate the so-called ‘‘Matchof the Day’’ surcharges, but models club-leveladmission prices to be constant within aseason.28

In addition, we include ‘‘home marketsize,’’ Hmarket to measure the home team’smarket potential, that is, the number of inhabi-tants within the home team’s hometown(in 100,000’s). Here, we follow the approachby Brandes, Franck, and Nuesch (2008) inincluding male inhabitants, only. Finally,Unemployed measures the unemployment ratein the home team’s hometown and thus servesas an income proxy. In comparison to thesemeasures, DBtime and Midweek might beviewed as indirect cost factors: From casualevidence we know that most visiting fanstravel by train. However, there are significantdifferences in train infrastructure betweenEastern and Western Germany resulting insignificant differences in required travel timefor visiting fans. It is thus questionablewhether a measure of absolute distance, suchas distance in kilometers, should be adopted.Our measure is based on the timetable fromDeutsche Bahn, the German Railway ServiceProvider.29 We also include the squaredtraveling distance, as we expect marginal dis-utility to decrease with the travel time. Mid-week matches, that is, matches played on

26. The derivation of the values for Relegation isobtained by a similar reasoning.

27. We are aware of the fact that this might appear tobe a rather restrictive criterion for the definition of cham-pionship contention. However, we decided to rely on thisnarrow definition in order to avoid the inclusion of addi-tional teams that would have had only a theoretical chanceof winning the championship under ‘‘extremely beneficialconditions.’’

28. As a team’s admission price is an important policyvariable, we readily followed the suggestion of an anony-mous referee to exclude a team-specific fixed effect fromEquation (1) as this would otherwise have captured a pos-sible price effect.

29. See the Appendix for a detailed description ofDBtime.


Monday-Thursday, are assumed to requireadditional ‘‘organizational effort’’ from con-sumers as there is usually less time to leavefrom work and reach the stadium in time.In addition, people will need to get to workthe next day, which might make a match start-ing at 20:30 possibly less attractive.

Following Gartner and Pommerehne (1978),weather-related variables might also be viewedas ‘‘indirect quality indicators.’’ Within ourspecification, we control for average tempera-ture (Temp) before kick-off in the home team’shometown as well as whether there had beenrain (Rain) and/or snow (Snow) before kick-off. Finally, the variable Fixture accountsfor a possible trend in within-season matchattendance.

In Table 2, we give descriptive statisticsfor our control variables.30

C. Measuring Match Uncertainty of Outcome

Within our study, we will rely on a varietyof measures of match uncertainty of outcome.This is done to account for a possible sourceof heterogeneity in previous results: In the sur-vey by Borland and Macdonald (2003) theapplied measures of match uncertainty differsignificantly across different studies.

TABLE 2

Descriptive Statistics

Variable Mean Standard Deviation Min. Max. N

Dependent variable

log(adjusted match attendance) 9.48 0.594 7.863 10.834 1369

Team quality

Hstand 9.683 5.234 1 18 1369

Astand 9.774 4.989 1 18 1369

Hstand (LS) 9.968 6.058 0 21 1369

Astand (LS) 10.439 5.84 0 21 1369

HGLM 1.703 1.367 0 6 1328

AGLM 1.118 1.101 0 9 1285

Hbudget 29.375 12.186 7.600 62.8 1369

Abudget 28.036 10.745 7.600 51.6 1369

HREP20 22.339 22.571 0 101.276 1369

AREP20 18.124 13.807 0 53.203 1369

Hseries3 0.031 0.174 0 1 1369

Aseries4 0.009 0.097 0 1 1369

Entertainment proxies

Hprom 0.17 0.376 0 1 1369

Aprom 0.176 0.381 0 1 1369

Championship 0.012 0.111 0 1 1369

Relegation 0.081 0.273 0 1 1369

Economic factors

Dbtime 5.41 3.296 0.17 15.8 1369

(DBtime)2 40.124 46.753 0.029 249.64 1369

log(Price) 2.885 0.286 1.92 3.666 1369

Unemployed 11.69 4.066 3.1 20 1369

Hmarket 2.995 3.723 0.098 16.515 1369

Midweek 0.062 0.241 0 1 1369

Weather variables

Temp 89.689 60.423 �86 309 1368

Rain 0.336 0.473 0 1 1369

Snow 0.061 0.24 0 1 1369

Within-season trend

Fixture 18.04 9.516 3 34 1369

30. For all seasons, we dropped the first two fixtures inorder to obtain values on Home: goals last home matchand Away: goals last away match. This explains the smalldifference in means for some variables.


As a starting point, we will use a very sim-ple measure of match uncertainty, namely,the absolute difference in league standings(ADSTAND). This measure is given by

ADSTAND5 jASTAND�HSTANDj;ð3Þ

where HSTAND and ASTAND denote thepre-kick-off league position of the home andaway team, respectively.

Another measure is based on the approachby Forrest, Simmons, and Buraimo (2005) andcalculated as follows:

FSBijs 5 jPPGi

s þHAs � PPGsjj;ð4Þ

where PPGsi and PPGs

j denote the points pergame records for home team i and visitingteam j in season s before the match, respect-ively. HAs (Home Advantage) was calculatedas the difference between the average numberof points won at home and the number ofpoints won on the road for all teams in the pre-vious season.

