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ACC JOURNAL 2021, Volume 27, Issue 2 DOI: 10.15240/ ul/004/2021-2-009
PERFORMANCE OF CZECH FOOTBALL CLUBS: MALMQUIST INDEX APPROACH
Michal Tomíček1; Na alie Pelloneo á2
Technical Uni e si y o Libe ec, Facul y o Economics,
Depa men o Business Adminis a ion and Managemen ,
S uden ská 1402/2, 461 17 Libe ec, Czech Republic
e-mail: 1[email p o ec ed]; 2na alie.pellone[email p o ec ed]z
Abs ac
Spo has become an impo an pa o ou li es in he mode n imes and spo ing si es
con ibu e signi ican ly o he image and ex u e o mode n ci ies. Rega ding he popula i y o
spo , and oo ball in pa icula , i has become an impo an mode n place whe e speci ic
ypes o economic and social in e ac ion ake place. The aim o his a icle is o p opose a
me hod o e alua ing he pe o mance o oo ball clubs based on DEA and Malmquis index.
P o essional Czech oo ball clubs playing in he Czech oo ball compe i ion Fo una:Liga
we e selec ed o empi ical analysis. To analyze he ela i e e iciency o oo ball clubs, BCC
and CCR models we e employed. The s udy was conduc ed on a sample o 20 clubs h ough 2
inpu s and 1 ou pu collec ed du ing he 2015/16 – 2019/20 seasons. Fo some clubs he
alues o he Malmquis index we e calcula ed. Wi h help o MI i was possible o quan i y
he o al p oduc i i y change ac o and o decompose i o echnological change and echnical
e iciency change. The esul s show ha Czech oo ball clubs achie ed a ela i ely high le el
o e iciency in he pe iod moni o ed and ha adi ional clubs achie ed he highes e iciency
sco e. These esul s could help club manage s imp o e he pe o mance o hei eams.
Keywo ds
DEA; Spo s s a is ics; Foo ball; Czech p o essional oo ball clubs; Malmquis index.
In oduc ion
P o essional spo s compe i ions a ac millions o spec a o s wo ldwide. Spo s ac i i ies
hen expand u he and each o he c i ical economic sec o s, such as hospi ali y, he media,
o ou ism. One o he wo ld’s mos impo an spo s compe i ions is mainly oo ball
compe i ions, which a e ex emely impo an o hei economic and social ac i i y. In he
Czech Republic, p o essional oo ball clubs a e ep esen ed by a p o essional oo ball league
called Fo una:Liga.
16 eams pa icipa e in he Czech highes oo ball compe i ion Fo una:Liga. His o ically, he
mos success ul club has been P ague AC Spa a wi h 36 i les, ollowed by SK Sla ia P ague
wi h 20 i les. In he las i e seasons, he Czech leagues ha e been domina ed by he FC
Vik o ia Plzeň and SK Sla ia P aha eams [1]. Only h ee eams ha e pa icipa ed in all 27
yea s o he independen Czech league (since 1993): AC Spa a P aha, SK Sla ia P aha and
FC Slo an Libe ec [1].
Al hough oo ball clubs ope a e wi hin he same legal amewo k as o he companies, hey a e
a pa icula ype o business due o being mainly condi ioned by spo ing ac i i ies. The
ques ion, he e o e, a ises as o how o measu e he pe o mance o oo ball clubs. Some
s udies mainly show a posi i e ela ionship be ween spo s and inancial pe o mance. In his
con ex , he e is a need o ecommend oo ball manage s’ p ac ices ha could help clubs
achie e bo h spo s and business achie emen s. In his a icle, a me hod o e alua ing he
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pe o mance o oo ball clubs based on da a en elopmen analysis and Malmquis index will
be p oposed.
