productive efficiency of english football teams - a data envelopment analysis approach (haas)

7/26/2019 Productive Efficiency of English Football Teams - A Data Envelopment Analysis Approach (Haas)

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MANAGERIAL AND DECISION ECONOMICS

Manage. Decis.

Econ.

24: 40 3^ 10 (2003)

Published online 15 May 2003 in Wiley InterScience (wvv-w.interscience.wiley.com). DOI: 10.1002/mde.l 105

Productive Efficiency of English Football

TeamsA Data Envelopment

Analysis Approach

Dieter J. Haas*

Institute of Public Finance University of Innsbruck. A ustria

This paper investigates how close to their potential English Premier League Clubs play. Using

a deterministie Data Envelopment A nalysis Approach, the productive efficiency of 20 teams in

the 2000/2001 season is measured and weaknesses of individual teams are disclosed. The

sensitivity of results is analyzed with regard to different model specifications and variable

combinations. Copyright 20 03 John Wiley Sons, Ltd.

INTRODUCTION

Du ring the last decade professional football

entertainment has become a major business in

Europe andalthough to a lesser extent

throughout the world. The financially strongest

football clubs can be found in the European top

leagues in Spain, Italy, Germany and especially in

the English Premier League. Manchester United

e.g., the most valuable team in Europe, showed

revenue figures of almost 200 million in the year

2000 (Deloitte and Touche, 2001).

Year after year clubs invest in their squads in

order to improve the performance of the team in

the field, which in turn stimulates the interest of

supporters and sponsors in the respective club.

Nevertheless, some of the attempts aiming at

increasing a team's success fail and the heavy

investments do not pay off. In such a case the

supporters will be highly unsatisfied and compar-

isons between a (theoretical) potential of a team

and its actual achievements will be the conse-

quence.

'Correspondence to: Institute of Public Finance (Finanzwis-

senschaft), University of Innsbruck, Universitaetsstrasse 15/4,

A 6020 Innsbruck, Austria/Europe. E-mail: Dieter.Haas@

uibk.ac.at

From an economic perspective the transforma-

tion of inputs into outputs is a production process

described by either a production function or a

production frontier. When making use of the latter

deviations of a constructed frontier can be

regarded as inefficiencies in production. In the

case of football, discussions about the possible

performance of a team with a given playing and

management talent, as well as comparisons be-

tween the actual performance and the possible one

are common. These discussions ultimately run

along one of the most fundamental economic

concepts, namely productive efficiency. Further-

more, if teams do not meet the expectations of

supporters and sponsors the question is, who

can be blamed for that. Is it the players in the

field who do not perform up to their potential? Is it

the manager who did not combine the factors of

production in an optimal way? Or is it a

combination of both?

In this paper the productive efficiency of teams

in the English Premier Leagueone of the most

important professional football leagues in the

worldis investigated. In the literature, at least

three different approaches to efficiency measure-

ment in sports can be found. These approaches

include efficiency measurement on the level of

single games (e.g., Carmichael

et al

2000),

Cop yright 2003 John W iley & Sons, Ltd.


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D.J. HAAS

measurement of managerial or coaching efficiency

(Dawson et al 2000; Fizel and D'itri, 1996;

Hadley et al 2000; Koning, 2000) and the analysis

of a team's efficiency over an entire season

(Carmichael and T hom as, 1995; Hofler and Payne,

1997).

The approach chosen in this paper corre-

sponds to the latter as it appears to be the most

interesting from an economic point of view

and allows to analyze the squads as well as the

coaches.

Most of the above-mentioned studies analyze

efficiency on the basis of pro duc tion functions

which need to be specified in advance and

problems of misspecification may occur (e.g.,

Carmichael and Thomas, 1995). In order to avoid

the problem of misspecification, incorrect assump-

tions on distribution and wrong w eighting schemes

of inputs and outputs, this study uses data

envelopment analysis (DEA) to measure the

productive efficiency of football teams. The use

of DEA has proved especially valuable when

production involves multiple inputs and/or multi-

ple outp uts, in cases where non-mark eted inputs or

outputs are being considered and, therefore, the

correct weighting of inputs and output cannot be

defined. DEA, originally developed by Charnes

et al (1978), estimates a production efficiency

frontier for teams and calculates the deviations

from that frontier for inefficient teams. The above

mentioned appealing properties of DEA have

made it a widely used efficiency measurement tool

in a variety of different fields, like, e.g., public

education, health care institutions (e.g. Hollings-

worth

et al

1999) or in the private transportation

sector (e.g. Fethi, 2000). The applications of DEA

in the field of sports economics have been rare up

to now (e.g. Haas et al 2001) and most of them

concentrate on efficiency measurement on the level

of individuals (Anderson and Sharp, 1997;

