measuring the productivity of spanish first division soccer teams

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Measuring the Productivity of SpanishFirst Division Soccer TeamsManuel Espitia-Escuer a & Lucía Isabel García-Cebrián aa Departmento de Economía y Dirección de Empresas , Universityof Zaragoza , SpainPublished online: 18 Sep 2008.

To cite this article: Manuel Espitia-Escuer & Lucía Isabel García-Cebrián (2008) Measuring theProductivity of Spanish First Division Soccer Teams, European Sport Management Quarterly, 8:3,229-246, DOI: 10.1080/16184740802224142

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ARTICLE

Measuring the Productivity of SpanishFirst Division Soccer Teams

MANUEL ESPITIA-ESCUER &LUCIA ISABEL GARCIA-CEBRIAN

Departmento de Economıa y Direccion de Empresas, University of Zaragoza, Spain

ABSTRACT This study examines the Total Factor Productivity evolution of SpanishFirst Division Soccer teams employing the values of the Malmquist Index. The footballseasons from 1998 to 2004 are used as the time horizon. The breakdown of the twocomponents of the Malmquist Index Values (efficiency change and technical change)enable one to understand the influence of these factors on productivity and conclusionscan be drawn about the relationship between the values of efficiency and the playingfield strategy adopted by the analysed teams.

Introduction

The sporting activity of professional football teams is carried out within acompetitive framework in which the performance level of each team is asdependent on the individual abilities of its members as its collectivemanagement. The level of management professionalism achieved by theseorganizations means that they may be assessed and evaluated by using themethodologies and parameters that are commonly employed in the field ofbusiness management.

In the competitive framework of the activity, the analysis of productivityand its determinants becomes a basic tool for understanding the influencethat each individual factor has on the final result. The resources availableand decisions taken as to how they are employed are contributing factors tothe success or failure of the organization.

Improving results is the challenge that faces all professional managementteams in these types of organizations. With the aim of activating a process ofimprovement in the use of available resources, complex analysis techniques

Correspondence Address: Lucıa Isabel Garcıa-Cebrian, Departmento de Economıa y Direccion de

Empresas, Facultad de Economicas, University of Zaragoza, Gran Vıa, 2, 50.005 Zaragoza, Spain. Email:

[email protected]

ISSN 1618-4742 Print/ISSN 1746-031X Online # 2008 European Association for Sport ManagementDOI: 10.1080/16184740802224142

European Sport Management Quarterly,

Vol. 8, No. 3, 229�246, September 2008

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are applied, which constitute a basis for an improvement in the decision-taking procedure. This study is based on a productivity analysis of SpanishFirst Division football teams. The analysis compares each team’s results inleague competition over a number of seasons.

The objective is to measure the productivity of Spanish First Divisionteams, taking the 1998/1999 to 2003/2004 seasons as the time horizon forthe analysis. We will employ deterministic non-parametric frontiers. Frontierfunctions measure efficiency with respect to the best observations andcorrespond to optimization processes. Deterministic non-parametric fron-tiers do not consider a specific functional form for the frontier; they areformed through linear programming techniques, such as the envelopment ofthe observed values. Firms lying on the frontier established in this way areconsidered as efficient. The use of this type of frontier has given rise to themethodology known as Data Envelopment Analysis (DEA). Having in-formation from several years will allow us to study, not only which teamshave been the most efficient every season, but also to analyse the evolutionof their productivity, in other words, the evolution of their efficiency and thechanges perceived in the efficient frontier itself.

The structure of the study is as follows: the next section contemplates theliterature that deals with the efficiency of soccer teams; the third sectioncovers a brief presentation of the Malmquist Index*the ratio that measuresthe change in Total Factor Productivity if a non-parametric frontier focus isused to measure efficiency; the fourth section shows the results of theSpanish First Division soccer teams in relation to changes in Total FactorProductivity, efficiency changes and technical changes; the last section setsout the conclusions drawn from the analysis.

Review of the Literature

Interest in the analysis of the economic aspects of professional sport is notnew: the works of Neale (1964), El-Hodiri and Quirk (1971) and Cairns,Jennett, and Sloane (1986) are early examples of the application of economictheories and models to this discipline.

The evaluation of the activity of sports clubs and the measurement of theirefficiency through frontiers has been of particular interest due to the varietyof sports studied. For example, Mazur (1994), Anderson and Sharp (1997),Sueyoshi, Ohnishi, and Kinase (1999), Lewis and Sexton (2004) and Lewis,Sexton, and Lock (2007) focused on baseball, whilst Zak, Huang, andSiegfried (1979), Fizel and D’Itri (1997) and Hofler and Payne (1997) allconsidered the evaluation of the efficiency of basketball teams. There arealso many works that deal with the efficiency of soccer teams, includingDawson, Dobson, and Gerrard (2000a, b), Haas (2003a,b), Haas, Kocher,and Sutter (2004), Espitia-Escuer and Garcıa-Cebrian (2004, 2006), Bosca,Liern, Martınez, and Sala (2006) and Guzman (2006). Hadley, Poitras,Ruggiero, and Knowles (2000) looked at American football, Fried,Lambrinos, and Tyner (2004) concentrated on golf and Scully (1994)analysed baseball, basketball and American football.

230 M. Espitia-Escuer & L.I. Garcıa-Cebrian

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The basic methodologies employed for the measurement of efficiency havebeen deterministic non-parametric frontiers (DEA) or stochastic frontiers.Among the already mentioned works that used the former are those ofMazur (1994), Anderson and Sharp (1997), Fizel and D’Itri (1997), Sueyoshiet al. (1999), Haas (2003a, b), Haas et al. (2004), Fried et al. (2004), Lewisand Sexton (2004), Espitia-Escuer and Garcıa-Cebrian (2004, 2006), Boscaet al. (2006), Guzman (2006) and Lewis et al. (2007). Hofler and Payne(1997) and Dawson et al. (2000a, b) used stochastic frontiers. Although theuse of stochastic frontiers is less common, other frontier types have also beenutilized in the calculation of the efficiency of sports teams*Scully (1994)and Hadley et al. (2000) applied deterministic frontiers (in the second case inconjunction with stochastic frontiers) and Zak et al. (1979) employeddeterministic parametric frontiers.

