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Valuations of Soccer Players from Statistical Performance Data

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Based upon contingent claims methodology and standard techniques in statistical modeling and stochastic calculus, we develop a framework for determining the financial value of professional soccer players to their existing and potential new clubs. The model recognizes that a player's value is a product of a variety of factors, some of them more obvious (i.e. on-field performance, injuries, disciplinary record), and some of them less obvious (i.e. image rights or personal background). We provide numerical examples based upon historical statistical performance indicators that suggest the value of a soccer player is not the same for all potential clubs present in a market. In other words this is a special case where the law of one price for one asset does not function. Our modeling employs the vast database of soccer players' performance maintained by OPTA Sportsdata; the same database has been used by major clubs in the English Premiership such as Arsenal and Chelsea. From a statistical point of view, our model can be applied to identify the relative value of players with similar characteristics but different market valuations, to explore patterns of performance for individual star players and teams over a run of games, and to explore correlations or interactions between pairs of players or small groups of players on the team. Moreover, it offers a tool to value players from a financial point of view using their past performance; hence this model can be also used to inform contractual negotiations.
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Volume 6, Issue 2 2010 Article 10
Journal of Quantitative Analysis in
Sports
Valuations of Soccer Players from Statistical
Performance Data
Radu S. Tunaru, City University, Cass Business School
Howard P. Viney, Open University Distance Learning
Recommended Citation:
Tunaru, Radu S. and Viney, Howard P. (2010) "Valuations of Soccer Players from Statistical
Performance Data," Journal of Quantitative Analysis in Sports: Vol. 6: Iss. 2, Article 10.
Available at: http://www.bepress.com/jqas/vol6/iss2/10
DOI: 10.2202/1559-0410.1238
©2010 American Statistical Association. All rights reserved.
Valuations of Soccer Players from Statistical
Performance Data
Radu S. Tunaru and Howard P. Viney
Abstract
Based upon contingent claims methodology and standard techniques in statistical modeling
and stochastic calculus, we develop a framework for determining the financial value of
professional soccer players to their existing and potential new clubs. The model recognizes that a
player's value is a product of a variety of factors, some of them more obvious (i.e. on-field
performance, injuries, disciplinary record), and some of them less obvious (i.e. image rights or
personal background). We provide numerical examples based upon historical statistical
performance indicators that suggest the value of a soccer player is not the same for all potential
clubs present in a market. In other words this is a special case where the law of one price for one
asset does not function. Our modeling employs the vast database of soccer players' performance
maintained by OPTA Sportsdata; the same database has been used by major clubs in the English
Premiership such as Arsenal and Chelsea. From a statistical point of view, our model can be
applied to identify the relative value of players with similar characteristics but different market
valuations, to explore patterns of performance for individual star players and teams over a run of
games, and to explore correlations or interactions between pairs of players or small groups of
players on the team. Moreover, it offers a tool to value players from a financial point of view using
their past performance; hence this model can be also used to inform contractual negotiations.
KEYWORDS: English Premier League, OPTA performance index, team performance, financial
valuation
1. Introduction
Many industries are increasingly dependent upon human assets rather than more
traditional tangible or intangible assets for the development and maintenance of
organizational competitive advantage. However, human assets are vulnerable
(Barone et al, 1998, Cherubini and Luciano, 2003, Hung and Liu, 2005), making
their control and use difficult, and accurate pricing complex. This is particularly
the case in any professional sports industry. This paper describes a framework to
enable an analyst to determine a link between the performance of an individual
sports player and their financial market value. While the framework illustrated
here can be applied more generally, we focus our discussion on the European
soccer industry. One of the main reasons for doing this is the availability of a
statistical performance index for all players playing in the main soccer leagues in
Europe to provide us with a source of rich and consistent data, but also because
these leagues are among the highest revenue generating professional leagues
within world sport outside of the professional leagues in the USA. European
soccer is also an increasingly attractive product across the world, with revenues
from TV rights and marketing increasing in particular in Asia and through the
global broadcasting of matches via the internet.
Our valuation model is based upon contingent claims methodology and
standard techniques in stochastic calculus (Dixit and Pindyck, 1994). This
approach is of particular relevance in noisy environments; i.e. uncertain
environments where there are many sources of information, and where the value
of much of this information is questionable (Childs et al, 2001, 2002, 2004). Our
focus is on the Vulnerable Asset (VA), a critical human asset, represented in our
paper by a soccer player, who possesses a degree of self-determination over their
contractual relationship with their owner, and who has the power to default upon
that contractual relationship (the authors, forthcoming).
