Freedom of entry, market size, and competitive outcome: evidence from English soccer.

1. Market Size in Sports Economics

Market size has been accorded central importance in the analysis of professional leagues. The two-team-league model of El-Hodiri and Quirk (1971), popularized in Quirk and Fort (1992) and still the framework for contemporary analysis, predicted that the larger market club would achieve a higher win-ratio. It had the incentive to hire more talent than the smaller club because greater success on the field could be more effectively converted to dollars where the customer base was bigger. In equilibrium, the superiority of the big club would be more marked, the wider the discrepancy in populations. Hence, the perceived problem of competitive imbalance in sports leagues came to be identified in the literature with the dominance of big city clubs.

Fort and Quirk (1997) and Quirk and Fort (1999), building on testimony to U.S. Congressional hearings by Roger Noll and Ira Horowitz in 1976 and by Steven Ross in 1989 and 1991, (1) argued for the breakup of U.S. major leagues to encourage new entry into large markets. More recently, Ross and Szymanski (2002, 2005) discussed introducing European-style promotion and relegation into American sports as a means to the same end. Each of these proposals is a response to the current situation where franchises confer territorial monopoly. If leagues were broken up, each of the new competing organizations would be expected to ensure a presence in each of the biggest cities. If promotion into the top level of play were permitted, entrepreneurs would be expected to be attracted by the monopoly rents of large market clubs and would invest in squads of players that could gain them entry. Either way, multiple franchises would presumably emerge in the largest metropoles, as has long been the case in open European soccer leagues. With the market divided between competing clubs, there would be more chance of even competition for championships.

Here we illuminate the debate by testing how closely playing success is linked to market size in practice. Further, we are able to test whether such a relationship exists in a long established open sports league that conforms to the European rather than American model of sport. This provides evidence on how radically the breaking of territorial monopoly in America would in fact ameliorate competitive imbalance.

In the United States, experience appears to be consistent with the notion that size matters (a lot). For example, Sandy, Sloane, and Rosentraub (2004), generalizing across the major team sports, remark that "teams that consistently win have been those with access to either the largest markets, revenue sources that are not shared with other teams, or heavily subsidized facilities" (p. 172). But despite such generalizations, there has been no direct systematic quantification of the relationship between market size and success in American sport. Impediments include that the number of clubs in each sport is small (about 30) relative to the requirements of econometric testing and that it is hard to compare market size across clubs. For example, Schmidt and Berri (2001) suggest that, in the attendance demand literature, "a common proxy for size of a team's market is the size of its metropolitan statistical area" (p. 158). They accordingly enter this in linear form in a baseball demand equation. But this is a misspecification. If one club is located in an standard metropolitan statistical area (SMSA) with twice the population of another, it cannot be considered as having double the market size. The bigger SMSA will cover a wider area, and the mean travel cost for residents to reach the stadium will be higher, implying that the ticket demand curve will not be pushed as much to the right as the population figures alone might suggest. SMSA population is, therefore, an inadequate proxy for market size.

In fact, total team revenues, not just gate revenues, are ultimately driven by local fan base as proxied by local population. Teams in European and North American leagues generally derive revenues not just from gate attendance but also from merchandise sales, sales of broadcast rights, and commercial sponsorship. (2) The potential broadcast revenues that a team can command will depend fundamentally on the fan base of the team as proxied by gate attendance. For example, in the English Premier League the biggest teams (Arsenal, Chelsea, Manchester United, and Liverpool) are shown disproportionately often in televised games and consequently earn larger broadcast revenues than smaller teams (Forrest, Simmons, and Buraimo 2005). In European soccer, teams with larger gate attendances tend to earn more merchandise revenues and larger sponsorship deals and larger broadcast revenues (despite collective selling of broadcast rights by the league as a whole; Buraimo, Simmons, and Szymanski 2006).