Works that study the efficiency of soccer teams are distinguished by theirobjective and study reference unit, something which means that therepresentative variables of input and output are different. For example,Dawson et al. (2000a, b), took data by team for their analysis, though theiraim was the evaluation of the efficiency of the coaches. In contrast, Haas(2003a,b), Haas et al. (2004), Espitia-Escuer and Garcıa-Cebrian (2004,2006), Bosca et al. (2006) and Guzman (2006) evaluated the efficiency ofsoccer teams (although from differing points of view). Haas (2003a, b) andHaas et al. (2004) argued that soccer teams pursue three objectives (sportingor the results of matches; economic or financial results; social results relatedwith offering entertainment to the public) so the outputs to be taken intoaccount have a relationship with the points won, with income and withattendance at matches, whilst inputs are concerned with the remuneration ofthe players and the coach. Haas (2003a) took Major League Soccer in theUSA as the sample; Haas (2003b) focused on the English League and Haaset al. (2004) used the German League. Guzman (2006) concentrated solelyon the financial performance of Spanish First Division teams and evaluatedefficiency by taking turnover as output and staff costs and general expensesas inputs. Espitia-Escuer and Garcıa-Cebrian (2004, 2006) and Bosca et al.(2006) evaluated the efficiency of the play developed by the teams; the firsttwo studies used the Spanish First Division as the sample, the latter workused the Spanish and Italian leagues. In the works of Espitia-Escuer andGarcıa-Cebrian, output is measured as the sporting results obtained in eachseason, inputs are the number of players used and the number of plays madeduring the season. Bosca et al. (2006) differentiated between the efficiency ofattacking and defensive plays. Espitia-Escuer and Garcıa-Cebrian (2006)calculated the efficiency of Spanish First Division teams with the aim ofevaluating their sporting potential and determining the position that theyshould have reached in the season if they had made efficient use of theresources at their disposal.

With the objective of evaluating the productivity of the play in thematches of Spanish First Division soccer teams, we have followed the ideasof Schofield (1988), Carmichael and Thomas (1995) and Carmichael,Thomas, and Ward (2000) in their characterization of the production

Productivity of Spanish Soccer Teams 231

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function. These authors do not aim to evaluate the efficiency of the sportsteams*they estimate a production function through an average function,though they consider a recursive system in which the success of the teamdepends on the performance of the players during the game and this, in turn,depends both on their abilities and on the work of the coach. Therefore, ifthis is applied to the production function of soccer teams, we can considerthat such a function is made up of two different components, each with itsown inputs and outputs.

. In the first part, we can consider the abilities of the players (sportingtalent, physical condition and form, experience, etc.) together with thework of the coach (work during training sessions, tactics, line-up, etc.) asthe inputs to obtain a result, where this is the performance during thematch, that is to say, attacking and defensive moves against the opposingteam.

. In the second part, we take as inputs the attacking and defensive moves(result of the first component), which are transformed into success duringthe matches, in such a way that they can be considered as output.

Our analysis of the productivity of the professional soccer teams playing inthe Spanish First Division focuses on the second of the aforementionedcomponents of the production function. With reference to the measurementof output as success in the competition, according to Dawson et al. (2000a),a draw is a common result in a match and the rules of the League allow thisresult with no obligation to find a way to determine a winner and loser ofeach game; Dawson et al. (2000a) therefore consider the number of pointsaccumulated during a season as a variable that conveniently measures afootball team’s results as its calculation contemplates the three possibleresults of a match (win, lose and draw) with each result being rewarded witha different number of points and, in this work, this variable is taken asrepresentative of output. We do not consider the number of goals scored asan output variable because the final position of the team in the League doesnot depend on this but on the difference between goals for and goals against.On the other hand, we have taken as input variables the number of playersused throughout the length of the season (the human factor is a productionresource present in all activity), the number of attacking moves, the numberof minutes during which the teams had possession of the ball and the numberof shots and headers. With reference to defensive plays, the proposal ofEspitia-Escuer and Garcıa-Cebrian (2004, 2006) has been followed and theyare not included as inputs due to the fact that in the Spanish First Division allteams have to play against each other twice so it is possible to consider thatthe influence of the opposition is homogeneous throughout the sample.

It is also worth contemplating a theoretical position that would allow theincorporation of defensive plays as an input through adapting DEAmethodology to its peculiarities; a proposal along these lines was advancedby Lewis and Sexton (2004) with their methodology for working withreverse inputs and outputs, applied to the world of sport. This solution,however, was not considered adequate for our research for a number of


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reasons. First, reverse inputs are those for which an increase in qualitysupposes a reduction in the quantity of product obtained, in the case of ateams’ defensive plays, this relationship does not exist: if a team is defensiveit will concede less goals and gain more points. In other words, it has thesame effect on output as attacking play. Secondly, it must be said that it ispossible to consider the defensive plays of all the rival teams during theseason as reverse input because an increase in these types of actions has anegative effect on the product (points obtained by the team that is the objectof analysis). Nevertheless, a more profound consideration of this questionled to ruling out the incorporation of rivals’ defensive plays as input becauseit is a variable that is not under the control of the team whose efficiency isbeing calculated and it can therefore not be considered as a factor ofproduction but as a variable of the operational environment. Finally, thedetermination of the variables to be taken as inputs and outputs representa-tive of the productive process of soccer teams during matches can be basedon the premise that a team has two tactical options in order to gain points:attacking play (implying an attempt to score more goals than the opposition,irrespective of the opponents’ play) and defensive play (with the aim ofstopping the opposition scoring goals irrespective of the goals scored by theteam in question). Attacking plays mean that the team takes the initiative,while defensive plays are an adaptation to the opposition with the aim ofcounteracting their strategy; in other words; defensive plays can be seen asan adaptation to the environment more than the resources involved in theproductive process. These are the arguments that led us to discount theinclusion of defensive plays as inputs.

