1
DETERMINANTS OF COMPETITIVE BALANCE IN THE NATIONAL HOCKEY
LEAGUE
Thomas Preissing
Department of Economics and Business, The Colorado College
Aju J. Fenn*1
Department of Economics and Business, The Colorado College
Economics and Business
Abstract
Abstract: Previous sports studies on competitive balance have focused on the
standard deviation of wins, but this paper uses a more sensitive measure of
parity. This paper calculates the deviations of the Herfindahl-Hirschman Index
of team points (dHHIp) for the years 1942-2002 in hopes of better understanding
the determinants of competitive balance for the National Hockey League. This
paper finds the three major factors affecting parity in the league are the
concentration of goals scored, the concentration of goals allowed, and the major
expansion of 1967-1968. Also of note, free agency was found to be insignificant
in determining competitive balance using the dHHIp model.
* Corresponding author: Aju J. Fenn, Department of Economics and Business, 14 E Cache La Poudre
Street, Colorado Springs, CO 80903. Phone: 719 389 6409 (voice), E-mail: [email protected]..
2
I. Introduction
One of the major appeals of professional sports is what is referred to as the
“uncertainty of the outcome”. In other words sports fans prefer to be uncertain of who
will prevail in a given game. This “uncertainty” goes hand-in-hand with competitive
balance. The more unpredictable the outcome of a sporting league’s events are, the more
competitively balanced that particular league is assumed to be. A perfectly competitive
league would be one where every team wins exactly half their games. Recently, a
concern for competitive parity in the National Hockey League has emerged. As
columnist Scott Taylor wrote,
Currently, the NHL has almost a dozen teams that will never win the Stanley Cup.
Because of the unworkable economic model, teams such as Nashville, Tampa, and
Atlanta can only hope to have the stars align as they did for Carolina last year
and, on a rare occasion, get to a final or maybe a conference championship.1
It is not in the National Hockey League’s best interest to have particular teams
winning or losing a disproportionate number of games from year to year. 2
In order for the NHL to develop increased competitiveness, it is important to investigate
the factors that affect the league’s parity. The purpose of this study is to examine the
determinants of competitive balance for the National Hockey League.
This paper will be the first to 3explore the determinants of competitive balance in
the National Hockey League using the Herfindahl-Hirschman Index (HHI). Section two
will examine previous research on competitive balance. Section three will describe the
data and model used, and section four will present the results of the regression analysis.
Finally, section five will discuss any conclusions that can be drawn as well as possible
pitfalls of this study.
3
II. Current Research on Competitive Balance
There have been a number of studies in the recent past that have looked at the
issue of competitive balance. Andrew Zimbalist (2002) recently wrote an article in the
Journal of Sports Economics that focuses not on competitive balance in any one
particular sport but looks at each of the four major professional sports leagues. He asserts
that the optimal level of balance in a sports league is “a function of the distribution of fan
preferences, fan population base, and fan income across host cities”.4 Zimbalist (2002)
discusses some of the more common ways of measuring competitive balance. The
methods include the Gini coefficient, the Herfindahl-Hirschman Index, the range of
winning percentages within a league, and standard deviation of winning percentage
within a league. Zimbalist (2002) suggests that factors like technology, playing
conditions, and playing rules are all influences on competitive balance yet almost
impossible to quantify.5 One of Zimbalist’s (2002) final points was that competitive
balance should be closely scrutinized due to the difficulty in assessing it.6
In the past few decades, there have been a number of more empirical studies done
involving competitive balance in Major League Baseball. Balfour and Porter (1991)
compare the variation of winning percentages of teams before and after free agency in
hopes of finding whether the reserve clause is necessary in professional sports to achieve
competitive balance.7 Their study finds that during free agency the variance of winning
percentages was actually lower than before free agency. Therefore, Balfour and Porter
(1991) reject the hypothesis that “the dispersion of winning percentage is higher with free
agency” and conclude that it “is indeed lower (i.e. that divisional races are closer) during
the period of free agency. It appears free agency promotes competitive balance.”8
4
In response to previous articles looking at competitive balance in Major League
Baseball, Michael Butler (1995) uses a regression equation to look at the “standard
deviation of a team’s winning percentage, and the season-to-season correlation of team
winning percentages over the period 1946-92.”9 His aim is to pinpoint the actual cause of
the increase in competitive balance by looking at free agency, a narrowing of team
market sizes, and a compression of baseball talent.10 When he examines competitiveness