1 Li e a u e Re iew
In he las ew yea s, a conside able numbe o pape s ha e been published ha de e mine he
economic and manage ial e iciency by da a en elopmen analysis in a ious spo s. Bha ,
Sul ana and Da [2] p esen an ex ensi e s udy on he applica ion o a ious models o DEA
in baseball, baske ball, c icke , cycling, oo ball, gol , handball, and ennis. I is ound ha
DEA iden i ied he sou ces o ine iciency and p o ided possible di ec ions o imp o emen .
A summa y o selec ed au ho s who apply he DEA me hod in hei esea ch ollows. Espi ia-
Escue and Ga cia-Ceb ian [3] apply he DEA me hod and Malmquis indices o he
e alua ion o he oo ball eams ha ha e pa icipa ed in he UEFA Champions League.
B osed Láza o, Espi ia-Escue and Ga cia-Ceb ian [4] e alua e he pe o mance o Spanish
i s -di ision baske ball eams, in e ms o e iciency. The second aim is o examine he o al
ac o p oduc i i y e olu ion ha ing in o ma ion om se e al yea s. In hei a icle, Ga cia-
Ceb ian and Espi ia-Escue [5] analyze p oduc i i y le els and i s componen s o eams ha
pa icipa ed in he UEFA Champions League be ween 2003 and 2012. A s udy by Kang [6]
measu ed he ela i e e iciency and p oduc i i y change o Ko ean p o essional spo s eams
using he DEA model and he Malmquis Index o 2006-2009. Ja din [7] e alua e he
e iciency o F ench oo ball clubs om 2004 o 2007 using da a en elopmen analysis. Then,
in his esea ch, s udies he dynamics o clubs’ pe o mance using he Malmquis index. Ba os
and Dou is [8] es ima e changes in p oduc i i y using da a en elopmen analysis applied o a
ep esen a i e sample o oo ball clubs ope a ing in he wo Eu opean coun ies: Po ugal and
G eece. Ba os and Dou is ank he oo ball clubs acco ding o hei change in p oduc i i y
be ween he 1999/2000 and 2002/2003 seasons, concluding ha some clubs expe ienced
p oduc i i y g ow h while o he s expe ienced a dec ease in p oduc i i y. Ba os, Assa and
Sá-Ea p [9] p esen a wo-s age boo s apped DEA model o analyze he echnical e iciency
o B azilian p emie league oo ball clubs o he pe iod 2006–2007.
2 Me hodology
The da a used o he pu poses o he esea ch come om he o icial da abases o he Czech
Fo una:Liga and a e supplemen ed by p i a e da abases o companies om he oo ball
en i onmen . The esea ched pe iod includes he seasons om 2015/16 o 2019/20. The
esea ch is di ided in o he ollowing i e s eps.
S ep 1: De ining he esea ch sample and compiling a lis o oo ball clubs o be
e alua ed.
The esea ch included a g oup o 20 oo ball clubs playing in he highes Czech oo ball
league called Fo una:Liga. In o ma ion abou hese clubs was subsequen ly ob ained o he
en i e selec ed pe iod. The co e is da a om InS a [10], which analyzes he pe o mance o
a hle es and spo s eams. They a e supplemen ed by he da abase o he T ans e ma k .com
se e [11] and he da abases o he Czech Fo una:Liga [1].
S ep 2: De e mina ion o ou pu and inpu a iables.
Due o he numbe o DMUs (16 clubs in one season), wo inpu and one ou pu a iable we e
included in he DEA model. Fo he model wi h 16 oo ball clubs (DMUs) and h ee a iables
included in he e iciency model, he model has su icien disc iminan powe . The i s inpu
a iable is he numbe o playe s (he eina e I1). The second inpu a iable is o al squad
ma ke alue (he eina e I2). The numbe o poin s achie ed in he season was chosen as he
ou pu a iable (he eina e O1).
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S ep 3: Selec ion and cons uc ion o DEA models.