The reason why this work analyses the actions of soccer teams on the fieldof play is not sporting but economic. As Espitia-Escuer and Garcıa-Cebrian(2004) explained, we must consider that the income of a football club isbased on season ticket sales, attendance at matches and advertising and thatthese things are fundamentally dependent on previously obtained results.Therefore, the only way to maximize profits is to minimize costs and oneway to do this is through the elimination of waste detected by the calculationof efficiency.

With reference to works that have measured the efficiency of Spanishsoccer teams, Guzman (2006) analysed efficiency in teams’ financialactivities, whilst this work evaluates sporting activities on the field ofplay. There are a number of articles that have studied the efficiency ofSpanish First Division football teams on the field of play and this work hasclosely followed the approach of Espitia-Escuer and Garcıa-Cebrian (2004,2006) in terms of the selection of the representative variables as inputs andoutputs, disregarding the differentiation of offensive and defensive play andtaking the points obtained throughout the course of the season asrepresentative variables of the sporting results. This work also considersthat defensive play is a reaction to the environment rather than a factor ofproduction. Espitia-Escuer and Garcıa-Cebrian (2004, 2006) used season-by-season data on the teams and obtained an efficiency ratio for each unitfor each of the analysed years (in the first work, with the aim of detecting


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inefficiencies, in the second, in order to analyse the sporting potential of theteams). This research takes advantage of the availability of complete data fora number of seasons in order to analyse changes in the total productivity ofthe factors affecting soccer teams in a more extensive time frame.

Table 1 shows the descriptive statistics for the data utilized in this work.

Measurement of Total Factor Productivity Using the Malmquist Index

As Grosskopf (1993) indicated, productivity has been an issue for quite sometime and a number of different approaches have been used in order tomeasure it. The same author mentions that she does not follow the focus thatconsiders that growth in productivity and technical progress are equivalentbut an approach that considers productivity growth as the net change inoutput due to changes in efficiency and technology; a change in efficiency isinterpreted as a modification in the distance between an observation and itsproduction frontier, while technical change is demonstrated through changesin the production frontier itself (Grosskopf, 1993). This study favours thelatter approach. From these definitions it is clear that the focus for themeasurement and evaluation of efficiency is by means of frontier functions.This focus is based on real data taken from a unit sample in which the inputquantities used and the output quantities obtained determine the isoquantthat represents the productive process of the analysed sample, based on thesupposition that no best observation can be found below the frontier orisoquant thus established and therefore can be found only on the frontieritself (corresponding to those units that are considered efficient) or above it(inefficient units). According to Førsund, Lovell, and Schmidt (1980), thepossible methods that can be used to establish the isoquant based on realdata, such as the frontier, are deterministic non-parametric frontiers,deterministic parameter and stochastic frontiers. For the purposes of thisstudy, deterministic non-parametric frontiers*or the model known asDEA*will be employed; it proposes the construction of non-parametricdeterministic frontiers based on the data of the study sample, no previoushypotheses about the functional form of the frontier will be put forward andall possible data deviations in respect of the frontier will be considered as theresult of inefficiency.

Table 1. Descriptive statistics of the data used

Number ofattacking plays

Numberof players

Minutes ofpossession

Number ofgoal attempts

Numberof points

Average 4476.12 26.13 1006.05 485.20 51.90Typical deviation 374.56 2.80 91.41 62.50 11.81Maximum value 5227 32 1271 637 80Minimum value 3765 19 851 342 26

Source: GecaSport.


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In order to calculate the efficiency ratio of a sample study unit, DEAproposes the resolution of the following linear programming problem forone period t:

Min Eti(y

ti ; xt

i)subject to yt

i 5zYt

Eti(y

ti ; xt

i)y]zXt:z � Rt

�

(1)

where yti is the vector of the quantities of the m products produced by the

unit i under analysis, Yt is the k.m matrix of the quantities of the m productsfor the k units of the sample, xt

i represents the quantities of the n productivefactors used by the unit i whose efficiency is being measured, Xt is the k.nmatrix of the quantities of the n productive factors used by the units of thesample, and z is a vector of parameters which determines the combinationsof factors and products observed, giving rise to a unit of reference for theunit under analysis which is on the efficient frontier, and which wouldobtain the quantities of products calculated as z Yt; using productiveresources in the quantities calculated as z Xt: The value Et

i(yti ; xt

i) is theefficiency ratio for the analysed unit i in period t and is the parameter to becalculated with the resolution of the linear programming problem putforward. All these variables use the data corresponding to the period t. Theproblem corresponds to the supposition of constant returns to scale andinput orientation and, based on these hypotheses, the interpretation ofEt

i(yti ; xt

i) is the proportion by which the input quantities used by theobserved units should be reduced in order to continue to obtain the sameoutput quantity, though in some way it can still be classed as efficient. Inaddition, when Et

i(yti ; xt

i)�1, the unit under analysis lies on the isoquant andis classed as efficient. Nevertheless, the formulation of the problem woulddiffer in accordance with changes in the suppositions that are made withrespect to production technology and the orientation of input and output.With reference to the first question, this work assumes performances that areconstant to scale because the aim is to value the efficiency assigned to eachsoccer team. The aim is not to identify which part of that efficiency is due tothe absence of waste in the utilization of resources and which part is due tothe selected technology (that would be represented by its size); this is adifferentiation that is allowed by a calculation of efficiency that is based onthe supposition of performances that are variable to scale. Once the decisionwas made to use the supposition of performances constant to scale, the valueof the ratio of efficiency orientated to input is the reverse of that orientatedto output. The adoption of one orientation or another is therefore irrelevantfrom the point of view of identifying inefficient teams and the explanation oftheir situation, although the value of the ratio and its interpretation differ: inthe case of orientation to input, the inefficient teams show a ratio inferior tothe unit that is interpreted as the proportion in which they could reduce thequantities of resources in order to obtain their current output in an efficientform; if orientation is to output, the ratio is superior to the unit, indicatingthe proportion by which the quantities of the product obtained could be


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increased by using the current quantities of input. In the case of efficientteams, both scenarios present a value of the ratio that is equal to the unit.

