Measuring efficiency in the Finnish Ice Hockey

There are at least two types of efficiency: full stand and winning ratio. Full stand refers to the number of spectators in relation to the venue capacity and the winning ratio to the points per game or standing in the series at the end of the season. It is important that sports and financial resources are combined. The team’s success is driving financial and operational performance. Given the dichotomous targets that the ice hockey teams have, it is important to study how Finnish ice hockey teams in men’s highest league have achieved these objectives. The scope of this research involves combining both sports and spectator variables to evaluate the efficiency of men’s ice hockey in Finland where ice hockey is the biggest sports in terms of spectator number and also truly the only large professional sports.

We are using a stochastic distance function approach with two targets: winning ratio and stadium capacity utilisation ratio and a ten year period from 1990/91 to 1999/2000 regular season data. Each sport team is using m inputs xj to produce two interrelated goods, a winning percentage or brand qi1 and arena capacity utilisation ratio qi2. An input distance function defined in the context of m inputs and two outputs and the Dobb-Douglas function is chosen. The results show that the characteristics of players are related to winning ratio, and these characteristics are also significant in explaining capacity utilisation. At the same time the winning ratio is related to capacity utilisation. The two output measures are interrelated which makes interpretation difficult.

Measuring efficiency in the Finnish Ice Hockey

Introduction and motivation

Research on the efficiency of professional ice hockey teams is relatively rare – there

are some studies, such as Jones and Ferguson 1988, Kahane 2005, Büschemann and

Deutcher 2011, Leard and Doyle 2011, Kahane, Longley and Simmons 2013 or

Mongeon 2015 - and far less common than in other professional sports (for a survey

see Barros & Leach 2006, Collier, Johnson and Ruggiero 2011 or Lee 2014) but no

studies have been carried out using Finnish data. In Europe sport leagues in general

are characterised by a system of relegation (worst teams drop to the second league

level) and promotion (best of the second go up) while the American leagues are

closed. Therefore any efficiency is important since the worst team is subject to

relegation which typically results in dramatic fall in spectators and advertising

revenue and therefore a substantial drop in the financial performance. For example

the average spectator number of all teams in the highest league, SM-liiga during the

regular season 2007/08 was 5144 while the same number of all teams in the second

highest league, Mestis was 1092. However, there has been a period in the Finnish

men’s ice hockey when the league was closed. The last relegation took place in 1999

when the worst of 12 dropped. During a 25 year period from the season 1990/91 to

2014/2015 there has been 18 different teams from 15 different towns in the men’s

highest league. Despite the fact that a relegation has been uncommon in Finnish ice

hockey the teams must pursuit efficiency.

There are at least two types of efficiency: full stand and winning ratio. Full stand

refers to the number of spectators in relation to the stadium capacity and the winning

ratio to the points per game or standing in the series at the end of the season. It is

important that sports and financial resources are combined. The team’s success is

driving financial and operational performance. However, if the ambitious in sport is

beyond the financial resources and the talent level of the team is far too expensive in

the relation to the team’s revenues, the combination of sporty and financial resources

is imbalanced. Therefore the team’s management must have two targets. The first is

to ensure that the team has enough revenues, the stand is relatively full and

advertising and broadcasting revenues are reasonable. The second is to ensure that

the team’s talents are sufficient in order to achieve a satisfactory winning ratio. The

empirical evidence as outlined by Garcia-del-Barrio and Szymanski (2009) is in line

with teams optimizing both profits and wins. However, there seems to a trade-off

between these two targets (Dietl, Grossmann and Lang 2011). Profit maximising club

behaviour can be affected by revenue sharing which has a dulling effect on the

competitive balance and hence on talent investment and winning probability. Dietl,

Grossmann and Lang show that revenue sharing does not always lead to dulling

effect. A sharpening effect increases investments in talents and produces a more

balanced league if the league is not fully balanced in equilibrium.

Given the dichotomous targets that the ice hockey teams have, it is important to

study how Finnish ice hockey teams in men’s highest league have achieved these

objectives. The scope of this research involves combining both sports and spectator

variables to evaluate the efficiency of men’s ice hockey in Finland where ice hockey is

the biggest sports in terms of spectator number and also truly the only large

professional sports. The outputs of the team (winning ratio and arena capacity

utilisation ratio) and data on the inputs (both players and circumstantial factors) are

transparent which allows us to study efficiency of the team conveniently. The aim of

this research is twofold. First, the efficiency of Finnish ice hockey teams in the men’s

highest league is studied using a data covering 10 seasons from 1990/91 to

1999/2000. Second, the determinants of technical efficiency are evaluated using

stochastic frontier analysis. As far as the writer of this study knows no studies have

been carried out using Finnish data.

Previous studies on sport team efficiency have used data envelopment analysis (DEA)

or stochastic frontier analysis (SFA). Rottemberg (1956) was perhaps the first who

introduced the idea of a sporting production function in the context of U.S. baseball:

“a baseball team, like any other firm, produces its products by combining factors of

production”. Since Scully (1974), who empirically tested how inputs (salary) were

related to performance (winning ratio) in baseball, most of the empirical studies have

applied the sporting production function idea.

Literature

After Rottemberg (1956) and Scully (1974) several studies have estimated production

functions in sports, such as soccer (Dawson, Dobson and Gerrard 2000, Haas 2003,

Espitia-Escuer and García-Cebrián 2004, Carmichael and Thomas 2005, Barros and

Leach 2006, Ascari and Gagnepain 2007, Barros, del Corral and Garcia-del-Barrio

2008, Frick and Simmons 2008, Barros, Garcia-Barrio and Leach 2009, Barros, Assaf

and Sá-Earp 2010, González-Gómez and Picado-Tadeo 2010, Lee, Jang and Hwang

2014, Zambom-Ferraresi, García-Cebrián, Lera-López and Iráizoz 2015), American

football (Depken 2001, Collier, Johnson and Ruggiero 2011), basketball (Hofler and

Payne 1997, McGoldrick and Voeks 2005, Fort, Lee and Berri 2008, Rimler, Song and

Yi 2010, del Corral, Maroto and Gallardo 2015), baseball (Depken 2000, Lewis,

Sexton and Lock 2007, Jane 2012), ice hockey (Kahane 2005, Leard and Doyle 2011,

Kahane, Longley and Simmons 2013, Mongeon 2015), golf (Park and Lee 2012),

triathlon (Sowell and Mounts 2005) and Summer Olympics (Wu, Zhou and Liang

2010).

In the efficiency analysis the input variables have varied substantially. Most of the

soccer studies have used players’ or coach’s characteristics, such as age, career

experience, goals scored, wage, or team attributes, such as points achieved, goals

scored, players used, shots made, stadium facilities expenditure. Sports specific

inputs have been also used, like ratio of field goal percentage, steals, blocked shots,

or ratio of free throw percentage in basketball, driving distance or driving accuracy

in golf. In addition to above mentioned input variables, efficiency studied using ice

hockey data have used among others franchise age, new location, ownership type and

competition from other professional sports in the same city (Kahane 2005), co-worker

heterogeneity (Kahane, Longley and Simmons 2013) or the share of rookies

(Mongeon 2015). The output variable in ice hockey has been winning percentage

(Kahane, Longley and Simmons 2013 or Mongeon 2015) or related (“proportion of

possible point won”, Kahane 2005). Production output measures, such as the

winning percentage of the whole season has been regarded as directly the team’s

objective or indirectly relevant since winning percentage has a major impact on

team’s revenue and profit. The issue in these studies has been the production

process efficiency. The management or the coach has been responsible to transform

the relevant inputs into outputs. Therefore both the players’ quality and the coach’s

quality are important in this transformation process into performance.

The survey indicates that a combination of arena capacity utilisation ratio and

winning percentage simultaneously as the output variable in ice hockey has not been

used previously, therefore it is important to study how this two-part objective is

related to its determinants using stochastic frontier analysis.

There are two main methods to evaluate relative efficiency of a decision making unit:

data envelopment analysis (DEA) and stochastic frontier analysis (SFA). DEA uses

linear programming methods to construct a non-parametric frontier over data.

Efficiency is relative to this frontier. DEA makes no assumptions concerning the

input-to-output transformation, hence DEA does not assume any production process

or production function. The linear programming method creates an efficient frontier

based on the historical best performance and evaluates the efficiency of each

decision making unit relative to this frontier (Coelli, Rao, O’Donnell and Battese

2005). One of major deficiency of DEA is that the method is deterministic and no

statistical evaluation on the significance of input variables can be made. Due to that

shortcoming the stochastic frontier analysis (SFA) developed independently by

Aigner, Lovell and Schmidt (1977) and by Meeusen and van den Broeck (1977) is

largely used to evaluate efficiency. The frontier refers to maximum attainable output

that a team can achieve given its players, coaches and environmental circumstances.

SFA assumes that there exists some functional form for production relationship. The

common used functional forms are linear, the Cobb-Douglas, and the translog due to

their convenience. The technological change or substitutability of inputs or other

relevant indicators are easily estimated. The SFA in the case of Cobb-Douglas form is

(1 ) ln qi=A0+∑n=1

N

βn ln xn−ui

Where qi is the output of a team, xn are the inputs used and ui is inefficiency. Distance

functions d iI can be used to estimate a multiple-output production relationship. When

there are two outputs a conventional Cobb-Douglas form takes the form:

(2 ) ln d iI=β0+∑

n=1

N

βn ln x¿+∑m=1

2

φm ln qmi+υi

where υi is a random variable to account for errors and statistical noise (Coelli, Rao,

O’Donnell and Battese 2005, 264). This function is non-decreasing, linearly

homogeneous and concave in inputs if βn≥0∧∑n=1

N

βn=1.However, the distance is

unobserved but the homogeneity assumption allows to re-arrange the model (2) to be

written in the following form:

(3 ) ln x¿=β0+∑n=1

N−1

βn ln( x¿

x¿)+∑

m=1

2

φm ln qmi+υi−ui

where ui = lnd iI is a non-negative variable associated with technical inefficiency. An

input-oriented measure of technical efficiency is

(4 )TEi=exp ¿)

The estimation of distance functions is not trouble-free since the explanatory

variables may be correlated with the composite error term: υi−ui. A team has two

objectives as proposed above: winning ratio and full stand. The winning ratio is a

function of player in relation to other teams in the league. The arena stand capacity

utilisation ratio is related to winning percentage but also on ice hockey’s position in

the eyes of consumers. They have a possibility to choose between various leisure

activities a town can offer. How consumers choose between different alternatives can

be justified with a model to be presented next.

A Model

A team’s production uses n inputs xj to produce one output, a differentiated activity qi

in a town. There is a single, representative consumer whose preferences denote a

favour for variety indicating that a sports team has a given number of competing

firms offering other leisure activities. The monopolistic competition assumption is

suitable for analysing the equilibrium number of different leisure activities (brands)

in a town. Excess capacity is often associated with monopolistic competition model

and therefore the assumption is useful to analyse teams’ efficiency, especially the

arena capacity utilisation ratio. Following Shy (1995) a simplified version of Dixit and

Stiglitz (1977) model is used to analyse a town with differentiated activities (sport

event, theater performance, movies at a cinema, etc.) i = 1,2,3, …, S. The number of

activities s is determined endogenously and qi ≥ 0 is the attendance of an activity

(the quantity consumed of brand i) and pi is the ticket price (price of one unit of

activity i). The utility function of the spectator is given by a CES (constant elasticity

of substitution) utility function:

(5 )u (q1 , q2 , q3 ,…)=∑i=1

S

√qi

The marginal utility of each brand is infinite at a zero consumption level indicating

that the utility function expresses dignity for variety.

(6 ) lim ¿qi→0∂u∂qi

=lim ¿qi→012√q i

=쨨

The indifference curves are convex to the origin meaning that spectators favour

mixing the brands in their consumption. It is possible that spectators gain utility even

when some brands are not consumed due to the summary procedure of the utility

function. The representative consumer’s income is made up of total wages paid by

the firms producing these brands and the sum of their profits. The wage rate is

normalised to equal 1, hence all monetary values are all denominated in units of

labour. The budget constraint is then:

(7 )∑i=1

S

pi qi≤ I=L+∑i=1

S

pi q i

Where L denotes labour supply. The sport spectators maximise their utility (5)

subject to budget constraint (7). The Lagrangian (Ł) is the following.