The cen al pa o his is he esea ch o pe o mance o Czech p o essional oo ball clubs
playing he highes compe i ion Fo una:Liga, h ough he me hod o da a en elopmen
analysis and Malmquis index. Da a en elopmen analysis (he eina e DEA) is used as
a specialized modelling ool o e alua ing he e iciency o a g oup o compa able decision-
making uni s (i.e., oo ball clubs).
In gene al, DEA models a e based on he inpu s and ou pu s o he e alua ed uni s. Fu he ,
he e iciency wi h which he oo ball club can ans o m i s inpu s in o ou pu s is compa ed,
i.e. he ex en o he ou pu s he oo ball club can achie e wi h he numbe o a ailable inpu s
[12].
Gene ally, DEA models can be di ided acco ding o he model’s o ien a ion in o inpu -
o ien ed, ou pu -o ien ed, and non-o ien ed models. Fu he so ing o DEA models can be
done based on he na u e o he p oduc ion p ocess. In his case, a dis inc ion can be made
be ween models based on he assump ion o cons an e u ns o scale (CCR model), and
models based on he assump ion o a iable e u ns o scale (BCC model) [13].
In he p esen ed a icle, he CCR-I and BCC-I models wi h inpu o ien a ion we e applied o
he ob ained da a. In he basic inpu -o ien ed CCR-I model wi h he assump ion o cons an
e u ns o scale, he objec i e unc ion is maximized unde es ic i e condi ions (1) [12]. In
he case o conside ing a iable e u ns om scale (BCC-I model), i is su icien o ex end
he p e ious model by he condi ion o con exi y [14]. The CCR-I and BCC-I models di e
only by alid con exi y condi ion (2).
𝐸0=𝑚𝑖𝑛.𝜃−𝜀(∑ 𝑠𝑖−
𝑚
𝑖=1 +∑𝑠𝑟+
𝑠𝑟=1 )
𝑠.𝑡.∑𝜆𝑗𝑋𝑖𝑗+𝑠𝑖−=𝜃𝑋𝑖0,𝑖=1,…,𝑚
𝑛
𝑗=1
∑𝜆𝑗𝑌𝑟𝑗−𝑠𝑖+=𝑌𝑟0,𝑟=1,…,𝑠
𝑛
𝑗=1
𝜆𝑗,𝑠𝑖−,𝑠𝑖+≥0,𝑗=1,…,𝑛,𝑖=1,…,𝑚,𝑟=1,…,𝑠. 𝜃 un es ic ed in sign. (1)
∑𝜆𝑗=1
𝑛
𝑗=1 (2)
In his model, λj a e he weigh s o all DMUs, s-i and s+ a e slack a iables, ε > 0 is an
in ini esimal cons an de ined o be smalle han any posi i e eal numbe and θ is he
e iciency sco e ha exp esses he educ ion a e o inpu s in o de o his uni o each he
e icien on ie .
S ep 4: Technical e iciency sco e calcula ion.
Technical e iciency and scale e iciency sco es we e de e mined o each oo ball club. All
necessa y calcula ions we e pe o med using OSDEA-GUI so wa e. The echnical e iciency
sco e de e mined using he CCR-I model is called he o e all echnical e iciency (he eina e
OTE). In con as , he sco e de e mined using he BCC-I model is called pu e echnical
e iciency (he eina e PTE). The o e all echnical e iciency sco e can, he e o e, be di ided
in o he pu e echnical e iciency sco e and he scale e iciency sco e (he eina e SE), see
ela ion (3). The scale e iciency measu es he deg ee o which a uni can imp o e i s
e iciency by changing i s size [15].
𝑆𝐸=𝑂𝑇𝐸
𝑃𝑇𝐸 (3)
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S ep 5: Calcula ion o he Malmquis Index.
Basic DEA models do no ake in o accoun ends o changes in he e iciency o clubs’
ac i i ies o e ime. This de iciency is elimina ed using he Malmquis Index (he eina e MI),
which e alua es changes in e iciency o e ime. The MI can be di ided in o wo pa s [16].