With the aim of measuring the productivity of the professional soccerteams playing in the Spanish First Division, this paper will use theMalmquist Index of the change in Total Factor Productivity. Grosskopf(1993) and Coelli, Rao, and Battese (1998) outlined a Malmquist Indexformula as a geometric measure of two indexes calculated from the distancefunctions between an observation and the isoquant that represents theproductive process. Given the existing relationship between the aforemen-tioned distance functions and the efficiency ratio calculated by means ofDEA, for the purposes of this study, the Malmquist Index for unit i iscalculated through the following expression:

Mi ��Et

i (yt�1i ; xt�1

i )

Eti (yt

i ; xti)

�Et�1

i (yt�1i ; xt�1

i )

Et�1i (yt

i ; xti)

�1=2

(2)

where the notation Eti (yt�1

i ; xt�1i ) represents the technical efficiency for the

period t�1 observation in respect of the period t technology. Similarly toGrosskopf (1993) and Coelli et al. (1998), the Malmquist Index used is, inreality, the geometric measure of the two Malmquist Indexes that evaluatethe observations of a determined unit at two different moments (t and t�1);the first being in respect of the technology of period t, the second being inrespect of the technology of period t�1.

A value of M greater than one will indicate positive Total FactorProductivity growth from period t to period t�1, while a value less thanone indicates a decline in Total Factor Productivity.

According to Grosskopf (1993) and Coelli et al. (1998), another way ofwriting this productivity index is:

Mi �Et�1

i (yt�1i ; xt�1

i )

Eti (yt

i ; xti)

��

Eti(y

t�1i ; xt�1

i )

Et�1i (yt�1

i ; xt�1i )

�Et

i(yti ; xt

i)

Et�1i (yi

t; xti)

�1=2

(3)

where the ratio outside the square brackets measures efficiency changebetween periods t and t�1 for unit i. The remaining part of the index is ameasure of technical change in unit i because it is the geometric mean of theshift in technology between the two periods. If the ratio corresponding tochanges in efficiency takes a value that is superior to the unit, it means thatefficiency for unit i has improved in the period from t to t�1; the contrarywill be the case if the ratio has a value inferior to the unit. Similarly, atechnical change value that is superior to one means that there has beentechnical progress in the period t�1 in respect of t; in the case where thevalue is inferior to one, it would mean a technical decline between the periodt and t�1.

In actual fact, the term that allows the calculation of technical change iscomposed of two coefficients; each one measures the relationship betweenthe efficiency ratio that, with respect to the isoquants in t and t�1, obtainedthe values (yt�1

i ; xt�1i ) and (yt

i ; xti): The Malmquist Index shows that for a

given sample, in the same period, the value of the ratio corresponding to


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technical change can demonstrate technical progress for some units of thesample and technical regression in others. The explanation for this is basedon the fact that on evaluating efficiency in relation to isoquants or frontiersof a different period, they can be cut and, therefore, depending on thesituation of each unit with respect to them, the technical change experiencedby them may be different. This would be the case for units i and j representedin Figure 1, if two inputs are considered.

Points it and it�1 represent the combinations of inputs 1 and 2 that theunit i has utilized in the periods t and t�1, respectively, to obtain thequantity of output represented by the isoquants. Points jt and jt�1 representexactly the same for unit j of the sample. Applying the expression thatappears in parenthesis in equation (3), the ratio of technical change of theunit i is inferior to 1, so it has undergone a technical regression between tand t�1, the value of the technical change of unit j is greater that 1 and ithas therefore experienced technical progress between the periods t and t�1.In the case represented in Figure 2, all the units experience the same technicalchange (technical progress).

Nevertheless, from some empirical results in which all the units show thesame type of technical change, it cannot be assumed that the isoquants thatrepresent technology do not cut; this can be the predominant case of a typeof technical change on situating all the units studied in a sector where thereis only one type of technical change*as in the situation represented inFigure 3.

As a consequence, the fact that in the same period, not all units exhibitedthe type of technical change clearly shows that the isoquants referring to thetwo periods were cut. On the other hand, if all units show the same type oftechnical change in the same period, it is not possible to determine if this isdue to a change in the position of the isoquants to the following periodwithout being cut or due to the predominance of the tendency that is clearlynoticeable in the global value of the technical change. This is the reason whythe section on conclusions refers to the technical change experienced by eachunit and not to that produced throughout the sample or sector. Onconsidering the formulae put forward, it can also be concluded that a

Input 2

Input 1

Isoquant t

Isoquant t+1

·it

·it+1

·jt+1 · jt

Figure 1. Existence of units that present technical progress and regression


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growth in Total Factor Productivity can be produced in spite of a technicaldecline or a drop in efficiency as long as the respective aforementionednegative effects are compensated for by gains in efficiency and technicalprogress. Obviously, the same possibility applies in the case of a fall in TotalFactor Productivity.

Results

The time horizon used for this study is the 1998/1999 to 2003/2004 footballseasons. The panel data are incomplete, as every season sees some teamspromoted from the Second Division and some teams relegated from the First.Given this fact, this study has opted to keep the study sample as all the teamsthat in one or more of the seasons analysed has played in the First Division*only the teams that played in the First Division in all six of the seasons underanalysis. This decision was made for two reasons: first, given that theevolution of the team’s efficiency is made with respect to the technologyrepresenting one season, it was considered that the said technology was

Input 2

Isoquant t+1

Isoquant t

· it

· it+1· jt+1

· jt

Figure 3. Case in which all units show the same type of technical change, despite the fact thatthe isoquants are cut

Input 1

Input 2

Isoquant t

Isoquant t+1

· it+1

· it

· jt+1

· jt

Figure 2. Case in which all units show the same type of technical change


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representative of all the teams that in that particular moment played in theFirst Division; secondly, as more Malmquist Index values are obtained if allthe teams that played at least one season in the First Division are included inthe sample, the results would therefore be more consistent.