In this paper, our model is used to determine the financial value of
professional soccer players to their existing and any prospective owners. The
model attempts to recognize that a player’s value is a product of a variety of
factors, some of them obvious (such as on-field performance, injuries, disciplinary
record), some of them less obvious (such as image rights, personal background, or
language attainment for example). The profusion of variables which may
influence the value of a VA such as a professional sportsman is an indication of
the noise prevalent within industries of this type. An important aspect of the
model is that it permits us to speculate upon the relative value of these playing
assets for employers other than the VA’s current employer. Traditional measures
of the value of an ‘income-producing asset’ assert that value is a product of
market conditions of supply and demand, and hence the value of a methodology
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which provides an evaluation of the asset for both the supplier and the demander
is clear.
The paper is organized as follows. In the following section we briefly
discuss relevant literature, focusing upon research on prediction within the
sporting industries, as well as the application of financial concepts to soccer. We
also introduce the source of the data described in this paper. This is followed by a
description of the context of the research; namely the European soccer leagues
and the English Premier League (hereafter EPL) in particular focusing upon the
characteristics of success in these leagues. In Section Four we discuss our model
formulation including an extended application of it to explain the value of a
soccer player (Thierry Henry) during a specific EPL season, followed by a range
of other applications in a variety of situations. This is followed by a brief
assessment of the managerial implications of this work, before we draw the paper
to a close and establish the future direction of the research.
2. A Brief Review of Relevant Literature
We briefly discuss relevant literature in two areas, highlighting some key research
on the prediction of results and performance, and upon the application of financial
analysis within the soccer industry. We also introduce the Opta Index, which
provides us with our data on the soccer players we discuss in this paper.
2.1 Research on Predicting Results and Performance
Statistical analysis in the soccer industry initially focused upon finding statistical
models for predicting the results of games. Important contributions on this theme
can be found in Crowder et.al. (2002), Andersson et.al. (2005) and McHale and
Scarf (2007). Dixon and Coles (2002) developed a Poisson regression model that
was fitted to English league and cup soccer data from 1992 to 1995. The model
was then used to exploit potential misalignments in the soccer betting market
using bookmakers' odds from 1995 to 1996. Maher (1982) proposed a model in
which the home and away team scores follow independent Poisson distributions with
means reflecting the attacking and defensive capabilities of the two teams. Forrest
and Simmons (2000a, 2000b) analyzed the predictive information contained in
newspaper tipsters' match forecasts, and the performance of the Pools Panel, an
official body tasked with providing hypothetical results for matches that were
postponed to enable these results to contribute to the various soccer betting pools
that dominated the UK betting industry for most of the post Second World War
period.
The development of the Opta Database (please see Section 2.3), allowed
analysts to establish a direct link between a player’s on-field actions and
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performance, including team results to which they have contributed. Previous
studies along this line include those by Barros and Leach (2006), Espitia-Escuer et
al. (2006), McHale (2007), and Szczepaski (2008). While these studies focused
more on the characteristics of individual players another stream of the literature
looked at the entire team performance. The idea that performance is a productive
function of various inputs has been advocated for soccer analysis since Sloane
(1971, 1997). Another seminal paper on this topic is by Carmichael et al. (2000)
who considered the linkage between EPL team performance together with the
skills and other characteristics of the team members, and the result (a victory or
loss) of the match in head-to-head competitions between clubs. Dawson et al.
(2000) and Hass (2003) also analyzed the efficiency of the EPL. Ultimately it is
the team’s performance that matters and various ways to identify performance
drivers for team success have been discussed in Haddley et al. (2000), Crowder et
al. (2002), Hirotsu and Wright (2002, 2003), Hope (2003), Barros and Leach
(2006), Fitt et al. (2006). Recently, Oberstone (2009) investigated the key factors
of success in the EPL by developing a multivariate regression model based on an
array of twenty-four pitch actions, collected during the 2007-08 season. One-way
ANOVA is used to identify those specific pitch actions that statistically separate
the top four clubs from the clubs classified in the middle of the pack and also
from the bottom four clubs. Using ANOVA it was possible to identify thirteen
pitch actions contributing significantly to the differentiation of the top four clubs
from the other clubs.
