P. Antonioni and J. Cubbin, "The Bosman Ruling and the emergence of a single market in soccer talent", European Journal of Law and Economics, 9(2): 157-73, 2000.
This paper discusses the effect of the Bosman Ruling on the nature of contracts between club and player under the modeling framework of options pricing theory. It uses the framework to formulate club strategies in contract negotiations in the post-Bosman landscape. (It's worth asking if the findings continue to hold in 2011.)
Review after the jump.
The Bosman ruling in 1995 marked the beginning of the free-agent era in European football and forced a fundamental change in how football clubs handled their most important asset -- the players. This publication was one of the first to examine the effects of the ruling by adapting models from modern investment theory, in particular, options theory. In this respect it is a predecessor of the player valuation work of Radu Tunaru et al. that was first presented in 2005 and later refined in 2009, but those papers do not reference this early work by Antonioni and Cubbin.
At the time of this paper's publication, Peter Antonioni and John Cubbin were in the Department of Economics at the City University of London (UCL). Cubbin has since retired, while Antonioni has remained at UCL where he is now a senior teaching fellow in the Department of Management Science and Innovation. This work is listed prominently in his list of publications, which indicates that it has gained him some notoriety, but I haven't seen any follow-on work that he has done. That is unfortunate, because after ten years we have more data to test the methodologies that he has developed.
Pre-Bosman ruling, a club could impose a transfer fee on a player at the end of his contract in order to recoup training expenses and other investment in the player's development. Post-Bosman, those out-of-contract transfer fees are no longer permitted, which in turn decouples investment and training costs from the transfer fee and creates an environment that forces clubs to answer the following question: What are the best investment and/or trading strategies for my club? Antonioni and Cubbin seek to answer that question in their paper.
Antonioni and Cubbin address the contract strategy problem by modeling the contract as an option. The analogy doesn't hold exactly, but there are some elements of the option that make it useful for analysis. The club has the option to exercise the option and sell the contract to an interested buyer, or let it expire which would allow the player to leave for free. There is an underlying asset -- the player -- whose value is difficult to model. Pre-Bosman, player contracts were essentially put options, for which the club had the option to sell with a non-zero payoff at expiration. Now, clubs not only have the option to sell, they also have the option to renegotiate -- to exchange the current option for another one. Most importantly, in the post-Bosman era the payoff of the option at expiration is zero. (One could think of loaned players as analogous to a call option, but I haven't thought through the concept completely.)
The first major modeling contribution of this publication is the formulation of player value. Antonioni and Cubbin claim that the objective of the club is to "maximize its discounted level of utility over the life of the contract", which makes sense to most observers. I have written about utility before in the context of goalscoring metrics, but in this situation utility is assumed to have a direct relationship with a player's market value, which in itself is assumed to have a direct relationship with a player's performance. (Here I would disagree with the authors; there are other financial contributors that should be accounted for, such as merchandising, sponsorship and endorsements, ticket revenue contribution, to name a few.)
The second major modeling contribution is the derivation of an optimal investment strategy for clubs. Antonioni and Cubbin define player value as a state variable (a variable that describes the condition and behavior of a time-varying system) and club investment, whether salary, training expenses, or development expenses, as an input variable. Player value is assumed to evolve as a Markov process which means essentially that the current value of the state depends only on previous values and that the amount of investment depends only on the current value of the state. Because clubs are interested in how the value of the contract evolves with time, we must model its discounted utility -- "discounted" is an application of the principle of time value of money, from which we obtain an interest rate. Clubs are also interested in maximizing the discounted utility of the contract, which is an optimization problem. I'm not going to include the derived formula here, but the formula follows from what is called Bellman's principle of optimality, which states that given an initial state, the best (optimal) decision one step in the future depends only on that initial state. One ends up with a recursive optimal solution that starts at the terminal point and works backwards to the beginning. It's a little difficult to wrap your mind around at first, but the solution is actually quite elegant.
Antonioni and Cubbin do not plug in real data in their analysis, but they use the expressions from their derivation to make conjectures about club investment behavior in a post-Bosman world. The authors point out that most transfers in English football occurred mid-contract pre-Bosman, and after the ruling the clubs made the decision to pay transfer fees for players who they would have purchased at the end of their contracts previously. Long-term contracts are the norm in European football now, an event that can be explained by modern investment theory. Transfer fees, rather than collapsed, have increased substantially since the ruling.
Progression of world record transfer fees in association football. Source: Wikipedia
Many readers of this paper will ask about the effect of the Bosman ruling on small clubs and clubs in small European markets, and it is here that I think the authors might have failed to appreciate the impact of the ruling of those teams. The authors said that the clubs would be motivated to sell their players to bigger clubs before their contracts expired, and that the rate of players moving on to big clubs on a free transfer is minimal. The viability of these small (or small-market) clubs depends on their ability to keep the conveyor belt of talent identification and development operating and to develop new revenue streams. The challenges of clubs not named Real Madrid or Barcelona in Spain and just about all of the Eredivisie teams in the Netherlands indicate how difficult this challenge is. The Bosman ruling may not have changed the investment strategy of many football clubs all that much, but it has changed rather substantially the timing of these decisions which has had an impact on competitiveness in domestic and European football.
This paper was written in 2000, and in the 10 years since there have been more data on club financials and their decision-making during numerous transfer windows. It would be worth to see if clubs actually do follow the investment strategy outlined in this paper, and whether there might be some inefficiencies to be exploited in the transfer market.