From the results presented in Table 2, it can be seen that until the 2001/2002 season, the average Malmquist Index for each team in each season wasless than the unit although it was growing; in the last two seasons studied,the value was superior to the unit and was also growing year by year. Thesevalues indicate that until the 2001/2002 season, Total Factor Productivity ofSpanish First Division soccer teams fell with respect to the previous seasons,although the fall was less each season and from the 2002/2003 season,productivity increased. In terms of the evolution of technical and efficiencychanges during the period studied, it was observed that, on average, therewas an increase in efficiency compared to the values of the previous period inthe 1999/2000, 2001/2002 and 2003/2004 seasons; the contrary being thecase in the other seasons. The evolution of the technical change average isthe opposite in practically all the analysed sample*with the exception of2003/2004 (when there was an increase in technical progress and efficiencycompared to the previous year)*when there is technical progress, there is adecline in efficiency, and vice versa. The fact that the Malmquist Indexpresented average values close to the unit when its components moved inopposite directions indicates that no component predominated in the TotalFactor Productivity variations.

Nevertheless, the average results mask great differences in the individualvalues of each team. In the 1999/2000 and 2001/2002 seasons, there was anaverage improvement in efficiency compared with previous seasons andthere was no team that presented technical progress; all Total FactorProductivity improvements were exclusively due to improvements inefficiency and we can find individual cases in which the positive change inefficiency was transcended by a technical decline leading to a fall in totalproductivity factors (this was the case with Real Madrid, Oviedo, Racing deSantander and Valladolid in the1999/2000 season and Celta in 2001/2002).In the 2000/2001 and 2002/2003 seasons there was an average decline inefficiency and all the teams showed technical progress; in 2000/2001, therewere seven teams that improved Total Factor Productivity but with adifferent component structure: five of which also showed an improvement inefficiency (Celta, Deportivo, Real Madrid, Malaga and Mallorca) while intwo of them the decline in efficiency did not impede the increase in TotalFactor Productivity (Barcelona and Espanol); in the 2002/2003 season, onlythree teams showed an improvement in efficiency (Celta, Real Madrid andReal Sociedad), although five more also showed a Total Factor Productivityimprovement, in spite of only showing technical progress (Atletic de Bilbao,Deportivo, Mallorca, Osasuna and Valladolid). In 2003/2004, seven teamsimproved efficiency and showed technical progress (Atletico de Madrid,Deportivo, Malaga, Osasuna, Racing de Santander, Sevilla and Valencia);five more teams had a Malmquist Index superior to the unit, for some thiswas solely due to improvements in efficiency (Barcelona and Villarreal), for


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Table 2. Malmquist Index value and its components for Spanish First Division soccer teams

Teams Changes in the 99/00

season compared to

the 98/99 season

Changes in the 00/01

season compared to

the 99/00 season


season compared to

the 00/01 season


season compared to

the 01/02 season


season compared to

the 02/03 season

Efficiency

change

Tech-

nical

change

Malm-

quist

Index

Efficiency

change

Tech-

nical

change

Malm-

quist

Index

Efficiency

change

Tech-

nical

change

Malm-

quist

Index

Efficiency

change

Tech-

nical

change

Malm-

quist

Index

Efficiency

change

Tech-

nical

change

Malm-

quist

Index

At. Bilbao 0.8105 0.9216 0.7470 0.8967 1.0439 0.9361 1.2373 0.9662 1.1954 0.9128 1.1426 1.0431 0.9562 1.0522 1.0062

Alaves 1.5583 0.8061 1.2561 0.7473 1.0534 0.7872 1.1823 0.9616 1.1369 0.5717 1.2044 0.6886

At. Madrid 0.8806 0.9127 0.8038 1.2126 1.0662 1.2930

Barcelona 0.9903 0.8250 0.8170 0.8347 1.2157 1.0148 1.0743 0.9378 1.0076 0.8809 1.0903 0.9605 1.2456 0.9965 1.2413

Betis 0.9494 0.8227 0.7812 0.8599 1.0433 0.8972 0.9611 1.0338 0.9936

Celta 0.8585 0.9066 0.7784 1.0108 1.1133 1.1254 1.0444 0.9445 0.9866 1.0168 1.1186 1.1375 0.6282 0.9834 0.6178

Deportivo 1.0993 0.9399 1.0333 1.0000 1.0471 1.0471 0.9792 0.9427 0.9231 0.9511 1.1275 1.0725 1.0736 1.0342 1.1103

Espanol 0.7894 0.9517 0.7514 0.9540 1.0977 1.0472 1.0952 0.9837 1.0774 0.8111 1.0717 0.8693 0.9710 1.0835 1.0522

Las Palmas 0.9216 0.9662 0.8904

Real Madrid 1.0816 0.8557 0.9256 1.0960 1.1658 1.2777 0.9549 0.8853 0.8454 1.0472 1.1877 1.2438 0.9208 0.9967 0.9177

Malaga 1.1590 1.0684 1.2383 0.9533 0.9662 0.9211 0.8029 1.1032 0.8857 1.1253 1.0500 1.1816

Mallorca 0.8417 0.8008 0.6740 1.1880 1.0881 1.2927 0.7707 0.9662 0.7446 0.9566 1.1968 1.1449 0.9883 1.0177 1.0058

Numancia 0.7561 1.0506 0.7944

Osasuna 0.9671 0.9662 0.9344 0.8663 1.1751 1.0181 1.0348 1.0197 1.0552

Oviedo 1.0375 0.7780 0.8072 0.7956 1.0677 0.8495

Racing S. 1.1036 0.8888 0.9809 0.7819 1.0982 0.8587 1.0197 1.0470 1.0677

Rayo V. 0.8426 1.0475 0.8826 1.0533 0.9662 1.0177 0.6256 1.1337 0.7093

Real Soc. 0.9620 0.8548 0.8224 0.8345 1.0777 0.8994 1.0917 0.9699 1.0589 1.4289 1.1512 1.6450 0.6323 1.0062 0.6362