2.2 Finance and Football
Despite the research discussed in Section 2.1, it is surprising to note that there has
been very little research to establish a linkage between player or team
performance and player or club financial market value. Part of the difficulty
perhaps lies with the fact that sportsmen are not tangible assets and valuation is
consequently difficult. Paxson (2001) considered a real options view on soccer
players, emphasizing the difficulty of decision making when the main assets are
the players themselves. Amir and Livne (2005) considered an accounting
perspective on football players as intangible assets that might need to be
capitalized in a uniform regulatory manner. They failed to detect evidence
between the investment in player contracts and future benefits for their clubs. The
relationship between future economic benefits and prior investment in soccer
players is based on the assumption that the club’s level of production is
determined a by current portfolio of tangible assets, such as stadia, commercial
shops, TV channels et cetera, and the portfolio of intangible assets, i.e. the soccer
players. Forker (2005) discussed some weaknesses of their conclusions
emphasizing that their results came from accounting-based tests. These are under
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researched themes and issues such as amortization and economic replacement
costs deserve further investigation from an accounting point of view, and there is
also a need for econometric tests to be improved. A seminal paper providing a
framework for determining a player’s financial value from the dynamics of his
performance is Tunaru et al. (2005), and it is upon the methodology proposed in
this paper that we intend to draw.
2.3 OPTA Performance Index
Opta Sportsdata describe themselves as Europe's leading compiler of sports
performance data, with a presence in England, Germany and Italy and a plan to
expand to new countries. Opta Index was born in 1996, a football-based version
of the successful Coopers & Lybrand cricket statistics. In 2001, Opta Index was
purchased by BSkyB, the UK broadcaster, who ran the company until 2003 when
SportingStatz purchased the brand. BSkyB continue their association with Opta
by retaining a shareholding. The database compiles every touch of the ball during
over 2,000 games of soccer a year resulting in over 4,000,000 individual events.
Opta provides the full analysis from the EPL, Italy's Serie A, the German
Bundesliga, France's Ligue One and the UEFA Champions League.
3. Research Setting
To give an idea of the value of Europe’s soccer industry, and of the biggest clubs
in particular, it is instructive to quote some figures from the latest Deloitte
Football Money report (Deloitte, 2009). This reports that the combined revenue
of the 20 highest grossing clubs in Europe (6 from England, 4 each from Germany
and Italy, 2 each from Spain and France, and 1 from Turkey) was €3.9b in season
2007-08, a 6% increase on the previous year. This compares to the total revenue
from the ‘big five’ European soccer leagues (England, France, Germany, Italy,
and Spain) in season 2003-04 of €5.8b, giving an indication of the rapid growth
particularly among the elite clubs frequently contesting the UEFA Champions
League competition. The largest revenue generating league is the EPL, which
Deloitte estimated generated revenues of £1.9b during this season, and it is upon
this league that the remainder of the paper focuses. Despite this growth in
revenues, the profitability of many EPL clubs is either negligible or negative, with
Deloitte suggesting that many leading clubs are essentially ‘not-for-profit’
organizations (Deloitte, 2009: 36) due to their excessive ‘cost of sales’,
principally player salaries and transfer fees.
However there is some suggestion that clubs are increasingly aware that
this situation, and in particular the share of revenue lost to player wages, is
unsustainable. For example, player wages in the EPL accounted for £811m in
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season 2003-04, a rise of 7% on the previous season. This represented a slight
decrease in the growth trend, and “well below the astonishing compound annual
growth rate of 23% seen in the previous decade” (Deloitte, 2005:7). That season,
the average wages/turnover ratio in the EPL was 72%, down from a previous high
of 82%, and Deloitte suggest that this proportion was diminishing as clubs were
becoming increasingly aware that they must control the amount of revenue paid to
their players if they are to retain any form of financial stability (Crawford, 2006).
The recent example of EPL side Portsmouth Football Club, where financial
security has been severely weakened due to overspending on player salaries
without a consummate increase in club revenues is a case in point.
However the share of revenue dedicated to wages is a clear indicator of the
extent to which the EPL is dependent upon its players. As we have suggested, the
players are VAs, and the competitive advantage of the clubs is directly related to
their on-field, and increasingly to their off-field, performance. The dilemma for
clubs is that a greater control over cost must be achieved while at the same time
maintaining on-field performance, as the principal means of maintaining status.
The professional soccer industry, as with all professional sports industries,
exhibit characteristics which indicate their differences from more conventional
businesses, while at the same time sharing some key similarities. One key
difference is that of organizational purpose, as reflected by key performance
indicators. Sports, crucially, possess a more visceral appeal. Supporters of a
soccer club (who may or may not also be shareholders) demand entertainment,
and are hence customers in a conventional sense. They have relatively little
interest in the financial wellbeing of the club and its key shareholders except
when the financial wellbeing of the club threatens its long term viability, such as
happened with several high profile clubs including Leeds United, Newcastle
United, and the aforementioned Portsmouth in the UK, Parma and Fiorentina in
Italy, and the Montreal Expos baseball team.