Regarding the interpretation of our resultson this variable, it is important to understandthe underlying idea of this measure: Thegreater the value of this measure, the lessuncertain the outcome of the match is. Anex-ante perfectly balanced match should showan FSBs

ij-value of 0. For reasons of readabil-ity, we will drop the subindexes on FSB in theremainder of this paper.

In addition to these two measures, we willalso use information from the sports bettingmarket. Based on quotations from the leadingGerman bookmaker in the sports betting mar-ket, ODDSET, we calculate the measure pro-posed by Theil (1967) by

THEIL 5X3i51

pilog

�1

pi

�;ð5Þ

where pi, i5 1,. . .,3 denotes the probabilities31

for the three possible match outcomes (homewin, draw, and away win). The smaller thedifference between these probabilities, thelarger the value for THEIL. Thus, we expecta positive effect from THEIL on attendancedemand.

However, Roy (2004) criticizes Theil’s mea-sure with respect to its reliance on all possible

match outcomes and proposes an adjustment,which focuses on the winning probabilities forthe home and away team, only.32 His relativewinning probability measure (REL.WINPROB)is given by

REL:WINPROB5X2k51

pk

p1 þ p2log

�p1 þ p2

pk

�:

ð6Þ

Finally,wealsodecided to includeaquadraticspecification of the home team’s winning proba-bility (WINPROB, WINPROBSQR). This isdone to allow for a comparison with previousresults in the literature, which show a concaverelationship between this winning probabilityand consumer demand.

We conclude this subsectionwith anoverviewof the expected results on the uncertainty meas-ures for our empirical analysis (see Table 3).

D. Estimation Procedure

Within this section, we shortly discuss theunderlying idea behind (censored) quantileregression33 and how this estimation procedurecan be implemented for empirical analyses.Recall that within our empirical frameworkwe are interested in estimating the effect ofvarious measures of match uncertainty (UOO)on different quantiles of aggregate (adjusted)match attendance demand in professionalGerman soccer. The quantile regression modelwas originally introduced by Koenker andBassett (1978). They argue that the estimationof regression quantiles yields a much morecomplete view of the relationship betweenthe observations on a dependent variable, hereDit and a set of regressors, here x, z, e, w,UOO. For the hth-quantile, the model can bewritten as

QuanthðDitjUOOit; xit; zit; eit;witÞ5 UOOitbþ x#itfþ z#itcþ e#itnþ w#itk;

31. In Germany, bookmakers do not give probabili-ties but betting quotes only. For a derivation of the cor-responding probabilities, see the Appendix.

32. His argument is based on the fact that, given equalwinning probabilities for the home and away team,a changing value for the draw probability would resultin a decrease of THEIL. Thus, a decrease in THEILmay not always be driven by a decrease in match uncer-tainty of outcome. Consider, for instance, the draw prob-ability changing from 50% to 60% while home and awaywin probabilities change from 25% to 20% each. In thiscase, the relative uncertainty of home and away win willnot be affected.

33. For excellent introductions, the interested readeris referred to Koenker (2005) and Buchinsky (1998).


which holds if

QuanthðeitjUOOit; xit; zit; eit;witÞ 5 0:ð7Þ

However, due to the existence of capacityconstraints at stadiums, we may not alwaysbe able to observe ‘‘true’’ ticket demand, assome observations may be censored. Thismeans that we observe values on all exogenousvariables for every observation within oursample, whereas for some observations ofthe dependent variable, we only know thatticket demand was at least as high as thematch-specific stadium capacity Ct. In the lit-erature, Dit is thus referred to as a limiteddependent variable. This requires us to distin-guish between attendance demand for a match,denoted by D*it and attendance at this match,denoted by Dit, where ticket demand equalsattendance as long as the stadium’s capacityconstraint is not met. This point can be mademore precisely by writing down the followinglatent variable model:

D*it 5 UOOitbþ x#itfþ z#itc

þ e#itnþ w#itkþ eit

ð8Þ

and

Dit 5Cit : D

*it � Cit

D*it : D*it ,Cit

:

8<:

Based on this latent variable model, we canwrite our estimation model as

QuanthðDitjUOOit; xit; zit; eit;witÞ5 minðCit;UOOitbþ x#itfþ z#itc

þ e#itnþ w#itkÞ

ð9Þ

and it follows that

@Quanth½D*it jUOOit; xit; zit; eit;wit�@UOOit

5 b;ð10Þ

that is, b is the partial effect from UOO onattendance demand rather than attendance.

With respect to the implementation of ourestimation procedure, it is important to pointat the fact that the censored quantile regression(CQR) coefficient estimate, for example, onUOO, b, can only be calculated from thoseobservations within a sample for which the con-ditional quantile is not in the unobserved partof the distribution. Therefore, we need to drop

that portion of the data for which the condi-tional quantile is in the unobserved part ofthe distribution. ‘‘It follows that the calculatedasymptotic covariancematrix has to be adjustedfor the fact that the estimation is conditionedon the inclusion of only the observations forwhich’’ the conditional quantile is in the ob-served part of the distribution.34 Of course, theset of observations for which the conditionalquantile exceeds the censoring point is notknown ex-ante. However, Buchinsky (1994)suggested an iterative linear programmingalgorithm (ILPA) that uses an iterative proce-dure to determine the set of observations thatcould have been excluded from the estimation.In particular, he proposes a design matrixbootstrap estimator for the asymptotic covari-ance matrix. Within this paper, we follow hisempirical strategy (see also below).