(8 )Ł (qi , p i , λ )=∑i=1

S

√q i−λ [I−∑i=1

S

p iq i]The first order conditions for every brand i is

(9 ) ∂Ł∂qi

= 12√q i

−λ p i=0 , i=1 ,2,…. N

The demand and price elasticity (ε i) for each brand are given i by

(10 )qi ( pi )=1

4 λ2( pi)2 , εi=

∂qi∂ pi

p iqi

=−2

It is assumed that the Lagrange multiplier λis a constant. Each brand is produced by

a single firm (e.g. sport club). All firms have identical cost structure with increasing

returns to scale. Formally, the cost function (C i) of a firm producing q i units of brand i

is given by

(11)C i (q i )=F+c qi ,if qi>0 ,∨Ci (q i )=0 , if q i=0

Each firm behaves as a monopoly over its brand and maximises its profit (10)

(12 )maxqi π i=p i (qi )qi−(F+c qi)

In the monopolistic competition model free entry of firms offering different leisure

activities will result in each club making zero profits in the long run and each firm

has excess capacity. The demand of each firm producing brands (sport events or

other leisure activities) depends on the number of brands in the town, S. As S

increases, the demand of each firm shifts downward indicating that spectators

substitute higher consumption levels of each brand with a lower consumption spread

over a larger number of brands. Free entry of firms increases the brands until the

demand curve of each firm becomes tangent to the firm’s average cost function. At

this point entry into the activity market stops and each firm is making zero profit and

they are producing on the downward sloping part of the average cost curve. Since

each firm that is making some production and maximising its profit the marginal

costs must equal marginal revenue.

(13 ) MC (qi )=MRi (qi )=pi(1+ 1εi )=p i(1+ 1−2 )= p i

2=c

Therefore, at equilibrium, the price of the activity is twice the marginal cost: pi=2c.

The zero profit condition denotes thatq i=F /c. The labour market equilibrium

presumes that labour supply (L) equals labour demanded for production:

∑i=1

S

(F+c qi )=L which implies thatS[F+c (Fc )]=L.

The monopolistic competition equilibrium is therefore given by

(14 ) pi=2c∧qi=Fc

∧S= L2F

The Dixit-Stiglitz model presented above implies that when fixed costs (F) are high,

the number of leisure activities (brands) offered in town is low but each brand is

produced in a large firm. If the town is small in terms of labour supply, the number of

brands is also low and there is a minor variety of different brands offered. The

following hypothesis can be presented.

H1: If the town is small in terms of population (L), the variety of leisure

activities offered in a town is small (S).

H1B: Ice hockey teams in a small town have a higher efficiency in terms of full

stand

H2: When the fixed costs (F) due to nature of the leisure event are high, the

variety of activities offered in a town is low (S).

H2B: Ice hockey teams’ efficiency is related to other leisure activities offered

in the town.

These fixed costs are related to building and maintaining a (sports, opera, and

theater) house or to the number of staff, like coaches or physiotherapists (singers,

players, musicians) needed in this sport (cultural activity).

The equilibrium of the Dixit-Stiglitz model is Nash-Cournot in prices. Each firm sets

price on assumption that other prices do not change. Moreover, entry drives profit

down to normal level. Hence the combination of Nash-Cournot in prices and zero

profits gives the number of activities offered in the town. However, the monopolistic

competition model does not have any criterion for defining the group of competing

brands. In our model the different activities are simply assumed to form this group.

The form of marginal utility function results in representative consumer purchasing

some of every brand which is analytically rational but in real life not sensible. Despite

these shortcomings the Dixit-Stiglitz model is still a reasonable theoretical setting to

study capacity utility ratio of sports since the excess capacity theorem entails from

the monopolistic competition model. Anyway the model proposes that the town size –

or population – and other competing leisure activities, such as theater performances

or cinema are relevant variables in explaining ice hockey teams’ efficiency.

Each sport team is using m inputs xj to produce two interrelated goods, a winning

percentage or brand qi1 and arena capacity utilisation ratio qi2. An input distance

function defined in the context of m inputs and two outputs takes the form if Dobb-

Douglas function is chosen.

(15 ) ln d iI=β0+∑

n=1

N

βn ln x¿+∑m=1

2

φm ln qmi+υi

The distance function approach and the propositions of the Dixit-Stiglitz model

compose the theoretical setting of the empirical testing.

Method and data

The distance function affords the advantage of using only quantities and no

information about prices or wages is needed. We can accommodate the multi-target

nature of the professional sport industry. However, should we have data on input

cost-shares, cost efficiency could be decomposed into technical and allocative

efficiency components. Allocative inefficiency is caused by the wrong mixture of

inputs in use. The technical efficiency can be decomposed into two elements: pure

technical efficiency and scale efficiency assuming variable returns to scale. The scale

efficiency indicates if the management is operating in the right scale. The frontier

contains an error term that represents a combination of technical and allocative

inefficiencies. Unfortunately, it is very difficult to model and estimate the

relationships between these two error terms (Coelli et al 2005, 269).

The problem with the distance function in efficiency evaluation is that the dependent

variable in (15) is unobserved. By substituting the homogeneity assumption ∑n=1

N

βn=1

into the distance function (15), a homogeneity-constraint model can be written and

also estimated.

(16 ) ln x¿=β0+∑n=1

N−1

βn ln( x¿

x¿)+¿∑

m=1

2

φm ln qmi+υi−ui ¿

Where ui= ln d iI is a non-negative variable associated with technical inefficiency. An

input-oriented measure of technical efficiency is TEi=1d iI=exp (−ui).

The data set covers 10 regular seasons from 1990/91 to 1999/2000 of men’s highest

league (SM-liiga) teams. During the 1990’s there were 12 teams playing regular

season games. The playoff games followed the regular season but the data covers

only regular season starting usually in early September and ending in early March.

Each team played 44 games during the 1990/91 season. The number of games

increased by jumps to 54 in 1999/2000. The primary data is taken from

www.quanthockey.com –website. Some auxiliary data is taken from official statistics

Finland and other semi-official websites such as www.sm-liiga.fi (spectators, points at

the end of the regular season), www.elokuvauutiset.fi (spectator number of the

movies at a cinema, annual), www.tinfo.fi (spectator number in the theatres, annual).

For each team the average age, the number of games played before the beginning of

the season (bbs), the number of goals scored (bbs), the number of assists (bbs), the

total points (goals + assists, bbs), the penalty minutes (bbs), the plus-minus statistics

(bbs) of the first line forwards (3 players), of the 12 forwards (lines 1 to 4) and of all

the forwards are counted. A similar statistics is counted for defencemen, 2 first

defenders and all defenders. The age of the main goalkeeper and the save percentage

(bbs) is counted. There are some foreign players without published statistics else

than their age. In these cases the average statistics of those players with the same

age is used. The missing data problem is most common if the player is a Russian. The

Swedish ice hockey league statistics does not contain the plus minus statistics (if a

player is on the ice when the own team scores then player receives one plus mark

and if the visitor team scores then the player receives one minus mark).

Age Games played

Goals scored

Goals assisted

Points

Penalty min

Plus minus

Forwards 3

26.41↑

(2.21)

238.07↑

(87.02)

83.79(41.2

9)

102.90

(51.42)

186.00

(88.88)

156.99↑

(76.49)

20.82↓

(26.84)

Forwards 12

25.16↑

(1.32)

193.40↑

(54.19)

61.47↓

(21.94)

71.12(27.4

7)

131.96

(48.06)

121.02↑

(46.57)

12.74↓

(18.82)

Forwards all

24.21(1.10)

157.56

(42.09)

49.54↓

(17.97)

57.06(21.8

8)

106.08↓

(38.74)

97.86↑

(34.24)

9.32↓

(13.41)

Defencem 27.04 286.7 45.4 86.22 131.7 230.3 21.83

en 2 (3.00) 8(136.91)

7↓

(33.23)

(64.73)

1(95.7

6)

1(144.38)

(46.28)

Defencemen all

24.31↓

(1.39)

162.37↓

(55.55)

20.53↓

(11.51)

39.08↓

(19.40)

59.61↓

(30.40)

122.89

(48.66)

9.91↓

(19.62)

Main goalkeeper

26.38(3.82)

162.31

(126.51)

Save percentage: 0.893↑

(0.013)

Table 1, Descriptive statistics of players characteristics: mean (std), seasons 1990/91 – 1999/2000

There is a low but significant increase in the average age of the first line (forwards 3)

from 1990/91 to 1999/2000: β = 0.187 / per year. This is indicated by ↑ in table 1. Also

the number of games and penalty minutes have increased significantly in the 1990’s.

Moreover, there is a significant increase in the age of all four forward lines (forward

12), their games played and penalty minutes. The number of goals scored has

diminished in the 1990’s (↓). A similar change is seen in the figures of all forwards.

The plus minus statistics has been diminishing over the period from 1990 to 2000.

The games played, goals scored and assisted by all defencemen has diminished

during this period although the number of regular series games has increased from

44 (1990/91) to 54 (1999/2000). It seems that forward players on average have

become more experienced and defencemen less experienced during this period. As a

rule, most teams have had one, main goalkeeper who has been on the ice in almost

all games. His save percentage has improved (↑) over time. The other goalkeepers

have had a minor ice time and therefore their input is neglected in the analysis.

Points per game

Capacity ratio

Population

Unemployment rate

Movies

Theatres

Points per game

1.00(0.26)

1 0.407 0.214 -0.198 0.188 0.151

Capacity utilisation ratio

0.68(0.13)

1 -0.042 -0.102 -0.019 -0.029

Population 536143(447844)

1 -0.365 0.988 0.946

Unemployment rate

16.24(5.44)

1 -0.406 -0.350

Movies 5805170(578423)

1 0.935

Theatres 2549060(100207)

1

Table 2: Descriptive statistics of output and province or city related input variables, and correlation statistics.

The output measures are points per game and capacity utilisation ratio. Since in the

1990’s the winner got 2 points and the loser 0 points and the points were split if

there was a tie game, the average points per game is 1.0. The best figure was 1.53

and the worst 0.29. The average stadium capacity utilisation ratio was 68%. The

population statistics refers to the province (NUTS3). The biggest province was

Uusimaa with roughly 1.4 Million inhabitants and the smallest less than 300000

citizens. The decade was economically weak in Finland, the economic growth in the

early 1990’s was negative and thus the unemployment rate was considerable. In table

2 the figure is the province unemployment rate and it is negatively correlated with

province population. The theater or movie attendance figures refer to the city where

the ice hockey team is located. The province population is highly positively correlated

with theater or movie attendance in the city. It is most plausible that movies and ice

hockey games have a similar audience (Suominen 2013). The variables listed in table

2 are not related to time while some of the player characteristics are as shown in

table 1, e.g. there is no trend during the 1990’s.

Results

A preliminary analysis is carried out with using only one output measure. First the

points per game is studied. The forward player characteristics except the plus minus

statistics are highly positively correlated with age therefore each of the other

variables are used separately. Second the stadium capacity utilisation ratio is

studied using player characteristics and circumstantial factors, like the area (NUTS3)

unemployment rate, population statistics and the spectator number of movies at a

cinema and theatres. Usually the theater season begins in autumn and ends in spring

which is in line with the ice hockey season. The theater statistics used here are

annual from January to December and therefore an average of two consecutive

annual figures is used in the analysis. In addition the stadium capacity utilisation

ratio is studied in relation to points per game and the above mentioned

circumstantial factors using a standard regression analysis. In the table 3 (below) the

columns on the left use the characteristics of the players in the first line: 3 forwards

and 2 defencemen. In the middle the characteristics of the 12 first forwards (probably

meaning lines 1 to 4) and all defencemen are used to explain the success of the team:

points per game in the regular season. It is fairly common that the first line of players

are best in the team. Usually a team uses 12 forward players (lines 1 to 4) and 7

defencemen and 2 goalkeepers in a game. Due to injuries or weak performance the

coach is able to use more than 12 + 7 + 2 players during the whole season. These

replacement players do not take part in each game during the season. However, the

in table 4 the stochastic frontier analysis use all players available in explaining points

per game.

Average, log ( )

First line forwards (only 3) and first line defencemen (only 2) 12 first forwards (4 lines) and all defencemen

ForwardsAge 0.029

2***

(0.0055)

-0.2019(0.3471)

#games 0.0638***

(0.0082)

0.1267(*)

(0.0705)

#goals 0.0997(*)

(0.0515)

0.0586***

(0.0045)

#assisted 0.0838(*)

(0.0485)

0.1222*

(0.0517)

#points 0.1035(*)

(0.0529)

0.1227*

(0.0572)

Penalty minutes

0.0602***

(0.0164)

0.1651**

(0.0624)

Plus/minus if positive

0.0294***

(0.0001)

0.0362***

(0.0010)

0.0071(0.0224)

0.0094(0.0218)

0.0056(0.0226)

0.0342****

(0.0061)

0.0367*(0.0179)

0.0259(0.0183)

0.0410***

(0.0133)

0.0197(0.0200)

0.0201(0.0206)

0.0251(0.0184)

Plus/minus if negative (oppos.)

0.0083***

(0.0005)

0.0168***

(0.0014)

-0.0080(0.0244)

-0.0041(0.0238)

-0.0082(0.0245)

0.0146*

(0.0063)

0.0282(0.0214)

0.0156(0.0206)

0.0459***

(0.0017)

0.0124(0.0220)

0.0136(0.0226)

0.0138(0.0206)

DefencemenAge -

0.0120***

(0.0042)

0.0358(0.4050)

#games -0.0044***

(0.0010)

0.1282*

(0.0634)

#goals 0.0469(0.0320)

0.0364***

(0.0049)

#assisted 0.0358(0.0356)

0.0801(*)

(0.0457)

#points 0.0412(0.0358)

0.0830(*)

(0.0479)

Penalty minutes

-0.0205(0.0161)

0.0105(0.0537)

Plus/minus if positive

0.0114***

(0.0014)

0.0096***

(0.0013)

0.0065(0.0216)

0.0133(0.0224)

0.0110(0.0223)

0.0162(*)

(0.0094)

0.0094(0.0153)

0.0014(0.0155)

0.0079***

(0.0022)

-0.0010(0.0168)

-0.0003(0.0167)

0.0154(0.0135)

Plus/minus if negative (oppos.)