Hence, market size can be considered as a fundamental determinant of revenue and, therefore, team performance. In European soccer, increased market size generates a larger fan base and greater gate and other revenues, and this in turn facilitates increased budgets to spend on playing and coaching resources that help deliver improved team performance. Section 3 formalizes these relationships into a structural model for empirical estimation. In our particular study, it is notable that teams in the top tier generated substantial broadcast revenues over our sample period, teams in the second tier obtained modest broadcast revenues, and teams in the third and fourth tiers earned negligible income from televised matches (Buraimo, Simmons, and Szymanski 2006). This scaling of broadcast revenues suggests that the relationship between team performance and market size is likely to be nonlinear, and we address this point explicitly in our empirical model below.

2. Evidence from England

English soccer provides a good context for formal testing of the relationship between success and size for three reasons. First, English soccer has the world's largest professional league structure: With 92 clubs, there is an adequate number of observations for meaningful estimation of the slope of the relationship. Second, it is an appropriately challenging environment in which to test the size hypothesis because it is an open league: Teams play in four hierarchical divisions (with the best and worst performing teams moving up or down a tier at the end of each season) and the bottom two of the 92 are replaced each year by the two clubs at the top of the structure of "minor" (semiprofessional and amateur) leagues. Third, the richness of United Kingdom (UK) census microdata and the availability of suitable geographic information system software permits precise measurement of both market size and overlap of markets between clubs.

In our principal regressions, the dependent variable is [POSITION.sub.it], which reflects the ranking of club i at the end of season t, taking the value 92 for the champion club of the top tier and the value 1 for the bottom team in the fourth tier. Strictly, this is an ordinal measure that we treat as cardinal, but this is unlikely to pose serious problems given the large number of ranks and given that there is no systematic difference across the structure in what is meant by a one-rank improvement. Nevertheless, to show that our results are robust to a different way of representing ranking, we also show estimates of our models for a specification that uses a transformation of the position variable, [TRANSRANK.sub.it], which is the negative logit of league rank (-log(rank/(93-rank))), a continuous variable proposed by Szymanski and Smith (1997) for the context of English soccer and employed in Szymanski (2000). (3)

Our data derive from seven seasons, 1997-1998 to 2003-2004. We restrict analysis to three seasons on either side of the 2001 census so that population measures capturing the market size of each club are based on reasonably contemporary enumeration. Standard errors of coefficients are clustered on clubs because consecutive seasonal outcomes are not independent; for example, a club promoted to the top tier from [POSITION.sub.it] = 72 must finish in the range 73-92 the following year. Clustering accounts for this distinctive feature of the data that would be impractical to represent by inclusion of conventional lagged dependent variables in the specification.

Employing census microdata for 175,000 output areas and manipulating them using stadium ordnance survey map references and the MapInfo software package, we measured the characteristics of two concentric rings, defined by radial distances 0-5 and 5-10 miles, around each stadium. According to Forrest, Simmons, and Feehan (2002), the bulk of attendance at games originates within 10 miles; dividing the catchment area into two ensures rough homogeneity of travel costs from each zone.

In model 1 (Table 1), we regress [POSITION.sub.it] on (log) population (millions) in the inner/ outer zones of a club's catchment area (model 1A reports results from the alternative specification where [TRANSRANK.sub.it] is the dependent variable). Additional regressors in each version of the model are the proportion of the catchment area's population aged over 64 (seniors are more likely to suffer mobility restrictions that make attendance difficult) and the number of years since the club first joined the league (support may build up over time because interest is passed between generations). (4) In either model 1 or 1A, only inner zone catchment area is significant, though it is strongly so. The point estimate from model 1 is that a 100,000 population increase from the mean (434,000) is associated with an improvement of 2.66 places in league position (3.50 according to model 1A). The implication is that the size of the community in which a club is located is a factor in determining club ranking, just as the two-team model predicted. While it may be that we are not observing equilibrium in the study period, the theory appears to hold true even in this context, where there are less rigid barriers to entry into heavily populated areas than in American sports.