Sevilla 0.8679 1.0423 0.9047 1.1047 1.0550 1.1655

Valencia 0.9793 0.9473 0.9278 0.9049 1.0741 0.9720 1.1477 0.9628 1.1050 0.8063 1.0234 0.8252 1.2402 1.0879 1.3492

Valladolid 1.1733 0.8441 0.9904 0.7555 1.0604 0.8012 1.2929 0.9675 1.2509 0.8813 1.1968 1.0548 0.7927 1.0824 0.8580

Villarreal 0.8750 0.9217 0.8065 0.8357 1.1583 0.9680 1.2722 0.9932 1.2636

Zaragoza 1.1184 0.9439 1.0557 0.5929 1.0949 0.6492 0.9878 0.9608 0.9492

Average 1.0147 0.8750 0.8845 0.8912 1.0861 0.9690 1.0370 0.9550 0.9912 0.8896 1.1275 1.0040 1.0106 1.0356 1.0479

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others the result was exclusively due to technical progress (Atletic de Bilbao,Espanol and Mallorca).

If the results obtained individually team by team are examined, no teamshowed a Total Factor Productivity increase in all the seasons analysed bythis study; the team that had a Malmquist Index value superior to the unitmost often in the time horizon was Deportivo: the increase in Total FactorProductivity for this team in the 1999/2000 season was due to improvementin efficiency, in the 2002/2003 season it was due to technical progress, in the2000/2001 season, there was no change in efficiency with respect to theprevious season and there was technical progress that generated an increasein Total Factor Productivity, while in the 2003/2004 season it was due to acombination of the two factors.

During the period studied, nine teams were relegated to the SecondDivision (Atletico de Madrid and Betis in 1999/2000, Numancia, Oviedoand Racing in 2000/2001, Las Palmas and Zaragoza in 2001/2002 andAlaves and Rayo Vallecano in 2002/2003), so it is possible to analyse themin terms of Total Factor Productivity, technical change and efficiency changein the season that they were relegated. In every case, in the season ofrelegation, the Malmquist Index value was inferior to the average of the FirstDivision teams as a whole and the value of the ratio that represents thechange in efficiency was also less than the average; only in three cases (Betis,Numancia and Oviedo) were these circumstances accompanied by a smallerthan average technical change.

Another interesting result was the fact that, with the exception of the2003/2004 season, the type of technical change was the same for each of theteams that played in the First Division. In the 1999/2000 and 2001/2002seasons, when there was technical decline in all teams, the isoquantrepresenting the production technology utilized either went up in compar-ison to the previous year without being cut or, if it was cut, the part in whichthe isoquant from the previous period was above is predominant. Technicalprogress in the 2000/2001 and 2003 seasons showed the opposite behaviour.

It is therefore worth considering if technical behaviour during the periodstudied corresponds to any factor involved in the on-field play of the teams.With this in mind, it was decided that the maximum number of goals scoredby the teams playing in the league could be taken as a proxy of on-fieldstrategy: in those seasons where there is a high number of goals scored it canbe considered that there was a predominance of attacking play; a lownumber of goals scored being an indicator of predominantly defensive play.The logic for taking this variable as a proxy of the playing strategy is asfollows: in the extreme case that all the teams in a competition adopteddefensive tactics, no team would score any goals and at the end of the seasonthe number of goals scored would be nil; the contrary case would be if allteams adopted attacking play, then the number of goals scored in a seasonwould be very high. It can therefore be argued that the greater the number ofgoals scored in a season, the greater would be the number of teams that havefollowed an offensive strategy. At the same time, we decided against usingany of the variables taken as inputs in the calculation of efficiency as proxy


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variables of the type of strategy followed by the teams because they arevariables that measure the offensive plays of the teams. From a methodo-logical point of view, this would lead to problems due to using the samevariables to both calculate efficiency (and therefore, productivity) andexplain the results obtained. Table 3 illustrates the value of the proxyvariable. As can be observed, if the maximum number of goals that a teamscores in a season is over 80, the strategy can be considered as offensive,while 70 or less goals indicates defensive play. The highest number of goalsscored varies from season to season and a curious alternate pattern can beobserved. We can see that the seasons in which technical progress wasobserved are those in which attacking play predominated and vice versa. Theresults and data that refer to the 2003/2004 season are worthy of additionalcomment: the number of goals scored by one team was 72, a number that,according to previously established criteria, indicates neither defensive norattacking play. In addition, the value of average technical change for theteams in this season indicates that there was progress, but if the values areconsidered individually, by team, there are some teams that demonstratetechnical progress and there are others that show a technical regression. As aconsequence, it can be concluded that when there is evidence that there is noclear style of play there is also a lack of unanimity in the technical changesexperienced by the teams.

Given that during the time period studied, Total Factor Productivitymeasured with the Malmquist Index showed no clear evolution, on averageor by individual team, it was worth considering the total variation during allseasons, taken as a whole. This was done using the data from 1998/1999 and2003/2004 as periods to be compared and the Malmquist Index wascalculated according to expression (3) with the two seasons being consideredas if they were concurrent. The values are shown in Table 4.

The average Total Factor Productivity fell between 1998 and 2004,despite the technical progress that was observed. The results by each teamwere as follows: Atletico de Madrid, Deportivo, Real Madrid, Racing deSantander, Valencia and Villarreal increased Total Factor Productivity withboth an increase in efficiency and technical progress; these were also the onlyteams that increased efficiency between 1998 and 2004. For the other teams,the fall in Total Factor Productivity can be attributed to the fall inefficiency*only three teams (Betis, Mallorca and Real Sociedad) experi-enced a technical decline. For the Malmquist Index calculations for the 1998and 2004 seasons, only the teams that played in the First Division in bothwere used*in the sample there are as many teams that played in the Second

Table 3. Maximum number of goals scored by an individual team

Season1998/1999 1999/2000 2000/2001 2001/2002 2002/2003 2003/2004

87 70 80 69 86 72

Source: GecaSport.