0.0043**

(0.0016)

0.0006(0.0015)

0.0002(0.0218)

0.0076(0.0228)

0.0052(0.0226)

0.0074(0.0091)

-0.0011(0.0169)

-0.0120(0.0171)

0.0031(0.0025)

-0.0149(0.0179)

-0.0143(0.0179)

0.0051(0.0152)

GoalkeeperAge -

0.0574***

(0.0149)

-0.0448***

(0.0059)

0.0234(0.1531)

-0.0232(0.1572)

-0.0079(0.1569)

0.0076(0.0571)

-0.1295(0.1498)

-0.2358(0.1571)

-0.3535***

(0.0107)

-0.2588(0.1585)

-0.2447(0.1585)

-0.1971(0.1474)

Save% 1.2702***

(0.1316)

0.5257***

(0.1515)

4.4616**

(1.4152)

4.0887**

(1.4087)

4.2735**

(1.3605)

1.0965***

(0.2263)

4.1781**

(1.5250)

4.1295***

(1.2735)

1.3978***

(0.1136)

3.9626**

(1.2962)

4.2065**

(1.2991)

3.2695*

(1.3269)

Constant 0.5827(0.0633)***

0.2005***

(0.0360)

0.0702(0.5687)

0.2707(0.5617)

0.0334(0.6004)

0.2300(0.2984)

0.7368(1.6965)

0.1951(0.5947)

1.3976***

(0.0328)

0.7429(0.5226)

0.6035(0.5493)

0.4907(0.5497)

Lambda; λ 231499***

(2168)

203764***

(2059)

4.7951**

(1.6975)

4.6835**

(1.6142)

4.3689**

(1.4036)

97019***

(2292)

6.0431**

(2.006)

5.4899***

(1.6293)

252953***

(2422)

4.7083***

(1.2469)

4.5146***

(1.1779)

5.5341**

(1.7340)

Sigma, σ 0.4616***

(0.0032)

0.4580***

(0.0032)

0.4132***

(0.0029)

0.4145***

(0.0029)

0.4087***

(0.0028)

0.4527***

(0.0031)

0.4290***

(0.0029)

0.4093***

(0.0029)

0.4580***

(0.0034)

0.4010***

(0.0028)

0.4003***

(0.0027)

0.4132***

(0.0029)

Table 3: Stochastic frontier analysis, output measure is points per game, 10 seasons from 1990/91 to 1999/2000, and 12 teams.

Average, log ( )

All forwards and all defencemen

ForwardsAge -0.3776

(0.3831)

#games 0.1678**

(0.0602)

#goals 0.1209*

(0.0556)

#assisted 0.1286**

(0.0487)

#points 0.1278*

(0.0522)

Penalty minutes

0.1755***

(0.0114)

Plus/minus if positive

0.0507***

(0.0150)

0.0429***

(0.0123)

0.0428*

(0.0169)

0.0402**

(0.0156)

0.0405*

(0.0165)

0.0451***

(0.0012)

Plus/minus if negative (oppos.)

0.0459*

(0.0198)

0.0340**

(0.0153)

0.0411*

(0.0197)

0.0363*

(0.0180)

0.0374*

(0.0189)

0.0383***

(0.0003)

DefencemenAge 0.3612

(0.4026)

#games 0.0806(0.0648)

#goals 0.0689(0.0448)

#assisted 0.0599(0.0433)

#points 0.0666(0.0452)

Penalty minutes

-0.0460***

(0.0095)

Plus/minus if positive

0.0562(0.0169)

-0.0047(0.0157)

-0.0036(0.0182)

-0.0090(0.0186)

-0.0074(0.0190)

0.0146***

(0.0015)

Plus/minus if negative (oppos.)

-0.0043(0.0184)

-0.0156(0.0180)

-0.0160(0.0195)

-0.0221(0.0200)

-0.0204(0.0203)

0.0056*

(0.0026)

GoalkeeperAge -0.1622

(0.1380)

-0.2870(*)

(0.1547)

-0.2490(*)

(0.1487)

-0.2982*

(0.1499)

-0.2776(*)

(0.1519)

0.0211(0.0209)

Save% 4.5209**

(1.5387)

4.4272**

(1.4611)

5.3812***

(1.3354)

4.6762***

(1.2713)

4.9652***

(1.2980)

3.0923***

(0.1367)

Constant 1.4782(1.6664)

0.5274(0.5139)

1.0963*

(0.5174)

1.0943*

(0.5083)

0.9354(*)

(0.5233)

0.1094*

(0.0539)

Lambda, λ 7.1502*

(3.2654)

13.072(*)

(7.412)

6.1849**

(2.2434)

7.7021*

(3.4000)

6.8365(*)

(2.8373)

170240***

(2045)

Sigma, σ 0.4270***

(0.0029)

0.4278***

(0.0029)

0.4106***

(0.0028)

0.4148***

(0.0028)

0.4121***

(0.0028)

0.4331***

(0.0030)

Table 4: Stochastic frontier analysis, output measure is points per game, 10 seasons from 1990/91 to 1999/2000, and 12 teams.

The results in table 3 and 4 show that almost all forward player related variables

(age, the number of games, goals, assisted goals, points or penalty minutes) are

statistically significant and have the correct sign. A positive coefficient indicates that

experience however you measure it has a positive impact on performance or points

per game. Only the average age of 12 first forward players or the average age of all

forward players is not significant. The plus – minus statistics of forward players is

also significant and plausible in almost all equations. If the plus – minus statistics is

negative the absolute value has been used before transforming the variable into its

logarithm. Therefore if the coefficient of the “plus-minus if negative” has a positive

sign indicates that a large negative plus-minus statistics has a harmful consequence

on points per game. The defencemen related variables seem to have a plausible sign

and are significant if there is a combination of 12 first forwards and all defencemen.

The goalkeeper age seems to have a negative impact on points per game while a high

previous (before the season, bbs) save percentage has a positive impact on

performance. In the case of assisted goals explaining the frontier, the technical

efficiency scores vary from 0.654 to 0.876. The average score is 0.761. Teams that

were newcomers in the league have rather low efficiency scores.

In the stochastic frontier function the error term ε i=υi−ui has two components in

which ui measures the percentage (due to logarithms) by which the ice hockey team

fails to achieve the frontier, the ideal production rate. The variance of the error term

can be divided into two parts: σ=√ (σ u2+σv

2 ) and λ=σu /σv in which the first part (σ u)

counts for inefficiency and the second (σ v) counts for disturbance. If λ is zero, there

are no technical inefficiency effects. The results in tables 3 and 4 present that the

inefficiency is notable.

The stadium capacity utilisation ratio (s-ca%) is related to points per game (ppg) and

circumstantial factors as the following regression equation reveals. All variables are

in logs.

Points per game

0.3184***

(0.0594)0.2968***

(0.0594)0.3053***

(0.0596)0.2952***

(0.0600)0.2950***

(0.0597)Unemployment rate

-0.0265(0.0397)

-0.0145(0.0402)

-0.0209(0.0430)

-0.0027(0.0398)

-0.0098(0.0406)

Population -0.0594*

(0.0260)Theater attendance

-0.0167(0.0149)

Movie attendance

-0.0238(0.0151)

Theater attendance / population

0.0060(0.0247)

Movie attendance / population

-0.0171(0.0316)

Constant 0.4508(0.3771)

-0.1520(0.2273)

-0.0297(0.2454)

-0.3736***

(0.1082)-0.3655(0.1093)

R” / F 0.1923 / 10.45***

0.1650 / 8.84***

0.1735 / 9.33***

0.1564 / 8.36***

0.1581 / 8.45***

Table 5: Regression analysis, output = stadium capacity utilisation ratio, n = 120, 12 teams, 10 seasons 1990/91 – 1999/2000, all variables in logs.

The regression equation shows that stadium capacity utilisation ratio is positively

related to points per game and negatively to area (NUTS2) population. The

unemployment rate, theatre or movie attendance are not related to capacity

utilisation ratio of the arena.

In tables 6 and 7 the stadium capacity utilisation ratio is studied using player related

variables and circumstantial factors. The player related variables refer to first line,

three forwards and two defencemen. In table 6 the area (circumstantial) factors are

either area population, theater attendance in the area or movies at a cinema

attendance in the area. The theater attendance figure takes into account only those

theatres that belong to the state subsidy system. The theatre and orchestra law

(705/92) that came into force in 1993 brought considerable changes to theatre

financing in Finland. The income share of the state and municipal subsidies has been

more than 50 % for theatres in the system during the sample period. Before 1993 the

state subsidies were more incidental, however the above mentioned state subsidy

system theatres are included in the sample.

The results indicate that penalty minutes of the first line forward (3) players are

significant in all stochastic frontier estimations regardless of the area variables. A

negative plus/minus statistics also seems to be significant. Since the absolute value

(always positive) of the plus/minus statistics is used in the estimations and the

coefficient is unambiguously negative the interpretation is the following: if the

plus/minus statistics of the first line forwards is weak (negative) before the actual ice

hockey season the impact on stadium capacity utilisation ratio (or attendance) is

negative. The plus/minus statistics used in the estimation is the figure covering all

earlier seasons, i.e. history of the players’ characteristics or talents.

The goals scored by first line defenders (2) or penalty minutes of the first line

defenders seem to have a negative impact on stadium capacity utilisation ratio. The

plus/minus statistics of the first line defenders is significant and positive in all models

in the tables 6 and 7. A positive plus/minus statistics but also a negative statistics

seems to attract audience since the coefficients are positive. The latter is surprising

since a negative plus/minus statistics indicates that the defender pair’s talents are

not great. Still that seems have a positive impact on stadium capacity utilisation ratio

or audience interest. A younger and perhaps less experienced goalkeeper seems to

attract more audience since goalkeeper’s age has a negative coefficient in tables 6 or

7.

Other variables in the analysis do not have a plausible and almost always significant

coefficient.

First line forwards (only 3) and first line defencemen (only 2)Forwards

Age 0.0109(0.1280)

0.1994***

(0.0475)

0.0809***

(0.0185)

#games 0.0225(0.0320)

0.0138***

(0.0039)

0.0137(0.0171)

#goals 0.0094(0.0173)

0.0075(0.0222)

0.0092(0.0145)

#assisted 0.0027(0.0169)

0.0036(0.0471)

0.0024(0.0210)

#points 0.0019(0.0139)

0.0054(0.0112)

0.0040(0.0123)

Penalty minutes

0.0357***

(0.0076)

0.0253***

(0.0047)

0.0312***

(0.0067)

Plus/minus if positive

-0.0018(0.0039)

-0.0016(0.0035)

-0.0022***

(0.0002)

-0.0019***

(0.0003)

0.0011(0.0009)

-0.0007(0.0050)

-0.0017(0.0072)

-0.0009(0.0095)

-0.0215(0.0067)

0.0007(0.0040)

0.0007(0.0196)

0.0006(0.0052)

-0.0002(0.0037)

0.0005(0.0013)

0.0004(0.0019)

-0.0003(0.0015)

0.0006(0.0008)

-0.0009(0.0016)

Plus/minus if negative (oppos.)

-0.0120(0.0035)

-0.0137***

(0.0039)

-0.0131***

(0.0004)

-0.0117***

(0.0003)

-0.0079**

(0.0004)

-0.0096(0.0072)

-0.0123(*)

(0.0065)

-0.0112(0.0082)

-0.0124(*)

(0.0066)

-0.0097*

(0.0041)

-0.0095(0.0209)

-0.0098(0.0061)

-0.0107**

(0.0036)

-0.0097***

(0.0013)

-0.0099***

(0.0023)

-0.0116***

(0.0016)

-0.0101***

(0.0012)

-0.0118***

(0.0015)

DefencemenAge -0.1153

(0.1198)

-0.2414***

(0.0279)

-0.1710***

(0.0256)

#games -0.0458(0.0302)

-0.0280(0.0225)

-0.0399***

(0.0106)

#goals -0.0129***

(0.0021)

-0.0085*

(0.0042)

-0.0101**

(0.0037)

#assisted -0.0077(0.0059)

-0.0096(0.0281)

-0.0082(0.0063)

#points -0.0094(*)

(0.0057)

-0.0092***

(0.0013)

-0.0085***

(0.0029)

Penalty minutes

-0.0371***

(0.0093)

-0.0215***

(0.0059)

-0.0292**

(0.0091)

Plus/minus if positive

0.0316*

(0.0154)

0.0352***

(0.0019)

0.0341***

(0.0028)

0.0430***

(0.0113)

0.0351*

(0.0141)

0.0418***

(0.0079)

0.0286***

(0.0061)

0.0265**

(0.0096)

0.0283***

(0.0056)

0.0237*

(0.0101)

0.0254(0.0239)

0.0242*

(0.0110)

0.0260**

(0.0082)

0.0254***

(0.0044)

0.0249***

(0.0047)

0.0409***

(0.0078)

0.0323***

(0.0059)

0.0392***

(0.0089)

Plus/minus if negative (oppos.)