Does this mean that reducing entry barriers would not, in fact, weaken the size-success relationship and thereby improve competitive balance? Not necessarily. Model 2 (2A is the alternative version with the transformed position variable) is more revealing in that it explicitly includes a measure of competition from neighboring clubs. Again using MapInfo, we constructed a variable, overlap. Each club was given a 10-mile radial catchment area. The variable overlap is the proportion of the catchment area population shared with another club. Where there is more than one neighboring club, these intersections of population are aggregated: overlap may then exceed I. Indeed it often does. Arsenal generated the highest value of overlap, 7.88, reflecting the extent to which clubs have found it worthwhile to enter the crowded London market.

Model 2 is more precisely determined than model 1 because of the inclusion of a measure of competition. Holding this and other variables constant, we now predict an increase in a club's performance when population increases in either inner or outer zones of the catchment area. Adding 100,000 to the inner and outer mean population values boosts predicted club performance by 4.81 and 1.38 places, respectively (the corresponding estimates for version 2A are 3.78 and 1.05 places). These are larger impacts than in model 1 (and 1A) because we now hold the degree of competition constant, whereas, in fact, the number of clubs will be greater in densely populated areas. The overlap variable attracts a strong negative coefficient, signifying that competition indeed mitigates the advantage of population size. For example, suppose population in both inner and outer zones increases by 100,000 (from mean values) but another club exists in the same location as the subject club. All of the beneficial impact of the higher population is then cancelled out.

Our panel data set comprises seven seasons, and this is too short a panel for formal testing of unit roots and potential within-sample break points to be carried out. Nevertheless, to check the stability of the model, we sequentially pooled the data, year to year, to see if it (model 2) generated different coefficient estimates over time. The results were reassuring. For example, when we used a Hausman test to compare the set of coefficients estimated from using the first five years of data and the set generated by the first six years of data, we could not reject that they were unchanged ([chi square] = 0.01, p = 1.00). When comparing the result to year six with that of year seven, the outcome was similar ([chi square] = 3.99, p = 0.55).

Model 2 demonstrates, then, that permitting freedom of entry to large population markets weakens the relationship between size and outcomes. But model 1 shows that there is insufficient response in the spatial distribution of clubs to eliminate the importance of market size altogether. Market size remains important across the league structure. In fact, in terms of the identity of the champion team, market size appears decisive. In only one of the last ten seasons has a champion emerged from outside the London and Manchester conurbations, and that club benefited from substantial subsidy from a benefactor. A clue to why there is insufficient entry is found in the club age variable. Incumbent teams have an advantage over new entrants because fans are reluctant to change allegiance given that much of their utility derives from the feeling of identity with the club they follow. We would predict that, for example, entry into the New York baseball market would indeed weaken the resource base of the Yankees. But any entry would be limited by the difficulty of weaning fans away from "their" team. Territorial monopoly power would not be eroded completely, and deregulation would still leave existing big city teams with disproportionate resources and success.

3. Underlying Structural Model

The policy debate on sports leagues and competition has taken as its starting point the hypothesis that large market size generates success on the field. We have sought to test this directly for the world's largest professional league. But of course, large population size does not generate wins in matches directly. Sports economics posits a series of relationships that comprise a mechanism by which larger market size leads to greater sporting success. The details vary according to whether one adopts the perspective of the American or the European model of sport, (5) but either generates the reduced form that success depends on market size, which we have tested.

A structural North American model can be developed from the pioneering contribution of Scully (1974). For Major League Baseball (MLB), Scully specified, first, team wins as a function of a vector of player productivity measures and, second, team revenues as a function of team wins. An extended version specifies, first, wage bill as a function of market size (since market size and fan base generate the resources with which to acquire talent), second, team wins as a function of team payrolls (since player productivity should be correlated with team payrolls), (6) and, third, team revenues as a function of team performance. (7)

For a European context, the above model specification is only slightly altered. Equations 1 to 3 capture that market size determines revenue, that revenue drives the wage bill (a measure of the quality of the playing squad), and that this in turn determines the degree of playing success:

