The impact of pooling and sharing broadcast rights in professional team sports.

Kesenne, Stefan

Introduction

In the White Paper on Sports (2007) of the European Commission, it is stated that: "While joint selling of media rights raises competition concerns, the Commission has accepted it under certain conditions. Collective selling can be important for the distribution of income and can be a tool for achieving greater solidarity within sports:' Although the Commission does not reject the individual selling of broadcast rights by clubs, it clearly prefers the pooling of rights in order to facilitate the distribution. In most national football championships in Europe, as well as in the US major leagues, the broadcast rights are pooled by the league and distributed in one way or another among all clubs. In a few countries, like Spain, Portugal, and Italy, the individual football clubs can individually sell the media rights of their home games. In a few court cases, in Holland, Germany, and Spain, it has been confirmed that the legal owner of the broadcast rights of a team's home game is the club and not the league. In several other court cases, the leagues won. From an economic point of view, individual selling is preferable because collective selling creates a monopoly that can cause welfare losses with prices that are too high and output that is too low (see Noll, 1999). On the other hand, the peculiar economics of professional team sports can also justify that part of the rights can be assigned to the league (see Neale, 1964). One team cannot play a game--a team needs an opponent--and together they supply the product. Moreover, the value of a game is much higher if it is part of a championship, organized by the league as a cartel of clubs, than if it is just an occasional game. Also, a certain competitive balance between the teams is necessary to make the games and the championship more attractive. From this point of view, a shared ownership and some distribution of broadcast rights by the league can be justified (see Jeanrenaud & Kesenne, 2006).

In this paper, we analyze the impact that can be expected from the selling and the distribution of broadcasting rights on the demand for talent and the competitive balance. We will only concentrate on profit maximization as the objective of club owners. If clubs are win maximizers, under a zero or non-zero profit constraint, it is obvious that any sharing arrangement that makes the small-market clubs richer and large-market clubs poorer improves the competitive balance because win-maximizing clubs spend all their (net) revenue on talent.

In an earlier study, Falconieri, Palomino and Sakovics (2004) investigated the welfare effects of collective versus individual sale of television rights, and conclude that the collective sale is socially preferable if leagues are small and homogenous, and if teams receive little performance-related revenues. Our analysis only concentrates on the impact of selling and sharing broadcast rights on competitive balance, because the need for a competitive balance in a sports league has always been the main argument to justify the monopolization of broadcast rights. This competitive balance is only one of the variables that positively affect the demand for broadcast games in the Falconieri et al. (2004) paper. However, these authors do not consider the possibility that the broadcasting money can be distributed if it has been collected individually by the clubs. The conclusion of our paper is that the best guarantee to improve the competitive balance is the individual sale of the rights with a performance-related sharing system.

In the Model Specification section, a simple 2-club Nash equilibrium model is specified with the demand for talent as the only decision variable. Following that, four different scenarios are compared regarding the selling of broadcasting rights and the distribution of the rights among the clubs. The final section includes the discussion and conclusion.

Model Specification

Some studies start from the equilibrium where the only club revenue are gate receipts and then analyze the impact on the competitive balance of sharing broadcast rights. But they do not consider how this money is collected; the money seems to appear out of nowhere. In our opinion, these approaches do not adequately analyze the impact of pooling and sharing broadcast rights; sharing means that money is taken away from somebody and given to somebody else. So, if one wants to analyze the impact of pooling and sharing broadcast rights, one has to start from the benchmark case of a non-pooling/non-sharing equilibrium.

We start from a 2-club league with x being the large-market club and y the small-market club. Each club has two basic sources of season revenue: gate receipts and broadcast rights. We assume that the broadcast revenue of each club, in the benchmark case, is proportional to the number of stadium spectators with a different proportionality factor in each club. See Garcia and Rodriguez (2002) and Forrest and Simmons (2006) for useful empirical evidence on the relationship between broadcasting and gate attendances in Spanish La Liga and English Championship, respectively. In our reference or benchmark case, the sale of broadcast rights is decentralized without any sharing. So, if R is season revenue, p the ticket price, A season attendances, B the broadcasting rights, and k the proportionality factor, total season revenue of each club can then be written as:

[R.sub.i] = [[p. sub.i][A.sub.i]] + [B.sub.i] with [B. sub.i]]= [k.sub.i][A.sub.i]

i : x, y

so : [R.sub.i] = ([p.sub.i] + [k.sub.i]) with [p.sub.x] > [p.sub.y] and [k.sub.x] > [k.sub.y] (1)

It is reasonable to assume that the ticket prices are higher in the large-market clubs. Also, the proportionality factor is higher for large-market clubs because broadcast games of successful teams have a larger drawing potential for spectators than just local supporters. We further assume that televising the games does not affect stadium attendances. Season attendance depends on the size of the market ([m.sub.i]) of the club, which cannot be changed by club management, and on the winning percentage ([w.sub.i]) of the team because spectators prefer winning teams. Following Szymanski (2003), we start from a very simplified attendance function which is linear in winning percentage, but concave in talent:

[A.sub.x] = [[m.sub.x][w.sub.x]] and [A.sub.y] = [[m.sub.y][w.sub.y]]

with [w.sub.x] = [t.sub.x]/[t.sub.x] + [t.sub.y], [w.sub.y] = [t.sub.x]/[t.sub.y] + [t.sub.y], and [m.sub.x] > [m.sub.y] (2)

The season winning percentages of a team depend on their relative playing strength, where the number of talents in a team, not the number of players, is given by [t.sub.i].

This specification implies a positive but decreasing marginal effect of talent on attendance. The total supply of talent ([t.sub.x] + [t.sub.y]) is flexible or fixed.

On the cost side, we only consider a variable player cost and a flied capital cost [c.sub.i.sup.0], so the total cost can be written as:

[C.sub.1] = [ct.sub.i] + [c.sub.i.sup.0] i: x, y (3)

where c is the equilibrium unit cost of talent in a competitive player market where all teams are wage takers.

In this partial approach, we assume that all clubs, at the start of the season, decide on the number of talents, with an exogenously given ticket price and proportionality factor ([k.sub.i]). Clearly, in this model, the winning percentage of one team also depends on the talents of the other team. We therefore derive the non-cooperative Nash equilibrium, assuming Nash conjectures, to derive the clubs' reaction functions and the competitive balance in the league. If clubs are profit maximizers, the optimum is found where the marginal revenue of talent equals the marginal cost. So the benchmark (no-sharing) solution of the model can be found by deriving the two reaction functions:

[partial derivative][R.sub.x][t.sub.x], [t.sub.y]/[partial derivative][t.sub.x] = ([p.sub.x] + [k.sub.x])[m.sub.x] [t.sub.y]/[([t.sub.x] + [t.sub.y]).sup.2] - c = 0

[partial derivative][R.sub.y][t.sub.x], [t.sub.y]/[partial derivative][t.sub.y] = ([p.sub.y] + [k.sub.y])[m.sub.y] [t.sub.x]/[([t.sub.x] + [t.sub.y]).sup.2] - c = 0 (4)

Solving this system of reaction equations results in the competitive balance:

[W*.sub.x]/[W*.sub.y] = [t*.sub.x]/[t*.sub.y] = ([p.sub.x] + [k.sub.x])[m.sub.x]/([p.sub.y] + [k.sub.y])[m.sub.y] (5)

Based on (1) and (2), it can be derived that [t.sub.x] > [t.sub.y], or the large-market club is more talented and successful than the small-market club.

Comparing Four Different Scenarios

Starting from this benchmark case above, different scenarios regarding the selling and distribution of broadcast rights can be distinguished:

1. Centralized selling and equal sharing (some US major leagues)

2. Centralized selling and performance-related sharing (most EU football leagues)

3. Decentralized selling and equal sharing

4. Decentralized selling and performance-related sharing.

We will consider these scenarios one by one and compare their impact on the competitive balance.

In reality, however, the sharing and selling of broadcast rights in the North American major leagues and the national football leagues in Europe follow more complicated lines then any of the four extreme scenarios in our simplified model.

In some countries like Spain, the selling of broadcast rights is a mixture of the two extreme scenarios considered in this model. In Spain, the largest and richest clubs sell their broadcast rights individually, while the smaller teams pool their rights and share the money among each other. Also the distribution of the pooled broadcast rights is more complicated than just equal sharing or just performance-related sharing. In England's Premier League, 50% is equally distributed, another 25% is related to the television appearances of the teams, and the other 25% depends on the performances of the teams or their ranking in the championship at the end of the season. In France, 75% is equally shared and 25% is split according to the last season's nnal ranking. We will not consider these mix systems in the model below, because we think it is worthwhile, first of all, to see and understand the impact of the extreme scenarios.

1. In the case of centralized selling of broadcast rights by the league and equal sharing of the total broadcast revenue (B), the total revenue of each team after sharing (indicated by the superscript a), with lump-sum broadcast revenue B, is then:

[R.sub.i.sup.a] = [p.sub.i][A.sub.i] + B/2 i : x,y with [B.sub.y] < B/2 < [B.sub.x] (6)

where B is the total broadcast revenue of the league. In this case, the Nash equilibrium [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] results in the following competitive balance:

[t.sub.x.sup.a]/[t.sub.y.sup.a] = [p.sub.x][m.sub.x]/[p.sub.y][m.sub.y] (7)

Compared with the benchmark in (5), this is only an improvement of the competitive balance if [k.sub.x] / [k.sub.y] > [p.sub.x] / [p.sub.y]. This selling and sharing arrangement worsens the competitive balance if [k.sub.x] / [k.sub.y] > [p.sub.x] / [p.sub.y]. Which inequality holds is an empirical question; a first quick check of the figures shows that the difference between the proportionality factors is larger than the differences in ticket prices between large- and small-market clubs. Theoretically, however, the outcome is indeterminate.