0.0228(0.0161)

0.0287***

(0.0017)

0.0262***

(0.0025)

0.0372**

(0.0143)

0.0280(*)

(0.0161)

0.0358***

(0.0085)

0.0207***

(0.0055)

0.0183(*)

(0.0101)

0.0202**

(0.0069)

0.0150(0.0098)

0.0164(0.0239)

0.0155(0.0098)

0.0174*

(0.0083)

0.0166***

(0.0040)

0.0162***

(0.0037)

0.0361***

(0.0089)

0.0259***

(0.0059)

0.0337***

(0.0101)

GoalkeeperAge -

0.2756***

(0.0420)

-0.3043***

(0.0184)

-0.2901***

(0.0206)

-0.2985***

(0.0530)

-0.2730***

(0.0447)

-0.2924***

(0.0490)

-0.2366***

(0.0214)

-0.2240***

(0.0338)

-0.2269***

(0.0262)

-0.2271***

(0.0311)

-0.2379*

(0.0957)

-0.2292***

(0.0601)

-0.2342***

(0.0240)

-0.2353***

(0.0202)

-0.2318***

(0.0314)

-0.2878***

(0.0132)

-0.2528***

(0.0294)

-0.2630***

(0.0115)

Save% 0.2578(0.1902)

0.1720(0.1907)

0.2169*

(0.1018)

-0.6290(0.8779)

-0.1893(0.6103)

-0.4925(0.5039)

0.0310(0.1645)

0.1591(0.2558)

0.0878(0.4138)

0.4545***

(0.0731)

0.3754(1.0633)

0.4426(0.3625)

0.3390(0.3452)

0.2968***

(0.0333)

0.3414(0.2313)

-0.3294(0.2423)

-0.0160(0.2972)

-0.2498(0.2703)

AreaPopulation -0.0043

(0.0072)

0.0129(0.0106)

0.0045*

(0.0017)

-0.0002(0.0021)

0.0011(0.0039)

0.0075*

(0.0029)

Unemployment

0.0079(0.0236)

-0.0124(*)

(0.0064)

-0.0010(0.0072)

0.0010(0.0108)

0.0044(0.0115)

0.0021(0.0154)

0.0169***

(0.0024)

0.0176(0.0128)

0.0171(*)

(0.0101)

0.0167*

(0.0071)

0.0134(0.0409)

0.0161(0.0198)

0.0162**

(0.0060)

0.0147***

(0.0042)

0.0160***

(0.0100)

-0.0019(0.0080)

0.0071(0.0088)

0.0007(0.0090)

Theatre -0.0106***

(0.0027)

0.0038(0.0050)

0.0019(0.0025)

-0.0012(0.0126)

-0.0004(0.0003)

0.0023(0.0014)

Movies -0.0055*

(0.0024)

0.0070(*)

(0.0039)

0.0023(0.0017)

-0.0002(0.0078)

0.0001(0.0036)

0.0040(*)

(0.0021)

Constant 1.1426***

(0.2565)

1.1525***

(0.1285)

1.1795***

(0.1375)

0.7178***

(0.0240)

0.7435***

(0.1760)

0.8065***

(0.2190)

0.5075**

(0.1672)

0.5081*

(0.2154)

0.5015***

(0.1387)

0.6000***

(0.1903)

0.6525(*)

(0.3433)

0.6109***

(0.3440)

0.6077***

(0.1650)

0.6133***

(0.1356)

0.6002***

(0.1762)

0.6825(0.0205)***

0.6074***

(0.1392)

0.6271***

(0.0318)

Lambda 55397***

(2765)

157690***

(2033)

85619***

(2275)

34167***

(3422)

49530***

(2954)

113540***

(2599)

96458***

(2169)

81119***

(2376)

111232***

(2234)

63949***

(2602)

29846***

(3768)

60999***

(2699)

78674***

(2383)

106696***

(2103)

108200***

(2138)

93926***

(2214)

117423***

(2046)

86791***

(2289)Sigma 0.315

6***

(0.0021)

0.3151***

(0.0021)

0.3155***

(0.0021)

0.3148***

(0.0021)

0.3165***

(0.0021)

0.3155***

(0.0022)

0.3178***

(0.0021)

0.3178***

(0.0021)

0.3176***

(0.0021)

0.3182***

(0.0021)

0.3181***

(0.0021)

0.3182***

(0.0021)

0.3180***

(0.0021)

0.3180***

(0.0021)

0.3180***

(0.0021)

0.3155***

(0.0021)

0.3160(0.0021)

0.3155***

(0.0021)

Table 6: Stochastic frontier analysis, output measure is stadium capacity utilisation ratio, 10 seasons from 1990/91 to 1999/2000, and 12 teams, all variables is logs

First line forwards (only 3) and first line defencemen (only 2)Forwards

Age 0.0243(0.0533)

0.0270(0.0579)

#games 0.0118(0.0098)

0.0108(0.0196)

#goals 0.0065(0.0040)

0.0104(0.0202)

#assisted 0.0103(0.0147)

0.0020(0.0105)

#points 0.0056***

(0.0007)

0.0032(0.0076)

Penalty minutes 0.0220**

(0.0080)

0.0221*

(0.0091)

Plus/minus if positive -0.0016(0.0014)

-0.0017(*)

(0.0010)

0.0031(0.0056)

0.0013(0.0035)

0.0004*

(0.0001)

-0.0000(0.0005)

0.0002(0.0063)

0.0004(0.0031)

0.0002*

(0.0001)

0.0005(0.0073)

0.0016(0.0025)

0.0011(0.0046)

Plus/minus if negative (oppos.)

-0.0119***

(0.0017)

-0.0120***

(0.0016)

-0.0070(0.0051)

-0.0075(*)

(0.0041)

-0.0097***

(0.0001)

-0.0103***

(0.0003)

-0.0103(*)

(0.0057)

-0.0100***

(0.0029)

-0.0100***

(0.0001)

-0.0099(0.0063)

-0.0089***

(0.0021)

-0.0093*

(0.0040)

DefencemenAge -

0.1238**

(0.0398)

-0.1281**

(0.0493)

#games -0.0152(*)

(0.0087)

-0.0253(0.0184)

#goals -0.0060***

(0.0001)

-0.0071***

(0.0007)

#assisted -0.0155(*)

(0.0079)

-0.0083***

(0.0013)

#points -0.0101***

(0.0005)

-0.0075(0.0109)

Penalty minutes -0.0157*

(0.0066)

-0.0191*

(0.0064)

Plus/minus if positive 0.0303***

(0.0049)

0.0307***

(0.0038)

0.0250***

(0.0065)

0.00357***

(0.0104)

0.0241***

(0.0007)

0.0245***

(0.0033)

0.0278***

(0.0066)

0.0244**

(0.0092)

0.0261***

(0.0004)

0.0241*

(0.0096)

0.0281***

(0.0058)

0.0310***

(0.0074)

Plus/minus if negative 0.021 0.021 0.016 0.028 0.015 0.016 0.018 0.015 0.017 0.015 0.021 0.024

(oppos.) 4***

(0.0054)

9***

(0.0040)

3***

(0.0064)

4**

(0.0104)

7***

(0.0005)

3***

(0.0022)

9**

(0.0065)

7(*)

(0.0092)

3***

(0.0004)

5(*)

(0.0085)

1***

(0.0062)

3**

(0.0078)

GoalkeeperAge -

0.2889***

(0.0288)

-0.2894***

(0.0404)

-0.2590***

(0.0429)

-0.2685***

(0.0512)

-0.2194***

(0.0072)

-0.2153***

(0.0357)

-0.2481***

(0.0451)

-0.2290***

(0.0026)

-0.2376***

(0.0036)

-0.2281***

(0.0516)

-0.2443***

(0.0343)

-0.2510***

(0.0350)

Save% 0.0753(0.1931)

0.0843(0.3226)

0.2838**

(0.1003)

-0.1335(0.6269)

0.2756***

(0.0214)

0.1931(0.1239)

0.2128(0.2407)

0.4453***

(0.0555)

0.2686***

(0.0164)

0.3851(0.5492)

0.1739(*)

(0.0905)

0.0271(0.2744)

AreaUnemployment 0.0129

(0.0079)

0.0119(0.0088)

0.0104(0.0099)

0.0036(0.0156)

0.0180***

(0.0006)

0.0185**

(0.0028)

0.0100(0.0085)

0.0162(*)

(0.0085)

0.0142***

(0.0010)

0.0173(0.0166)

0.0103(0.0092)

0.0084(0.0090)

Theatre/Population -0.0009(0.0067)

-0.0014(0.0049)

0.0024***

(0.0002)

-0.0045(0.0069)

-0.0007*

(0.0002)

0.0023(0.0041)

Movies/Population -0.0017(0.0133)

0.0087(0.0151)

0.0035**

(0.0012)

-0.0001(0.0037)

0.0008(0.0081)

0.0049(0.0062)

Constant 1.0675***

(0.1106)

1.0887***

(0.1939)

0.7034***

(0.2217)

0.7877***

(0.1690)

0.5251***

(0.0447)

0.4855***

(0.2249)

0.6533***

(0.2002)

0.6094***

(0.0973)

0.6169***

(0.0094)

0.5891***

(0.1884)

0.6044***

(0.1502)

0.6340***

(0.1344)

Lambda 134622***

(2005)

121480***

(2121)

112251***

(2108)

84630***

(2502)

70762***

(2465)

72686***

(2436)

103464***

(2195)

76925***

(2391)

92217***

(2207)

78968***

(2365)

114482***

(2062)

105450***

(2215)Sigma 0.316

4***

(0.0021)

0.3166***

(0.0021)

0.3171***

(0.0021)

0.3167***

(0.0021)

0.3180***

(0.0021)

0.3177***

(0.0021)

0.3188***

(0.0021)

0.3182***

(0.021)

0.3178***

(0.0021)

0.3180***

(0.0021)

0.3168***

(0.0021)

0.3160***

(0.0021)

Table 7: Stochastic frontier analysis, output measure is stadium capacity utilisation ratio, 10 seasons from 1990/91 to 1999/2000, and 12 teams, all variables is logs

In tables 8 and 9 the stochastic frontier analysis is otherwise similar than in tables 6 and 7 except that the statistics or characteristics of 4 lines of forwards (12 players) and 7 (all) defenders are used.

12 first forwards (4 lines) and all defencemen

ForwardsAge -0.1073

(0.1354)

-0.1948(0.1522)

-0.1828(0.1538)

#games 0.1348***

(0.0309)

0.0570***

(0.0118)

0.0694***

(0.0244)

#goals 0.0306(0.0216)

-0.0103(0.0122)

-0.0098(0.0146)

#assisted 0.1349***

(0.0435)

0.0586(0.0509)

0.0606(*)

(0.0341)

#points 0.0884*

(0.0419)

0.0443***

(0.0124)

0.0424(0.0264)

Penalty minutes

0.1181***

(0.0066)

0.0762***

(0.0065)

0.0738**

(0.0133)

Plus/minus if positive

0.0078(*)

(0.0046)

0.0120***

(0.0035)

0.0114*

(0.0045)

-0.0123*

(0.0057)

-0.0006(0.0010)

-0.0044(0.0031)

-0.0041(0.0044)

0.0055*

(0.0022)

0.0052(*)

(0.0030)

-0.0196(*)

(0.0117)

-0.0112(0.0168)

-0.0109(0.0152)

-0.0140(0.0119)

-0.0055(*)

(0.0032)

-0.0073(0.0059)

-0.0046**

(0.0016)

-0.0108***

(0.0017)

-0.0108***

(0.0034)

Plus/minus if negative (oppos.)

0.0037(0.0067)

0.0105(*)

(0.0055)

0.0094(0.0071)

-0.0117*

(0.0053)

-0.0041(*)

(0.0021)

-0.0076(*)

(0.0040)

-0.0108**

(0.0041)

-0.0017(0.0023)

-0.0021(0.0026)

-0.0211*

(0.0098)

-0.0157(0.0101)

-0.0158(0.0141)

-0.0177*(0.0081)

-0.0098***

(0.0027)

-0.0128*

(0.0051)

-0.0029(*)

(0.0015)

-0.0094***

(0.0016)

-0.0096**

(0.0033)

DefencemenAge -

0.2092*

(0.0999)

-0.3077**

(0.1074)

-0.2872*

(0.1148)

#games 0.0095(0.0136)

-0.0075(*)

(0.0045)

-0.0070(0.0063)

#goals -0.0057(0.0039)

-0.0124***

(0.0024)

-0.0123***

(0.0020)

#assisted 0.0033(0.0183)

-0.0175(0.0188)

-0.0176(0.0268)

#points 0.0005(0.0142)

-0.0130***

(0.0033)

-0.0148***

(0.0036)

Penalty minutes

-0.0318***

(0.0027)

-0.0363***

(0.0023)

-0.0364***

(0.0047)

Plus/minus if positive

0.0053*

(0.0022)

0.0066**

(0.002

0.0064*

(0.0026)

0.0111***

(0.003

0.0051***

(0.001

0.0065**

(0.002

0.0040*

(0.0018)

0.0020(*)

(0.001

0.0021**

(0.000

0.0111*

(0.0045)

0.0071(0.0075)

0.0069(0.0052)

0.0081*

(0.0038)

0.0052***

(0.001

0.0051***

(0.001

0.0138***

(0.0007

0.0115***

(0.000

0.0112***

(0.001

7) 0) 0) 2) 2) 7) 1) 3) ) 9) 8)Plus/minus if negative (oppos.)