Sueyoshi

et al

1999).

It appears to be straightforward to employ DEA

for revealing weaknesses and indicating areas for

potential improvement within football clubs. DEA

therefore is used in this paper to answer the

following important questions: Which Premier

League teams are on the efficiency frontier and

which teams could have performed better in the

period of observation? What are the particular

weaknesses of the inefficient teams and to which

extent should improvements be made? How robust

are the results with regard to different inpu t/

The remainder of the paper is organized

follows. Section 2 briefiy introduces the method

DEA. In Section 3 the data base is describ

Section 4 presents efficiency results along w

optimization proposals using DEA and fina

Section 5 concludes.

D T ENVELOPMENT N LYSIS

The application of a specific DEA-model provi

a single measure of technical efficiency wh

dealing with multiple inputs and multiple o

puts,

and obviates the need to assign pre-specif

weights to either. The efficiency of a decis

making unit (DMU; in this paper a footb

team) is measured relative to all othe r D M

under the restriction that all DMUs lie on

below the efficient frontier, hence measures

relative efficiency are obtained.' The indica

optimization, then, accords the evaluated DM

the most favorable weighting that the constrai

al low. Note that the DEA-approach has prov

especially valuable in cases where non-marke

inputs or outputs are taken into account and

where correct weighting of inputs and outputs

unknown or cannot be derived as is supposed

some of the variables used here.

Basically, an input-oriented DEA modeP wh

can process non-discretionary variables is employ

in order to get the efficiency score assum

constant returns to scale which represents the glo

technical efficiency

(TE) of a DMU. Additiona

an input-oriented variable returns to scale mo

is used to get the corresponding efficiency sco

representing

loc al pure technical efficie

(PTE).

Decomposing

global technical efficie

into loca l pure technical efficiency and sc

efficiency

provides valuable information on

sources of inefficiencyeither an inefficient tra

formation process of inputs into outputs or

inefficiently small scale of operation, or both

those teams being inefficient.

DATA

The data^ have been provided by the 'Deloitte

Touche Football team', which publishes revie

on the financial situation of English footb

teams twice a year and the population data wh


3/9

PRODUCTIVE EFFICIENCY OF ENGLISH FOOTBALL TEAMS 405

correspond to the year 1998 are taken from

www.statistics.gov.uk. As team inputs the clubs

total wages and salaries reduced by the amount

paid to the head coach and the salary of the head

coach are considered. In doing so, the approach

pioneered by Szymanski and Smith (1997) and

Szymanski and Kuypers (1999) to proxy the talent

available to a team by data on financial expendi-

tures is taken. The salary of the head-coach is a

separate input variable * as evidence indicates that

coaches significantly influence the performance of

teams in the field (e.g. Clement and McCormick,

1989 and Ruggiero et al. 1996). Although, the

proxy for the playing talent available to a team is

not perfect in the sense that also non-playing

employees are included in the total wages and

salaries, it appears to be the best proxy available

as alternative proxies are highly subjective, like

pre-season estimates of playing success as fre-

quently published in newspapers, do not include

all players in the squad and/or depend heavily on

the average length of the contract, as e.g.