within the season (the standard deviation of a team’s winning percentage), he finds only
the rookie draft to be statistically significant.11 However in season-to-season data, all
three of the factors in Butler’s equation are statistically significant.12
Brad Humphreys (2002) applies a novel approach when looking at competitive
balance in baseball using the Competitive Balance Ratio (CBR). He argues that,
although many other measures of competitive balance (like the standard deviation of
yearly win-loss records) are fine to use for specific years, the CBR is a more proficient
indicator of competitive balance.13 This is because CBR is able to pick up variations in
balance over time.14 Humphreys (2002) uses a ratio of average team-specific variation in
won-loss ratio during a number of seasons (over) the average within-season variation in
won-loss percentage during the same period. The ratio is a number between zero and
one, with one being perfect competitive balance over time and zero being no competitive
balance over time.15 Humphreys (2002) also finds that variations in the CBR over time
offer a better explanation than previous models of the variation in the attendance for
Major League Baseball.16
Danielle Carbonneau and Paul Sommers (1997) use the Gini index, normally used
for income or wealth distributions, to look at competitive balance in baseball. Their
5
findings agree with the majority of other baseball studies in that “the absences of
restrictions in baseball such as the reserve clause (does not) have a disruptive effect on
the evenness of the competition in Major League Baseball.”17 Martin B. Schmidt (2001)
also uses the Gini index when looking at competitive balance in MLB. In contrast to a
majority of the other studies on baseball, which have examined factors like the reserve
clause, free agency, or the rookie draft, Schmidt (2001) chose to investigate the effect
expansion has on competitive balance in Major League Baseball. 18 He concludes that the
“rise in competitive balance began with the movement toward expansion.”19
In one of the few articles focusing on the National Football League, Kevin Grier
and Robert Tollison (1994) look specifically at the effect of the rookie draft on
competitive balance. They find “higher draft choices raise winning percentages
significantly over time”20 and concluded that the rookie draft in the National Football
League helps advocate competitive balance.21
Fort and Quirk (1995) examine the effect of revenue distribution, the reserve
clause, salary caps, and the rookie draft on competitive balance for different professional
sports leagues.22 They come to the conclusion that “an enforceable salary cap is the only
one of the cross-subsidization schemes currently in use that can be expected to
accomplish (financial viability for weak-drawing markets) while improving competitive
balance in a league.”23 As with Kesenne (2000), Fort and Quirk (1995) argue that the
problem with a salary cap is proper enforcement because teams are not allowed to
maximize revenues with a salary cap.24 This discrepancy would naturally cause
management to look for loopholes, like deferred payment, in the cap.25
6
David Richardson (2000) is the first to use the National Hockey League as a focus
for exploring competitive balance. He finds the long-term trend leaned towards more
competitive balance in the National Hockey League when looking at winning
percentages, and he finds no significant patterns for playoff games.26 When looking at
the impact the entry draft had on competitive balance in the NHL, Richardson (2000)
finds some support that the draft helps maintain competitive balance in the league.27
The most relevant journal article for this paper is Craig A. Depken’s (1999)
study on the competitiveness of Major League Baseball. He uses a deviation of the
Herfindahl-Hirschman Index (HHI), which has previously been used to find the market
share of a firm in an industry, to account for competitive balance. 28 If the HHI measures
1/N (where N is the number of firms), then it can be assumed the league is perfectly
competitive.29 On the other hand, if the HHI equals one, it can be assumed there is no
competitive balance in the league.30
In Depken’s (1999) article, however, he points out that the number of firms in the
industry can skew the actual HHI.31 In other words, as the number of firms in the market
grows, the HHI will decline. Since there are expansion waves, the HHI will tend to
decrease. To fix this problem, Depken (1999) uses the dHHI.32 He finds that the
variation in parity has been decreasing over time.33 Depken (1999) also looks at the
effects of free agency in baseball, finding statistical evidence that free agency has
reduced equality in the American League, while having no significance in the National
League.34
In the studies on competitive balance in professional sports, the findings of the
reviewed material are not consistent. The conflicting conclusions probably stem from the
7
lack of a universal system for gauging competitive balance. The literature has different
findings for all sports regarding free agency, the amateur draft, and expansion of the
league. The next section will describe the adaptation of Depken’s model, which this
study will employ to examine the NHL.