Relative revenue = f (market size), (1)

Relative wage bill = g(relative revenue), (2)

League position = h(relative wage bill). (3) (8)

Together, this system of equations generates the reduced form League position = F(market size), (4)

which is the relationship estimated in this paper. Market size is captured by population, demographic, and competition variables that together appear to explain much of the difference in performance across clubs, which we take to be linked to the differences in revenue streams across clubs. As noted in section 1, revenue for all clubs comes from a mix of ticket sales, attendance-related spending such as on food and beverages, merchandising, and broadcasting fees. All are likely to be related to the size of the potential fan base, which, in turn, is related to local population.

It would be of interest to estimate this system of structural equations underpinning our model. However, we were handicapped by the incomplete availability of relevant data since not all clubs declared their wage bills and revenue for every year in the sample period of seven seasons. This makes estimation less reliable than that for the reduced form, since there could potentially be selection bias from employing an incomplete sample. Nevertheless, we report in Table 2 the results from estimating, by three-stage least squares (3SLS), the system of structural equations, with a reduced sample size (449 rather than 644 observations). They illustrate sharply the importance of the key relationships underlying our main model. Population, within 5-10 miles and, more crucially, local population within 5 miles, matters significantly (both in the economic and statistical sense) for determining club revenue. A high proportion of seniors in the population or the presence of rival clubs has a marked negative effect on revenue. The second equation reveals a very well determined and high marginal propensity to spend revenue on player wages. And the third confirms the well-established proposition that playing success is closely related to what is spent on wages, as is to be expected given a competitive labor market with free agency. (9)

4. Conclusions

A concern with competitive balance pervades debate on major league sports in the United States. Two policies--the enforced breakup of leagues and the adaptation of the European model of hierarchical open leagues linked by promotion and relegation--have been proposed, with the goal of encouraging new clubs to emerge in large population centers. The argument is that this would benefit consumers in those markets by offering a choice of supplier and would also benefit fans nationally by intensifying competition for championships, at present won disproportionately often by lucrative monopoly franchises located in the largest metropolitan areas.

Study of European sport, where typically there is open entry based on merit shown in feeder leagues, can illustrate the extent to which allowing competitive forces to operate mitigates the advantages of location in an area with access to (the spending power of) large numbers of fans. Our case study for English soccer shows both the potential and the limitations of policy reforms proposed for the United States. In the English case, market size still matters for sporting success, but the effect is clearly mitigated by clubs having to share markets with rivals. An obstacle to complete elimination of the importance of population size in delivering sporting success is the barrier to entry represented by the allegiance to incumbent clubs built up over time: History as well as geography is significant in understanding which teams fall where in the hierarchy of English soccer clubs.

We predict, then, that either style of reform designed to facilitate entry into large U.S. markets would enjoy partial success in terms of weakening the relationship between population numbers and sporting success. Our analysis cannot distinguish between the merits of the two styles of policy. Much would depend on the details of the respective schemes to be implemented. However, we note that breaking up a major league sport into two competing organizations may lead to only two clubs being available in each of the biggest cities, whereas European-style promotion and relegation can induce a much bigger scale of entry. For example, in the top division of 20 clubs in England, there are currently seven teams based in London and four in Greater Manchester County. In the United States, there are few examples of more than one franchise of a sport being located in a given conurbation, a stark illustration of the different worlds that emerge according to whether markets are organized as monopolies or with freedom of entry.

