On the Science & Mathematics blog: Football LTDA
This article was published on the Science and Mathematics blog of the newspaper O Globo, coordinated by the deputy director of IMPA, Claudio Landim.
Carlos Frederico Rocha, full professor at the Institute of Economics.
In recent months, fans and analysts have witnessed a radicalization of the movement of football teams being acquired by companies and individuals. This phenomenon (no pun intended) had been circulating in the national football scene for some years, but remained restricted to smaller teams that frequented state tournaments or lower divisions and rarely had the capacity to fill stadiums. The novelty is its extension to prestigious clubs, former Brazilian and/or continental champions, such as Cruzeiro, Botafogo, and Vasco. The change in ownership of these clubs' football operations has been received with a mixture of joy and skepticism. On the one hand, some claim it is the last hope for the recovery of financially broken clubs, whose maintenance of expensive and competitive squads is unfeasible; on the other hand, there is nostalgia and distrust that it is simply a transfer of ownership and a possible loss of identity, with some even talking about a wave of "privatization."
First, it's important to dispel the myth that the word "privatization" cannot be used in these cases. You cannot privatize what is already private. Clubs are owned by individuals; their statutes define the rights and duties of these individuals. The major Brazilian clubs have been controlled by families for at least a century, serving diffuse interests and with various types of compromises. One could list a huge number of cases of misappropriation by unpaid club directors; furthermore, the way the clubs are run, as the situation of the aforementioned clubs clearly demonstrates, borders on irresponsibility, with the assumption of unpayable debts. Therefore, the process we are witnessing is a change of ownership between private entities.
So, what distinguishes these two entities? We economists meddle in any subject, even football. Let's start with the objective function. The objective function of a club is difficult to define, but the economic literature has addressed the subject in a series of articles. An interesting example is Solberg and Haugen (2010). There, they differentiate European teams from North American ones. The former would be club organizations, as prevailed here in Brazil, in which individuals become members, but which also have fan bases that can influence their decisions. These clubs would have an objective function guided by results, that is, they would seek to obtain the best possible result, regardless of the financial outcome. North American teams, on the other hand, are business-oriented teams. Their objective function would be profit maximization. The revenue of a club or a sports company would be a function of two variables: the size of the market and the result obtained. The result obtained would, in turn, be a function of talent acquisition.
Let's not analyze the market size for the moment. In short, the strategies of each can be described by examining the graph, which keeps monetary units on the vertical axis and talent volume (whether by quality or quantity of players) on the horizontal axis. In a simplified way, it is assumed that the marginal cost of acquiring talent is constant, represented by a horizontal line. Also in a simplified way, we consider diminishing marginal returns, that is, as you acquire new talent, your revenue increases, but at increasingly lower rates. Thus, the average revenue curve (revenue per unit of talent) and the marginal revenue curve (revenue per additional unit of talent) are derived. A company would hire the quantity TL of talent, obtaining the profit represented by the green box, while a club, in the traditional model, would hire the quantity TR, equating revenue and costs, and obtaining zero profit. Thus, at first glance, skeptics of the recent changes in their clubs may be right: the change in ownership in the management of companies will lead clubs to worse results.
However, there are three complicating factors in the case of the traditional model:
(i) Often, benefactor members decide to make donations to clubs, leading to the recruitment of talent beyond TR. There are a number of examples of this type in Brazil. This should be the case with the relationship between Unimed and Fluminense, the recent wave of signings by Atlético Mineiro, or even the relationships established between Crefisa and Palmeiras. In all these cases, football lovers and their clubs have made or are making financial contributions that allow for the extension of spending on talent recruitment. The cessation of these contributions can cause crises, given the clear expenditure exceeding revenue;
(ii) Hiring talent does not guarantee results, but rather the expectation of results. Failure to meet expectations can lead to future revenue shortfalls, potentially causing a leftward shift in average and marginal revenue curves, resulting in losses for the club; and
(iii) Contracts with football players and technical teams tend to have extended terms, which can lead to adjustment difficulties in the event of revenue shortfalls. Recent examples can be cited, such as the case of Fluminense with the departure of Unimed, the case of Grêmio, with the frustration of not qualifying for the Cups after the departure of Renato Gaúcho, or the drama experienced by Cruzeiro in its relegation with no prospect of return.