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Division at some point (Atletico de Madrid, Betis, Racing de Santander,Villarreal and Zaragoza) as teams that played only in the First Division inthe six seasons studied. The results show that being in the First Division orSecond Division is not enough to explain the differences observed in TotalFactor Productivity*there was no relationship between an increase ordecrease and the division in which the teams played during the periodstudied.

Also, the fact that the highest number of goals scored varies from seasonto season could explain that in the Malmquist Index calculations for the firstand last seasons studied there are also teams that showed a technical decline,in spite of the fact that there was an average technical improvement overall.

Conclusions

This study has analysed the evolution of Total Factor Productivity forSpanish First Division soccer teams between the years 1998 and 2004. Theanalysis has been based on the calculation of the Malmquist Index, usingefficiency values calculated through Data Envelopment Analysis (DEA). Inaddition to the Malmquist Index itself, the values of its two components,technical change and efficiency change have also been determined.

First, without giving details for individual teams, we can say that theaverage Malmquist Index and average technical and efficiency change valueshave allowed us to make a series of observations, comments and conclu-sions. Between the 1998/1999 and 2001/2002 seasons, there was a fall inTotal Factor Productivity; in the 1999/2000 and 2001/2002 seasons the fallcan be attributed to technical decline while in the 2000/2001 season it wasdue to a decline in efficiency. Results for the 2002/2003 and 2003/2004

Table 4. Malmquist Index value and its components for Spanish First Division soccer teams(seasons 1998/1999 and 2003/2004)

Teams Efficiency change Technical change Malmquist Index

At. Bilbao 0.7851 1.0768 0.8454At. Madrid 1.1889 1.0828 1.2873Barcelona 0.9747 1.0252 0.9993Betis 0.9935 0.9982 0.9917Celta 0.5792 1.0202 0.5909Deportivo 1.0994 1.0536 1.1583Espanol 0.6498 1.1074 0.7195Real Madrid 1.0916 1.0295 1.1238Mallorca 0.7287 0.9480 0.6908Racing S. 1.0170 1.0542 1.0721Real Soc. 0.7920 0.9921 0.7857Valencia 1.0172 1.1170 1.1362Valladolid 0.8008 1.0245 0.8204Villarreal 1.3324 1.0193 1.3581Zaragoza 0.7481 1.0819 0.8094Average 0.9199 1.0420 0.9593


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seasons show an increase in Total Factor Productivity, in 2002/2003 this isdue to technical progress, while 2003/2004 produced an increase in bothtechnical progress and efficiency. The fact that there was contrary evolutionin technical change and changes in efficiency (with the exception of the lastseason studied), together with the fact that the Malmquist Index values wereclose to the unit value, led to the conclusion that the evolution of year-by-year Total Factor Productivity for Spanish First Division soccer teams is notdetermined by changes in efficiency nor by technical changes.

Given that in the period studied there were seasons when Total FactorProductivity rose and others when it fell, a Malmquist Index andcomponents calculation was made using the first and last season of thetime horizon, in order to determine the evolution of the Total FactorProductivity between 1998 and 2004 as a whole. From the results, we areable to conclude that on average there was a decline in efficiency andtechnical progress that led to a decline in Total Factor Productivity. Analysisof individual results for each team shows that only six increased Total FactorProductivity; the same six teams that showed an increase in efficiency in theperiod studied. It can therefore be concluded that a change in efficiency wasa determining factor in the variation of Total Factor Productivity between1998 and 2004; as much with average as individual values, Total FactorProductivity increased only if there was an increase in efficiency.

Given that this work has studied the performance of teams on the field ofplay, the results obtained can be used to improve sporting performance and,as a consequence, the teams’ economy. With reference to the former,conclusions can be established which are relevant for two specific concerns:avoiding relegation to the Second Division and improving the sportingresults. It has been shown that (although they were not the only ones) theteams that were relegated presented a Malmquist Index and efficiencychange that were inferior to the average in that season. It can therefore berecommended that the coaching and training staff pay particular attention tothese variables with the aim of taking corrective action as soon as possible.

The improvement in efficiency of each team can contribute to animprovement in their sporting results and this would not only avoidrelegation. Given that the change in efficiency of some teams is below theunit, there are opportunities to increase it: Espitia-Escuer and Garcıa-Cebrian (2006) have established that until it is the case that all soccer teamsefficiently use their inputs, any of them can improve their sporting results bymaximizing the potential of their productive playing resources. Once thishypothetical situation is achieved and all the teams have eliminated waste,Espitia-Escuer and Garcıa-Cebrian (2006) predicate that the sporting resultswould correspond to that permitted by the potential of the productivefactors employed. In this situation, the only way to obtain an improvementin sporting performance would be to increase the quantities of inputs utilizedon the field of play, without reducing their efficiency of use. Therecommendations of Espitia-Escuer and Garcıa-Cebrian (2006) are valid inthe context of their study, which calculated the efficiency of soccer teams ona season-by-season basis only. In this present work, the calculation of the


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Malmquist Index and its two components has revealed that the improvementof sporting results (even when all possible improvements in efficiency havebeen exhausted) can be achieved with technical progress. This means that toimprove their sporting results, football teams must not only be situated onthe efficiency frontier but they should also experience technical progress; inother words, they should be situated on frontiers that are ever closer to theorigin of the coordinates, something that also represents a saving in utilizedresources. Analysis indicates that offensive play could be related to thetechnologies that represent the technical progress recommended.

In conclusion, the results of this study suggest that soccer teams willimprove their sporting results by taking greater advantage of their resourcesand the application of an offensive strategy on the field of play; even if theyare not in a problematic situation, such as being threatened with relegation.Moreover, these recommendations that refer to the strategy employed in thematches would also have a positive influence on the economic resultsbecause (as shown by Espitia-Escuer and Garcıa-Cebrian, 2004) goodsporting results lead to improved income through sales of season-tickets,attendance at matches and advertising. At the same time, the betterutilization of resources, implied by the improvement in efficiency andtechnical progress, generates savings and so both sets of circumstances resultin an increase in profits.