Another comment is required on specificobservations forwhich there isnot sufficientvari-ationinthedependentvariable,asnoinformationabout the coefficients of interest can be inferredfrom such observations. For example, withinour data set, matches involving Bayern Munichas the visiting team are found to be sold out in95% of all times. As a result, the introductionof an additional regressor controlling for BayernMunichbeing the visiting teamwouldnot lead toa reasonable estimate for theassociatedmarginaleffectas95%oftheseobservationsdonotcontaininformation on the influence from BayernMunich being the visiting team (and all otherregressors) on ticket demand: Theoretically, thecoefficient on Munich could have been ‘‘þ‘,’’thereby leading to ticket demand exceeding sta-dium capacity. As a result, we decided to dropthose observations35 fromour sample.However,weneedtoemphasizethattheexclusionofDerbiesand Bayern Munich’s away matches is not inher-ently driven by the fact that those are censoredobservations but by their lack of variation forthe dependent variableDit. As a result, our pop-ulation under study can best be characterized asall matches that are neither Derbies or BayernMunich’s away matches in the German Bunde-sliga. The reader should note that although thesize of bred for the reduced sample will generallybedifferent from btot for the total sample,36 thees-timator is still

ffiffiffin

p-consistent and asymptotically

34. See Buchinsky (1998) p. 120–1.35. A similar reasoning applies to so-called ‘‘Derbies,’’

leading to the exclusion of Derby matches from our sam-ple, too.

36. See, for example, Preisser and Qaqish (1996).


normal for the new population parameters(Buchinsky, 1998).

To estimate the model in Equation (1) weuse Stata 9. However, obtaining estimateson CQR with observation specific censoringvalues has not yet been implemented in Stata.Therefore, we rely on the ILPA implemen-tation for Stata by Robert Vigfusson.37 Thiscode is then adjusted38 to allow for observa-tion-varying censoring values. In additionwe adjust the ILPA code such that it becomesthe modified iterative linear programmingalgorithm.39 Standard errors on all estimatesare obtained by performing 2000 bootstrap-ping replications. Due to this procedure, thepossible existence of heteroskedasticity isalready taken into account for the calculationof the standard errors.

Concluding this section, we would like tocomment on the existence of clustered obser-vations within our data set. Clustering affectsthe standard errors of our estimates as it refersto a situation in which there are ‘‘groups’’ ofobservations, which are correlated within thegroup but are uncorrelated across groups.Within our sample, clustering should be ex-pected to be present for the following reason:Each season, each team plays 17 matches athome, which results in 17 attendance figuresfor our data set. However, these attendancefigures comprise two different groups of con-sumers, namely, season ticket and matchday–ticket holders. Given that the numberof season ticket holders remains constantfor all 17 matches, shocks in season ticketdemand will in general affect match day–ticketavailability for the whole season. An alterna-tive source of shocks affecting the ‘‘group’’ ofhome matches by a team in a particular seasonmight be the kind of media coverage withina season: The way that team performance isjudged by the media may depend on theirexpectations, which are often based on playertransfers for a particular season. This mightalso affect consumer demand for match daytickets. To allow for such types of clustering,we calculate clustering adjusted bootstrappedstandard errors.

IV. EMPIRICAL RESULTS

Within this section, we present our estima-tion results for CQR, OLS regression and cen-sored normal regression (Tobit). Followingour reasoning from Section III, the dependentvariable in all models is the logarithmic numberof adjusted match attendance.

When interpreting the results, the readershould recall from Equation (10) that the esti-mated marginal effects in censored quantileand censored normal regression models referto the percentage change in attendance demand,whereas the estimated coefficients from theOLS model refers to a percentage change inactual attendance. For this reason, we placemore emphasis on the CQR and Tobit results,as from a team owner’s perspective, knowingthe behavior of the underlying demand func-tion should be particularly interesting as, forinstance, it is relevant for the adoption of opti-mal pricing schemes. Observed attendance, onthe contrary, should already be seen as theconsumers’ response to such schemes.

An additional note is required concerningthe number of observations used in each esti-mation.40 As the reader will note from Table 4below, these numbers differ across Tobit, OLSand different quantile estimations. This isbecause we rely on the ILPA algorithm toimplement the CQR estimators (see alsoabove). The iterative nature of this algorithmcomes from the fact that at the beginning ofthe algorithm an uncensored quantile regres-sion model is fitted to the data and the asso-ciated predicted values for each observationare calculated. In case that the predicted valueis greater than the corresponding censoringvalue, this observation is excluded from thedata set and, in the next iteration step, themodel is estimated again based on the remain-ing observations. Convergence is then defined

TABLE 3

Expected Signs for b-Coefficients

Variable Expected Sign

ADSTAND (�)

FSB (�)

THEIL (+)

REL.WINPROB (+)

WINPROB (+)

WINPROBSQR (�)

37. The code is available from http://faculty.chica-gogsb.edu/timothy.conley/research/qrcode/quantile.html

38. The software code is available from the authors onrequest.

39. Fitzenberger (1994) has shown that this algorithmis more likely to achieve convergence than ILPA. 40. See also Buchinsky (1998), p. 121.


to be achieved if the set of observations is thesame for two subsequent iteration steps. Ascan be seen fromTable 4, the number of obser-vations used is decreasing in the quantile ofinterest. However, even for the 90% quantile,the number of observations is always strictlygreater than 400, which we regard as suffi-ciently high in order to yield reliable results.