What is so striking about sport is that the main focus of most owners of
professional sporting teams is also upon performance measures such as
‘entertainment’ and ‘glory’ rather than upon the bottom line. Indeed, economists
have argued that soccer clubs have never been run as pure profit maximisers
(Szymanski, 2003; Dobson and Goddard, 2001). Formerly, in the UK at least,
club owners had been life-long supporters of their club and prepared to make
business decisions that they would never countenance in a more conventional
business environment. The success of Blackburn Rovers, in winning the EPL in
1995, was directly attributable to the financial support of Jack Walker, an
industrialist whose investment in his club was never intended to yield financial
returns of the nature he was accustomed to from operating Walkersteel, his
family-owned steel business. In Italy the ‘owner-supporter’ is even more
common. For example, prior to being listed on the Borsa Italiana, Juventus of
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Turin was owned and operated by the Agnelli family, owners of the Fiat
automobile company.
Add to this recent statements by senior soccer officials (particularly
Michel Platini, President of UEFA) that clubs should be penalized for funding
their expenditure by a reliance upon debt, and a perspective emerges that suggests
that only seeking to manage a football club like a traditional competitive business
creates the environment for financial survival and success. Pressures are
mounting upon major soccer teams to become more ‘business like’, by which we
mean that pressure exists for soccer teams to be aware of the need for the financial
side of the club to be run as effectively as possible to support the performance of
the sporting side of the club. Indeed, in recent years new types of owners have
entered the EPL, many of whom are familiar from US sports (e.g. Malcolm
Glazier, owner of the Tampa Bay Buccaneers NFL team owns Manchester
United, Randy Lerner, owner of the Cleveland Browns NFL team also owns EPL
side Aston Villa, while George Gillett, former owner of NHL team The Montreal
Canadiens and Tom Hicks, owner of the Texas Rangers, co-own EPL side
Liverpool) and all of whom appear to expect to operate these teams on a more
financially rigorous, and business like fashion than traditional EPL owners. This
is not universally the case, and the EPL has also seen other new owners, mainly
from the middle-east or rapidly developing economies (such as Roman
Abramovich at Chelsea or Mansour bin Zayed Al Nahyan at Manchester City),
whose investments appear to be motivated by ownership status and is perhaps
more akin to old-style owners, but without the local affiliations.
We suggest that the key performance criterion for all soccer teams is the
maintenance of status. In arriving at this conclusion we looked at the purpose of a
soccer team, and determined that there are several that can be pursued. These are
(1) winning competitions, (2) operating profitably or (3) maintaining their status
in the hierarchy. In the professional soccer leagues of Europe in the early 21st
century, relatively few clubs have the opportunity of winning competitions; for
example since its inception in 1992, only four clubs have won the EPL. The
numbers of clubs that operate profitably are also relatively low, and the return on
investment (ROI) for these clubs would be unacceptable for traditional businesses.
This leaves us to conclude that while winning competitions and operating
profitably are the purpose of a small group of clubs, the majority of clubs satisfice
(Simon, 1957), which we interpret as seeking to maintain their status in the soccer
hierarchy even if achieving this goal is at the expense of operating profitably.
This is because status can be an extremely valuable commodity, with for example
TV revenues which closely reflect a club’s status in the soccer hierarchy for the
20 largest European clubs accounting for 41% (or €1.6b) of total revenue for
season 2007/08 (Deloitte, 2009, p.33); these clubs are possibly prioritizing
revenue growth over profitability.
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At the same time as status has assumed greater importance, so the
resources required to maintain that status have become more expensive to control
and use. A variety of factors are important here. They include:
x The changing nature of investment in soccer: numerous clubs have sought
to differentiate their sources of revenue and have floated their clubs on
stock markets. This has brought into soccer more investors that view
clubs more as traditional financial investments than emotional
investments, hence a subtle change in the purpose of these clubs;
x The development of meaningful international competition for finance and
resources: clubs have always competed on the field for trophies; they now
compete off the field for access to players and to funds and revenues. The
UEFA Champions League (founded in 1992) was the catalyst for this
major change; and
x The rising cost of playing assets: as has been noted (the authors,
forthcoming) players are no longer the chattels of clubs, but effectively
independent contractors who can sell their skills and expertise into an
almost open market (it is not a fully open market due to national
employment regulations, but as an effect of the development of trading
blocks and legislation to promote the international mobility of labor, and
even human rights legislation, this market is becoming much more open).
All of these factors have impacted upon each other, and have perpetuated
the growth and importance of each other. Maintaining status now depends upon
exploiting the appropriate assets, which requires access to ever greater funds, or
the development of a more sophisticated approach in using limited resources to
finance the use of those assets. This problem is complicated even further by the
fact that the assets in question are vulnerable.
4. Model Formulation
It is our contention that statistical analysis of past performance can help develop a
model for more accurately determining the financial value of a soccer player.