Appendix
Data Description and Sources

Variable                            Description

League position        League positions are in reverse order
                         with the first place club in the highest
                         division, the Football Association
                         Premier League, taking a value of 92,
                         the second place club taking a value
                         of 91, and so on, to 1

Inner zone             The inner zone population is the
population               number of people within 5 miles of
                         a club's stadium

Outer zone             Outer zone population is the number of
population               individuals residing between 5 and
                         10 miles of a club's stadium

Proportion of 65       The proportion of all individuals within
and over                 10 miles of a club's stadium who are
                         aged 65 or over

Overlap                Overlap is the proportion of all
                         individuals residing within a 10-mile
                         radius of a club who also live within
                         a 10-mile radius of another club.
                         Where there is more than one
                         neighboring club, these intersections
                         of population are aggregated

Years of               Years of membership is the number
membership               of years since the club was first
                         admitted to the football league

Relative revenue       Relative revenue is the ratio of a
                         club's revenue in a given season to
                         the average club revenue across all
                         divisions in English football

Relative wage bill     Relative wage bill is a club's wage bill
                         in a given season divided by the
                         average wage bill in English football
                         that season

Variable                          Source

League position        Teams' league positions are
                         taken from various editions
                         of the Rothmans (now Sky
                         Sports) Football Yearbooks
                         (Rollin and Rollin, various
                         years)

Inner zone             Population information is from
population               the UK's 2001 Census;
                         census information used is
Outer zone               aggregated as appropriate
population               across output areas (the
                         smallest geographical unit
                         for publication of data) and

Proportion of 65       provided by the Office of
and over                 National Statistics

Overlap                Overlap is constructed using
                         the program MapInfo and
                         UK census information
                         provided by the Office of
                         National Statistics

Years of               Information on the duration of
membership               teams' league membership is
                         taken from various editions
                         of the Rothmans (now Ski,
                         Sports) Football Yearbook

Relative revenue       Revenue information was
                         taken from various issues of
                         Deloitte and Touche Annual
                         Review of Football Finance
                         (Deloitte & Touche LLP,
                         various years)

Relative wage bill     Wage bill information was
                         taken from various issues of
                         Deloitte and Touche Annual
                         Review of Football Finance

The authors would like to thank an anonymous referee for valuable suggestions that greatly improved this manuscript. We also acknowledge comments from audiences at the International Association of Sports Economists, Ottawa, 2005, and the Economic and Social Research Council Urban and Regional Economics Study Group, Leeds, 2005.

Received May 2006; accepted October 2006.

References

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(1) The contributions of Noll, Horowitz, and Ross are summarized in Fort (1999).

(2) Lack of data prevents a precise decomposition of revenues by category at club level in English soccer, the subject of our case study below.

(3) In Szymanski (2000) and Szymanski and Smith (I997) the negative logit measure of position delivers an S-shaped relationship in position-relative wage bill space with reflecting barriers at the extreme positions of 1 and 92 and a point of inflection at position 46, halfway through the league rankings. This corresponds to a linear relationship in logit position-relative wage bill space. We prefer to model negative logit of position against log population rather than level of population as the former generates a negative, convex relationship between (actual) league rank and population. A sufficient, not necessary, condition for convexity is that the marginal effect of population is less than or equal to unity and the estimated impact of inner zone population in our model 2A is not significantly different from unity. We find this nonlinear relationship more plausible than the S-shaped form where the second derivative changes sign at an arbitrary league position. Our version predicts that a given increase in population generates a greater improvement in league position from lower levels, ceteris paribus.

(4) Income levels represent another dimension of market size. Initially we included a measure of (occupational) social class, from census data, as another regressor. This was to serve as a proxy for income, information on which is not collected in the UK census. However, the coefficient on social class was not significant, and this variable was consequently deleted from the model.

(5) A key point of contrast in the present context is that the American model starts from an assumption of profit maximization, whereas Europeans, working in countries where ownership and forms of governance of sports clubs are different than they are in the United States, tend to presume that decisions are based on win maximization subject to resource constraints. For contrasting implications of the two types of models for league competitive balance and income redistribution (revenue sharing) policies see Kesenne (2000).