'amortisation of players registrations' where

young home-grown players are not accounted

for. Furthermore, the data on wages appear to

be the most realistic as club managers have pre-

season estimates of success in mind and will

accordingly plan the team roster.^

Some additional input variables may be applic-

able,

e.g. ex ante players' ability or the manage-

ment capabilities. These possible inputs were

rejected partly because of their short-term nature,

their subjectivity or their uneven distribution

among the teams investigated. Note that not only

the value, but also the size of the player squad,

which is an important factor in determining the

performance in sport leagues, is implicitly reflected

in the variable ' total wages and salaries' . Finally,

when measuring technical efficiency of football

teams it has to be accounted for the fact that those

teams come from different parts of the country

with accordingly varying population densities and

ultimately differing demand for football entertain-

ment, which in turn influences the revenue

potential of the teams. Therefore, the population

of the clubs' home town is introduced as a non-

discretionary input variablea variable represent-

ing an input which is beyond the control of the

club management, but still has some influence on

the production process.

The outputs include points awarded during the

2000/2001 Premier League season and the season

total revenues. The first output variable aims at

capturing a team's

athletic output

in the national

league over the entire season. The number of

points lead to a ranking which determines the

national champion, those teams which qualify for

an international tournament in the following

season (usually teams ranked first to fifth), and

those two or three teams which are relegated to

Division One, the second highest league in

England, in the next year.^ From the importance

of points in the national league it is evident that

this is the core output of any (European) football

team and that this output variable is positively

correlated to fan interest and a clubs revenue

potential. Nevertheless, taking points awarded in

the national Premier League as the only output

variable would be misleading, because European

football competitions on team level are organized

hierarchically with national and international

matches played simultaneously.

Some teams, especially the big ones, not only

aim at success on the national level but also in

international competitions and are therefore will-

ing to employ more and better players. These

teams would come out very inefficient when only

variables representing national outputs are taken

into account.^ Therefore a variable capturing a

team's output, irrespective of whether the team is

engaged nationally or additionally plays on the

international level had to be found and total

revenues appear to suit best.^

Total revenue figures serve as an indicator

for a team's

commercial output

and include

revenues from ticket sales, merchandising, TV

rights sales, advertising and sponsoring. ' Further-

more, total revenues include also revenues from

national cup tournaments and so a team which

plays only in the national league, but is rather

successful in one ofthe national cups can also raise

its total revenues significantly. Therefore, total

revenue figures promise to be a very encompassing

variable in order to measure outputs of football

t eams. '

Table

1

reports the input and ou tput da ta taken

from the 2000/2001 season and ranks the teams

according to their final rank at the end of that

season. As the drawing potential of the Premier

League teams varies considerably, the absolute

number of spectators during the entire season is

indicated as an additional information. The

column ' International ' in Table

1

states whether

a team had participated in an international


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406

D.J. HAAS

Table

Final

rank

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1. Raw Data for

Club

Manchester United

FC Arsenal

FC Liverpool

Leeds United

Ipswich Town

FC Chelsea

Sunderland

Aston Villa

Charlton Athletic

FC Southampton

Newcastle United

Tottenham Hotspur

Leicester City

FC Middlesbrough

West Ham United

FC Everton

Derby County

Manchester City

Coventry City

Bradford City

the Premier

Total wages

and salaries

(excl. coach)

in Mio.

44.6

33.7

39.9

27.5

9.9

46.6

22.1

21.4

10.9

13.7

28.6

25.9

20.3

24.7

25.0

22.2

17.3

14.7

15.7

21.9

League Season 2000/2001

Coach

salary

in 1000 e

232

266

140

276

69

346

70

138

104

140

266

208

150

138

125

91

191

166

111

96

Home town

Population' '

in 1000 e

427

7122

46 3

727

117

7122

293

1014

7122

215

279

7122

294

144

7122

464

236

428

304

48 3

Points

80

70

69

68

66

61

57

54

52

52

51

49

48

42

42

42

42

34

34

26

Spectators

in 1000

1282

721

830

740

428

659

889

600

380

287

975

669

389

584

669

649

542

647

391

352

Revenue in

Mio. e

194.6

101.8

77.5

94.9

45.4

127.5

62.0

59.6

19.5

28.7

74.9

19.1

43.3

46.0

59.3

46.7

36.1

52.9

33.5

12.7

Inter-

national

CL

CL

U C

CL

UC

U C

CL (Champions-League) , UC (UEFA-Cup) .

' 'Refers to the year 1998.

Source: Annu al Review of Footb all Financ e 2001, www .footballtransfers.net and w ww.statistics.gov.uk.

competition in 2000/2001, for which the teams

have qualified in the previous season.