III. The Empirical Model and Data
As its primary model, this study uses the deviation of Herfindahl-Hirschman
Index of points (dHHIp) to look at the competitiveness of the National Hockey League.
dHHIp = f(HHIgf, HHIga, Amateur Draft, Racial Integration, European
Influence, Expansion, World Hockey Association, Free Agency, Special
Expansion)
(3.1)
The dependent variable, dHHIp, is the deviation of the Herfindahl-Hirschman
Index of team points from the ideal distribution of points in any given time period. 35
Equations 3.2-3.4 are mathematical representations of the dHHIp.
dHHIp = HHIp −
N
1
, where
N
HHIp = ∑ (MS i ) , where
2
(3.2)
(3.3)
i =1
MS i =
POINTS OF TEAM i
TOTAL LEAGUE POINTS
(3.4)
8
where N is the number of teams or firms in the industry. MSi is the market share of the ith
firm, where market share is defined as points gained by a teami divided by the total
league points.
Independent Variables
Goals Scored (HHIgf) and Goals Allowed(HHIga)
HHIgf is the Herfindahl-Hirschman Index for goals scored, or the distribution of
goals scored. Equations 3.5-3.6 are mathematical representations of the HHIgf.
N
HHIgf = ∑ (MS i )
2
(3.5)
i =1
MS i =
GOALS SCORED BY TEAM i
TOTAL LEAGUE GOALS
(3.6)
On the other hand, HHIga is the Herfindahl Hirschman Index for goals allowed, or the
distribution of goals allowed . Equations 3.7-3.8 are mathematical representations of the
HHIga.
N
HHIga = ∑ (MS i )
2
(3.7)
i =1
MS i =
GOALS ALLOWED BY TEAM i
TOTAL LEAGUE GOALS
(3.8)
One would expect that the more concentrated goals scored become over time, the more
evenly distributed offensive talent in the league becomes, and the lower the HHIgf value
9
should be. It is expected, then, that as the HHIgf decreases, the dHHIp will become
smaller. In other words, the predicted sign of the coefficient for HHIgf is positive.
Similarly, one would expect that the more concentrated goals allowed becomes, the more
evenly distributed defensive talent is in the league, and as such will cause the HHIga
approach zero. Therefore, the predicted sign of the coefficient for HHIga is positive.
Amateur Draft (AD)
The dummy variable AD begins in 1963, when the inception of a rudimentary
form of the current Entry Draft was introduced.36 Years 1963 and after have a value of
one. Years before 1963 have a value of zero. The launch of the amateur draft in 1963
may have had a positive effect on competitive balance. Before the draft, NHL teams
could sponsor entire amateur teams and could sign any player from that team to a
contract.37 After the onset of the draft, teams were only allowed to pick individual
players, e.g. if the two best available players played on the same amateur team, two
different National Hockey League teams could draft these players (whereas in the old
system both players would have ended up playing for the same team). A testable
hypothesis is that the amateur draft would increase the level of competitive balance in the
National Hockey League. In other words, the expected sign of the coefficient for the
amateur draft is negative.
⎧1 if year ≥ 1963
AD = ⎨
⎩0 if year = otherwise
(3.9)
10
Racial Integration (RI)
In 1958, the first non-white hockey player entered the National Hockey League.38
The dummy variable RI equals one for every year after 1957 and zero for 1957 and
before. With the establishment of a racially integrated league, a larger labor pool would
theoretically be available for teams. Although it cannot be assumed that all teams would
necessarily integrate at the same time or rate, it can be expected that integration by all
teams would improve the overall quality of play. As Depken (1999) notes in his work,
“if all teams improved at the same absolute rate, then the poor quality teams (those with
lower winning percentages) would improve at a greater percentage rate than the preintegration teams of high quality.”39 Integration can therefore be expected to improve
parity, or decrease the dHHIp. Consequently the predicted sign of the coefficient for
racial integration is negative.
⎧1 if year ≥ 1958
RI = ⎨
⎩0 if year = otherwise
(3.10)
European Influence (EURO)
The European influence on the National Hockey League has been enormous in the
past few decades. The dummy variable EURO equals zero for every year through 1989,
and one for every year after. In the 1940’s and 1950’s there were only a handful of
European born and trained players in the National Hockey League. Although always
increasing slightly, the percentage of Europeans in the NHL stayed below 10 until 1990.
It was finally in 1990 that the percentage of Europeans in the NHL increased to over 10
percent. 31.6 percent of the National Hockey League is currently European and that
11
number continues to rise.40 The influx of Europeans has caused a major rise in the talent
pool, hopefully bringing more balance to the league (in form of more top-level players).
The anticipated sign of the coefficient for EURO is negative.