-0.0001(0.0022)

0.0026(0.0024)

0.0020(0.0026)

0.0003(0.0011)

0.0005(0.0005)

0.0006(0.0009)

-0.0012(0.0019)

-0.0026*

(0.0013)

-0.0027*

(0.0012)

0.0043(0.0046)

0.0014(0.0010)

0.0023(0.0029)

0.0013(0.0040)

0.0010(0.0012)

0.0010(0.0025)

0.0083***

(0.0008)

0.0058***

(0.0005)

0.0059***

(0.0012)

GoalkeeperAge -

0.2295***

(0.0501)

-0.2140***

(0.0687)

-0.2178***

(0.0570)

-0.2666***

(0.0678)

-0.1954***

(0.0182)

-0.2303***

(0.0337)

-0.2162***

(0.0327)

-0.1988***

(0.0246)

-0.2018***

(0.0232)

-0.2261*

(0.0883)

-0.2699*

(0.1298)

-0.2577*

(0.1037)

-0.2219**

(0.0685)

-0.1997***

(0.0204)

-0.2287***

(0.0345)

-0.3889***

(0.0164)

-0.3773***

(0.0195)

-0.3714***

(0.0370)

Save% 0.4759*

(0.2358)

0.2619(0.3080)

0.3029(0.2916)

1.1938**

(0.4476)

0.7639***

(0.1967)

0.9663**

(0.3595)

1.0901**

(0.4034)

0.2633(0.2636)

0.2925(0.2580)

2.1701***

(0.6266)

1.3551***

(0.3300)

1.4656*

(0.5784)

1.7969***

(0.3618)

1.0013***

(0.1937)

1.1735**

(0.3945)

1.0348***

(0.0938)

0.7147***

(0.1041)

0.7162**

(0.2278)

AreaPopulation -0.0030

(0.0062)

-0.0468***

(0.0139)

-0.0170*

(0.0083)

-0.0678***

(0.0194)

-0.0447*

(0.0177)

-0.0277***

(0.0031)

Unemployment

-0.0344***

(0.0056)

-0.0370***

(0.0071)

-0.0366***

(0.0068)

-0.0439*

(0.0182)

-0.0184***

(0.0050)

-0.0247**

(0.0093)

-0.0238(*)

(0.0123)

-0.0341***

(0.0087)

-0.0340***

(0.0047)

-0.0103(0.0262)

-0.0152(0.0335)

-0.0148(0.0241)

-0.0176(0.0189)

-0.0169*

(0.0072)

-0.0187*

(0.0077)

-0.0110*

(0.0046)

-0.0284***

(0.0046)

-0.0292**

(0.0092)

Theatre 0.0023(0.0046)

-0.0143***

(0.0041)

-0.0003(0.0043)

-0.0181(0.0218)

-0.0139***

(0.0035)

-0.0044(*)

(0.0023)

Movies 0.0008(0.0037)

-0.0145*

(0.0065)

-0.0005(0.0035)

-0.0159(0.0133)

-0.0102*

(0.0050)

-0.0029(0.0039)

Constant 1.8270*

(0.8162)

2.3116*

(1.0039)

2.2362***

(0.9700)

0.8267***

(0.2322)

0.5477***

(0.0769)

0.6427***

(0.1140)

0.8489***

(0.1545)

0.7119***

(0.1042)

0.7242***

(0.1031)

1.1483***

(0.3077)

0.9467*

(0.4640)

-0.9000(*)

(0.4796)

0.9635***

(0.2542)

0.6686***

(0.0823)

0.7592***

(0.1626)

1.2555***

(0.0518)

1.1195***

(0.0635)

1.0990***

(0.1220)

Lambda 89186***

(2337)

66386***

(2602)

78168***

(2450)

74250***

(2624)

131932***

(2138)

85804***

(2445)

108369***

(2238)

140841***

(2113)

137129***

(2077)

60399***

(2903)

18136***

(4950)

59613***

(2847)

66738***

(2758)

157338***

(2106)

92698***

(2320)

227964***

(2295)

192396***

(2103)

124878***

(2130)Sigma 0.349

9***

(0.0023)

0.3500***

(0.0023)

0.3500***

(0.0023)

0.3457***

(0.0023)

0.3493***

(0.0024)

0.3487***

(0.0023)

0.3508***

(0.0023)

0.3515***

(0.0023)

0.3515***

(0.0023)

0.3463***

(0.0023)

0.3502***

(0.0023)

0.3507***

(0.0023)

0.3490***

(0.0023)

0.3514***

(0.0024)

0.3513***

(0.0023)

0.3462***

(0.0025)

0.3474***

(0.0024)

0.3474(0.0024)

Table 8: Stochastic frontier analysis, output measure is stadium capacity utilisation ratio, 10 seasons from 1990/91 to 1999/2000, and 12 teams, all variables is logs

12 first forwards (4 lines) and all defencemenForwards

Age -0.0433(0.1334)

-0.1508**

(0.0535)

#games 0.0153(0.0129)

0.0235(0.205)

#goals 0.0091(0.0073)

-0.0098**

(0.0034)

#assisted 0.0235(0.0267)

0.0287***

(0.0075)

#points 0.0155(0.0132)

0.0227(0.0195)

Penalty minutes 0.0553***

(0.0128)

0.0466*

(0.0233)

Plus/minus if positive 0.0068(0.0053)

0.0113***

(0.0024)

0.0013(0.0021)

0.0025(0.0036)

0.0026(0.0016)

0.0068*

(0.0027)

-0.0054(0.0098)

-0.0051(0.0033)

-0.0006(0.0041)

-0.0004(0.0045)

-0.0117***

(0.0035)

-0.0069(*)

(0.0040)

Plus/minus if negative (oppos.)

0.0027(0.0076)

0.0094**

(0.0030)

-0.0041(*)

(0.0025)

-0.0020(0.0043)

-0.0034(0.0021)

0.0002(0.0044)

-0.0126(0.0087)

-0.0116**

(0.0039)

-0.0070*

(0.0032)

-0.0059(0.0041)

-0.0122***

(0.0033)

-0.0083*)

(0.0036)

DefencemenAge -

0.2424(0.1620)

-0.2822***

(0.0545)

#games -0.0262***

(0.0054)

-0.0216**

(0.0074)

#goals -0.0180*

(0.0075)

-0.0145***

(0.0035)

#assisted -0.0289(0.0195)

-0.0262***

(0.0022)

#points -0.0251***

(0.0028)

-0.0206***

(0.0030)

Penalty minutes -0.0381***

(0.0049)

-0.0325***

(0.0070)

Plus/minus if positive 0.0040(0.0026)

0.0058***

(0.0008)

0.0030***

(0.0006)

0.0024**

(0.0009)

0.0015(0.0015)

0.0014(0.0010)

0.0040(0.0037)

0.0036***

(0.0009)

0.0026(*)

(0.0014)

0.0021(*)

(0.0011)

0.0091***

(0.0021)

0.0066*

(0.0033)

Plus/minus if negative (oppos.)

0.0012(0.0030)

0.0021***

(0.0005)

0.0013**

(0.0005)

0.0012(*)

(0.0007)

0.0015(0.0021)

-0.0015(0.0017)

0.0018(0.0015)

0.0016***

(0.0004)

0.0021**

(0.0006)

0.0016(0.0020)

0.0057***

(0.0012)

0.0045*

(0.0018)

GoalkeeperAge -

0.1991***

(0.0544)

-0.1979***

(0.0269)

-0.2032***

(0.0295)

-0.1979***

(0.0482)

-0.1441***

(0.0244)

-0.1701**

(0.0661)

-0.2624**

(0.0855)

-0.2675***

(0.0433)

-0.1883***

(0.0338)

-0.1979***

(0.0380)

-0.3435***

(0.0459)

-0.3093***

(0.0803)

Save% 0.2765(0.1999)

0.1866(0.1329)

0.4405**

(0.1472)

-0.2021(0.2817)

0.2339(0.2737)

0.0055(0.5143)

0.7912(*)

(0.4418)

0.2407(0.3871)

0.5014(*)

(0.2571)

-0.1883(0.3571)

0.5757*

(0.2405)

-0.0854(0.5301)

AreaUnemployment -

0.0318***

(0.0096)

-0.0354***

(0.0036)

-0.0292***

(0.0088)

-0.0134(0.0112)

-0.0314***

(0.0097)

-0.0335*

(0.0132)

-0.0239(0.0177)

-0.0095(0.0089)

-0.0294***

(0.0077)

-0.0093(0.0116)

-0.0427***

(0.0121)

-0.0223*

(0.0096)

Theatre/Population 0.0121(0.0109)

0.0162***

(0.0037)

0.0198***

(0.0058)

0.0149(0.0190)

0.0191***

(0.0042)

0.0258*

(0.0127)

Movies/Population 0.0051(0.0062)

0.0227***

(0.0053)

0.0082(0.0232)

0.0212(0.0168)

0.0264(*)

(0.0155)

0.0319**

(0.0115)

Constant 1.5715(*)

(0.8945)

2.0480***

(0.3100)

0.7224***

(0.0744)

0.5168***

(0.0763)

0.4816***

(0.1525)

0.5951***

(0.1734)

0.8735*

(0.3535)

0.7482***

(0.0801)

121467***

(2051)

0.4875***

(0.1265)

1.1041***

(0.1460)

0.8615***

(0.1702)

Lambda 87297***

(2321)

144882***

(2048)

109024***

(2116)

79349***

(2382)

122252***

(2104)

75657***

(2476)

78554***

(2396)

103416***

(2200)

121467***

(2051)

113548***

(2154)

109518***

(2135)

73141***

(2466)Sigma 0.349

4***

(0.0023)

0.3495***

(0.0023)

0.3490***

(0.0023)

0.3493***

(0.0023)

0.3504***

(0.0023)

0.3512***

(0.0023)

0.3507***

(0.0023)

0.3510***

(0.0023)

0.3507***

(0.0023)

0.3515***

(0.0023)

0.3466***

(0.0023)

0.3470***

(0.0023)

Table 9: Stochastic frontier analysis, output measure is stadium capacity utilisation ratio, 10 seasons from 1990/91 to 1999/2000, and 12 teams, all variables is logs

The results in tables 8 and 9 confirm the importance of penalty minutes of forwards in explaining stadium capacity

utilisation ratio. A large penalty minutes figure seems to attract audience. However, the opposite is true with the

defencemen penalty minutes. A large figure is harmful for raising the attendance of home games. The plus/minus statistics

of 12 forwards and 7 defenders seems to be less significant than the same statistics for first line (3 forwards and 2

defenders).

All forwards and all defencemenForwards

Age -0.4016***

(0.0304)

-0.3880***

(0.0473)

-0.3846***

(0.0451)

#games -0.0297***

(0.0053)

-0.0252**

(0.0094)

-0.0254***

(0.0067)

#goals -0.0170***

(0.0016)

-0.0186(*)

(0.0098)

-0.0174***

(0.0008)

#assisted 0.1074*

(0.0510)

0.0798(0.0501)

0.0859(*)

(0.0510)

#points -0.0136*

(0.0063)

-0.0215(0.0205)

-0.0176**

(0.0056)

Penalty minutes

-0.0415(*)

(0.0238)

-0.0365(0.0315)

-0.0372(0.0323)

Plus/minus if positive

0.0120***

(0.0013)

0.0128***

(0.0015)

0.0128***

(0.0017)

0.0067***

(0.0012)

0.0064***

(0.0004)

0.0070***

(0.0008)

0.0074***

(0.0009)

0.0078(0.0062)

0.0074***

(0.0003)

0.0034(0.0145)

0.0045(0.0147)

0.0033(0.0146)

0.0102**

(0.0033)

0.0090(0.0069)

0.0077*

(0.0036)

0.0049(0.0051)

0.0038(0.0047)

0.0054(0.0050)

Plus/minus if negative (oppos.)