RESULTS

For calculating efficiency scores the software

DEA-solver, professional version 1.0 is used.

Table 2 reports the results for both variable

returns to scale (VRS) and constant returns to

scale (CRS). The efficiency scores between teams

engaged additionally in international competition

and those which compete only on the national

level are not significantly diffe ren t and so

considering total revenueswhich includes also

revenues from international competitionas

output variable does not systematically bias

efficiency results in favor of teams competing

internationally.

Global technical efficiency (CRS) is achieved by

four teams: Charlton Athletic, Ipswich Town,

Manchester United and Sunderland. The variable

driving the efficiency of the 2000/01 champion

Manchester United is the highest total revenues of

all teams which can partly be attributed to the

performance in international competitions and th

worldwide reputation of the club. Teams lik

Arsenal, Liverpool or Leeds Unitedwhich ended

up between second and fourth, thus qualifying fo

international competition in 2001/2002are quit

far away from the efficiency frontier, indicatin

that they had invested too much resources (inputs

compared to the output finally achieved in th

particular year under investigation.

Teams' efficiency scores rise slightly whe

allowing for variable returns to scale (VRS)'^ bu

only the same four teams lie on the VRS frontier

As already explained in Section 2, inefficiency ca

be decomposed into technical inefficiency an

scale inefficiency by relating CRS-efficiency score

to VRS-efficiency scores (see column 'scale efficiency

in Table 2). Tho se team s being globally technica

efficient (CR S) are , of course, also locally technica

efficient and consequently scale efficient. On

teamAston Villais perfectly scale efficien

although the production process as such show

quite clear inefficiencies and some more team

se.g. Manchester City or Tottenham Hot

spurare inefficient under both CRS and VRS

bu t are very close to the scale efficiency frontie

with efficiency scores ranging from 0.96 to 0.99


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P R O D U C T I V E E F F I C I E N C Y O F E N G L I S H F O O T B A L L T E A M S

7

Table

Final

rank

1

2

3

4

5

6

7

8

9

10

II

12

13

14

15

16

17

18

19

20

2.

DEA Results for

Club

Manchester United

FC Arsenal

FC Liverpool

Leeds United

Ipswich Town

FC Chelsea

Sunderland

Aston Villa

Charlton Athletic

FC Southampton

Newcastle United

Tottenham Hotspur

Leicester City

FC Middlesbrough

West Ham United

FC Everton

Derby County

Manchester City

Coventry City

Bradford City

Three Inputs

CRS-efficiency

1

0.68

0.64

0.75

1

0.61

1

0.62

1

0.57

0.57

0.70

0.47

0.44

0.59

0.68

0.45

0.78

0.47

0.29

and Two Outputs

VRS-efficiency Scale-efficiency

1

0.70

0.75

0.78

1

0.64

1

0.62

1

0.72

0.59

0.71

0.49

0.5

0.63

0.79

0.57

0.79

0.63

0.72

1

0.97

0.85

0.96

1

0.95

1

1

1

0.79

0.97

0.98

0.96

0.88

0.94

0.86

0.79

0.99

0.75

0.40

r e f e r e n c e - s e t V R S

A, = 1.00

A, = 0 . 3 9 , As= 0 . 5 1 ,

A i = 0 . 2 1 , As = 0.7 8,

A,

= 0 . 3 3 ,

As = 0.6 6,

As = 1 . 0 0

A, = 0.5 7, As = 0.3 4,

AT= 1 . 0 0

A,

= 0.09, As = 0.8 9,

A9 = 1.00

As = 0.99, A9 = 0.01

A, = 0.20, As = 0.80,

A, =0 .2 5 , As = 0 .65 ,

As = 0.9 9, A9 = 0.0 2

As =

0 . 9 5 ,

A7 =

0 . 0 5 ,

A, = 0 . 0 5 ,

As

= 0 .62 ,

As = 0. 67 , A7 =

0 . 2 3 ,

As = 0.9 9, A9 = 0.01

A, = 0 . 0 5 , As = 0 .95 ,

As = 0.9 9, A9 = 0.0 2

As = 0.9 9, A9 = 0.01

A9 = 0.10

A9 = 0.01

A9 = 0.01

A9 = 0.0 9

A9 = 0.01

A9 = 0.01

A9 = 0.10

A9 = 0.01

A7 = 0.3 2, A9 = 0.01

A9 = 0.10

A9 = 0.01

Figures may not add up to 1.00 due to rounding. CRS; constant returns to scale; VRS: variable returns to scale.