⎧1 if year ≥ 1990
EURO = ⎨
⎩0 if year = otherwise
(3.11)
Expansion (EXPAN)
As Depken (1999) points out in his Major League Baseball paper on competitive
balance,
Although the parity measure dHHI arithmetically accounts for the expansion of a
league, it does not control for any statistical influences of expansion on the
league’s competitive balance. Expansion teams are staffed with players drafted
from existing teams which are able to protect (supposedly high-quality) players
from being drafted. Thus, one may suspect expansion teams to be at a
competitive disadvantage.41
The disadvantage created by expansion may have more of an effect on parity than by just
calculating the dHHIp. In order to account for this, a dummy variable for expansion has
been added.42 In any year that a new NHL team starts play the dummy variable EXPAN
equals one; for all other years EXPAN is equal to zero. The predicted sign of the
coefficient for EXPAN is positive.
⎧1if year = 1968,1971,1973,1975,1980,1992,1993,1994,1999, 2000, 2001
EXPAN = ⎨
⎩0 if year = otherwise
(3.12)
12
World Hockey Association (WHA)
In 1972-73, the World Hockey Association (WHA) was established. It was the
first and only direct competition in North America that the National Hockey League
faced in the 20th century. The league lasted through the 1978-79 season before folding.43
Drawing upon the reasoning from the dummy variables for Europeans and racial
integration, the WHA took away from the talent pool in the National Hockey League.
WHA equals one for seasons 1972-73 to 1978-79 and zero for all other seasons. It is
expected that the inception of the World Hockey Association will cause a decrease in
parity. Therefore, the predicted sign of the coefficient for the WHA variable is positive.
⎧1 if year = 1973 − 79
WHA = ⎨
⎩0 if year = otherwise
(3.13)
Special Expansion (D68)
From 1942-43 until 1967-68, there were only six teams in the National Hockey
League.44 The league experienced its largest expansion ever during the 1967-68 season,
when six more teams were added to the league.45 Special consideration should be given
to this expansion, as the league doubled in size in one year. The dummy variable D68 is
equal to zero before the 1967-68 season and one thereafter. For reasons similar to the
expected effect of other expansionary years (in which the dummy variable EXPAN is
used), the expansion of 1967-1968 can be projected to have the same effect on parity. As
such, it is predicted that the major expansion in the 1967-68 season will cause an increase
in the dHHIp, which will make the league less competitive. Hence, the predicted sign of
the coefficient of D68 is positive.
13
⎧1if year ≥ 1968
D 68 = ⎨
⎩0 if year = otherwise
(3.14)
In some regression equations, D68 integrated with HHIgf and HHIga. The D68
variable is multiplied by HHIgf and HHIga, respectively, to account for a gap that
occurred in the two independent variables when the league expanded in 1967-68.
Combining D68 with HHIgf and HHIga allows for changes in the slope of the
independent variables. Examples of the dHHIp with the integrated D68 variable are
given in equation 3.15.
dHHIp = β 0 + β 1 HHIgf + β 2 HHIga + ... + γ 1 ( HHIgf * D68) + γ 2 ( HHIga * D68)
(3.15)
Free Agency (FA)
The dummy variable FA controls for the system of free agency currently in use by
the National Hockey League. FA equals one for years after the CBA (see footnote 14)
was ratified, and zero otherwise. With increased restriction on movement, it is assumed
that teams will be able to retain their top end players more easily. Hence, it will be more
challenging for the better teams to lure talent away from the bottom place teams,
hopefully increasing competitive balance. Therefore, the predicted sign of the coefficient
for free agency is negative.
14
⎧1if year ≥ 1995
FA = ⎨
⎩0 if year = otherwise
(3.16)
IV. Results
Table 4.1 is a summary of the OLS regression results for various regression runs
based on model one. The name of the variable is followed by a brief definition of it. A
dash through the cell indicates a variable that has been left out of that particular
regression.