From a modeling point of view what is needed is a variable that is reliable,
observable and calculated consistently across discrete but similar activities (such
as the 38 games each EPL side plays per season) to allow for appropriate
comparisons between the parallel games/events.
Fortunately OPTA Sportsdata, introduced earlier, provides an answer to
these requirements. The OPTA Index results from a database where over 400
variables are recorded for all games in a given league such as the EPL. This index
encapsulates numerically the individual performance of players and teams. Since
the same calculation is made for each player in each game included in the index,
one can make relative value calculations and develop methodologies for financial
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value calculation of players and of clubs. As previously noted, we will make
extensive use of the valuation formulas established in Tunaru et al. (2005). Their
methodology makes an important distinction between valuations made by the
incumbent owner of the player’s rights and the potential club that is looking into
transferring the player into their team.
In Figure 1 we show the Opta Index value of Thierry Henry for the EPL
season 2003-04, which was that season won by Henry’s club, Arsenal. We may
observe that he had an outstanding second half of the season, scoring consistently
above the 1500 OPTA point threshold and even breaching the 2000 points barrier.
This performance is all the more impressive in comparison with his
teammates. Figure 2 depicts the total Opta points for the entire Arsenal team.
Their maximum achieved in any one game over that season was about 15000 and
their average was roughly 11000, thus giving an average per player per match of
1000 points (as a soccer team has 11 starting players). From these descriptive
statistics it is obvious that Thierry Henry was a very influential player for Arsenal.
In fact the statistical analysis shows a correlation coefficient between the return
on his performances and the return on Arsenal team performances of almost 60%,
which is very high in this context. If we remember that these are variables
quantifying human behavior, in this case individual soccer performance, then this
correlation is very strong.
Figure 1: Opta Index Scores f or Thie rry Henry over season 2 003/0 4
when playing for Arsenal Football Club
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Moreover, Henry missed only one week through injury so the injury
arrival rate was estimated as one game per season. The size of the fall in value due
to an injury event was taken as 10%. This means that 10 injuries in a season will
completely wipe out the value of the player to the owning club. The issue of how
much potential value (in terms of the intrinsic value of the player and the value of
the player as an asset to his owner) is lost through injuries requires further
analysis, as it may be possible to differentiate the potential impact of different
types of injuries and their timing, and so add a further level of sophistication to
the analysis. Nevertheless the major question in the soccer industry, “How much
is a player worth?”, needs deeper consideration.
Tunaru et al (2005) developed a methodology for quantifying dynamically
Henry’s value to his own club. The financial value of a single OPTA point for
Arsenal during season 2003-04 was calculated as being £417. There was about an
80% correlation between the turnover of the club, week by week, and the team
performance as measured by OPTA. Post 2007 this value will be considerably
higher as the club has moved to a new stadium with a much higher capacity and
consequently additional revenue generating operations. Figure 3 illustrates the
financial market value for Henry and we can see how this monetized value
fluctuates with his performance as measured by the OPTA index. The financial
value varies between £10m and £20m over season 2003-04 with an average value
of £16.33m. It is worth pointing out that this calculation was done from the point
of view of his then employers, Arsenal. Hence, based on the statistical analysis of
Op ta Arsenal
0
2000
4000
6000
8000
1000 0
1200 0
1400 0
1600 0
16/08/2003
16/09/20 03
16/10/20 03
16/11/2003
16/12/20 03
16/01/2004
16/02/2004
16/03/2004
16/04/2004
Opta A rsenal
Figure 2. Opta Points fo r the enti re te am o f Arsenal ove r the season 2003-04.
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his performance over the season 2003-04 Arsenal should have valued Henry at
close to £17 million, in any notional sale to a new employer. In fact, this is exactly
the figure for which he was sold to Barcelona in June 2007.
We can expect that the calculation will be different for a potential new
employer willing to transfer the player. The reason behind this argument is that if
Henry is either transferred to a new club or he is considering defaulting on his
current employer by entering into a strategy that is loss making for his current
club1, the current club is losing one member of the squad and to keep things the
same at least numerically they will have to transfer in a new player from outside.
In the soccer industry this may be a problem because similar players may not be
available or if they are available they may be more expensive than usual due to
market liquidity constraints or the scarceness of appropriately highly skilled
assets. This is in essence the basis of our argument that players are vulnerable
assets (VAs). For the new employer however, the transfer means that the new
1 The player may decide that his future lies elsewhere and he may refuse to train with his team,
refuse to play at his potential and create a state of unrest among his team mates and club fans.
Figu re 3. The evolution of Thierry Henry’s financial val ue to
Arsenal Football Club over the entire season 2003-04.