Source: Own calculation.

Thus , the scale of their production is (almost)

optim al and their relatively high global inefficiency

is purely caused by inefficient operation. For all

other teams inefficiency is caused both by ineffi-

cient operation and by operating on a sub-optimal

scale. However, scale efficiencies are, on average,

very close to one, indicating that m ost ofth e teams

operate on, or close to, the optimal scale.

The optimal values of Xj in the outer right

column of Table 2 provide the linear combination

of teams on the efficiency frontier (assuming VRS)

closest to a particular team. The linear combina-

tion is also referred to as the 'peer group' or

'reference set' for this team. The A-subscript

j

denotes the final Premier League rank of team /

The highest of the /i-values indicates to which of

the efficient teams an inefficient team is closest in

its combination of inputs and outputs.

In order to provide the inefficient clubs with

information about how to improve their perfor-

mance and how to reach the efficiency frontier, the

optimization results of the input-oriented DEA

model assuming constant returns to scale are

indicated in Table 3. The figures repre sent the

percentage of input-reduction (-) or percentage of

output-increase +) necessary for the inefficient

tea m s to reach the efficiency fron tier.

The fact that observed inefficiencies are sug-

gested to be removed mainly by input reductions

comes from employing an input-oriented DEA

model and in case the input reductions do not lead

the inefficient teams completely to the frontier,

output increases are proposed. The optimization

results suggest that none of the teams will reach

the efficient frontier by input reduction only. For

most inefficient teams, in addition to input

reductions, improvements in the points awarded

are suggested and some even should have higher

revenue figures in order to become efficient. An

extreme case is the team of Bradford City, which

shows the lowest revenue of all teams. There, only

a substantial increase in revenues and points,

together with sharp salary cuts would lead the

team to the efficient frontier. The optimization

results for that team also make clear that higher

revenues should be possible given the relatively

large home town population. Generally, no clear

optimization pattern can be detected on the input

side,

where particular weaknesses of the teams

either of the players or the coach are revealed

and improvements are suggested accordingly. On

the output side, a clear tendency towards higher

proposed increases concerning the points awarded

can be seen at the lower end of the league table.

Finally, the issue of sensitivity of efficiency

scores with respect to the chosen output variables

should be addressed. As argued in Section 3, the

choice of three inputs and two outputs aimed at


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408

D.J. HAAS

Table 3.

Final rank

2

3

4

6

8

10

11

12

13

14

15

16

17

18

19

20

DEA Optimization Results

Club

FC Arsenal

FC Liverpool

Leeds United

FC Chelsea

Aston Villa

FC Southampton

Newcastle United

Tottenham Hotspur

Leicester City

FC Middlesbrough

West Ham United

FC Everton

Derby County

Manchester City

Coventry City

Bradford City

Total wages

and salaries

- 2 9 . 6 0

-5 6 .2 0

- 2 1 . 9 4

- 3 6 . 3 9

- 3 7 . 8 4

- 2 7 . 5 3

- 4 1 . 2 3

- 2 8 . 3 9

-5 1 .0 1

- 5 7 . 6 8

- 3 6 . 7 4

- 4 2 . 1 2

- 4 2 . 7 8

- 2 0 . 9 3

- 3 6 . 7 5

-5 4 .6 4

Coach salary

-4 8 .4 4

-2 4 .8 2

- 5 5 . 1 3

-5 2 .2 2

-3 8 .2 9

-5 0 .4 4

-6 1 .79

-4 5 .6 4

-5 3 .72

-4 9 .74

-3 6 .74

-2 0 .4 7

-6 3 .8 2

-5 3 .4 1

-3 7 .4 0

-2 8 .0 9

Points

+ 0.25

+ 3.76

+ 19.00

+ 24.42

+ 26.89

+ 34.81

+ 38.97

+ 37.43

+ 56.06

+ 52.22

+ 48.86

+ 57.13

+ 96.09

+ 93.94

+ 153.57

Revenu

+ 0.5

+ 58.1

+ 4.8

+ 25.7

+ 35.3

+ 257.3


Table 4.