(6) The relationship between team wage bills and team performance appears to be stronger for European soccer leagues than for North American leagues, as revealed by goodness of fit criteria (Simmons and Forrest 2004). This is intuitively plausible, since markets for soccer player talent are open and global with fewer restrictions than in North America. Hence, player productivity and player salaries should be highly correlated in European soccer. In North American sports, major leagues have few teams, restrictions on free agency remain, and the player labor market continues to be predominantly closed, implying monopsonistic divergence of salaries from marginal revenue products. Even in North America, though, Simmons and Forrest (2004) found that team payroll was a significant predictor of team success for all four major sports leagues and including the highly interventionist and restrictive National Football League.

(7) Some U.S. studies have estimated reduced form team revenue functions, for example, Burger and Waiters (2003) for baseball total revenues and Berri, Schmidt, and Brook (2004) for National Basketball Association (NBA) gate revenues. Setting aside our reservations over use of metropolitan area population measures, Berri, Schmidt, and Brook found (log) population to be a significant determinant of NBA revenues, while Burger and Walters found that population significantly affected MLB team revenues when interacted with team wins.

(8) Because our analysis is multiseason, and inflation of revenue and wage bills was a feature of the study period, it is important to recognize that it is not absolute revenue streams and wage bills that matter but rather revenue streams and wage bills relative to other clubs that compete for (relative) league position.

(9) See Simmons and Forrest (2004) for evidence across Europe on the wage bill-team performance relationship.

Babatunde Buraimo, Lancashire Business School, University of Central Lancashire, Preston, PR1 2HE, United Kingdom; E- mail [e-mail].

David Forrest, Salford Business School, University of Salford, Greater Manchester, M5 4WT, United Kingdom; E-mail [e-mail].

Robert Simmons, Department of Economics, The Management School, Lancaster University, LA1 4YX, United Kingdom; E-mail [e-mail]; corresponding author.

Table 1. Regression Results

                                        Model 1

Dependent variable:                            [absolute
  [POSITION.sub.it]             Coefficient   value of t]

Log inner zone population           11.54        2.39
Log outer zone population            1.35        0.49
Proportion 65+                    -106.60        1.23
Years of membership                  0.26        4.10
Overlap
Constant                            55.74        4.19
[R.sup.2]                                  0.38

                                       Model 1A

Dependent variable:                            [absolute
  [TRANSRANK.sub.it]            Coefficient   value of t]

Log inner zone population            0.75        2.58
Log outer zone population            0.08        0.48
Proportion 65+                      -7.32        1.40
Years of membership                  0.02        3.97
Overlap
Constant                             0.81        0.98
[R.sup.2]                                  0.38

  Number of observations                    644
  Clusters                                   98

                                        Model 2

Dependent variable:                            [absolute
  [POSITION.sub.it]             Coefficient   value of t]

Log inner zone population           15.64        3.08
Log outer zone population            7.57        2.42
Proportion 65+                    -172.43        2.13
Years of membership                  0.21        3.17
Overlap                             -5.28        3.13
Constant                            91.72        6.83
[R.sup.2]                                  0.42

                                      Model 2A

Dependent variable:                            [absolute
  [TRANSRANK.sub.it]            Coefficient   value of t]

Log inner zone population            1.01        3.31
Log outer zone population            0.47        2.38
Proportion 65+                     -11.48        2.39
Years of membership                  0.01        3.03
Overlap                             -0.33        3.08
Constant                             3.08        3.87
[R.sup.2]                                  0.41

  Number of observations                    644
  Clusters                                   98

Table 2. Structural Model (estimation by 3SLS)

                                                           [absolute
                                            Coefficient   value of t]

Stage one
  Dependent variable: RELATIVE REVENUE
     Log inner zone population                 0.56          4.61
     Log outer zone population                 0.38          4.81
     Proportion 65+                           -9.38          3.80
     Years of membership                       0.01          6.47
     Overlap                                  -0.24          6.54
     Constant                                  2.83          6.85

Stage two
  Dependent variable: RELATIVE WAGE BILL
     Relative revenue                          0.87         29.22
     Constant                                  0.11          3.02

Stage three
  Dependent variable: POSITION
     Relative wage bill                       27.00         16.56
     Constant                                 27.90         14.72
Number of observations                                449