15
Table 4.1
Variable
C
dHHIp(-1)
HHIgf
HHIga
FA
AD
EURO
RI
W HA
EXPAN
D68
YEAR
Definition
Constant
Lag variable for effects on parity
Concentration of offensive talent
Concentration of defensive talent
Dum m y for free agency
Dum m y for am ateur draft
Dum m y for European Influx
Dum m y for Racial Integration
Dum m y for W orld Hockey Association
Dum m y for expansion
Dum m y for expansion of 1967-1968
Tim e trend
HHIgf*D68 Allows changes in the slope of HHIgf
HHIga*D68 allows changes in the slope of HHIga
Model 1
Equation 1
Equation 2
Equation 3
0.2307
0.0081
-
Equation 4
-0.5294
(1.0464)
(0.0448)
-
(-3.5633)*
-
-0.1831
-
-
(-1.4266)
-
-
-
-1.1702
-0.9537
-0.1582
1.7547
(-5.5687)*
(-5.4748)*
(-1.1163)
(5.0122)
1.1776
0.9769
1.1688
1.3047
(5.7103)*
(5.6085)*
(8.4518)*
(10.6375)*
0.00001
-0.0004
-0.0004
-0.0001
(0.00176)
(-0.2417)
(-0.3434)
(-0.1136)
-0.0018
-0.0006
-0.0011
0.0019
(-0.9876)
(-0.3800)
(-0.8155)
(1.3703)
0.00003
-0.0009
-0.0005
-0.0003
(0.0140)
(-0.4734)
(-0.4396)
(-0.2618)
0.0028
-
0.0017
-
(1.4593)
-
(1.3969)
-
0.0014
0.0016
0.0011
0.0016
(1.0090)
(1.2061)
(1.0639)
(1.7741)
0.0003
0.0003
-0.00001
0.0001
(0.2355)
(0.3083)
(-0.0140)
(0.1387)
-
-
-
0.5097
-
-
-
(8.494 8)*
-0.0001
-0.000003
0.0000003
0.000008
(-1.0360)
(-0.0325)
(0.3762)
(0.1141)
-
-
-
-2.18 60
-
-
-
(-1.80 60)
-
-
-
-0.79 93
-
-
-
(-0.67 17)
R-squared
0.7109
0.6953
0.9989
0.8861
Adjusted R-squared
0.6507
0.6475
0.9987
0.8600
F-statistic
11.8051
14.5457
5789.080
33.9347
16
Table 4.1 (continued)
Variable
Definition
C
Constant
dHHIp(-1)
Lag variable for effects on parity
HHIgf
Concentration of offensive talent
HHIga
Concentration of defensive talent
FA
Dummy for free agency
AD
Dummy for amateur draft
EURO
Dummy for European Influx
RI
W HA
Dummy for Racial Integration
Dummy for W orld Hockey Association
EXPAN
D68
YEAR
Dummy for expansion
Dummy for expansion of 1967-1968
Time Trend
HHIgf*D68 Allows changes in the slope of HHIgf
HHIga*D68 Allows changes in the slope of HHIga
Model 1
Equation 5
Equation 6
-0.5047
-0.5139
Equation 7
-0.5294
(-3.3626)*
(-8.76580)*
(-3.5633)*
-0.1114
-
-
(-1.3848)
-
-
1.6262
1.7664
1.7547
(4.4880)*
(5.3305)*
(5.0123)*
1.3894
1.2987
1.3049
(10.1411)*
(11.9200)*
(10.6375)*
-0.0008
-0.0001
-0.0001
(-0.0691)
(-0.0943)
(-0.1136)
0.0017
0.0020
0.0019
(1.2164)
(2.0354)*
(1.3703)
-0.0003
-0.0003
-0.0003
(-0.2292)
(-0.2383)
(-0.2618)
-
-
-
-
-
-
0.0017
0.0016
0.0016
(1.8621)
(1.8215)
(1.7741)
0.0001
0.00009
0.0001
(0.1851)
(0.1288)
(0.1387)
0.5018
0.5109
0.5097
(8.3220)*
(8.7530)*
(8.4948)*
0.00000005
-
0.000008
(0.00005)
-
(0.1141)
-2.0905
-2.1912
-2.1860
(-1.7137)
(-1.8300)
(-1.8060)
-0.8442
-0.8035
-0.7993
(-0.7046)
(-0.6825)
(-0.6717)
R-squared
0.8888
0.8860
0.8861
Adjusted R-squared
0.8598
0.8628
0.8600
F-statistic
30.6485
38.0942
33.9347
Offensive Talent
In the first three equations, the results show the Herfindahl-Hirschman Index for
goals scored (HHIgf) has a negative impact on the model. In equations one and two,
HHIgf is significant at the 95% confidence level. The regression coefficient for equation
one is –1.1702 with a t-statistic of –5.5687. This result was puzzling, since the predicted
relationship between HHIgf and dHHIp is a positive one. However, once the structural
17
break due to the 1967-68 expansion is accounted for by multiplying HHIgf with the D68
variable, the coefficient value changes to positive. The HHIgf and D68 variables are
multiplied together to allow for changes in the slope of HHIgf. In the last four equations,
the HHIgf is significant at the 95% confidence level, and it exhibits a positive
relationship with dHHIp. These findings suggest that the concentration of offensive
talent in the National Hockey League has an effect on parity. However, HHIgf*D68 is
insignificant.