The i s componen measu es echnical e iciency changes (E) and he second componen
measu es echnological changes (T) be ween pe iods and + 1.
In his a icle, inpu -o ien ed MI was used, which can be exp essed by equa ion (4). Whe e x
a e inpu s in pe iod , y a e ou pu s in pe iod , x +1 a e inpu s in pe iod + 1, y +1 a e ou pu s
in pe iod + 1. Eq is he change in he ela i e e iciency o uni q wi h espec o o he uni s
be ween pe iods and + 1, Tq is he change in p oduc ion possibili y on ie as a esul o
echnology de elopmen be ween pe iods and + 1, o in o he wo ds echnological change.
In his equa ion, he MI is calcula ed as he p oduc o Eq and Tq, and i p o ides se e al
ad an ages o e o he indices [16]. Componen s Eq and Tq a e gi en by equa ions (5) and (6).
𝑀𝐼𝑞(𝑥𝑡+1,𝑦𝑡+1,𝑥𝑡,𝑦𝑡)=𝐸𝑞𝑇𝑞 (4)
𝐸𝑞𝐷𝑞
𝑡+1(𝑥𝑡+1,𝑦𝑡+1)
𝐷𝑞
𝑡(𝑥𝑡,𝑦𝑡) (5)
𝑇𝑞=√ 𝐷𝑞
𝑡(𝑥𝑡+1,𝑦𝑡+1)𝐷𝑞
𝑡(𝑥𝑡,𝑦𝑡)
𝐷𝑞
𝑡+1(𝑥𝑡+1,𝑦𝑡+1)𝐷𝑞
𝑡+1(𝑥𝑡,𝑦𝑡) (6)
Fo selec ed clubs and each pe iod, he alues o he dis ance unc ions and o each
componen o he MI we e de e mined in he MaxDEA 7 Ul a so wa e en i onmen . Finally,
he alue o he Malmquis Index was calcula ed using equa ion (4). A alue o MIq > 1
indica es an inc ease in p oduc i i y; MIq = 1 means he e has been no p oduc i i y change;
and MIq < 1 means a dec ease in p oduc i i y [17].
3 Resul s
This pa o he a icle is de o ed o empi ical esea ch, whe e he nonpa ame ic DEA
me hodology was used. Table 1 shows he esul ing e iciency sco es o CCR-I model o all
clubs examined om all seasons o he Fo una:Liga. The las ow o Table 1 shows he
a e age alues o OTE sco e. The CCR-I model esul ed in he iden i ica ion o up o ou
e icien clubs in a single season. This means ha he size o hese clubs is op imal and a he
same ime, he clubs a e able o ans o m he gi en inpu s in o ou pu s e icien ly.
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Tab. 1: OTE sco e o Czech clubs playing Fo una:Liga
Club
OTE
A e age
2015/16
2016/17
2017/18
2018/19
2019/20
1. FC Slo ácko
0.85
0.89
0.87
0.72
0.85
0.84
1. FK Příb am
0.52
0.71
-
0.74
0.50
-
AC Spa a P aha
0.69
0.63
0.55
0.66
0.62
0.63
Bohemians P aha 1905
0.64
0.76
0.85
0.82
0.76
0.77
FC Baník Os a a
0.23
-
0.71
1.00
1.00
-
FC Fas a Zlín
0.69
0.99
0.58
0.85
0.54
0.73
FC H adec K álo é
-
0.96
-
-
-
-
FC Slo an Libe ec
0.85
0.60
0.63
0.71
0.72
0.70
FC Vik o ia Plzeň
1.00
0.78
1.00
1.00
1.00
0.96
FC Vysočina Jihla a
0.65
0.89
0.70
-
-
-
FC Zb ojo ka B no
1.00
0.87
0.55
-
-
-
FK Dukla P aha
0.66
0.83
0.79
0.48
-
-
FK Jablonec
0.70
0.85
0.81
0.83
0.86
0.81
FK Mladá Bolesla
0.87
0.84
0.46
0.54
0.61
0.66
FK Teplice
0.51
1.00
0.60
0.63
0.67
0.68
MFK Ka iná
-
0.89
0.80
0.56
0.44
-
SFC Opa a
-
-
-
1.00
0.65
-
SK Dynamo Č. Budějo ice
-
-
-
-
1.00
-
SK Sigma Olomouc
0.53
-
1.00
0.68
0.73
SK Sla ia P aha
0.97
1.00
0.70
1.00
0.90
0.91
Mean
0.71
0.84
0.73
0.76
0.74
Sou ce: Own
Table 2 shows he esul ing e iciency sco es o BCC-I model o all clubs examined om all
seasons o he Fo una:Liga. The las ow o Table 2 shows he a e age alues o PTE sco e.