0.0115***

(0.0020)

0.0128***

(0.0023)

0.0128***

(0.0017)

0.0003(0.0026)

0.0003(0.0015)

0.0010(0.0019)

-0.0003(0.0005)

-0.0001(0.0066)

-0.0003(0.0003)

0.0114(0.0151)

0.0123(0.0155)

0.0110(0.0153)

0.0019(0.0039)

0.0010(0.0068)

0.0001(0.0022)

-0.0025(0.0054)

-0.0026(0.0045)

-0.0005(0.0050)

DefencemenAge -

0.2108***

(0.0146)

-0.2158***

(0.0267)

-0.2200*

(0.1039)

#games -0.0236***

(0.0035)

-0.0249***

(0.0039)

-0.0246***

(0.0026)

#goals -0.0125***

(0.0024)

-0.0113*

(0.0047)

-0.0125***

(0.0010)

#assisted 0.0410(0.0411)

0.0280(0.0416)

0.0300(0.0416)

#points -0.0018(0.0111)

-0.0099(0.0068)

-0.0157(0.0157)

Penalty minutes

-0.0057(0.0064)

-0.0131(0.0090)

-0.0130(0.0182)

Plus/minus if positive

0.0096***

(0.0007

0.0093***

(0.001

0.0092***

(0.001

0.0030***

(0.000

0.0028***

(0.000

0.0028***

(0.000

0.0020***

(0.0005

0.0022**

(0.000

0.0020***

(0.000

0.0116(0.0126)

0.0103(0.0123)

0.0101(0.0124)

0.0230**

(0.000

0.0024**

(0.000

0.0022***

(0.000

0.0005(0.0101)

0.0000(0.0019)

0.0003(0.0029)

) 1) 5) 3) 5) 4) ) 6) 8) 7) 9) 3)Plus/minus if negative (oppos.)

0.0004(0.0008)

0.0007(0.0013)

0.0009(0.0017)

-0.0035(*)

(0.0018)

-0.0026(0.0023)

-0.0026(0.0016)

-0.0036***

(0.0004)

-0.0042*

(0.0018)

-0.0037***

(0.0009)

0.0025(0.0124)

0.0014(0.0121)

0.0252(0.0121)

-0.0053**

(0.0019)

-0.0052*

(0.0024)

-0.0033(0.0037)

-0.0064(0.0103)

-0.0035(0.0045)

-0.0036(0.0056)

GoalkeeperAge -

0.2609***

(0.0380)

-0.2402***

(0.0509)

-0.2380***

(0.0430)

-0.2394***

(0.0465)

-0.2266***

(0.0452)

-0.2190***

(0.0411)

-0.2161***

(0.0088)

-0.2236***

(0.0450)

-0.2177***

(0.0040)

-0.1655(0.1268)

-0.2000(0.1313)

-0.1870(0.1300)

-0.1876**

(0.0671)

-0.2247***

(0.0503)

-0.2122***

(0.0093)

-0.1736***

(0.0510)

-0.1494**

(0.0583)

-0.1392(*)

(0.0768)

Save% 0.7055***

(0.2036)

0.5974*

(0.2778)

0.5857**

(0.2169)

0.3877(*)

(0.2287)

0.3440(*)

(0.1953)

0.2985(0.1920)

0.2414***

(0.0627)

0.2739(0.2789)

0.2446***

(0.0400)

2.1118(*)

(1.1334)

1.3517(1.0372)

1.5599(1.1193)

0.5138*

(0.2351)

0.3882(0.3286)

0.3049(0.2997)

0.4169(0.2965)

0.2616(0.3088)

0.2406(0.6167)

AreaPopulation -0.0025

(0.0023)

0.0015(0.0036)

-0.0006(0.0036)

-0.0532(*)

(0.0294)

-0.0153(0.0122)

0.0008(0.0055)

Unemployment

-0.0418***

(0.0012)

-0.0410***

(0.0011)

-0.0410***

(0.0029)

-0.0371***

(0.0019)

-0.0362***

(0.0024)

-0.0362***

(0.0021)

-0.0381***

(0.0032)

-0.0386***

(0.0036)

-0.0382***

(0.0004)

-0.0360(0.0371)

-0.0227(0.0369)

-0.0235(0.0375)

-0.0374***

(0.0039)

-0.0386***

(0.0078)

-0.0375***

(0.0013)

-0.0441***

(0.0100)

-0.0414***

(0.0125)

-0.0436*

(0.0192)

Theatre -0.0013(0.0032)

0.0024(0.0033)

-0.0019(0.0051)

-0.0196(0.0183)

-0.0048(0.0065)

0.0083(0.0077)

Movies -0.0007(0.0037)

0.0019(0.0020)

-0.0004(0.0009)

-0.0176(0.0174)

-0.0000(0.0115)

0.0058(0.0078)

Constant 2.9269***

(0.2222)

2.8065***

(0.2990)

2.7947***

(0.5025)

1.0354***

(0.2269)

0.9633***

(0.2338)

0.9394***

(0.1970)

0.8051***

(0.0539)

0.8506***

(0.1521)

0.8095***

(0.0250)

0.8655(0.6455)

0.5640(0.6373)

0.5057(0.6185)

0.9040***

(0.2262)

0.9386***

(0.1815)

0.8350***

(0.1760)

0.7837***

(0.1982)

0.6109***

(0.1971)

0.6143(*)

(0.3313)

Lambda 101620***

(2182)

77185***

(2433)

108074***

(2241)

83200***

(2370)

79625***

(2416)

91994***

(2272)

80089***

(2387)

98204***

(2302)

89016***

(2280)

3.8706**

(1.1204)

4.3346**

(1.6289)

4.2517**

(1.5827)

81292***

(2517)

99551***

(2293)

47311***

(3120)

88579***

(2603)

70581***

(2570)

69233***

(2595)

Sigma 0.3455***

(0.0023)

0.3456***

(0.0023)

0.3457***

(0.0023)

0.3499***

(0.0023)

0.3499***

(0.0023)

0.3497***

(0.0023)

0.3497***

(0.0023)

0.3496***

(0.0023)

0.3498***

(0.0023)

0.3072***

(0.0020)

0.3156***

(0.0021)

0.3149***

(0.0021)

0.3507***

(0.0023)

0.3509***

(0.0023)

0.3511***

(0.0023)

0.3506***

(0.0023)

0.3502***

(0.0023)

0.3503***

(0.0023)

Table 10: Stochastic frontier analysis, output measure is stadium capacity utilisation ratio, 10 seasons from 1990/91 to 1999/2000, and 12 teams, all variables is logs

All forwards and all defencemenForwards

Age -0.3948***

(0.0389)

-0.3818***

(0.0630)

#games -0.0169***

(0.0073)

-0.0148(*)

(0.0079)

#goals -0.0195**

(0.0075)

-0.0169**

(0.0063)

#assisted -0.0170(0.0186)

-0.0126(0.0155)

#points -0.0189(0.0110)(*)

-0.0155(0.0110)

Penalty minutes -0.0150(0.0253)

-0.0002(0.0116)

Plus/minus if positive 0.0123***

(0.0019)

0.0129***

(0.0029)

0.0059**

(0.0018)

0.0067***

(0.0002)

0.0084***

(0.0023)

0.0076***

(0.0007)

0.0079(0.0063)

0.0077*

(0.0036)

0.0078*

(0.0032)

0.0075(*)

(0.0042)

0.0035(0.0057)

0.0016(0.0019)

Plus/minus if negative (oppos.)

0.0124***

(0.0024)

0.0132***

(0.0028)

-0.0003(0.00263)

0.0013(0.0009)

0.0010(0.0025)

0.0000(0.0017)

0.0005(0.0013)

0.0010(0.0034)

0.0002(0.0039)

0.0002(0.0047)

-0.0035(0.0069)

-0.0032(*)

(0.0017)

DefencemenAge -

0.2478***

(0.0386)

-0.2347(0.1904)

#games -0.0230***

(0.0011)

-0.0250***

(0.0013)

#goals -0.0123***

(0.0017)

-0.0128***

(0.0033)

#assisted -0.0175(0.0116)

-0.0203**

(0.0071)

#points -0.0154***

(0.0035)

-0.0168***

(0.0042)

Penalty minutes -0.0123(0.013

-0.0259***

7) (0.0069)

Plus/minus if positive 0.0096***

(0.0011)

0.0092***

(0.0023)

0.0026***

(0.0002)

0.0025***

(0.0003)

0.0020***

(0.0006)

0.0020*

(0.0009)

0.0024(0.0027)

0.0022*

(0.0009)

0.0023**

(0.0009)

0.0021(0.0134)

0.0010(0.0026)

0.0011(0.0016)

Plus/minus if negative (oppos.)

0.0013***

(0.0002)

0.0130(0.0031)

-0.0019(*)

(0.0010)

-0.0012(0.0014)

-0.0040*

(0.0016)

-0.0034(*)

(0.0018)

-0.0030(0.0025)

-0.0017(0.0033)

-0.0037*

(0.0018)

-0.0028(0.0136)

-0.0017(0.0049)

0.0030(0.0026)

GoalkeeperAge -

0.2484***

(0.0470)

-0.2328***

(0.0670)

-0.2111***

(0.0244)

-0.1873***

(0.0330)

-0.2125***

(0.0233)

-0.2104***

(0.0468)

-0.2049***

(0.0482)

-0.1823***

(0.0499)

-0.2178***

(0.0279)

-0.2023***

(0.0613)

-0.1629*

(0.0670)

-0.1426***

(0.0356)

Save% 0.5787***

(0.1572)

0.5298***

(0.1556)

0.3740***

(0.0971)

0.1829(0.1388)

0.1785*

(0.0869)

0.2123(0.1637)

0.3524(0.4906)

0.2524(0.2799)

0.3084(0.2807)

0.2616(0.3292)

0.4404(0.6054)

0.1095(0.2847)

AreaUnemployment -

0.0405***

(0.0005)

-0.0405***

(0.0040)

-0.0352***

(0.0011)

-0.0346***

(0.0015)

-0.0384***

(0.0030)

-0.0380***

(0.0023)

-0.0367*

(0.0187)

-0.0358***

(0.0062)

-0.0378***

(0.0104)

-0.0371***

(0.0047)

-0.0357*

(0.0180)

-0.0343***

(0.0044)

Theatre/Population 0.0009(0.0033)

0.0073(0.0057)

-0.0038(0.0096)

0.0006(0.0098)

-0.0012(0.0085)

0.0134(0.0106)

Movies/Population -0.0001(0.0094)

0.0087*

(0.0040)

-0.0004(0.0052)

0.0050(0.0123)

0.0022(0.0090)

0.0377***

(0.0072)

Constant 2.9380***

(0.4043)

2.7999***

(0.8165)

0.8987***

(0.1002)

0.7979***

(0.1535)

0.7865***

(0.0821)

0.7765***

(0.1834)

0.8031***

(0.2094)

0.7128***

(0.1978)

0.8564***

(0.1169)

0.7928**

(0.2449)

0.6749*

(0.2822)

0.5680***

(0.1533)

Lambda 99310***

(2166)

78650***

(2446)

158672***

(1988)

107915***

(2142)

106717***

(2189)

90109***

(2299)

88143***

(2326)

63826***

(2669)

116868***

(2121)

64965***

(2856)

80349***

(2388)

122017***

(2076)Sigma 0.345

6***

(0.0023)

0.3456***

(0.0023)

0.3497***

(0.0023)

0.3496***

(0.0023)

0.3498***

(0.0023)

0.3496***

(0.0023)

0.3515***

(0.0023)

0.3519***

(0.0023)

0.3508***

(0.0023)

0.3510***

(0.0023)

0.3499***

(0.0023)

0.3484***

(0.0023)

Table 11: Stochastic frontier analysis, output measure is stadium capacity utilisation ratio, 10 seasons from 1990/91 to 1999/2000, and 12 teams, all variables is logs

Tables 10 and 11 use the statistics of all forwards (more than 12) and all defencemen

(usually 7 but also more than 7). The age, games played or goals scored of all

forwards seem to have a negative impact on stadium capacity utilisation ratio. The

plus/minus statistics of all forward players is significantly important and positive if

any the above variable (age, games, goals) is involved in the estimation. The same is

verified in the case of all defencemen. The age, games played or goals scores has a

negative impact on stadium capacity utilisation ratio. Since age, games played and

goals scored are positively correlated, they all measure the experience of a player

that seems to have a negative effect on attendance. This finding is in line with the

goalkeeper age that also has a negative coefficient.

The unemployment rate of the area where the ice hockey team has its home stadium

has a negative impact on stadium capacity utilisation ratio indicating that stadium

capacity utilisation ratio or the demand for an ice hockey game has probably a

positive income elasticity. The theatre or movie attendance in relation to population

have no or positive impact on stadium capacity utilisation ratio. These latter results

denote that ice hockey game demand seems to be positively income sensitive. If a

consumer has enough spare money to go to a cinema or theater, then the consumer

can also go to see an ice hockey game. Hypothesis H2B: “Ice hockey teams’

efficiency is related to other leisure activities offered in the town” receives some

support in the results presented in tables 6 to 11.

Hypothesis H1B: “Ice hockey teams in a small town have a higher efficiency in terms

of full stand” seems to be confirmed using the player characteristics of 12 forwards

and all defencemen (table 8). The area population variable is significantly negative. In

table 6 where the player characteristics are based on first line (3 forwards and 2

defencemen) talents the hypothesis is not verified. In table 10 where all forward

players (more than 12) and all defencemen talents are used to explain stadium

capacity utilisation ratio the results concerning the population variable are not

significant.

