Part 2 – Contest Theory and the economics of football

The second part of this series exploring what FFP means for the future of European football will look at Contest Theory, and will examine why the current structure is responsible for the financial turmoil in European football, not individual clubs.

You can be forgiven for assuming that this is a problem caused primarily by irresponsible ownership with much of the media attention falling on these clubs e.g. Rangers and Portsmouth. To some extent, it is true, bad owners do contribute to an industry that is blighted by poor financial performance, however, even clubs with very responsible owners fail to produce a profit. Nor is poor financial performance a new phenomenon, it has been a significant factor since professional football began in the 19^th century, yet football still exists today as the worlds most popular team sport.

FFP is said to be necessary to combat the unsustainable financial situation that football finds itself in, yet poor financial performance has been a sustained part of football since its inception, and yes individual clubs have fallen fowl of mismanagement, but overall the game has survived and thrived.

This piece will argue that it is not greed that drives clubs to over invest in players, but a necessary measure to maintain status due to the unrelenting pressure of sporting competition under the current structure of European football.

What is Contest Theory?

In sport, Contest Theory is concerned with identifying the optimal design of a sporting contest and its outcomes (Szymanski, 2003). So what do we consider to be a contest?

“A contest is a game in which players compete over a prize by making irreversible outlays; each player's outlay increases his probability of success and at the same time reduces the chances of the opponents” (Clark and Riis, 1998).

For sport, talent is an extremely important part of a contest; generally the individual or team with more talent will win, and the relative amount of talent employed by one individual or team will affect the performance of others. What differentiates team sports from individual sports is the ownership of that talent. In an individual sport competitors are in control of their own talent and choose when and where to apply it, however, teams must purchase players with talent creating an internal market whereby talent has obtainable economic value. In short, this means that teams are the entities that enter competitions, expend resources and receive prizes, and must employ individuals with talent to compete for them. It is fairly obvious to most people that clubs are spending too much on player acquisitions and wages, for example Manchester City spent 114% of its total revenue in the 2010/11 season on wages and made an overall loss of £197m. However, they did go on to win the FA cup in 2011 and the Premier League in 2012 as a result of this expenditure. The question we should all be asking is could they have achieved success without exceeding their means? The answer has got to be a resounding no.

Exploring a simple two-team model

Contest Theory is used in academic literature to explain why there is over investment in team sports. It uses a simple two-team model to replicate the mechanisms of a sporting contest. First, it is necessary to make some assumptions. These are not ad hoc assumptions but logical ones that anyone could make. In addition these assumptions can and have been proved using empirical data.

1. More talented teams are more likely to win than less talented teams.
2. Talent costs money and more talented players cost more to acquire and to maintain i.e. wages.
3. Clubs with higher turnover can afford better players; therefore they are more likely to perform better.
4. Teams finishing at the top of their respective leagues are likely to have larger turnover and higher wage bills than those lower down.
5. Increasing investment in talent will attract fans and increase income, but at a decreasing rate since more talent costs more money.
6. There is a sliding scale of returns based on a team’s league position i.e. finishing 1^st gives a higher return than finishing 10^th.

For an excellent and full explanation of Contest Theory and its application in sport read this by Dietl, Franck, Lang and Grossmann:

Contest Theory and its applications in sports
(Be warned it does require some understanding of economic theory)

• The first part of the model relates to the probability of success. As the probability of contestant i winning increases, the probability of contestant j winning must decrease.
• The second part of the model looks at expected payoff, which is dependant on the probability of success multiplied by the value of the contest prize, less the cost of effort. That is to say, the contestant that values the prize the most is likely to expend more effort and is more likely to win.
• Third, the model attempts to take different time periods into account i.e. effort in period T is likely to impact on performance capabilities in period T+1. Therefore, there is incentive to use resources that are predicted to be earned in the future to boost present performance.
• Next, the model examines the demand function of fans in terms of match quality. Theoretically, increasing the win percentage of one team will increase revenues for that club up to a certain point, at which, over dominance will lead to falling revenues for the dominant club.
• Subsequently, the model addresses the supply of talent. It is accepted that in European football the supply of talent is flexible (especially since the Bosman Ruling of 1995), since “the number of talent hired by club i has no influence on the talent pool that is available to the other club j” (Dietl et al, 2009).

 

How does this lead to over investment?

Imagine a two-team league where both teams have an equal amount of money, and both act as profit maximisers. The level of investment will be equal at the start of the season (period T). However, equal investment does not mean equal performance since only one team can win. If we assume that the winning team will receive a larger share in prize money, they will achieve a higher profit level. Once a team has achieved a higher income level they are able to spend a higher amount than their opponent and still maximise their profit. This creates two problems. Firstly, there is incentive to invest a higher amount in period T than is optimal to increase the likelihood of achieving a higher league position. Secondly, for all subsequent periods, T+1, T+2 etc, present performance will impact on total income, which in turn affects the amount of talent a team can afford, their performance relative to the other team and their profitability. This leads teams to over invest in playing talent to secure future income.

(Dietl, Franck and Lang, 2008) provide 5 key indicators that increase the level of over investment:

1. A stronger correlation between talent investments and league performance.

2.  A more unequal distribution of the league’s revenue.

3. An additional exogenous prize (e.g. participation to international competition) awarded to the winner of the domestic championship.

4. A system of promotion and relegation.

5. An increased inequality between first and second division of a domestic league.

They assert that over investment increases when the effects of these indicators increase.