2. The centralized broadcast rights B can also be distributed depending on the performance of the teams. Performance can be measured by the winning percentage, but the league can choose to take season attendances. The advantage of using season attendances is that it also creates an incentive for the price-setting clubs to keep their (local monopoly) ticket prices low.

If we assume that the broadcast rights each club receives from the league's sharing arrangement are proportional to attendances with a fixed proportionality factor [beta], as decided by the league, club revenue after sharing will be:

[R.sub.i.sup.a] = ([p.sub.i] + [beta])[A.sub.i] i : x,y

with [beta] = B / ([A.sub.x] + A.sub.y]), because [beta] ([A.sub.x] + A.sub.y]) [less than or equal to] B (8)

So, the win or talent ratio after sharing is now:

[t.sub.x.sup.a*]/[t.sub.y.sup.a*]= ([p.sub.x][beta])[m.sub.x]/([p.sub.y][beta])[m.sub.y] (9)

which can be an improvement of the distribution of talent compared with the benchmark (5). Indeed, it can be shown that ([p.sub.x] + [beta]) ([p.sub.y] + [k.sub.y]) < ([p.sub.y] + [beta]) ([p.sub.x] + [k.sub.x]) for whatever value of [beta], if [k.sub.x]/[k.sub.y] [greater than or equal to] [p.sub.x]/[p.sub.y]. So basically, the outcome is again theoretically indeterminate.

3. In the case of decentralized selling of the broadcast rights, the broadcasting revenue of the league is no longer lump-sum, but based on the individual rights collection of each team. With equal sharing, the teams' revenue after sharing can now be written as:

[R.sub.i.sup.a] = [p.sub.i][A.sub.i] + 1/2 ([k.sub.x][A.sub.x] + [k.sub.y][A.sub.y] i : x,y (10)

The reaction functions can now be derived as:

[partial derivative][R.sub.x.sup.a][[t.sub.x],[t.sub.y]]/[partial derivative][t.sub.x] = (2[p.sub.x][m.sub.x] + [k.sub.x][m.sub.x] - [k.sub.y][m.sub.y])[t.sub.y]/2([t.sub.x] + [t.sub.y] - c = 0

[partial derivative][R.sub.y.sup.a][[t.sub.x],[t.sub.y]]/[partial derivative][t.sub.y] = (2[p.sub.y][m.sub.y] + [k.sub.x][m.sub.x] + [k.sub.y][m.sub.y])[t.sub.x]/2([t.sub.x] + [t.sub.y] - c = 0 (11)

In order to find the Nash equilibrium, we equalize the two reaction functions and can find the following competitive balance:

[t.sub.x.sup.a*]/[t.sub.y.sup.a*] = ([p.sub.x] + [k.sub.x])[m.sub.x] - 1/2 ([k.sub.x][m.sub.x] + [k.sub.y][m.sub.y])/([p.sub.y] + [k.sub.y])[m.sub.y] - 1/2 ([k.sub.x][m.sub.x] + [k.sub.y][m.sub.y]) (12)

Compared with the benchmark in (5), this is clearly a worse competitive balance. This connrms the finding of Szymanski and Kesenne (2004) regarding the impact of revenue sharing on competitive balance.

4. Finally, with decentralized selling of the rights, the league can also redistribute the broadcasting money based on the season attendances of the teams. It follows that after-sharing revenues can be written as:

[R.sub.x.sup.a] = [p.sub.x][A.sub.x] + [[beta].sub.x][A.sub.x]

[R.sub.y.sup.a] = [p.sub.y][A.sub.y] + [[beta].sub.y][A.sub.y]

with [[beta].sub.x][A.sub.x] + [[beta].sub.y][A.sub.y] [less than or equal to] [k.sub.x][A.sub.x] + [k.sub.y][A.sub.y] (13)

Comparing club revenues after sharing in (13) with club revenues before sharing in the benchmark case (1), it is obvious that it must hold that [[beta].sub.y] > [k.sub.y] and [[beta].sub.x] > [k.sub.x]. Otherwise, the small-market club would be worse off after sharing than before sharing. Under these conditions, the Nash equilibrium can be found to be:

[t.sub.x.sup.a]/{t.sub.y.sup.a] = [p.sub.x][[beta].sub.x][m.sub.x]/[p.sub.y][[beta].sub.y][m.sub.y] (14)

which is a more balanced distribution of talent than the benchmark case in (5), because ([p.sub.x][[beta].sub.x])[p.sub.y] + [k.sub.y]) < ([p.sub.y] + [[beta].sub.y])[p.sub.x] + [k.sub.x]).