Defensive Talent
In all seven equations, the Herfindahl-Hirschman Index of goals allowed is
significant at the 95% confidence level. In addition, all seven coefficients possess a
positive relationship with the dHHIp. Using equation one as an example, the regression
coefficient for HHIga is 1.1776. Equation one also has a t-statistic of 5.7103. Similar
logic can be used for the other six model one equations in the same manner. These
findings imply that the defensive concentration of talent has an effect on parity in the
National Hockey League.
Player Mobility
The influence of free agency and the amateur draft on parity is also examined.
The current collective bargaining agreement deals a great amount with free agency and is
supposed to help alleviate some of the perceptions of the lack of competitive balance in
the league. This study has found free agency to be insignificant at the 95% confidence
level as a factor in determining the deviation from the ideal distribution of points
(dHHIp). Similar to free agency, the amateur draft is insignificant in six of seven
equations.
18
Talent Pool
Three dummy variables were added to help account for large or potentially large
changes in the overall talent pool teams have to draw from. Accounting for the infusion
of Europeans (EURO) into the National Hockey League is one of the talent pool dummy
variables. Six of the regressions have a negative regression coefficient, meaning that
since the number of Europeans in the National Hockey League has grown to over 10
percent, the dHHIp has decreased. Even though the coefficients are as predicted for the
EURO variable, all of them are insignificant. These findings suggest that the increased
participation by Europeans in the National Hockey League has not significantly affected
the equality level in the league.
A second dummy variable that accounts for a change in the talent pool is racial
integration (RI). Racial integration is used only in equation 1 and equation 3, and in both
cases their t-statistic is insignificant (at t-stat=1.4593 and t-stat=1.3969). The racial
integration variable is therefore dropped in the rest of the regressions. Compared to other
professional sports, hockey still has a very limited amount of integration.46 The
regression results for racial integration suggest that it has not had a major impact on
balance in the National Hockey League.
A dummy variable for the World Hockey Association (WHA) is the final variable
to account for a major change in the National Hockey League’s talent pool. For (WHA),
the regression coefficient matches the predicted sign, but again none of the equations
exhibit a significant t-statistic. Therefore, the WHA variable does not affect the parity in
the National Hockey League enough to be a noteworthy factor.
19
Number of Teams
Two dummy variables have been added to help account for the expansion in the
number of teams in the National Hockey League. The EXPAN variable is used in normal
years of expansion. 47 In six of the equations the regression coefficient for EXPAN
displays a positive relationship with the dependent variable, but they are all insignificant.
The insignificant t-statistics for EXPAN suggest that expansion is an insignificant factor
in determining parity in the National Hockey League.
The second variable used to account for the expansion of the league is D68.48 In
each of the four equations that included D68, all were significant at the 95 percent
confidence level. In addition, the predicted positive relationship between D68 and
dHHIp exists. In equation 5, for example, the regression coefficient is 0.5018 with a tstatistic of 8.322. This suggests that the expansion of the 1967-68 season has helped
cause a decrease in the parity of the National Hockey League.
Non-game Related Dummy Variables
In equations one and five, the lag variable dHHIp(-1) is included in the
regressions. This is done to show that lag effects for parity have been taken into account.
Neither of the two t-statistics is found to be significant, however, so the lag is dropped
from the other equations. A variable for year (YEAR) is also present in six of seven
model one equations. This precaution is added to account for certain things affecting
competitive balance that are not represented in the model. YEAR proves to be
insignificant in all six equations that it is represented in.
20
In the interest of being thorough, a second set of regressions was done using the
standard deviation for points as the dependent variable instead of the HerfindahlHirschman Index. A similar set of explanatory variables was employed, with the
difference being standard deviations for goals scored and allowed were substituted for the
HHI here as well. Results for the standard deviation model are presented in Table 4.2.
