Rooney, Finney, power & skill

Sir Tom Finney - widely regarded as the best English footballer of all time - earned £20 a week, or around £1000 in today's wages. Wayne Rooney is about to get a a pay deal worth £300,000 a week. Why the difference?

A useful framework for thinking about this is the Nash bargaining solution*.

Let's say that the joint surplus to both Manyoo and Rooney from Rooney's playing for Manyoo is A - (c + p), where c is the club's payoff if a contract is not agreed and p is the player's payoff if there's no agreement.

It can then be shown that Rooney's payoff will be:

p + b(A - (c + p))

where b is Rooney's bargaining power; this is a coefficient between 1 and 0, where 1 means he has all the power and Manyoo has none, and 0 means Manyoo has all the power.

This tells us that Rooney's wage depends upon three things:

 - his payoff if there's no agreement, p.

 - the size of the pie to be split, A.

 - his bargaining power, b.

Given the amount of money in the game, A is big. Similarly, Rooney's payoff if contract talks break down, p, is also big; he plays for Chelsea instead. And his bargaining power is also strong because Manyoo's is weak; if they let him go, the fans will be angry and the club will be signalling a lack of ambition and hence find it difficult to attract the new players they'll need in the summer. In the extreme but not implausible case of Rooney having all the bargaining power, he can extract all of the surplus from his playing for Manyoo for himself, leaving the club with nothing.

Now, contrast this to Sir Tom's position:

 - A was low, because there was less money around; there were no big TV revenues in his day.

 - p was low, because the maximum wage of £20 per week meant his outside options paid no better than Preston did.

 - b was low. When Sir Tom was offered big money by Palermo in 1952, his employers refused to let him go, and he acquiesced in this. How far this was because of the club's actual power and how far because of Sir Tom's placid nature and loyalty to the town needn't detain us here.

Now, here's the thing. The player's skill enters into our equation only indirectly - as one factor determining A; Manyoo gains more from employing a skilful player than it does from employing a clogger. But how much of the total surplus the skilful player can extract for himself depends upon the other factors determining A, outside payoffs c and p, and bargaining power.

These coefficients favour Rooney but did not favour Sir Tom. They depend upon institutional factors (whether there's a maximum wage or not); cultural ones (deference towards football club owners, willingness of fans to pay to see a game); temporary stength (such as Manyoo's desperation now); or individual character (a person's timidity or narcissism).

The message of all this should be obvious to anyone who isn't blinded by ideology. It's that incomes don't depend merely upon an individual's skill. Instead, they depend upon the power to extract a share of the surplus, or rent, which arises from job matches. As Robert Solow says (pdf):

Rents are pervasive...It is too nonchalant to presume that all market incomes reflect true productivity.

* I'm following ch 5 of Sam Bowles Microeconomics.

Comments

[Will Davies]

One might also apply a bit of Hirschman to the situation. In his famous analysis, there are two forms of power in economic situations: exit and voice. Clearly the general drift towards economic liberalisation leads to growing priority to exit over voice; the market's primary form of freedom is the freedom to withdraw from a relationship. So clearly that accounts for a lot of how Rooney (and his agents) have acquired power.

But I wonder if the sort of idiot savant element also helps, i.e. that 'voice' is probably not his trump card anyway. Arsene Wenger has always sought to manage players via dialogue, presenting them with an image of their future career. Supposedly this was how he lured Ozil. It never really works for more than about 5 years tops. Rooney does a very good impression of someone with whom it would never work for more than the duration of a single conversation...

[Alfred]

Skill also determines p, not just A.

[Socialism In One Bedroom]

"Supposedly this was how he lured Ozil"

Ozil must have a very understanding agent!

Rooney is a prime example of market failure, ridiculously over-rewarded by any rational measure of merit.

Your equations are very abstract it should be noted, behind size of the pie lies a number of factors. Football's massive global popularity being one.

[Dave Timoney]

Amusing to see Will Davies elide the role of intermediaries like Paul Stretford.
http://www.ippr.org/juncture/171/11905/the-tyranny-of-intermediaries-who-writes-the-rules-of-our-modern-capitalism

[chris]

@ Alfred - you're right.
@ FATE - the rise of agents can be seen as another institutional change that has raised the bargaining ppower of players since Finney's day.
@ Will - yes. Insofar as players have become more footloose because of neoliberalism (or the rise of narcissism or whatever) it's one of the cultural changes which has shifted bargaining power.

[Andrew]

I'm interested in exactly how bargaining power is separable from the utilities of various outcomes.

Every time I see high bargaining power discussed people really seem to mean relatively high payoffs for no agreement (p).

Even in the example of the offer from Palermo it is just an instance of reduced value of opportunities for Finney available elsewhere - because of loyalty or otherwise.

Similarly, institutional factors such as minimum wage legislation should all be expressed terms of payoffs.

Is bargaining power really a clearly defined factor? I can think off a few complications that aren't encapsulated in the payoffs, but not ones usefully summarised as a single bargaining power coefficient.

Yours faithfully,
Andrew

[Shinsei1967]

With regard to your point about players being more "footloose" these days isn't that more a function of technology & globalisation rather than narcissism.

1952 Palermo would have been a very strange environment for Finney. No recognisable food, drink, language, media (newspapers/radio), British ex-pats, British holiday makers etc.

A Wayne Rooney moving to Palermo today would probably speak the same amount of Italian as Finney (none) but could lead a lifestyle in an English ex-pat bubble. Skype-ing relatives at home, watching UK TV online, friends flying out on Easyjet every weekend.

Hence it is easier to be footloose today.

Same with bargaining power for footloose investment bankers. Moving from JPMorgan in Canary Wharf to a better offer at Citibank in Canary Wharf doesn't involve moving house, your spouse having to find a new job, or your kids having to move school.