Acknowledgements

This study has been undertaken within the framework of the CREVALOR research group. Ithas been funded by Project SEJ2005-07341, financed by the Spanish Ministry of Educationand Science and FEDER. The authors are grateful to Vıctor Munoz for his helpfulobservations.

References

Anderson, T.R., & Sharp, G.P. (1997). A new measure of baseball batters using DEA. Annals of

Operations Research, 73, 141�151.

Bosca, J.E., Liern, V., Martınez, A., & Sala, R. (2006). Increasing offensive and defensive efficiency? An

analysis of Italian and Spanish football. Omega, doi: 10.1016/j.omega.2006.08.002.

Cairns, J., Jennett, N., & Sloane, P.J. (1986). The economics of professional team sports: a survey of

theory and evidence. Journal of Economic Studies, 13, 3�80.

Carmichael, F., & Thomas, C. (1995). Production and efficiency in team sports: an investigation of rugby

league football. Applied Economics, 27, 859�869.

Carmichael, F., Thomas, D., & Ward, R. (2000). Team performance: the case of English Premiership

football. Managerial and Decision Economics, 21, 31�45.

Coelli, T., Rao, D.S.P., & Battese, G.E. (1998). An introduction to efficiency and productivity analysis.

Norwell, MA: Kluwer Academic Publishers.

Dawson, P., Dobson, S., & Gerrard, B. (2000a). Estimating coaching efficiency in professional team

sports: evidence from English association football. Scottish Journal of Political Economy, 47, 399�421.

Dawson, P., Dobson, S., & Gerrard, B. (2000b). Stochastic frontiers and the temporal structure of

managerial efficiency in English soccer. Journal of Sports Economics, 1, 341�362.


Dow

nloa

ded

by [

The

Uni

vers

ity o

f M

anch

este

r L

ibra

ry]

at 0

2:03

20

Dec

embe

r 20

14

El-Hodiri, M., & Quirk, J. (1971). An economic model of a professional sports league. Journal of

Political Economy, 79 (6), November�December, 1302�1319.

Espitia-Escuer, M., & Garcıa-Cebrian, L.I. (2004). Measuring the efficiency of Spanish First-Division

soccer teams. Journal of Sports Economics, 5, 329�346.

Espitia-Escuer, M., & Garcıa-Cebrian, L.I. (2006). Performance in Sports teams: results and potential in

the professional Soccer league in Spain. Management Decision, 44, 1020�1030.

Fizel, J.L., & D’Itri, M.P. (1997). Managerial efficiency, managerial succession and organizational

performance. Managerial and Decision Economics, 18, 295�308.

Førsund, F.R., Lovell, C.A.K., & Schmidt, P. (1980). A survey of Frontier Production Functions and of

their relationship to Efficiency Measurement. Journal of Econometrics, 13, 5�25.

Fried, H.O., Lambrinos, J., & Tyner, J. (2004). Evaluating the performance of professional golfers on the

PGA, LPGA and SPGA tours. European Journal of Operational Research, 154, 548�561.

Grosskopf, S. (1993). Efficiency and productivity. In H.O. Fried, C.A.K. Lovell, & S.S. Schmidt (Eds.),

The measurement of productive efficiency. Techniques and applications (pp. 160�194). New York:

Oxford University Press.

Guzman, I. (2006). Measuring efficiency and sustainable growth in Spanish football teams. European

Sport Management Quarterly, 6, 267�287.

Haas, D.J. (2003a). Technical efficiency in the Major League soccer. Journal of Sports Economics, 4,

203�215.

Haas, D.J. (2003b). Productive efficiency of English football teams. A Data Envelopment Analysis

approach. Managerial and Decision Economics, 24, 403�410.

Haas, D., Kocher, M.G., & Sutter, M. (2004). Measuring efficiency of German football teams by Data

Envelopment Analysis. Central European Journal of Operations Research, 12, 251�268.

Hadley, L., Poitras, M., Ruggiero, J., & Knowles, S. (2000). Performance evaluation of National Football

League teams. Managerial and Decision Economics, 21, 63�70.

Hofler, R.A., & Payne, J.E. (1997). Measuring efficiency in the National Basketball Association.

Economic Letters, 55, 296�299.

Lewis, H.F., & Sexton, T.R. (2004). Data Envelopment Analysis with reverse inputs and outputs. Journal

of Productivity Analysis, 21, 113�132.

Lewis, H.F., Sexton, T.R., & Lock, K.A. (2007). Player salaries, organizational efficiency and

competitiveness in Major League baseball. Journal of Sports Economics, 8, 266�294.

Mazur, M.J. (1994). Evaluating the relative efficiency of baseball players. In A. Charnes, W.W. Cooper,

A.Y. Lewin, & L.M. Seiford (Eds.), Data envelopment analysis: Theory, methodology and

application (pp. 369�391). Boston: Kluwer Academic Publishers.

Neale, W.C. (1964). The peculiar economics of professional sports. A contribution to the theory of the

firm in sporting competition and in market competition. The Quarterly Journal of Economics,

LXXVIII, 1�14.

Schofield, J.A. (1988). Production functions in the sports industry: an empirical analysis of professional

cricket. Applied Economics, 20, 177�193.

Scully, G.W. (1994). Managerial efficiency and survivability in professional team sports. Managerial and

Decision Economics, 15, 403�411.

Sueyoshi, T., Ohnishi, K., & Kinase, Y. (1999). A benchmark approach for baseball evaluation.

European Journal of Operational Research, 15, 429�448.

Zak, T.A., Huang, C.J., & Siegfried, J.J. (1979). Production efficiency: the case of professional basketball.

Journal of Business, 52, 379�392.


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measuring the productivity of spanish first division soccer teams

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