The goalkeeper save percentage is almost in each equation statistically significant.

Therefore that variable is used in the distance function the left hand side variable (

ln x¿). The λ statistics in tables 5 to 11 is extremely large indicating that inefficiency is

prominent, however the λ coefficient is implausible. The efficiency scores are huge

and implausible.

Finally the distance function approach is used to estimate the frontier and efficiency

scores. The equation below (16) is used in estimations.

(16 ) ln x¿=β0+∑n=1

N−1

βn ln( x¿

x¿)+¿∑

m=1

2

φm ln qmi+υi−ui ¿

The results of the estimations using only all forwards and defencemen talents as well

as area factors are presented in tables 12 to 16.

The distance function estimates have the correct sign, since the output measure

coefficients (φ1∨φ2 ¿are positive while the talent variables have a negative sign. The

points per game output measure coefficient (φ ¿¿1)¿ is significantly positive

regardless of which talent variable (age, games played, goals scored, goals assisted,

points achieved or penalty minutes) is used in the estimation. However, the second

output measure, stadium capacity utilisation ratio coefficient (φ2¿ is statistically

significant only if the talent variables are the ages of forward players and

defencemen (columns 1, 2 or 4 in table 12). The significance level is 10 percent, not

more. Plus/minus statistics measures are not significant. The goalkeeper’s age is

significant and it has the correct sign (negative). Theater attendance does not seem

to be significant but movies at a cinema variable seems to be significant and the

coefficient is positive indicating that cinema attendance is reducing the output of an

ice hockey team. The results propose that movies at a cinema attendance and ice

hockey games are interrelated. The theater attendance is not interrelated with ice

hockey which is plausible. They have a separate audience. The unemployment rate

has been controlled but the variable does not seem to be significant.

The plus/minus statistics is significant in the distance function approach estimation if

the talent variable is not age. In tables 13 to 16. Especially the negative plus/minus

statistics seems to explain nicely. The coefficient is negative showing that output

measures (points per game and “full arena”) and a negative plus/minus statistics are

positively interrelated. Perhaps the coach and the audience favour different outputs.

The coach seeks wins while the spectators favour outcome uncertainty (Rottenberg

1956).

We have many reasons to assume that theatre visitors and ice hockey game visitors

are two separate groups (Suominen 2013) and not overlapping, the results here

propose that they are not interrelated.

Average, log ( )

All forwards and all defencemen (25Nov2016)

ForwardsAge/GSave% -0.0615**

(0.0223)-0.0690**

(0.0219)-0.0673**

(0.0223)-0.0720***

(0.0214)-0.0725**

(0.0221)#games/GSave%#goals/GSave%#assisted/GSave%#points/GSave%Penalty minutes/ GSave%Plus/minus if positive/ GSave%

-0.0004(0.0009)

-0.0004(0.0009)

-0.0007(0.0009)

0.0001(0.0009)

-0.0007(0.0009)

Plus/minus if negative/ GSave%

-0.0011(0.0009)

-0.0011(0.0009)

-0.0013(0.0009)

-0.0005(0.0009)

-0.0014(0.0009)

DefencemenAge/GSave% -0.0477*

(0.0207)-0.0486*

(0.0209)-0.0455*

(0.0207)-0.0516*

(0.0207)-0.0464*

(0.0208)#games/GSave%#goals/GSave%#assisted/GSave%#points/GSave%Penalty minutes/ GSave%Plus/minus if positive/ GSave%

-0.0011(0.0008)

-0.0007(0.0008)

-0.0011(0.0008)

-0.0005(0.0008)

-0.0008(0.0008)

Plus/minus if negative/ GSave%

-0.0011(0.0009)

-0.0009(0.0008)

-0.0011(0.0009)

-0.0010(0.0009)

-0.0010(0.0008)

Goalkeeper Age/GSave%

-0.0245***

(0.0068)-0.0245***

(0.0068)-0.0221**

(0.0068)-0.0262***

(0.0065)-0.0216**

(0.0070)AreaPopulation/ GSave%

0.0043**

(0.0015)Unemployment/ GSave%

-0.0021(0.0026)

-0.0039(0.0027)

-0.0019(0.0026)

-0.0056*

(0.0027)-0.0030(0.0027)

Theatre/ GSave%

0.0014(0.0008)

Movies/ GSave%

0.0027**

(0.0009)Theatre/Pop /GSave%

-0.0008(0.0017)

Movies/Pop /GSave%

0.0045*

(0.0017)Points per game

0.0092*

(0.0036)0.0098**

(0.0036)0.0101**

(0.0036)0.0075*

(0.0038)0.0106**

(0.0036)Stadium capacity utilisation ratio

0.0092(*)

(0.0055)0.0088(*)

(0.0054)0.0083

(0.0054)0.0097(*)

(0.0051)0.0076

(0.0054)

Constant 0.2915***

(0.0829)0.3659***

(0.0756)0.3154***

(0.0778)0.4147***

(0.0734)0.3735

(0.0730)

Lambda 2.8189***

(0.7378)3.6219***

(1.0330)2.7292***

(0.7071)5.0639**

(1.8997)3.2174***

(0.9350)Sigma 0.0174***

(0.0001)0.0187***

(0.0001)0.0172***

(0.0001)0.0199***

(0.0001)0.0180***

(0.0001)Table 12: Stochastic frontier analysis, distance function approach, output measures are points per game

and stadium capacity utilisation ratio, 10 seasons from 1990/91 to 1999/2000 and 12 teams.

Average, log ( )

All forwards and all defencemen (25Nov2016)

ForwardsAge/GSave%#games/GSave%

-0.0025(0.0045)

-0.0016(0.0047)

-0.0027(0.0046)

-0.0011(0.0047)

-0.0021(0.0047)

#goals/GSave%#assisted/GSave%#points/GSave%Penalty minutes/ GSave%Plus/minus if positive/ GSave%

-0.0012(0.0010)

-0.0013(0.0010)

-0.0014(0.0010)

-0.0007(0.0011)

-0.0015(0.0010)

Plus/minus if negative/ GSave%

-0.0018(*)

(0.0010)-0.0020(*)

(0.0011)-0.0021*

(0.0010)-0.0014(0.0011)

-0.0022(*)

(0.0011)

DefencemenAge/GSave%#games/GSave%

-0.0068(*)

(0.0038)-0.0069(*)

(0.0039)-0.0064(*)

(0.0038)-0.0072(*)

(0.0040)-0.0065(*)

(0.0039)#goals/GSave%#assisted/GSave%#points/GSave%Penalty minutes/ GSave%Plus/minus if positive/ GSave%

-0.0018(*)

(0.0009)-0.0015(0.0010)

-0.0018(*)

(0.0009)-0.0014(0.0010)

-0.0016(*)

(0.0010)

Plus/minus if negative/ GSave%

-0.0018(*)

(0.0010)-0.0018(*)

(0.0010)-0.0018(*)

(0.0010)-0.0020(*)

(0.0010)-0.0018(*)

(0.0010)

Goalkeeper Age/GSave%

-0.0247***

(0.0074)-0.0234**

(0.0078)-0.0219**

(0.0074)-0.0252**

(0.0077)-0.0207**

(0.0077)AreaPopulation/ GSave%

0.0056***

(0.0017)Unemployment/ GSave%

-0.0007(0.0026)

-0.0026(0.0028)

-0.0007(0.0027)

-0.0037(0.0027)

-0.0017(0.0028)

Theatre/ GSave%

0.0015(0.0009)

Movies/ GSave%

0.0031**

(0.0009)Theatre/Pop /GSave%

-0.0012(0.0017)

Movies/Pop /GSave%

0.0044*

(0.0019)Points per game

0.0124**

(0.0040)0.0136**

(0.0042)0.0134**

(0.0041)0.0117**

(0.0043)0.0140***

(0.0042)Stadium capacity utilisation ratio

0.0086(0.0059)

0.0066(0.0059)

0.0073(0.0058)

0.0054(0.0057)

0.0057(0.0059)

Constant -0.0445(0.0428)

0.0075(0.0411)

-0.0223(0.0400)

0.0337(0.0387)

0.0141(0.0383)

Lambda 2.2126***

(0.4949)2.4688***

(0.5833)2.1337***

(0.4769)2.6405***

(0.6197)2.2039***

(0.5053)Sigma 0.0177***

(0.0001)0.0188***

(0.0001)0.0176***

(0.0001)0.0192***

(0.0001)0.0181***

(0.0001)Table 13: Stochastic frontier analysis, distance function approach, output measures are points per game and stadium capacity utilisation ratio, 10 seasons from 1990/91 to 1999/2000 and 12 teams.

Average, log ( )

All forwards and all defencemen (25Nov2016)

ForwardsAge/GSave%#games/GSave%#goals/GSave%

-0.0054(0.0034)

-0.0054(0.0036)

-0.0054(0.0035)

-0.0047(0.0036)

-0.0054(0.0036)

#assisted/GSave%#points/GSave%Penalty minutes/ GSave%Plus/minus if positive/ GSave%

-0.0008(0.0010)

-0.0009(0.0010)

-0.0011(0.0010)

-0.0004(0.0011)

-0.0011(0.0010)

Plus/minus if negative/ GSave%

-0.0017(*)

(0.0010)-0.0018(*)

(0.0011)-0.0020(*)

(0.0010)-0.0013(0.0011)

-0.0020(*)

(0.0011)

DefencemenAge/GSave%#games/GSave%#goals/GSave%

-0.0050*

(0.0024)-0.0048(*)

(0.0025)-0.0046(*)

(0.0024)-0.0049(*)

(0.0026)-0.0044(*)

(0.0025)#assisted/GSave%#points/GSave%Penalty minutes/ GSave%Plus/minus if positive/ GSave%

-0.0017(*)

(0.0009)-0.0015(0.0009)

-0.0017(*)

(0.0009)-0.0013(0.0009)

-0.0016(0.0010)

Plus/minus if negative/ GSave%

-0.0018(*)

(0.0010)-0.0018(*)

(0.0010)-0.0018(*)

(0.0010)-0.0020*

(0.0010)-0.0019(*)

(0.0010)

Goalkeeper Age/GSave%

-0.0216**

(0.0072)-0.0193*

(0.0076)-0.0191**

(0.0073)-0.0216**

(0.0076)-0.0176*

(0.0075)AreaPopulation/ GSave%

0.0058***

(0.0016)Unemployment/ GSave%

-0.0008(0.0026)

-0.0023(0.0027)

-0.0008(0.0026)

-0.0033(0.0027)

-0.0017(0.0027)

Theatre/ GSave%

0.0016(*)

(0.0009)Movies/ GSave%

0.0031***

(0.0009)Theatre/Pop /GSave%

-0.0010(0.0016)

Movies/Pop /GSave%

0.0045*

(0.0019)Points per game

0.0129**

(0.0040)0.0143***

(0.0042)0.0138***

(0.0040)0.0125**

(0.0043)0.0145***

(0.0041)Stadium capacity utilisation ratio

0.0076(0.0058)

0.0054(0.0059)

0.0063(0.0058)

0.0042(0.0057)

0.0047(0.0058)

Constant -0.0694(*)

(0.0363)-0.0183(0.0334)

-0.0447(0.0328)

0.0108(0.0300)

-0.0078(0.0302)

Lambda 2.0105***

(0.4375)2.0552***

(0.4600)1.9325***

(0.4184)2.2871***

(0.5199)1.9053***

(0.4157)Sigma 0.0170***

(0.0001)0.0178***

(0.0001)0.0169***

(0.0001)0.0184***

(0.0001)0.0173***

(0.0001)Table 14: Stochastic frontier analysis, distance function approach, output measures are points per game and stadium capacity utilisation ratio, 10 seasons from 1990/91 to 1999/2000 and 12 teams.