The BCC-I model esul ed in he iden i ica ion o up o six e icien clubs in a single season.
This means ha he clubs a e able o ans o m he gi en inpu s in o ou pu s e icien ly.

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Tab. 2: PTE sco e o Czech clubs playing Fo una:Liga
Club
PTE
A e age
2015/16
2016/17
2017/18
2018/19
2019/20
1. FC Slo ácko
0.99
0.92
1.00
0.80
0.88
0.92
1. FK Příb am
0.85
0.90
-
0.81
0.84
-
AC Spa a P aha
0.74
0.73
0.66
0.67
0.82
0.72
Bohemians P aha 1905
0.80
0.88
1.00
0.84
0.79
0.86
FC Baník Os a a
0.76
-
0.81
1.00
1.00
-
FC Fas a Zlín
1.00
1.00
0.84
0.86
0.84
0.91
FC H adec K álo é
-
1.00
-
-
-
-
FC Slo an Libe ec
0.88
0.70
0.75
0.77
0.76
0.77
FC Vik o ia Plzeň
1.00
0.83
1.00
1.00
1.00
0.97
FC Vysočina Jihla a
0.97
0.93
0.83
-
-
-
FC Zb ojo ka B no
1.00
0.91
0.81
-
-
-
FK Dukla P aha
0.86
0.84
0.91
0.79
-
-
FK Jablonec
0.86
0.97
0.81
0.83
1.00
0.89
FK Mladá Bolesla
0.95
0.87
0.64
0.59
0.74
0.76
FK Teplice
0.75
1.00
0.78
0.76
0.92
0.84
MFK Ka iná
-
0.91
0.95
0.65
0.69
-
SFC Opa a
-
-
-
1.00
1.00
-
SK Dynamo Č. Budějo ice
-
-
-
-
1.00
-
SK Sigma Olomouc
0.87
-
1.00
0.77
0.89
-
SK Sla ia P aha
1.00
1.00
0.76
1.00
1.00
0.95
Mean
0.89
0.90
0.85
0.82
0.89
Sou ce: Own
Table 2 also shows ha all clubs ha we e classi ied as e icien acco ding o he CCR-I
model a e also classi ied as e icien acco ding o he BCC-I model. I is appa en ha he
PTE sco e in he BCC-I model is highe han he OTE sco e in he CCR-I model, as he CCR-
I model conside s he scale e iciency (SE), which educes he OTE alue. Fo clubs ha a e
classi ied as ine icien acco ding o he CCR-I model ye as e icien acco ding o he BCC-I
model, i can be concluded ha hei echnical ine iciency is caused by scale ine iciency.
The e o e, i can be s a ed ha he size o hese clubs is no op imal and an inapp op ia e
spo s ac ic was chosen. Scale e iciency and scale ine iciency is shown in Table 3.
