**Quantitative Analysis… for football managers**

By Jasvin Josen

As the World Cup fever grips the world, it is worthy to reflect on how football has impacted the financial world and what it could mean for the future. The amount of money generated by the football industry grew exponentially in the late 1990s and early 2000s, and has been steadily growing since. Record-breaking financial deals have been negotiated between football clubs and players they sign. With the fast moving pace of the industry, clubs and players are bound to undergo some sort of financial advancement into the future. Shares in clubs are a reality now. Eventually, players will want to establish themselves as corporations and to issue shares in themselves. Sooner or later, it would make financial sense to hedge clubs or players’ performance with derivatives. Thus there is a real need to quantitatively evaluate a football player, to understand his value adding potential, and to put a price upon that capacity.

Existing conditions already show a growing need to measure the value of a football player. Chelsea spent £24m for Didier Drogba in 2004. Real Madrid spent £80 million on Cristiano Ronaldo in June 2009. We can only guess what the price may be for Lionel Messi if he leaves Barcelona. Yet at times, this spending is claimed to have contributed to financial problems, especially when the players do not sustain their success bringing about their subsequent sale by the club at a loss.

Moreover, instability came about in the football industry when the European Union (EU) legislation extended the right of free movement of labour enjoyed by other EU citizens to footballers. Formerly a player was a property of the club but now he is an employee like any other in the EU, working with a contract, and entitled to give due notice to leave that contract. Many see a strong link between this change in legislation and the increase in transfer fees of players. It is becoming more difficult for clubs to continue meeting rising wage demands while having to satisfy owners’ or shareholders’ aspirations and maintaining their performance on the pitch.

For both the above situations, an accurate assessment of players would help to ensure that huge financial outlays actually bring value to the club.

There is very little financial literature on how to value football players, except for a very interesting paper in the Review of Financial Economics in 2005 titled “An option pricing framework for valuation of football players” by R. Tunaru, E. Clark and H. Viney.

**The Opta Index**

The valuation centres on a performance indices such as the Carling Opta Index . This index, calculated specifically for footballers, uses many important statistical records such as:

- The number of minutes played

- The number of goals scored from action

- The number of goals scored from free kicks, including penalties

- The number of goals scored with a header

- The number of assists

- The number of good passes in the opposition half and in his own half

- The number of bad passes in the opposition half and in his own half

- the number of yellow and red cards received

- the number of successful crosses

- ingenious executions

- missed clear chances

and so on, the list is by no means exhaustive.

The Opta idex was established in 1996 as a quantitative indicator of the form of the player. It is already being used in the betting industry, the media and fantasy games. A player earns a total number of points called the Game Score. The Index score is then simply calculated as the total number of points from the last six Game Scores. It is a moving average type of statistical measure; with any new match, the previous oldest match is removed from the calculation.

**Valuing the player**

The intention here is for the reader to get a good idea of the key parameters involved in the valuation model, without getting into the details of the equations and problem solving methods. Aptly, this is a model of 2 halves.

The first half (or parameter) is the value (in money) for a single Opta index point for the club that is interested in buying the player (let us call this X). Intuitively X will depend on the club’s turnover and the Opta index generated by all its players. In other words, X is simply the ratio of the club’s turnover to the sum of Opta Index points of its players. One point of note here is that the quality of teamwork amongst the players could very well push this total higher or lower than just the sum of the individual players. For example Germany in the present world cup, with its seamless teamwork, and relative unknown players, would definitely command a higher number of index points than just its quantitative total.

Through the years, analysing several clubs, it has been observed that the club’s Opta index points show no specific pattern. In fact the performance over time looks very much like random movements with an upward drift; an example of such possible path is shown in

**Chart 1**.

**Chart 1 : Example of a random movement path with upward drift**

The second parameter is the number of Opta Index points for the individual player under evaluation (let us call this N). The movement of the player’s index points over time also exhibits a random movement with an upward drift except that there is an additional consideration for injuries. The injury is empirically observed to make the random process “jump” downwards, an example of such path is in Chart 2.

**Chart 2: Example of a random movement path with upward drift and downward jumps**

Both N and X is modelled with the respective random elements, drifts and jumps accordingly to produce a sort of forecast (or function) of their performances.

Now to obtain the value of the football player, we just multiply the player’s index points (N) with the value of a single index point of the club in question (X). Hence, both the functions of N and X will be incorporated into a new function, Y to reflect the value of the footballer. Based on the numerous simulated paths that function Y could take, a kind of an average value for the player is determined. The last step is then just to discount this value to arrive at its present value.

**Conclusion**

The quantitative valuation described above is the first step in the direction of independent valuation of football players. While this is just the beginning, and there will definitely be a need to consider other factors as the football market scene progresses, it does look like the game is afoot.