Our empirical results on the match uncer-tainty of outcome measures for the 10%,25%, 50%, 75% and 90% quantiles are givenin Table 4. The different UOO model specifi-cations are separated by two horizontal lines,where each model includes only one measurefor the ex-ante degree of match uncertainty ofoutcome. It is immediately revealed that UOOdoes not seem to be an important influencefactor for match attendance demand: Irrespec-tive of the underlying measure, we do not findany statistically significant effects for the 10%–75% quantiles. A noteworthy exception to thisis the 25% quantile in the FSB specification,for which we find the theoretically expectedeffect that an ex-ante less balanced match willface lower attendance demand. Interestingly,however, the results are much clearer for the90% quantile: Here, three out of five modelspecifications reveal a statistically significantinfluence from match uncertainty of outcomeon consumer demand; moreover, these effectssupport Rottenberg’s uncertainty of outcomehypothesis. For ADSTAND, we see thatincreasing ADSTAND by 1 leads to a 1.6%reduction in attendance demand.

Based on the FSB specification, we obtainthe result that an increase in FSB by 1 pointwill lower consumer demand by 12% (at the25% quantile) and by 20% (at the 90% quan-tile). Although these numbers may seemextraordinarily large, it should be mentionedthat within our sample period the averagevalue for FSB lay around 0.81 points, thatis, the current average FSB value is smallerthan the (hypothetical) change that is associ-ated with the marginal effect for FSB. Giventhat the measure is defined on the intervalbetween 0 (perfect uncertainty) and 3 (no un-certainty), a change of FSB by 1 point shouldcertainly be viewed as a strong decrease inmatch uncertainty. Intuitively speaking, andviewing match uncertainty to be continuouslydecreasing in FSB, we could say that increas-ing FSB, for example, from 0.81 to 1.81 pointswould correspond to a decrease in matchuncertainty from 73% [(3 � 0.81)/3] to 40%

TABLE

4

Estim

ationResults(A

djusted

Ticket

Dem

and)

Variable

Quantile

OLS

Tobit

0.10

0.25

0.50

0.75

0.90

b-C

oef.

b-C

oef.

b-C

oef.

b-C

oef.

b-C

oef.

b-C

oef.

b-C

oef.

ADSTAND

0.002(0.006)

�0.005(0.005)

�0.002(0.005)

�0.004(0.006)

�0.016(0.008)y

�0.004(0.004)

�0.002(0.004)

N5

1161,R25

.339

N5

1040,R25

.372

N5

860,R25

.397

N5

581,R25

.372

N5

408,R25

.426

N5

1284,R25

.417

N5

1284,R25

.378

FSB

0.033(0.075)

�0.120(0.067)y

�0.100(0.078)

0.015(0.076)

�0.199(0.104)y

�0.080(0.056)

�0.019(0.050)

N5

1162,R25

.341

N5

1037,R25

.374

N5

867,R25

.397

N5

579,R25

.373

N5

410,R25

.422

N5

1284,R25

.418

N5

1284,R25

.375

THEIL

�0.919(1.655)

�2.087(1.488)

�1.110(1.320)

�0.136(1.473)

�0.820(2.228)

1.168(1.047)

�0.887(1.048)

N5

1162,R25

.342

N5

1024,R25

.370

N5

857,R25

.401

N5

578,R25

.374

N5

425,R25

.422

N5

1284,R25

.418

N5

1284,R25

.375

REL.W

INPROB

�1.161,(1.448)

�1.836,(1.376)

�1.198,(1.131)

�0.990,(1.180)

�2.810,(1.820)

0.884,(0.956)

�1.135,(0.945)

N5

1158,R25

.346

N5

1024,R25

.371

N5

854,R25

.402

N5

586,R25

.376

N5

415,R25

.422

N5

1284,R25

.418

N5

1284,R25

.376

WIN

NIN

GPROB

0.079(2.292)

0.220(1.827)

�0.365(2.503)

2.456(3.085)

7.343(3.807)y

1.145(1.451)

1.583(1.610)

WIN

NIN

GPROB2

0.273(2.231)

0.736(1.850)

1.027(1.994)

�1.878(2.907)

�6.890(3.862)y

�1.497(1.324)

�0.888(1.594)

N5

1160,R25

.341

N5

1025,R25

.375

N5

866,R25

.399

N5

578,R25

.380

N5

415,R25

.432

N5

1284,R25

.418

N5

1284,R25

.377

Notes:Standard

errors

inparentheses:CQR

andTobitestimationstandard

errors

are

clusteringadjusted

standard

errors

basedon2000bootstrapreplications;OLSstandard

errors

are

whiteheteroskedasticity-robust

standard

errors

adjusted

forclustering.Coef.5

coefficient.

Significance

levels:y10%;*5%;**1%.


[(3 � 1.81)/3]. This means that match uncer-tainty is almost cut in half. Thus, in our opin-ion, the size of the marginal effects for FSBshould be attributed to the associated strongdeterioration in ex-ante match uncertainty.

