Are stars as shiny as they look?

The net expenditure of the Paris Saint-Germain (PSG) football team was equal to almost 400 million euros over the past three seasons. This amounts to roughly half of the total market valuation of the current team’s players. However, during the last three years, the PSG’s winning ratio has increased only from 71% to 79%. Clearly, the theoretical relationship between marginal cost and marginal productivity does not seem to hold: the team’s performance has not improved proportionally to its investments.  So why is the PSG willing to spend so much in transfer fees, and, more broadly, what impact do these prices have on the football industry as a whole?

Economic theory offers an explanation: the so-called “superstar effect”, originally articulated by Rosen in 1981. Every team wants the best player and thus small differences in performance translate into considerably higher prices, as a player can only play for one team – this phenomenon also arises in setups where the players are relatively homogenous. Additionally, teams are usually privately owned and thus also seek to make profits, encouraging them to pursue popular players who can increase their fan base and thus their revenues.

This superstar status means that the previous computations did not consider the revenue obtained from advertisements and attendance gained from these new superstars. On the one hand, the marginal attendance or publicity brought to a top team like the Real Madrid or the Barcelona could be very low, as they already have a very strong fan base. On the other hand, the income from all the player-related goodies, such as jerseys, could probably compensate the amounts paid for the players.

Can the effect of the superstar status fully explain the value paid for top players? Since details about teams’ revenue composition are almost impossible to obtain, it is difficult to check if the superstar effect is the only reason.

However, we can still think about additional explanations that go further from the main reasons – success and profitability – driving teams to buy certain players. There could be opportunity costs that were omitted so far, such as, for example, the fear of being left behind and allowing other teams to scoop the best players. Following this idea, buying a player would represent a utility gain from their contribution to the team, from the revenues related to their popularity, and from preventing another team to include a high-quality player and potentially becoming a stronger rival. This argument relies on the existence of incumbents who would preemptively hire more than they need in order to maintain their position.

But this preemptive hiring does not necessarily follow anticompetitive practices. After all, player selection is a human decision-making process and thus could be affected by behavioural biases arising when the decision-makers are particularly experienced. In fact, coaches or managers could follow their gut instinct instead of conducting a statistically based analysis of a player’s performance when looking for the next superstar. This could explain why they would be ready to pay considerably higher amounts than what the player’s performance seems to be worth. As performance is difficult to forecast, buying football players becomes similar to a common value auction where the winner’s curse may arise, as teams will base their valuations using incomplete information and will end up paying more than what players are really worth.

The progressive and steep increase in transfer value over time inevitably drives the poorer teams out of the superstar market. In most cases, these teams will not be able to become highly successful as they lack the competitive edge required to face the financially stronger teams. This, in turn, reinforces the financial differences between teams, as winners will always be more popular, and thus have higher incomes. Nevertheless, this “success concentration” does not necessarily arise in all sports.

In the National Basketball Association (NBA), all teams have a salary cap that varies accordingly to the total revenue perceived by the entire league in the previous years. In addition, players’ wages are capped according to their seniority. These two factors limit the distortion caused by the “superstar” effect, as showed by the literature, where performance tends to explain 50% more of wages’ variation than in football. This does not mean that players do not receive a superstar treatment, as advertisement contracts will represent an important source of revenue that can surpass their salaries.

However, this regulation means that teams do not directly bear an outrageous superstar premium and that financially weaker teams therefore have the ability to hire high performance players. In conjunction with the draft system, which allows the worst teams to choose the best incoming players before the best performing teams, the existing regulation allows the NBA to have more winner variety than football. These types of regulations are common in American sports leagues like the Major League Baseball (MLB) and the National Football League (NFL). As the following graph shows, these leagues have stronger competition than the European football counterparts, as more teams have the possibility to recruit stars and thus to avoid the scenario where only a handful of teams can win. France is no exception to the rule when we look at a larger time period: in the last five years, the PSG used its financial power to recruit more stars than any other team, winning four league titles in total. For all of the other main European leagues, there is a clear pattern where the same three or four teams always win the competition. However, the UEFA Champions League seems closer to the American level of winner variety, which could be explained by the fact that this competition gathers the best, and therefore richest, teams of each country.

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It is hard to imagine sports without stars: rooting for the best players of the team is an inherent part of being a fan. Superstars will always shine on the field, but should their allocation be regulated? Answering that question would inevitably lead to a discussion on which sports competition setup maximises welfare. Are consumers happier and their surpluses higher if there are super-successful teams like in the European soccer leagues, or is everyone better off in a league like the NBA, where most teams have a chance of winning?

by Nicolas Martinez

References:

Rosen, S. (1981). “The economics of superstars”. American Economic Review 71, 845–858.

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