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Tab. 3: Scale e iciency o Czech clubs playing Fo una:Liga
Club
SE
A e age
2015/16
2016/17
2017/18
2018/19
2019/20
1. FC Slo ácko
0.86
0.97
0.87
0.89
0.97
0.91
1. FK Příb am
0.60
0.78
-
0.91
0.59
-
AC Spa a P aha
0.93
0.86
0.84
0.98
0.76
0.87
Bohemians P aha 1905
0.80
0.86
0.85
0.98
0.96
0.89
FC Baník Os a a
0.30
-
0.87
1.00
1.00
-
FC Fas a Zlín
0.69
0.99
0.69
0.99
0.64
0.80
FC H adec K álo é
-
0.96
-
-
-
-
FC Slo an Libe ec
0.96
0.85
0.83
0.92
0.95
0.90
FC Vik o ia Plzeň
1.00
0,94
1.00
1.00
1.00
0.99
FC Vysočina Jihla a
0.67
0.96
0.85
-
-
-
FC Zb ojo ka B no
1.00
0.95
0.68
-
-
-
FK Dukla P aha
0.76
0.99
0.86
0.61
-
-
FK Jablonec
0.81
0.88
1.00
1.00
0.86
0.91
FK Mladá Bolesla
0.91
0,96
0.72
0.91
0.82
0.86
FK Teplice
0.68
1.00
0.76
0.83
0.72
0.80
MFK Ka iná
-
0.98
0.83
0.86
0.65
-
SFC Opa a
-
-
-
1.00
0.65
-
SK Dynamo Č. Budějo ice
-
-
-
-
1.00
-
SK Sigma Olomouc
0.61
-
1.00
0.89
0.82
-
SK Sla ia P aha
0.97
1.00
0.92
1.00
0.90
0.96
Mean
0.78
0.93
0.85
0.92
0.83
Sou ce: Own
To es ablish he p oduc i i y le els a ained by Fo una:Liga clubs, an addi ional s udy using
Malmquis index was ca ied ou o imp o e unde s anding o empi ical implica ions o
p oduc i i y measu es in p o essional oo ball. The sample was educed o he 10 clubs ha
pa icipa ed in he Fo una:Liga in all i e seasons.
The change in p oduc i i y and i s wo componen s we e calcula ed o he clubs ha
pa icipa ed in he Fo una:Liga in he seasons 2015/2016 and 2019/2020, as i hey had been
consecu i e yea s, wi h he objec i e o app oxima ing he e olu ion o hei p oduc i i y o e
he en i e pe iod analyzed in his a icle. The esul s a e shown in Table 4.
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Tab. 4: Malmquis index o he clubs pa icipa ing in he Fo una:Liga in he pe iod
analyzed
2015/2016 – 2019/2020
E iciency change
Technological change
Malmquis index
AC Spa a P aha
1.028
0.941
0.968
Bohemians P aha 1905
1.030
0.991
1.021
FC Fas a Zlin
0.983
0.930
0.914
FC Slo acko
1.000
0.951
0.951
FC Slo an Libe ec
0.971
0.932
0.905
FC Vik o ia Plzen
1.000
0.904
0.904
FK Jablonec
1.038
0.964
1.000
FK Mlada Bolesla
0.955
0.910
0.869
FK Teplice
1.073
0.926
0.993
SK Sla ia P aha
1.000
0.911
0.911
A e age
1.008
0.936
0.944
Sou ce: Own
On a e age, he esul s show a dec ease in p oduc i i y, an inc ease in e iciency and
echnological eg ession. I he esul s a e in e p e ed indi idually o each eam, only
Bohemians P aha 1905 inc eases i s p oduc i i y, due o an inc ease in e iciency ha
compensa es o i s echnological eg ession. On he o he hand, FK Jablonec expe iences no
change in p oduc i i y, inc ease in e iciency and show echnological eg ession.