Our results for the home team’s winningprobability (WINPROB) support a non-linearspecification for this measure: For the 90%quantile, we find a concave relationship betweenthe home team’s winning probability and atten-dance demand. The presented coefficients referto the percentage change in attendance demandfor a one percentage-point increase in the hometeam’s winning probability, for instance, from45% to 46%41. Based on this specification, wefind attendance demand to be maximized whenthe home team’s winning probability reaches53%. As can be seen from our literature review,this result is in line with previous findings in theliterature (see Section II).

In order to provide the reader with a moredetailed view on our empirical findings, wealso give a graphical illustration for our esti-mation results on the uncertainty measuresin Figure 1. For each uncertainty measure,the corresponding Tobit estimation results(point estimate and 95% confidence intervalbounds) were chosen as benchmark and quan-tile estimates were calculated in 10% steps,ranging from 10% to 90% quantiles.

Concluding this section, two importantaspects about our empirical results requirespecial mention. First, match uncertainty ofoutcome is only found to affect attendancedemand on a 10% level of significance. Com-bining this fact with our estimation results onteam quality factors from Tables A1-A3 inappendix, we come to a similar conclusionas Czarnitzki and Stadtmann (2002), namelythat a team’s reputation (and current rank-ing) seems to be the main driving force formatch attendance demand in the GermanBundesliga. In other words, uncertainty of out-come is obtained to be a ‘‘second-order’’ influ-ence factor only. This point is furtherstrengthened by the interesting result that in

the period 1999–2004 at least 75% of allmatches in the German Bundesliga did notshow any reliance onmatch uncertainty of out-come measures. On such empirical grounds,the question can be raised whether the exclu-sive adoption of revenue-sharing systems canbe expected to ‘‘get the job done’’ for associ-ation officials, a question to which we will turnnow in our concluding discussion.

V. CONCLUSION

The purpose of this study was to analyzewhether previous results describing the effectof uncertainty of outcome on match atten-dance could have been driven by heterogeneityin fan demand and/or the use of various meas-ures of uncertainty. To answer this question,we adopted quantile regression methods onindividual match attendance demand for avariety of uncertainty measures. Following thearguments by Koenker and Bassett (1978),we argued that quantile regression would pro-vide a much better understanding of the con-ditional distribution of match attendancedemand.

Based on data from professional Germansoccer in the period 1999–2004, our empiricalanalysis clearly reveals two importantfacts: First, match UOO is found to be only a‘‘second-order’’ influence factor for attendancedemand. Statistically much more important isa team’s reputation (in terms of its performancewithin previous years) and current ranking. Thisresult is in line with the previous findings byCzarnitzki and Stadtmann (2002). The secondaspect relates to the question whether UOO isa relevant influence factor for all quantiles inthedistributionof consumerdemand, aquestionthat is clearly negated by our findings: Matchuncertainty of outcome is consistently found(for three out of five UOO measures) to affecthigh-demandmatches only.42Unlike the findingfrom CQR methods, Tobit or OLS estimationprocedures do not obtain this result. In ouropinion, this stresses the importance of quantileregressionmethods for the analysis of consumerdemand in general, and the demand for sport, inparticular.

Regarding policy implications for associa-tion officials, we come up with the following

41. This can be seen as follows: Information on thehome team’s winning probability was included in decimalform, that is, 45% was expressed as 0.45 rather than 45.However, following Wooldridge (2003, p. 43), using 45instead of 0.45 would result in b45 5 1=100 � b0:45. Asthe dependent variable is measured as logarithmic matchattendance demand, the marginal effect from the hometeam’s winning probability (e.g. 45%–46%) on demandis given by b45 � 100 percent. Clearly this is equivalent tob0:45 percent.

42. As we are concernedwith this finding’s robustness,For reasons of simplicity, we abstract from the FSB resultfor the 25% quantile, as discussed in Section IV.


suggestions: If association and league officialsaim at increasing a league’s degree of matchuncertainty of outcome, it is not sufficientto simply redistribute revenues, for example,from the UEFA Champions League to non-participating teams. Our findings provide

strong evidence that redistribution schemeswill only affect attendance demand as far asteams facing low demand (call them ‘‘low-demand’’ teams) are able to efficiently investthis money into player talent. As long as thiscannot be achieved by those teams, they will

FIGURE 1

Results from Quantile Regression.–6

–4–2

02

4

Estimated Coefficients for THEIL

0 .2 .4 .6 .8 1

Quantile

Low/Hi Quantile Quantile Estimate

Low Tobit Tobit EstimateHi Tobit

–6–4

–20

2

0 .2 .4 .6 .8 1

Quantile

Estimated Coefficients for RELWINPROB



–.03

–.02

–.01

0.0

1

0 .2 .4 .6 .8 1

Quantile



Estimated Coefficients for ADSTAND



–.4

–.2

0.2

Estimated Coefficients for FSB

0 .2 .4 .6 .8 1

Quantile

–50

510

15

0 .2 .4 .6 .8 1

Quantile

Estimated Coefficients for WINPROB





–15

–10

–50

5

Estimated Coefficients for WINPROBSQR

0 .2 .4 .6 .8 1

Quantile


not be able to generate additional interest asa higher budget itself does not increase atten-dance demand (see the results in the appen-dix). Although this may seem obvious froma single team’s economic point of view, ourfindings suggest that the importance of effi-cient investment allocations by ‘‘low-demand’’teams is also relevant for the ‘‘high-demand’’teams, because of the UOOmechanism: Theseare the teams that exclusively profit from anincrease in match uncertainty of outcomewhen playing ‘‘previously low-demand’’ teamsat home, that is, teams that used to be ‘‘low-demand’’ ones but have learned to invest theirmoney more efficiently, thereby increasingtheir associated team quality. Such a scenariowould certainly qualify to be termed a classical‘‘win-win situation’’: ‘‘Low-demand’’ teamswould become ‘‘more interesting’’ for theirown customers at home and would also posea positive externality when playing ‘‘high-demand’’ teams on the road.