Table 4.2
Variable
C
DEVgf
DEVga
DEVp(-1)
FA
AD
EURO
RI
W HA
EXPAN
D68
YEAR
Definition
Constant
Concentration of offensive talent
Concentration of defensive talent
Lag variable for effects on parity
Dum m y for free agency
Dum m y for am ateur draft
Dum m y for European Influx
Dum m y for Racial Integration
Dum m y for W HA
Dum m y for expansion
Dum m y for expansion of 1967-1968
Tim e trend
Model 2
Equation 1
Equation 2
Equation 3
1.5877
-
-177.0445
Equation 4
1.4171
(0.8653)
-
(-1.3858)
(0.9332)
0.2737
0.2896
0.2764
0.2691
(5.3897)*
(6.4740)*
(5.4178)*
(5.7515)*
0.2134
0.2298
0.2107
0.2151
(5.9830)*
(8.3899)*
(5.8959)*
(6.5677)*
-0.0245
-
-0.0015
-
(-0.2961)
-
(-0.0173)
-
2.3419
2.8482
2.0695
2.0548
(2.1216)*
(2.2976)*
(1.4872)
(1.5536)
1.1485
1.2008
0.7361
0.4497
(0.8045)
(0.8523)
(0.5056)
(0.3597)
-
-0.1847
-1.4527
-1.2879
-
(-0.1625)
(-1.0204)
(-0.9655)
0.3595
0.5512
-0.5902
-
(0.3021)
(0.4770)
(-0.4297)
-
0.8458
0.3640
0.9930
0.9620
(0.7738)
(0.3672)
(0.8881)
(0.8993)
-0.1893
-0.2231
0.0413
0.0528
(-0.2375)
(-0.2762)
(0.0487)
(0.0651)
-2.7365
-3.0250
-4.1592
-3.8596
(-2.1137)*
(-2.4165)*
(-2.4261)*
(-2.6051)*
-
-
0.0914
0.0773
-
-
(1.3991)
(1.4340)
R-squared
0.7885
0.7877
0.7973
0.7986
Adjusted R-squared
0.7497
0.7544
0.7497
0.7623
F-statistic
20.3016
23.6533
16.8070
22.0279
In stark contrast to the model one equations, two of the four model two equations
find free agency to be statistically significant at a 95 percent confidence level. Moreover,
model two finds that free agency actually decreases the parity in the league. Although
21
the decrease in parity was not predicted, it is not entirely shocking. There seems to be no
continuity in the findings of the studies that look at the effect of free agency in
professional sports.
V. Conclusions
After analyzing the regression equations pertaining to the deviation from the ideal
distribution of points for the Herfindahl-Hirschman Index, some conclusions can be
made. In observing the regression equations, it is very apparent that the three variables
most affecting the dHHIp are the HHIgf, HHIga, and D68. Offensive and defensive
talent distribution are expected to be major factors in determining competitive balance.
As National Hockey League player agent Ben Hankinson stated, “The two most
important general game aspects of hockey are offense and defense.”49 Hankinson’s
statement seems to point out the obvious, since few would argue that defense and offense
are the two most important facets of the game of hockey. It therefore seems logical that
the more even the distribution of offensive or defensive talent is, the lower the dHHIp
will be. Hence, by creating more evenly distributed offense and more evenly distributed
defense the league will create better parity.
It also seems logical that when the National Hockey League doubled in size (D68)
in 1967-68, this would cause a decrease in league parity. The new expansion teams
would not have same resources as the original teams. Doubling the number of teams at
such a high level would also factor in the talent pool drying up, meaning that these new
teams would not get the same caliber players as the existing teams.
With regards to the unexpected results, the free agency (FA) variable was
surprising. Free agency has been the focus of many studies looking at competitive
22
balance. As previously stated, conclusions on the effects of free agency with regard to
competitive balance have been inconsistent. Similar to Fort and Quirk’s (1995) finding
for Major League Baseball,50 this study has shown that the current system of free agency
does not have an impact on competitive balance in the NHL. This information could
potentially be a used by the National Hockey League Players’ Association as leverage for
fewer player restrictions when the current collective bargaining agreement expires at the
end of the 2003-04 season.
In order to help determine factors in competitive balance within the National
Hockey League, the following should be analyzed: the offensive concentration of talent,
the defensive concentration of talent, and major expansion. Although free agency was
found to be insignificant in this study using the Herfindahl-Hirschman Index, a possible
combination of measures of competitive balance could potentially make free agency a
significant factor in competitive balance.
The National Hockey League and the National Hockey League Players’
Association would both benefit greatly if they were able to make the league more
competitively balanced. It would not only help the overall product of the game but also
create more interest in National Hockey League cities that currently have perpetually
losing teams. In the end, a more balanced league would also help generate more revenue
for NHL teams and, in turn, its players.
This research helps distinguish the determinants of competitive balance in the
National Hockey League. This is the first competitive balance study for the National
Hockey League that uses the Herfindahl-Hirschman Index as its basis for determining
parity. This study will hopefully act as a stepping-stone for future studies of the
23
determinants of competitive balance in the National Hockey League. Armed with the
knowledge of knowing how to improve parity, the league and its players could potentially
offer the public a superior National Hockey League product.