Henry's value for Arsenal
0
5000000
10000000
15000000
20000000
25000000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
Matches in the season 2003-04
Market Value
Henry's value for Arsenal
0
5000000
10000000
15000000
20000000
25000000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
Matches in the season 2003-04
Market Value
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club is either increasing the squad by one, or they are placed in a position where
they decide to sell one of their players in order to generate the capital needed for
the transfer. The difference in the positions vis-à-vis the market creates the
difference in the financial value of a player such as Thierry Henry to his current
club and any new potential club, everything else being equal.
Henry’s total money contribution (cumulative) via Opta points was £20.3
million during season 2003-04. His value could have been even higher if Arsenal
had been able to generate more income from their UEFA Champions League
matches. For example an increase of revenue leading to the increase in value of
one Opta point to Arsenal to £500 would increase Henry’s value to Arsenal to an
average of £19.12m.
Another subtlety is the location of the prospective new employer. If a club
is exploring whether or not to sign a player from another club playing in the same
national league competition as the player’s current club then the analysis at club
level is somewhat simplified because the financial economics of the game are
similar and the transaction will be conducted in the same currency. However, if
the new club is from a different country then the pricing methodology ought to be
adapted to take into consideration issues such as foreign currency exchange rates,
and also the financial and economic characteristics of that particular country2.
Human assets are difficult to price in a noisy environment such as the
soccer industry. Is the value of a vulnerable asset such as a soccer player the same
for all clubs present on the market? In other words does the law of one price
function here? Our empirical investigations show clearly that this is not the case.
In figure 4 we illustrate in parallel the value of Henry over the season 2003-04 for
Arsenal and for another club, in this case Manchester United. It is obvious that
Henry’s value would be less for Manchester United. Our heuristic explanation is
that if Manchester United were to buy Henry and not sell an existing squad player,
they would be adding to their current squad or roster of players while if Arsenal
were to sell or lose3 Henry they will be one player short.
2 As an example, until the UK government’s recent decision to increase the upper income tax
banding, players playing in France paid higher taxes on their income than their counterparts in the
EPL. At the time, taxes in the UK were much lower and therefore it was not surprising that there
were so many French players pursuing their careers in the EPL.
3 Players who have reached the end of their contracts are not obliged to sign new contracts, and are
able to assume what in US sport is called ‘free agency’ under the Bosman Ruling, named for the
Belgian soccer player (Jean-Marc Bosman) who originally took this case to the European Court of
Justice.
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0
5000000
10000000
15000000
20000000
25000000
1 357 9 111315171921232527293133
Figure 4. The Market Value of Thierry Henry for Arsenal ()
and for ManU () with the value of one point equal to £500)
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Let’s consider the same question, although this time for another EPL side,
Aston Villa. In 2003-04 the total revenue generated by Aston Villa was £84.4m.
Under the (unrealized) assumption that Aston Villa had an identical performance
on the pitch with Arsenal it would have meant that one Opta point during that
season was worth £200 for Aston Villa. Thus, Aston Villa could not recover the
same value from Henry’s performance as would Arsenal, so paying him similar
wages to those he received at Arsenal would have resulted in a loss. There are
various reasons for this: firstly Aston Villa would have had to transfer him to the
club, and there will always be some friction costs because other Aston Villa
players may have had to be sold at a discount to enable the transfer and there may
well be an accommodation period while the player settles in. However, perhaps
more important is the fact that the economic engine of Aston Villa is not
comparable with top clubs such as Manchester United and Arsenal.
Even in this brief example, we demonstrate that statistical analysis of this
nature can be useful to highlight the differential financial contribution such a VA
can make, which can assist in determining whether such an investment (i.e. the
transfer of a VA from one club to another) is a risk worth taking.
5. Further Insights from Statistical Analysis
In this section we show how statistical analysis can extract valuable information
about soccer teams and players by looking at the OPTA performance index. In
Figure 6 we compare the team index for the EPL champions in season 2003-04
(Arsenal) with their main competitor (Manchester United). It is evident that while
Manchester United enjoyed a slightly better first half of the season, Arsenal had a
better second half of the season. It is important to remember that in the EPL there
is no mid-season break.
There are several points that we would like to point out when
comparatively analyzing the performance of the two best teams in season 2003-04
in the EPL. First, both teams seem to have their equilibrium performance level
just about 11000 OPTA index points. This implies an average of 1000 OPTA
Index points per player per game so players producing well in excess of this
threshold are extremely valuable assets for their clubs. Secondly, counting the
number of consecutive downward jumps, Arsenal had four runs with two
consecutive drops (there is another one that can be easily attributed to noise in
data collection) while Manchester United had four runs with two consecutive
drops. Arsenal never had a team score below 8000 points while Manchester
United had had four such games. Additionally, Arsenal had three games with
performances above 14000 points while Manchester United never breached that
barrier.