In order to achieve this goal, however, webelieve that the promotion of additionalgovernance standards is indispensable forincreasing managerial professionalism inthe day-to-day operations of soccer clubs.At first sight, the idea that those in chargeof the team should use the redistributedmoney wisely and make the ‘‘right’’ invest-ment decisions might seem to be more anissue of ‘‘good judgment’’ and less an issueof governance standards.43

However, governance standards have thepotential to promote ‘‘good judgment’’ in soc-cer clubs by altering the selection proceduresand incentives for managerial candidatesand by improving the accountability and con-trol of decision makers. Currently, we still see alot of potential in improving the quality of theadopted governance standards: In Germany,for example, registered associations called‘‘eingetragener Verein’’ are still required byleague regulation to remain majority ownersof their specific Bundesliga teams. Managedby representatives, who are elected by themembers of the Verein, this special form ofnon-profit organization is not even requiredto publish its accounts. As there is no cheapand reliable mechanism to aggregate the pref-erences of a heterogeneous and large group ofpeople like the members, the elected represen-

tatives de facto seize control of German soccerclubs. They have the discretionary freedom toderive personal utility from the fame and pub-licity associated with sporting success. At thesame time they are not personally liable for thefinancial losses of the club.44 The history ofGerman clubs entering into insolvency pro-ceedings and accused of fraudulent practicesis rather rich. The appointment of managerialstaff without any formal training and withouta track record in management and account-ing is still common practice in this environ-ment. Against this background governancestandards leading to a selection of manage-rial staff with relevant skills and enhancingthe accountability of decision makers arelikely to increase the advent of ‘‘good judg-ment’’ in German football. As the lack ofprofessional management does not seem tobe a German exception in Europe, variousnational football governing bodies as wellas UEFA have started attempts to improvethis situation.45 Our findings thus sheda new and positive light on this currentattempt of UEFA to promote standards of‘‘good governance’’ in an industry witha poor track record concerning the selectionof managerial candidates and the monitoringof decision makers.

APPENDIX

Within this appendix, we show how to translate bettingquotations into probabilities, how the values on the vari-able DBtime have been obtained, and present estimationresults on team quality regressors and a team’s admissionprice.

A. Derivation of Probabilities from Betting Quotations

In the German betting market, bookmakers do notquote probabilities for the different match outcomes,

43. We are grateful to an anonymous referee whoattracted our attention to this issue.

44. See Dietl and Franck (2007) for an extensive dis-cussion of this aspect.

45. UEFA’s Club Licensing System was approved in2002 and first introduced in the 2004/05 season. The ideawas to set a common minimum standard in five key areasfor entry into UEFA competitions across Europe. The cri-teria used by UEFA fall into five areas—sporting, infra-structure, personnel and administration, legal, andfinancial. By setting a minimum standard, the license nec-essarily falls short of the most stringent standards set forsome criteria in some countries; however, it representsa significant regulatory hurdle for clubs in many countrieswhere regulation is less robust. To improve the perfor-mance of these standards, the UEFA Club Licensing sys-tem is monitored by spot checks to see that the system iscorrectly implemented by clubs and national associations.Finally, a new tougher licensing system (version 2.0) willcome into effect in the 2008/09 season.


but give payment quotations. Let us clarify the derivationby an example. In the 1999/2000 season, on December 4,Stuttgart (at home) played 1860 Munich. The quotationswere ‘‘2 to 1 for Stuttgart winning,’’ ‘‘2.75 to 1 for a draw’’and ‘‘2.6 to 1 forMunich winning.’’ In other words, book-makers would pay 2 Euro per Euro betted in the case ofStuttgart winning. Based on these quotations, the‘‘implicit probabilities’’ were 0.5 (1/2), 0.36 (1/2.75) and0.38 (1/2.6). However, these values would not satisfythe restriction that probabilities need to sum up to 1. Thisis due to the fact that these probabilities include earningspreads of the bookmakers. Thus, we need to adjust the‘‘probabilities’’ once more by

p1 50:5

0:5þ0:36þ0:38 5 :40

p2 50:36

0:5þ0:36þ0:38 5 :29

p3 50:38

0:5þ0:36þ0:38 5 :31:

These probabilities can be used to calculate THEILand REL.WINPROB.

B. Obtaining DBtime

Our measure is based on the timetable from DeutscheBahn, the German Railway Service Provider.