If we extend the two-team model to look at a league of 20 teams we can examine how these indicators work. If we assume that all 20 contestants are win maximisers i.e. willing to perform at a loss, are of equal size and all want to win the contest they would all commit to investing an amount that would maximise the chances of winning, and since they are all equal in size they would all invest equal amounts. However, only 1 team can win; hence 19 teams will under perform and make considerable losses since they do not receive the income they gambled on getting from a higher league position.

This gamble is not just in place for the overall winner, but is a significant function throughout all levels of hierarchical professional football. Say a club expects to finish 4^th in the Premier League and gain entry to the Champions League which is extremely lucrative. The difference in income between a club finishing 5^th and 4^th would be enormous since the income gained from the Europa League is almost insignificant in comparison; hence the club would need to invest an appropriate amount in order to achieve its aim of 4^th place. This means gambling on the income that it hopes to receive by spending it before they have it. Failure to finish 4^th would mean that the club does not receive the additional income it had hoped for and will therefore make significant losses.

Case Study – Leeds United

 

The experience of Leeds United exemplifies this. Having reached the UEFA Champions League semi-final in the 2000/01 season, the club narrowly missed qualification the following season and began an inexorable spiral of decline as players were sold at less than their purchase price to service debt, sporting performance then declined, until finally the club was relegated from the Premiership at the end of the 2003/04 season, entering administration in 2007.

The same can be argued for clubs at the bottom of the table. 3 teams are relegated from the Premier League every season, the costs of which are significant when you look at the revenue differential between Premier League and Championship teams (in 2011 total Premier League revenue = £2.3bn whilst Championship revenue = £423m). Clubs are forced to spend an amount that may well see their clubs over reaching themselves just to remain in the league and retain the significant revenues they receive from being there. Compare the 2011 figures to the same numbers from 2003 (PL = £1.25bn, C = £206m). As you can see the growth rate is pretty much the same, both leagues have more or less doubled their total income, however, this means the numbers are getting further and further apart, increasing the gap between the leagues and increasing the attraction and pressure on clubs to be in the Premier League.


Case Study – Tottenham Hotspurs

What would happen if a club decided not to operate in this way i.e. they act as a profit maximiser among win maximisers? This was a reality for Tottenham during the 1990’s under the ownership of Alan Sugar who wanted to run the football club as a business. Rather unsurprisingly this made him unpopular with the fans as the team’s performance deteriorated with not a single top 6 finish under Sugar after the 1980’s where Tottenham yo-yoed continuously from mid-table to as high as 3^rd place. In the 1997/98 season Tottenham were languishing near the relegation zone at Christmas and Sugar was forced to abandon his profit making strategy when he signed several high profile players including the resigning of former talisman Klinsmann on loan. Tottenham went on to finish 14^th but at the expense of Sugar’s business principles. When Sugar sold his controlling interest in Tottenham in 2001, he publicly stated that owning an English football club was not a viable business proposition, but a very expensive hobby or leisure pursuit.

Many of you will be pointing out that both Manchester United and Arsenal manage to operate at a profit year after year and are also relatively successful. To that I would say they are extraordinary cases. For the 2008/09, 2009/10 and 2010/11 seasons the average Premier League revenue (taken from the 14 clubs present in all 3 seasons) was £446m, whilst Arsenal made £1bn and Manchester United made £994m. For the majority of teams this sort of income is completely impractical and not at all representative, and as for Arsenal, they haven’t really been that successful when you consider how much income they have.

Conclusion

It is wrong to place the blame for poor financial performance and instability on clubs when the institutions themselves do so much to exacerbate the problem. Some would argue that FFP is an excellent solution to the problem. Clubs wouldn’t be allowed to gamble on future success, they wouldn’t be able to over spend and exceed their means, and therefore they cannot get into an unsustainable financial position. Part 3 of this series will explore why in the long-term the break-even restriction of FFP will diminish competition and actually make the current structure of European football unsustainable.

If you want to explore Contest Theory further I recommend these sources if you are lucky enough to have access to academic journals:

Ascari, Guido and Gagnepain, Philippe (2007) ‘Evaluating Rent Dissipation in the Spanish Football Industry’ (In Journal of Sports Economics, Volume 8, Issue 5, pp 468-490)

Dietl, Helmut M, Franck, Egon, and Lang, Markus (2008) ‘Over-investment in team sports leagues: A contest theory model’ (In Scottish Journal of Political Economy, Volume 55, Issue 3, pp 353-368)

Dietl, Helmut M, Franck, Egon, Lang, Markus and Grossmann, Martin (2009) ‘Contest Theory and its Applications in Sports’ (Institute for Strategy and Business Economics, University of Zurich, Accessed on 29th July 2012)

Grossmann, Martin and Dietl, Helmut (2009) ‘Investment Behaviour in a Two Period Contest Model’ (In The Journal of Institutional and Theoretical Economics, Volume 165, Issue3, pp 401-417)

Skaperdas, Stergios (1996) ‘Contest success functions’ (In Economic Theory, Volume 7, Issue 2, pp 283–290)

Szymanski, Stefan (2003) ‘The Economic Design of Sporting Contests’ (In Journal of Economic Literature, Volume 41, Issue 4, pp 1137-1187)

Tullock, G. (1980) ‘Efficient rent-seeking’ (In Buchanan, J, Tollison R, and Tullock, G. eds, Toward a Theory of Rent Seeking Society, Texas University Press, pp 97–112)