Final

rank

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Comparison of DEA Results

Club

Manchester United

FC Arsenal

FC Liverpool

Leeds United

Ipswich Town

FC Chelsea

Sunderland

Aston Villa

Charlton Athletic

FC Southampton

Newcastle United

Tottenham Hotspur

Leicester City

FC Middlesbrough

West Ham United

FC Everton

Derby County

Manchester City

Coventry City

Bradford City

When Using Different

Outputs

Points and revenue

CRS(2)

1

0.68

0.64

0.75

1

0.61

1

0.62

1

0.57

0.57

0.70

0.47

0.44

0.59

0.68

0.45

0.78

0.47

0.29

Outputs

VRS(2)

1

0.70

0,75

0.78

1

0.64

1

0.62

1

0.72

0.59

0.71

0.49

0.5

0.63

0.79

0.57

0.79

0.63

0.72

Points

C R S( I )

0.36

0.32

0.52

0.37

1

0.20

0.86

0.41

1

0.57

0.27

0.29

0.36

0.32

0.35

0.53

0.36

0.35

0.33

0.28

VR S(

1

0.69

0.75

0.55

1

0.21

0.99

0.50

1

0.72

0.34

0.39

0.49

0.5

0.55

0.79

0.57

0.67

0.63

0.72

CRS: constant returns to scale; VRS: variable returns to scale.


capturing team efficiency in a broader way.

Therefore,

athletic

and

commercial

output vari-

ables have been included in the calculation;

furthermore, the commercial output variable has

the appealing property that it includes success in

international competitions which would otherwise,

by focusing on points awarded in the national

league, be neglected. This in turn, as can be seen in

Tab le 4, would systematically bias the efficienc

scores in favor of those teams which pla

exclusively on the national level.

The data in Table 4 indicates rath er stabl

efficiency measurement results in the top Englis

football league which depend only to a mino

degree on the assumed type of technology (CRS o

VRS) . Concerning the efficiency scores when th


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PRODUCTIVE EFFtCIENCY OF ENGLISH FOOTBALL TEAMS

40 9

output variable revenue is dropped in the calcula-

tion two remarks have to be made: first, efficiency

scores tend to decrease as the space for possible

optimization is narrowed; second, the efficiency

scores of prominent and internationally reputed

teams like Manchester United, FC Arsenal, FC

Chelsea or Leeds United drop dramatically,

especially with CRS. Therefore, when technical

efficiency is measured in the field of sports the used

variables have to be selected carefully and as long

as this is done, DEA appears to be a suitable tool

for measuring efficiency and detecting weaknesses

in the context of football teams.

DISCUSSION AND CONCLUSION

From the football supporter 's point of view it can

be said, that at the end of a season 'The champion

was the best '. When trying to measure productive

efficiency of professional football teams in a

broader context by using DEA this simple state-

ment has to be revised as there is enough space for

improvementeven for very successful teams

and the Premier League ranking at the end of the

season is not significantly related to the ranking

based on efficiency scores.

Based on the 2000/2001 season in the English

Premier League the technical and scale efficiency

of football teams has been studied. Using proxies

for the playing talent and the coaching capabi-

lities available to a team as inputs and points won

and total revenues as outputs, while taking

the population size of the home town as a non-

discretionary input, i t can be shown that about a

quarter to one third of the teams are on the

efficiency frontier.

Ipswich Town and Charlton Athletic are the

only teams coming out efficient in all models and

specifications. The results of those teams are

mainly driven by relatively moderate expenditures

on both, players and the coach. In contrast, the

performance of Arsenal as well as Chelsea and

especially Newcastle United is surprisingly bad,

given the success in the field of the 2nd ranked

Arsenal. Their results are mainly driven by squad s,

whichin the sense of the underlying assump-

tionsare of highest quality but do not lead to the

corresponding success.