We obtained the travel times by submitting the follow-ing information on the internet site (http://www.bahn.de)of Deutsche Bahn:

1. From: Visiting Team’s Hometown (Main Station)2. To: Home Team’s Hometown (Main Station)3. Outward Journey: Saturday.46

4. Arrival Time: 14:30h to 15:00h5. Means of Transport: all except InterCity Express

(ICE).47

The arrival time was chosen to ensure between 30 and60 min for travel time frommain station to stadium beforekick-off. Usually, special ‘‘fan trains’’ are organized forvisiting teams. However, to the best of our knowledge,48

these trains do not include ICE-trains, which results inlonger travel times.

C. Estimation Results on Team Quality ControlRegressors and Admission Price

Within this subsection, we present our empirical resultson team quality factors and the home team’s admissionprice (Table A1–A3). As all empirical results are in line withpredictions from economic theory, we do not provide anyadditional interpretation of these results. Noteworthy, how-ever, is the fact that the insignificance of certain quality fac-tors cannot be attributed tomulticollinearity; for all models,we calculated variance inflation factors (VIFs) based on theOLS specification. For all team quality factors, we obtainedVIFs between 1 and 4. Following Neter, Wasserman, andKunter (1990), however, there is evidence for multicolli-nearity if the largest VIF is above the value of 10. Thesevalues were only obtained for our distance measure andthe home team’s winning probability (both of which followa quadratic specification, because it seems appropriate froman economic theory’s point of view). As a result, we are nottoo concerned about multicollinearity as an important fac-tor for our team quality regressors’ results.

46. It should be mentioned that for reasons of simplic-ity we did not adjust times for matches on other weekdays.Saturday matches account for 65% of all matches in oursample. In addition, travel times usually do not signifi-cantly differ across days.

47. The ICE is the fastest and most expensive traintype that is currently operated by Deutsche Bahn.

48. We are grateful to Norbert Schneider from Deut-sche Bahn for providing us with this information.


TABLE

A1

CQR

(adjusted

ticket

dem

and)—

ADSTAND

Variable

Quantile

OLS

Tobit

0.10

0.25

0.50

0.75

0.90

b-C

oef.

b-C

oef.

b-C

oef.

b-C

oef.

b-C

oef.

b-C

oef.

b-C

oef.

Hstand

�0.018(0.010)y

�0.030(0.008)**

�0.030(0.007)**

�0.028(0.008)**

�0.026(0.009)**

�0.019(0.010)y

�0.025(0.007)**

Astand

�0.007(0.005)

�0.014(0.005)**

�0.010(0.006)y

�0.012(0.006)*

�0.017(0.007)*

�0.010(0.003)**

�0.012(0.003)**

Hstand(LS)

�0.001(0.018)

0.014(0.013)

0.006(0.013)

0.001(0.013)

�0.008(0.017)

0.018(0.016)

0.007(0.012)

Astand(LS)

0.010(0.005)y

0.004(0.006)

�0.005(0.006)

�0.008(0.006)

�0.010(0.007)

�0.001(0.003)

�0.002(0.003)

HGLM

0.028(0.016)y

0.010(0.015)

�0.009(0.015)

0.016(0.019)

�0.004(0.025)

0.003(0.009)

0.009(0.010)

AGLM

0.006(0.021)

0.037(0.018)*

�0.010(0.017)

�0.023(0.021)

�0.033(0.028)

0.002(0.011)

�0.007(0.010)

Hbudget

0.006(0.006)

0.002(0.006)

�0.000(0.005)

�0.001(0.005)

�0.003(0.006)

0.006(0.005)

0.007(0.005)

Abudget

�0.000(0.002)

0.000(0.002)

0.001(0.003)

0.005(0.004)

0.013(0.005)**

0.001(0.001)

0.002(0.001)

HREP20

0.007(0.003)*

0.008(0.003)**

0.0070.003*

0.016(0.005)**

0.017(0.005)**

0.009(0.003)**

0.007(0.002)**

AREP20

0.013(0.002)**

0.008(0.002)**

0.007(0.002)**

0.006(0.002)**

�0.001(0.003)

0.005(0.001)**

0.007(0.001)**

Hseries3

0.123(0.102)

0.141(0.131)

0.219(0.144)

0.219(0.180)

0.048(0.213)

0.051(0.063)

0.115(0.075)

Aseries4

0.0.70(0.197)

0.305(0.129)*

0.184(0.152)

0.082(0.159)

�0.093(0.187)

0.121(0.139)

0.151(0.121)

log(Price)

�0.249(0.200)

0.013(0.198)

0.305(0.170)y

0.295(0.185)

0.340(0.217)

�0.281(0.173)

�0.060(0.165)

Notes:Standard

errors

inparentheses:CQR


errors

are

clusteringadjusted

standard

errors


errors

are


standard

errors

adjusted


coefficient.

Significance

levels:y10%;*5%;**1%.


TABLE

A2

CQR

(adjusted

ticket

dem

and)–FSB

Variable

Quantile

OLS

Tobit

0.10

0.25

0.50

0.75

0.90

b-C

oef.

b-C

oef.

B-C

oef.

b-C

oef.

b-C

oef.

b-C

oef.

b-C

oef.

