Monday, April 22, 2013

Marginal analysis of Premiere League Football in the UK

The Economist published the above graph, showing that the price per point varies across England's football clubs:

If the market for footballers resembled a textbook labour market, the players' wages should reflect their "marginal product": the amount they add to the firm's output. If the output of a Premier League side is points, then a player's wage should reflect his addition to the club's points-haul. But if that were the case, then every club would rack up the same points per pound.

Perhaps a better explanation is found in the fact that clubs don't maximize points, but rather payoffs, and there is a big payoff to being the best (e.g., more playoff games, more jerseys sold), and a big negative payoff to being the worst (relegation to Division I).

As a consequence, clubs near the top and bottom are locked into arms races with each other. If one club spends more to finish in the top four, its rivals must spend more also. In particular, it is worth spending a lot to finish first rather than second, as Manchester City did; or 17th rather than 18th, as Queens Park Rangers managed to do. It is worth rather less to finish 11th like Swansea rather than 12th like Norwich City, who finished just below the Swans in the points-per-pound ranking too. That may explain why the clubs near the top and bottom of the Premier league cluster near the bottom of our points-per-pound table. They're not necessarily inefficient or irrational. They're just playing a positional game.


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  3. According to The Economist article, English Premier League wins cost on average of $1.55 million euros per league win. Some clubs are able to maximize points per pound by earning a point for every $740,000 euros spent whereas some clubs gain rather expensive points where 1 point cost $2.4 million. Using marginal analysis, the cost of players wages should reflect the additional output (wins) that add to the clubs output. Team sports appear such as football are highly dependent on performance; clubs spend a lot of dollars to obtain the services of the most talented footballers, as a result they are realizing the most revenues and success. Clubs that are most fascinating to me are ones such as Swansea City that maximize the most out of their players, they keep payroll costs down while earning a lot of points. They are not experiencing the large revenues that are enjoyed by teams such as Arsenal. How does Swansea City get to the next level to compete for a league championship without breaking the bank? According to a recent article, one way could be through incentive pay. Andy Pettite of the New York Yankees signed a contract valued at $5.5 million USD but had incentives built in that could escalate his pay up to $12 million if he achieved certain levels of performance; clutch pitching, strikeouts, and ERA drove his pay and in effect the team’s success. Marginal analysis indicates that MR = MC; therefore the incentive pay model works for Swansea City. If they encourage players to maximize effort it will cost them more in pay, but they are earning more points per million euros spent and the more success the club experiences the more revenues and dollars in terms of marketing, tickets, apparel, etc.

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