Shortfalls concerning the

athletic output

have

been detected first of all for Manchester City,

Coventry City and Bradford City; thus, for those

teams being relegated at the end of the season.

Contrary to that, a team like Liverpool would

have to reduce primarily the value of the squad

when trying to get efficient, given the attained

output level of the 2000/2001 season. The

com-

mercial output

levels of most teams are satisfactory

and remarkable adjustments are proposed for a

handful of teams only. Those teams are mainly at

the end of the final league table, with the

exemption of Southampton for which an almost

60 percent increase of revenuesamongst other

adjustmentsis proposed.

Finally, when global technical efficiency scores

are analyzed in more detail and the sources of

inefficiency are revealed the results indicate that

most teams operate at, or close to, the optimal

scale. It follows that inefficient operation is the

m ain so urce of overall inefficiencies. Efficiency

scores and correspondingly the ranks based on

efficiency scores only change significandy when

essential parts of the outputs are dropped and so

the hierarchical structure of European competi-

tions is not accounted for. This leads to the

conclusion that data envelopment analysis appears

to be a suitable tool for measuring efficiency of

football teams although the applicable variables

must be treated with some caution.

ACKNOWLEDGEMENTS

The author would l ike to thank Mart in Kocher

and Matthias Sutterwithout implicating them

for their support and two anonymous referees

for their valuable comments on earlier drafts of

this paper.

N O TES

1. DEA-efficient D M U s are not necessarily efficient in

an absolute sense, but for a DEA-efficient DMU it

is impossible to detect a better performing D M U

within the same sample.

2. While output-oriented models lead to exactly the

same efficiency scores like input-oriented models

when assuming constant returns to scale and slacks

are zero, differences may occur concerning the

optimization and when variable returns to scale

are assumed (see Seiford and Thrall, 1990). In this

paper an input-oriented model is applied as inputs

appear easier to be varied in the context of football

teams.


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410

D.J. HAAS

3. The da ta has been taken from the 2000/01 season

only as DEA requires positive data on each DMU in

any period observed and this would not be the case

for English Premier League teams when looking at

more than one season due to promotion and

relegation.

4. Only the wage of the coach wh o was initially hired

for the season 2000/2001 is considered. In case a

coach was fired during the season, the wage of the

successor is disregarded. Note that Koning (2000),

for instance, does not find any econometric support

for the claim that firing a coach improves team

performance (in the Dutch football league). Hence,

the restriction on the initial coach's wage is seen as

unproblematic.

5. Dawson et al. (2000) criticized the approach to

proxy playing talent by players' wages as this

represents end-of-season data and, therefore, in-

clude bonuses depending on a team's success during

the season. This criticism does not hold for this

study as the financial data is taken from the year

2000 and b onus paym ents at the end of the

2000/01-

season are not included.

6. The reason behind taking only points of national

matches into account is that in the national

competition each team has to play the same rivals

twice. Rivals in international games, on the con-

trary, are drawn and chance plays a major role.

7.

As will be seen below, if DE A is applied to the da ta,

excluding total revenues those teams engaged in

international competition come out very inefficient.

8. The significantly higher financial expenditures of

internationally successful teams (one-sided Mann-

Whitney {/-test, N=2Q\

/>

= 0.05 for players and

p = 0.006 for coache s) is no t su rprising and the

direction of causality promises to be an interesting

field for further research, but appears to be out of

the scope of this paper.

9. The figures of the variables T o ta l wages & salaries

(excl. coach)' and 'Revenue' correspond to the

financial statements of the year 2000.

10. The entertainment 'produced' by a team could be

measured by attendance figures, but as the demand

for a team is implicitly refiected in the revenue

figures, a separate variable aiming at capturing the

social output generated by a team is not employed.

11. A one-sided Mann-Whitney [/-test reveals signifi-

cance levels of

/7

= 0.59) when con stant returns to

scale are assu med and of (p = 0.96) when a va riable

returns to scale model is employed.

12. As noted in Section 2 the VRS is the more general

model. Both models, VRS and CRS, are indicated

because there is no theoretic rationale for one of the

models and it is necessary to have both efficiency

scores to assess scale efficiency.

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productive efficiency of english football teams - a data envelopment analysis approach (haas)

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