Hstand

�0.013(0.011)

�0.038(0.009)**

�0.035(0.008)**

�0.027(0.008)**

�0.036(0.011)**

�0.024(0.009)**

�0.026(0.008)**

Astand

�0.009(0.006)

�0.004(0.006)

�0.005(0.007)

�0.013(0.007)y

�0.012(0.009)

�0.005(0.004)

�0.011(0.004)*

Hstand(LS)

0.000(0.017)

0.012(0.013)

0.004(0.012)

0.003(0.013)

0.000(0.015)

0.018(0.016)

0.007(0.012)

Astand(LS)

0.009(0.006)

0.004(0.006)

�0.003(0.006)

�0.006(0.006)

�0.010(0.008)

�0.001(0.003)

�0.002(0.003)

HGLM

0.031(0.016)y

0.005(0.014)

�0.001(0.014)

0.011(0.018)

0.011(0.026)

0.002(0.009)

0.009(0.010)

AGLM

�0.001(0.021)

0.033(0.017)y

�0.009(0.017)

�0.019(0.022)

�0.027(0.028)

0.002(0.011)

�0.007(0.010)

Hbudget

0.006(0.006)

0.002(0.006)

0.001(0.005)

�0.002(0.005)

�0.003(0.006)

0.006(0.005)

0.007(0.005)

Abudget

0.000(0.002)

0.001(0.002)

0.001(0.003)

0.006(0.004)

0.004(0.005)

0.000(0.001)

0.001(0.002)

HREP20

0.007(0.003)*

0.008(0.003)**

0.007(0.003)*

0.016(0.005)**

0.021(0.005)**

0.009(0.003)**

0.007(0.003)**

AREP20

0.012(0.002)**

0.009(0.002)**

0.007(0.002)**

0.006(0.002)**

0.001(0.003)

0.005(0.001)**

0.007(0.001)**

Hseries3

0.141(0.105)

0.146(0.132)

0.221(0.133)y

0.284(0.173)

0.062(0.190)

0.065(0.063)

0.120(0.074)

Aseries4

0.079(0.206)

0.400(0.135)**

0.149(0.160)

0.018(0.162)

0.067(0.243)

0.133(0.146)

0.149(0.125)

log(Price)

�0.256(0.186)

0.032(0.198)

0.318(0.163)y

0.300(0.186)

0.298(0.215)

�0.282(0.174)

�0.058(0.168)

Notes:Standard

errors

inparentheses:CQR


errors

are

clusteringadjusted

standard

errors


errors

are


standard

errors

adjusted


coefficient.

Significance

levels:y10%;*5%;**1%.


TABLEA3

CQR

(adjusted

ticket

dem

and)—

WIN

PROB

Variable

Quantile

OLS

Tobit

0.10

0.25

0.50

0.75

0.90

b-C

oef.

b-C

oef.

b-C

oef.

b-C

oef.

b-C

oef.

b-C

oef.

b-C

oef.

Hstand

�0.014(0.011)

�0.026(0.009)

�0.026(0.007)**

�0.024(0.010)*

�0.024(0.012)*

�0.020(0.009)*

�0.020(0.007)**

Astand

�0.010(0.006)y

�0.021(0.007)**

�0.015(0.007)*

�0.017(0.008)*

�0.019(0.009)*

�0.008(0.004)y

�0.017(0.004)**

Hstand(LS)

0.002(0.018)

0.016(0.013)

0.011(0.013)

0.004(0.013)

0.014(0.015)

0.017(0.017)

0.009(0.012)

Astand(LS)

0.009(0.006)

0.003(0.006)

�0.004(0.006)

�0.009(0.006)

�0.013(0.008)

�0.001(0.003)

�0.004(0.004)

HGLM

0.031(0.017)y

0.001(0.014)

�0.013(0.015)

0.008(0.019)

0.002(0.027)

0.003(0.009)

0.008(0.010)

AGLM

0.001(0.021)

0.017(0.018)

�0.006(0.018)

�0.021(0.022)

�0.018(0.026)

0.001(0.011)

�0.005(0.010)

Hbudget

0.006(0.006)

0.001(0.006)

0.000(0.006)

�0.002(0.005)

�0.005(0.006)

0.007(0.005)

0.007(0.005)

Abudget

(0.001)(0.003)

�0.000(0.003)

0.002(0.003)

0.006(0.004)

0.013(0.005)**

0.000(0.001)

0.003(0.002)

HREP20

0.007(0.003)*

0.007(0.003)*

0.006(0.003)y

0.015(0.005)**

0.020(0.005)**

0.009(0.003)**

0.007(0.003)**

AREP20

0.013(0.002)**

0.010(0.002)**

0.008(0.002)**

0.006(0.002)**

0.001(0.003)

0.004(0.001)**

0.008(0.001)**

Hseries3

0.091(0.108)

0.109(0.119)

0.215(0.150)

0.311(0.184)y

0.014(0.197)

0.055(0.064)

0.114(0.077)

Aseries4

0.103(0.200)

0.334(0.130)*

0.210(0.151)

0.106(0.181)

�0.061(0.185)

0.124(0.140)

0.168(0.129)

log(Price)

�0.257(0.198)

0.068(0.200)

0.310(0.169)y

0.260(0.198)

0.343(0.236)

�0.280(0.175)

�0.076(0.167)

Notes:Standard

errors

inparentheses:CQR


errors

are

clusteringadjusted

standard

errors


errors

are


standard

errors

adjusted


coefficient.

Significance

levels:y10%;*5%;**1%.


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