13
Tunaru and Viney: Valuations of Soccer Players
Published by Berkeley Electronic Press, 2010
Despite the apparently strong team performance, the key to Arsenal’s
success was Thierry Henry’s extraordinary season. One important lesson from
this comparison is that star players can make a difference. Henry’s performance in
this season, and others while at the club, as well as his off-field ambassadorial
performance and image rights fully justified his manager Arsene Wenger’s
decision to sign him for Juventus of Italy (for £10.5M in 1999), and to pay him a
high salary during his time with Arsenal.
6. Managerial Insights
The manager of a football club has a difficult balance to achieve. Within the
financial constraints of the club his objective is to maximize the performance of
the club’s team primarily, as we have noted, to maintain their status within the
soccer hierarchy but also, if the club is a member of the elite group in any league,
to attempt to win trophies and possibly also to operate profitably.
In the previous section we have seen the impact that Thierry Henry had for
his team, in particular in the second half of season 2003-04 of the EPL, so one can
extrapolate that his performance made the difference in the end to Arsenal
Figure 6. Arsenal OPTA performance ind ex versus Manch ester United
OPTA performance index for t he season 2003-2004.
14
Journal of Quantitative Analysis in Sports, Vol. 6 [2010], Iss. 2, Art. 10
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DOI: 10.2202/1559-0410.1238
winning the league. Another important factor that should not be overlooked is the
frequency and seriousness of the injuries experienced by players in the squad. In
Figure 7 we illustrate the week by week total number of injured players for
Manchester United in season 2003-04. There is a clear dichotomy between the
first half of the season and the second half. The volatility of the number of injuries
is much higher for the latter. This suggests that as some players were coming back
from injury, other players were getting injured. This creates a problem for the
manager who has to consider the probability that players coming back from injury
may still need a number of games to get to their standard level of performance and
also that changing the team on a frequent basis may be detrimental to the team, by
preventing them from developing a deeper understanding between them. It also
may help explain Manchester United’s relatively poorer second half to this
season.
Another question we can offer commentary upon is ‘does a superstar
player always help a team win competitions?’ Here we use the same tools as
utilized above for Thierry Henry but for another interesting case, that of Rio
Ferdinand, the current captain of Manchester United who we examine for season
2004-05 of the EPL. His value at the beginning of that season was zero, because
in the previous season he received a long ban for missing a drug-test and thus
Man U 2003-04
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
16/08/2003
16/09 /2003
16/10 /2003
16/11/2003
16/12/2003
16/01/2004
16/02/2004
16/03 /2004
16/04/2004
No of Inju rie
s
Figure 7. The evolution of injuries for the entire Manchester Unit ed
team in the 2003-04 season
15
Tunaru and Viney: Valuations of Soccer Players
Published by Berkeley Electronic Press, 2010
played no part in early season games. His transfer from Leeds United (for £30m in
2002) had dwarfed any previous transfer fees for a defender. His off-the-field
problems should not take away from his on-the-field performance, should it? Our
analysis suggests that this is not the case reinforcing the complexity of valuing a
human asset. Even allowing for this initial artificial ranking, his performance
during the season was relatively poor, as can be seen from Figure 8.
His relative value, as measured by our analysis, never reached £0.6m and
this was very low considering his high wages and his transfer fee. As can be seen
from Figure 9, there was no correlation between his performance and the team’s
performance. The scatter plot shows no association between the levels of his
performance and his team’s OPTA index score. This does not necessarily mean
that his intrinsic value was low or that he should be dropped from the team.
Defenders in soccer take longer to reach their peak and quite often they may be
penalized for making a relatively limited number of mistakes during a season.
However, his OPTA index scores were consistently so low that one may ask the
question whether he justified his high salary by virtue of his poor performances?
One could argue that it possibly was a bad season for the entire team, not
just for him. If that was the case then his performances would improve when the
Rio Ferdi nand Ster li ng Value to ManU
0
10000 0
20000 0
30000 0
40000 0
50000 0
60000 0
15/08/2004
15/0 9/ 20 04
15/1 0/ 2 004
15/11/2004
15/12/2004
15/0 1/ 20 05
15/02/2005
15/03/2005
15/0 4/ 20 05
15/0 5/ 20 05
Figure 8. Fi nancial Value of Rio Ferdinand for his club Manchester United
throu gh the seaso n 2004 -0 5.
16
Journal of Quantitative Analysis in Sports, Vol. 6 [2010], Iss. 2, Art. 10
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DOI: 10.2202/1559-0410.1238
team’s performance improved and vice versa. In other words the percentage
changes in OPTA index would then show some correlation. However, as shown in
Figure 10, once again we are unable to conclude that there was any synergy
between him and the team.