The es o he eams show a decline in p oduc i i y, some o hem due o a d op in bo h
e iciency and echnological eg ession (FK Mlada Bolesla , FC Slo an Libe ec, and FC
Fas a Zlin). Analyzing he in o ma ion in Table 4, one could conclude ha o e he pe iod
s udied he e is a widesp ead decline in p oduc i i y, which is also e iden in i s wo
componen s, bu p ima ily in a echnical eg ession.
Conclusion
Gi en oo ball clubs’ cu en economic and inancial si ua ion, he e is an inc easing need o
know how e icien ly a club uses i s esou ces. In addi ion, his analysis is also c ucial o
e alua ing he spo s pe o mance o clubs. Among he a ious ools ha a e widely used o
measu e e iciency, he da a en elopmen analysis and Malmquis index we e chosen in his
a icle.
In his a icle, he DEA was applied o he bes clubs in he Czech Republic, which pa icipa e
in he highes oo ball compe i ion Fo una:Liga. The e we e 20 di e en clubs ha played
Fo una:Liga in i e seasons (2015/16 o 2019/20). The esea ch p o ided se e al
conclusions.
The i s conclusion: om he analyzed pe iod om he poin o iew o he OTE sco e, he
winne o Fo una:Liga was always desc ibed as e icien wi h he excep ion o he 2019/20
season and he club wi h he lowes OTE sco e o Fo una:Liga mos ly le he league a he
end o he season.
The second conclusion can be d awn om he la ge numbe o seasons included in he
esea ch. As can be seen, in he i e seasons analyzed, no club was able o main ain e iciency
h oughou he pe iod unde e iew. I is impo an o no e ha he clubs and esou ces used
change om season o season, as do he opponen ’s eams. The e o e, when an e icien club
uses he same esou ces in he same way in pas seasons, i is no enough o be e icien in he
coming seasons.
110
110
As a hi d conclusion, a ious sou ces o ine iciency we e iden i ied. The i s sou ce o
ine iciency is obse ed in pu e echnical e iciency (PTE) and is ela ed o he was e o
inpu s. To achie e he same ou pu , a lowe alue o inpu s (i.e., a lowe o al squad ma ke
alue o a lowe numbe o playe s) should su ice. The second sou ce o ine iciency can be
obse ed by calcula ing scale e iciency and is associa ed wi h he selec ion o inapp op ia e
spo s ac ics. In his case, o cou se, he eam’s head coach is he mos in ol ed. The p oblem
is no jus how hey use hei spo s esou ces. These clubs should seek o de elop a medium-
and long- e m s a egy o de elop new and di e en ac ics wi h he esou ces hey ha e o
could ha e in he u u e. The pu chase o playe s should also ake place in he con ex o he
de elopmen o hese new spo s ac ics. The e a e also clubs ha su e om bo h sou ces o
ine iciency. In his case, clubs should educe esou ces and, in e ms o size, ind ou how
e ec i e clubs a e de eloping spo s ac ics.
In his a icle, changes in p oduc i i y in oo ball clubs playing in Fo una:Liga om
2015/2016 o 2019/2020 ha e been calcula ed by means o he Malmquis index. The esul s
ob ained in his a icle show no clea inc ease in p oduc i i y du ing he pe iod s udied, bo h
on he a e age and indi idually. In conclusion, i does no appea ha he o ganize o his
ou namen has been able o inc ease he p oduc i i y o he eams ha has pa icipa ed in i
du ing he pe iod analyzed. Consequen ly, he o e all ecommenda ion o he oo ball clubs
analyzed in his s udy would be o imp o e hei p oduc i i y. B eaking down he Malmquis
index in o e iciency change and echnical change and seeing ha nei he o he wo show a
clea inc ease. The e o e, he ecommenda ion would be o design ules o he ou namen
ha would imp o e he p oduc i i y o he pa icipa ing eams by linking spo s success o he
inc ease in p oduc i i y.
Li e a u e
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[6] KANG, H.-J.: P oduc i i y Change and Rela i e E iciency o P o essional Spo
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