Discussion and Conclusion

Comparing the outcomes of the Nash equilibrium scenarios in the previous section, decentralized selling with equal sharing worsens the competitive balance, whereas the impact of centralized selling with equal or performance-related sharing is theoretically indeterminate. Only the individual selling and performance-related sharing of broadcast rights seems to improve the competitive balance.

A simple numerical example can illustrate this point. In Table 1, the benchmark case is compared with the four scenarios in this paper. It shows that the case of decentralized selling with performance-related sharing offers the best guarantee to improve the competitive balance. Also, centralized selling and performance-related sharing has a, albeit smaller, positive effect on competitive balance, because in the numerical example [k.sub.x]/[k.sub.y] = [p.sub.x]/[p.sub.y]. It can also be seen in Table 1 that a more equal distribution of the collected broadcast money does not necessarily result in a better competitive balance.

However, one can expect that the total amount of broadcast revenue collected by a monopolist will be higher than the sum of the rights that can be collected by decentralized selling. The reason is that a profit-maximizing league will maximize total broadcast revenue given that the marginal cost is close to zero. Moreover, the transaction costs of an intensive decentralized bargaining process between all clubs and all broadcasters will be higher (see also Andreff & Bourg, 2006). To the extent that more club revenue increases the absolute quality of the games, this can also be favorable for the spectators. On the other hand, an important advantage of decentralized selling is that it does not cause the welfare loss one can expect in a monopoly market, with broadcast rights (and pay-per-view) that are too high and the number of broadcast games that is too low. If the televised sports are free-to-air, the higher broadcast rights do not result in any pay-per-view, but then again, consumers have to pay higher taxes to finance public television or higher prices given the marketing cost of the products that are advertised on television. What is good for the clubs and the league is not necessarily good for the spectators. So, a welfare economic approach is appropriate to find the optimal arrangement.

If improving the competitive balance is important, the analysis in this paper shows that the case for pooling and sharing broadcast rights in a sports league with profit-maximizing clubs is not very strong.

References

Andreff, W., & Bourg, J-F. (2006). Broadcasting rights and competition in European football. In C. Jeanrenaud & S. Kesenne (Eds.), Sports and the media (pp. 37-70). Cheltenham, UK and Northampton, MA: Edward Elgar.

Falconieri, S., Palomino, F., & Sakovics, J. (2004). Collective versus individual sale of television rights in league sports. Journal of the European Economic Association, 2(5), 833-862.

Forrest, D., & Simmons, R. (2006). New issues in attendance demand: The case of the English Football League. journal of Sports Economics, 7(3), 247-266.

Fort, R. (2003). Sports economics. Englewood Cliffs, NJ: Prentice Hall.

Garcia. J., & Rodriguez, P. (2002). The determinants of football match attendance revisited: Empirical evidence from the Spanish Football League. Journal of Sports Economics, 3(1), 1838.

Jeanrenaud, C., & Kesenne, S. (Eds). (2006). Sports and the media. Cheltenham, UK and Northampton, MA: Edward Elgar.

Neale, W. (1964). The peculiar economics of professional sports. Quarterly journal of Economics, 78(1), 1-14.

Noll, R. (1999). Competition policy in European sports after the Bosman Case. In C. Jeanrenaud & S. Kesenne (Eds.), Competition policy in professional sports, (pp. 17-43). Antwerp: Standaard Editions Ltd.

Szymanski, S. (2003). The economic design of sporting contests. journal of Economic Literature, XLI, 1137-1187.

Szymanski, S., & Kesenne, S. (2004). Competitive balance and gate revenue sharing in team sports. journal of Industrial Economics, 51(4), 513-525.

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Stefan Kesenne, University of Antwerp

Stefan Kesenne is an economics professor in the Department of Economics. His research interests include labor economics and sport economics.

Table 1. Numerical Example (Performance-Related Sharing)

[A.sub.x]      [p.sub.x]  [m.sub.x]  [B.sub  [B.sub   B      [T.sub.x]/
  = 500        = 10       = 8        .x]     .y]             [t.sub.y]
[A.sub.y]      [p.sub.Y]  [m.sub.y]
  = 100        = 9        = 6
0.Benchmark    [k.sub.x]  [k.sub.y]  10000   1800     11800  1.48
case           = 20       = 18

1. Collective
sale and                             5900    5900     11800  1.48
equal sharing

2. Collective
sale and
performance--    [beta] = 19.66      9833    1967     11800  1.38
related
sharing

3. Individual
sale and                             5900    5900     11800  4.07
equal sharing

4. Individual
sale and       [[beta].   [[beta].   9000    2800     11800  1.01
performance--  sub.x]     sub.y
related        = 18       = 28
sharing