Average, log ( )

All forwards and all defencemen (25Nov2016)

ForwardsAge/GSave%#games/GSave%#goals/GSave%#assisted/GSave%

-0.0032(0.0033)

-0.0022(0.0035)

-0.0031(0.0034)

-0.0013(0.0035)

-0.0024(0.00359

#points/GSave%Penalty minutes/ GSave%Plus/minus if positive/ GSave%

-0.0011(0.0010)

-0.0013(0.0010)

-0.0014(0.0010)

-0.0008(0.0011)

-0.0014(0.0010)

Plus/minus if negative/ GSave%

-0.0019(*)

(0.0010)-0.0021(*)

(0.0011)-0.0022*

(0.0011)-0.0015(0.0011)

-0.0022*

(0.0011)

DefencemenAge/GSave%#games/GSave%#goals/GSave%#assisted/GSave%

-0.0055*

(0.0027)-0.0054(*)

(0.0026)-0.0051(*)

(0.0027)-0.0054(*)

(0.0029)-0.0049(*)

(0.0028)#points/GSave%Penalty minutes/ GSave%Plus/minus if positive/ GSave%

-0.0017(*)

(0.0009)-0.0015(0.0010)

-0.0017(*)

(0.0009)-0.0014(0.0010)

-0.0016(*)

(0.0010)

Plus/minus if negative/ GSave%

-0.0019(*)

(0.0010)-0.0019(*)

(0.0010)-0.0019(*)

(0.0010)-0.0022*

(0.0010)-0.0020(*)

(0.0010)

Goalkeeper Age/GSave%

-0.0218**

(0.0073)-0.0201**

(0.0077)-0.0193**

(0.0074)-0.0227**

(0.0077)-0.0182*

(0.0076)AreaPopulation/ GSave%

0.0060***

(0.0017)Unemployment/ GSave%

-0.0003(0.0026)

-0.0020(0.0027)

-0.0003(0.0026)

-0.0033(0.0027)

-0.0013(0.0027)

Theatre/ GSave%

0.0017(*)

(0.0010)Movies/ GSave%

0.0032**

(0.0009)Theatre/Pop /GSave%

-0.0011(0.0016)

Movies/Pop /GSave%

0.0046*

(0.0020)Points per game

0.0124**

(0.0040)0.0138**

(0.0042)0.0134**

(0.0041)0.0118**

(0.0043)0.0140***

(0.0042)Stadium capacity utilisation ratio

0.0095(*)

(0.0059)0.0069

(0.0059)0.0081

(0.0058)0.0055

(0.0057)0.0061

(0.0059)

Constant -0.0764*

(0.0368)-0.0238(0.0341)

-0.0510(0.0334)

0.0053(0.0310)

-0.0135(0.0310)

Lambda 1.8975***

(0.4060)2.0426***

(0..4493)1.8441***

(0.0041)2.3059***

(0.5125)1.8846***

(0.4056)Sigma 0.0169***

(0.0001)0.0179***

(0.0001)0.0169***

(0.0001)0.0186***

(0.0001)0.0174***

(0.0001)Table 15: Stochastic frontier analysis, distance function approach, output measures are points per game and stadium capacity utilisation ratio, 10 seasons from 1990/91 to 1999/2000 and 12 teams.

Average, log ( )

All forwards and all defencemen (25Nov2016)

ForwardsAge/GSave%#games/GSave%#goals/GSave%#assisted/GSave%#points/GSave%

-0.0047(0.0034)

-0.0041(0.0036)

-0.0046(0.0035)

-0.0031(0.0036)

-0.0041(0.0036)

Penalty minutes/ GSave%Plus/minus if positive/ GSave%

-0.0009(0.0010)

-0.0011(0.0010)

-0.0012(0.0010)

-0.0006(0.0011)

-0.0012(0.0010)

Plus/minus if negative/ GSave%

-0.0018(*)

(0.0010)-0.0019(*)

(0.0011)-0.0020(*)

(0.0011)-0.0014(0.0011)

-0.0021(*)

(0.0011)

DefencemenAge/GSave%#games/GSave%#goals/GSave%#assisted/GSave%#points/GSave%

-0.0055*

(0.0026)-0.0053(*)

(0.0028)-0.0050(*)

(0.0026)-0.0054(*)

(0.0028)-0.0049(*)

(0.0027)Penalty minutes/ GSave%Plus/minus if positive/ GSave%

-0.0017(*)

(0.0009)-0.0014(0.0010)

-0.0017(*)

(0.0009)-0.0013(0.0010)

-0.0016(0.0010)

Plus/minus if negative/ GSave%

-0.0018(*)

(0.0010)-0.0018(*)

(0.0010)-0.0018(*)

(0.0010)-0.0021*

(0.0010)-0.0019(*)

(0.0010)

Goalkeeper Age/GSave%

-0.0216**

(0.0073)-0.0196*

(0.0077)-0.0190**

(0.0073)-0.0222**

(0.0077)-0.0178*

(0.0076)AreaPopulation/ GSave%

0.0060***

(0.0016)Unemployment/ GSave%

-0.0004(0.0026)

-0.0020(0.0027)

-0.0005(0.0026)

-0.0034(0.0027)

-0.0014(0.0027)

Theatre/ GSave%

0.0017(*)

(0.0009)Movies/ GSave%

0.0032***

(0.0009)Theatre/Pop /GSave%

-0.0011(0.0016)

Movies/Pop /GSave%

0.0046*

(0.0019)Points per game

0.0128**

(0.0040)0.0142***

(0.0042)0.0138***

(0.0040)0.0123**

(0.0043)0.0144***

(0.0042)Stadium capacity utilisation ratio

0.0090(0.0058)

0.0066(0.0059)

0.0076(0.0058)

0.0053(0.0057)

0.0058(0.0058)

Constant -0.0652(*)

(0.0373)-0.0136(0.0348)

-0.0402(0.341)

0.0156(0.0319)

-0.0031(0.0319)

Lambda 1.9402***

(0.4171)2.0422***

(0.4520)1.8733***

(0.4000)2.3137***

(0.5199)1.8857***

(0.4076)Sigma 0.0169***

(0.0001)0.0178***

(0.0001)0.0169***

(0.0001)0.0186***

(0.0001)0.0173***

(0.0001)Table 16: Stochastic frontier analysis, distance function approach, output measures are points per game and stadium capacity utilisation ratio, 10 seasons from 1990/91 to 1999/2000 and 12 teams.

Average, log ( )

All forwards and all defencemen (25Nov2016)

ForwardsAge/GSave%#games/GSave%#goals/GSave%#assisted/GSave%#points/GSave%Penalty minutes/ GSave%

0.0017(0.0034)

0.0028(0.0036)

0.0019(0.0034)

0.0035(0.0036)

0.0026(0.0036)

Plus/minus if positive/ GSave%

-0.0017(*)

(0.0009)-0.0019(*)

(0.0010)-0.0020*

(0.0009)-0.0013(0.0010)

-0.0021*

(0.0010)

Plus/minus if negative/ GSave%

-0.0023*

(0.0010)-0.0025*

(0.0010)-0.0026*

(0.0010)-0.0019(*)

(0.0011)-0.0027*

(0.0011)

DefencemenAge/GSave%#games/GSave%#goals/GSave%#assisted/GSave%#points/GSave%Penalty minutes/ GSave%

-0.0074**

(0.0028)-0.0066*

(0.0029)-0.0072*

(0.0028)-0.0058*

(0.0029)-0.0066*

(0.0029)

Plus/minus if positive/ GSave%

-0.0018*

(0.0008)-0.0017(*)

(0.0009)-0.0017*

(0.0008)-0.0017(*)

(0.0009)-0.0017(*)

(0.0009)

Plus/minus if negative/ GSave%

-0.0017(*)

(0.0009)-0.0018(*)

(0.0010)-0.0017(*)

(0.0009)-0.0023*

(0.0010)-0.0018(*)

(0.0010)

Goalkeeper Age/GSave%

-0.0272***

(0.0072)-0.0254***

(0.0076)-0.0244***

(0.0073)-0.0263***

(0.0077)-0.0230**

(0.0076)AreaPopulation/ GSave%

0.0061***

(0.0016)Unemploymen

t/ GSave%-0.0009(0.0026)

-0.0029(0.0027)

-0.0012(0.0026)

-0.0040(0.0027)

-0.0023(0.0027)

Theatre/ GSave%

0.0017(*)

(0.0009)Movies/ GSave%

0.0033***

(0.0009)Theatre/

Pop /GSave%-0.0008(0.0016)

Movies/Pop /GSave%

0.0046*

(0.0018)Points per

game0.0114**

(0.0040)0.0122**

(0.0043)0.0125**

(0.0041)0.0100*

(0.0044)0.0126**

(0.0042)Stadium capacity

utilisation ratio

0.0081(0.0059)

0.0057(0.0058)

0.0066(0.0058)

0.0040(0.0055)

0.0048(0.0058)

Constant -0.0617(*)

(0.0357)-0.0136(0.0335)

-0.0363(0.0329)

0.0047(0.0313)

-0.0022(0.0313)

Lambda 2.6946***

(0.6174)2.8628***

(0.7128)2.6639***

(0.6306)2.7984***

(0.6657)2.6729***

(0.6646)Sigma 0.0183***

(0.0001)0.0193***

(0.0001)0.0184***

(0.0001)0.0195***

(0.0001)0.0188***

(0.0001)Table 17: Stochastic frontier analysis, distance function approach, output measures are points per game and stadium capacity utilisation ratio, 10 seasons from 1990/91 to 1999/2000 and 12 teams.

The distance function approach explaining both stadium capacity utilisation ratio and

points per game does not seem to perform nicely. The stadium capacity variable is

not significant in most equations since these both output variables are interrelated as

the results in table 5 reveal. However, the results using the distance function

approach is appropriate since the variable coefficients are reasonable. Circumstantial

variables, especially movies at a cinema attendance has an impact on ice hockey

teams’ outcomes. The player characteristics are important. Age, the games played,

goals scored, and plus/minus statistics seem to explain the outcomes: points per

game and stadium capacity utilisation ratio. Both outcomes are important from the

management view.

The population variable (Population/ GSave%) in the distance function approach

estimation is statistically positive indicating that hypothesis H2B is verified. Since the

ice hockey team output measures (points per game and stadium capacity utilisation

ratio) also have a positive sign but all of these three variables are on the right hand

side in the equation, the positive population variable sign shows that in a small town

the efficiency of the ice hockey team is higher. There are less other leisure activities

offered in that town and consumers have to go to an ice hockey game if they wish to

get any amusement during their leisure time.

Summary and conclusions

Research on the efficiency of professional ice hockey has not emphasised the role of

player characteristics in explaining winning percentage. These studies (Kahane 2005,

Kahane, Longley and Simmons 2013 or Mongeon 2015) have had only one target

variable, winning percentage or similar. However, most ice hockey must pursuit two

targets: winning percentage or point per game and stadium capacity utilisation ratio.

A high winning percentage has a positive impact on the demand for ice hockey games

and hence on stadium capacity utilisation ration. Spectators seem to favour a team

that has a nice points per game figure. However, since Rottemberg’s (1956) seminal

contribution the role of outcome uncertainty has been noticed continuously and

significantly. Spectators seem to prefer uncertain games, there is more interest

towards a fair game and a rather balanced teams. Since spectator fulfil the stadium

the role of full stand is important from the point of revenues to the team. There are

therefore two targets: winning percentage and a high stadium capacity utilisation

ratio. This study uses a distance function approach that allows us to have two targets

that measure efficiency.

A combination of stadium capacity utilisation ratio and points per game

simultaneously as the output variable in ice hockey has not been studied previously,

therefore this study contributes the literature by using a stochastic frontier analysis

and especially how the determinants of these two outputs relate to ice hockey team

targets. The data set covers seasons from 1990/91 to 1999/2000 of men’s highest

league teams in Finland. During that period there were 12 teams playing regular

season games. For each team the average age, the numbers of games played before

the beginning of the season (bbs), the number of goals scored (bbs), the number of

assists (bbs), the total points (bbs), the penalty minutes (bbs) and the plus/minus

statistics (bbs) of the first line forwards (3) of all forwards (12, lines 1 to 4), and all

forwards (likely more than 12) are counted. A similar variable set is calculated for

defencemen: 2 defencemen (1 line) and all defencemen. The age and the save

percentage (bbs) of the main goalkeeper is also used to explain the efficiency of the

ice hockey team. However, these variables are enough to explain stadium capacity

utilisation ratio, since the consumers have other leisure activities, like going to a see

a theater play or going to see a movie at a cinema.

First the stochastic frontier analysis is carried out using only one target variable:

points per game. The results show that the above mentioned player characteristics or

talents do explain points per game. Almost all talent variables are statistically

significant and they have a plausible and correct sign. The second stochastic frontier

analysis uses the second target variable: stadium capacity utilisation ratio. The

results propose that the talent related variables are significant but the sign is

different. While the goals scored (bbs) seems to increase winning percentage the

same variable seems to decrease stadium capacity utilisation ratio. The area

population seems to have a negative impact on the demand for ice hockey game

(stadium capacity utilisation ratio) indicating that a bigger town offers other leisure

activities, like theatre or movies at a cinema that diminish the demand for ice hockey

game. Spectators have other options to choose during their leisure time. The

circumstantial variables, like the population, the theatre or movie attendance have

been justified using a monopolistic competition model proposed by Dixit and Stiglitz

(1977). Two hypothesis are derived based on the model. H1B: ice hockey teams in a

small town has a higher efficiency in terms of full stand and H2B: ice hockey teams’

efficiency is related to other leisure activities offered in the town. These hypothesis

seem to be supported by the data and estimation results.

Finally a distance function approach with two target variables is estimated. The

approach does not work well. Only the points per game is significant is most

estimation models. The stadium capacity utilisation ratio variable is barely significant

but it is significant in a model where the age variables of forwards and defencemen is

the talent variable explaining two targets. The movies at a cinema in relation to

population variable is also significant in that model proposing that ice hockey and

movies are interrelated. Theater attendance is not related to ice hockey.

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Statistics from:

www.elokuvauutiset.fi

www.quanthockey.com

www.sm-liiga.fi

www.tinfo.fi