Statistical analysis of the performance of players in the EPL and other
major European leagues can reveal important data and relationships that may help
a management team to identify key players, who not only help the team but also
display other behavioral characteristics that need to be considered for decision
making. For example, an excellent player who is hated in the dressing room, who
is extremely injury prone or is homesick, is unlikely to bring out the best in his
colleagues, and building an understanding of these criteria into transfer and salary
negotiations we suggest can have a valuable impact upon management’s role and
effectiveness. Moreover, we suggest that it is important to have a link between
the performance function of the players and their financial value. While every
supporter might wish to have the latest superstar in their team, it is important to
realize that some clubs may not have the economic engine to generate enough
revenues by which to pay the high wages of star players, nor the potential to
achieve and retain a high enough status in the soccer elite to justify the expense of
keeping a star player in the team.
0
200
400
600
800
1000
1200
1400
0 5000 10000 1500 0 2 000 0
Figur e 9. Scatterplo t of Rio Ferdinand’s OPTA perf orma nce poin ts on the vertical
versus the to tal OPTA perfo rma nce poin ts of the entire rest of his team.
17
Tunaru and Viney: Valuations of Soccer Players
Published by Berkeley Electronic Press, 2010
This kind of analysis is very important for the manager especially as
players may become more difficult to manage as their status and image grows.
Hence being able to pinpoint the qualities of the player and the performance ties
with the entire team is imperative in the current environment where spiraling
wages and increased revenues are linked, directly or indirectly, to performance.
7. Conclusion and Future Research
The OPTA performance index offers a tool to analyze statistically the
performance of soccer players and their teams. This is very important for
establishing a more realistic assessment of the financial value of players but also
for extracting useful information about what determines success on the pitch for a
given team or the potential linkages between individual players and their teams.
This paper represents a first attempt to highlight the potential we believe this
methodology offers.
This area of research is in a nascent phase but with the availability of more
accurate information there is scope for expanding this research in several
directions. First, we would like to continue our research by undertaking
evaluations of entire teams and implicitly of their parent clubs. After all, the clubs
main assets are their players. Secondly we would like to develop a ranking tool
-1
-0.8
-0.6
-0.4
-0.2
0
0. 2
0. 4
0. 6
0. 8
1
-0. 6 -0.4 -0. 2 0 0. 2 0. 4 0.6
Ma nU
Ferdi nand
Figure 10. Scatterplot of percentage returns of Rio Ferdinand’s OPTA
perf ormance points on th e vertica l versus the percent age returns of t ot al OPTA
performance points of the entire rest of his team.
18
Journal of Quantitative Analysis in Sports, Vol. 6 [2010], Iss. 2, Art. 10
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DOI: 10.2202/1559-0410.1238
that will identify the best and worst teams in terms of their financial performance,
rather than the more normal ranking by performance and we can estimate that this
ranking may not necessarily coincide with the actual ranking determined by match
results. Last but not least we would like to drill-down into the statistical
information contained in the OPTA database and identify the unsung heroes.
These are the ‘moneyball’ players who make a significant contribution but do not
receive either glory or very high financial rewards.
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This paper proposes a dynamic programming (DP) approach to find the optimal substitution strategy for a football match, which maximises the probability of winning or the expected number of league points, supported by real data of the English Premier League. We use a Markov process model to evaluate the offensive and defensive strengths of teams by means of maximum likelihood estimators. We develop a DP formulation to derive quantitatively the optimal substitution strategy of a team, in relation to the number required of each type of outfield player. We demonstrate how this approach may help to determine how many of each type of player should start a match and be substituted during a match. We also show how the expected league points would increase if the optimal strategy were followed.
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A football match is modelled as a four-state Markov process. A log-linear model, fed by real data, is used to estimate transition probabilities by means of the maximum likelihood method. This makes it possible to estimate the probability distributions of goals scored and the expected number of league points gained, from any position in a match, for any given set of transition probabilities and hence in principle for any match. This approach is developed in order to estimate the optimal time to change tactics using dynamic programming, either by making a substitution or by some other conscious change of plan. A simple example of this approach is included as an illustration.Journal of the Operational Research Society (2002) 53, 88–96. DOI: 10.1057/palgrave/jors/2601254
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A football match is modelled as a four-state Markov process. A log-linear model, fed by real data, is used to estimate transition probabilities by means of the maximum likelihood method. This makes it possible to estimate the probability distributions of goals scored and the expected number of league points gained, from any position in a match, for any given set of transition probabilities and hence in principle for any match. This approach is developed in order to estimate the optimal time to change tactics using dynamic programming, either by making a substitution or by some other conscious change of plan. A simple example of this approach is included as an illustration.
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