1
Scott Taylor, “New CBA era is crucial,” The Hockey News, 21 February 2003, 7.
2 The Stanley Cup is awarded to the National Hockey League’s playoff champion on a
yearly basis.
3
4 Andrew Zimbalist, “Competitive Balance in Sports Leagues: An Introduction,” Journal
of Sports Economics 3, no. 2 (May 2002): 111.
Allen Sanderson, quoted in Andrew Zimbalist, “Competitive Balance in Sports Leagues:
An Introduction,” Journal of Sports Economics 3, no. 2 (May 2002): 119.
5
6
Ibid., 120.
Alan Balfour and Philip K. Porter, “The Reserve Clause in Professional Sports: Legality
and Effect on Competitive Balance,” Labor Law Journal 41, no. 1 (1991): 8-18.
8 Ibid., 16.
9 Michael Butler, “Competitive Balance in Major League Baseball,” American Economist 39,
no. 2 (1995): 46-53.
7
10
11
12
Ibid.
Ibid., 49.
Ibid.
13 Brad R. Humphreys, “Alternative Measures of Competitive Balance in Sports
Leagues,” Journal of Sports Economics 3, no. 2 (May 2002): 133-148.
14Ibid., 133.
15
Ibid., 147.
16
Ibid.
Ibid., 165.
Martin Schmidt, “Competition in Major League Baseball: the Impact Expansion,”
Applied Economics Letters 8, no. 1 (2001): 21-27.
17
18
19
Ibid., 26.
20
Ibid., 298.
24
21
Ibid.
Rodney Fort and James Quirk, “Cross-Subsidization, Incentives, and Outcomes in
Professional Team Sports Leagues,” Journal of Economic Literature 33, no. 3 (1995): 1265-1300.
22
23
Ibid., 1282.
24
Ibid., 1266
25
Ibid.
26
Ibid., 405.
Ibid.
David Richardson, “Pay, Performance, and Competitive Balance in the National
Hockey League,” Eastern Economic Journal 26, no. 4 (Fall 2000): 393-418.
27
28
29
Ibid., 208.
Ibid.
David R. Kamerschen and Nelson Lam, “A Survey of Measures of Market Power,”
Rivista Internazionale di Scienze Economiche e Commerciali 22 (1975): 1131-1156, quoted in Craig A.
Depken. II, “Free-Agency and the Competitiveness of Major League Baseball,” Review of Industrial
Organization 14 (1999): 205-217.
30
31
dHHI = HHI – 1/N, where N is the number of firms (or teams) in the industry. This,
he says, measures the deviation from the ideal distribution of wins in any given time period.
32
33 Craig A. Depken II, “Free-Agency and the Competitiveness of Major League Baseball,”
Review of Industrial Organization 14 (1999): 209.
34
Ibid., 215.
As referred to in Chapter II, the dHHIp is used (as opposed to the HHIp) because as a
measure of concentration, the HHI will always decrease as the number of firms in the market
increase. It is therefore necessary to account for the influence of a change in the number of firms.
As such, the dHHIp = HHI – 1/N where n is equal to the number of NHL teams in the league.
35
36
Prior to 1963, NHL teams acquired player by sponsoring amateur players or teams. In
1963 the amateur draft was introduced to replace this system. Teams could select any amateur
player who would reach his 17th birthday between August 1st, 1963 and July 31st, 1964. Players
would then remain on the team reserve list until their 18th birthday, when contract negotiations
would begin. The name of the draft was changed to the NHL Entry Draft in 1979, and has
retained the name since. Under the current draft rules, a player must be 18 years of age by
September 15th of his draft year to be eligible.
36
An NHL team would pay an amateur team to become the amateur team’s sponsor.
The NHL team would then have the right to sign any player they wanted to off of that particular
team.
38
Willie O'Ree became the first black player in the history of the NHL when he played for
the Boston Bruins on January 18, 1958.
37
25
Craig A. Depken II, “Free-Agency and the Competitiveness of Major League Baseball,”
Review of Industrial Organization 14 (1999): 212.
40 Steve Hirdt, “Do the Math,” ESPN The Magazine, 17 February 2003, 16.
39
Craig A. Depken II, “Free-Agency and the Competitiveness of Major League Baseball,”
Review of Industrial Organization 14 (1999): 212.
41
Other than the original expansion in 1967-68, there have been 9 years of expansion. In
1970-71 franchises were established in Buffalo and Vancouver. In 1972-1973 franchises in Atlanta
(which moved to Calgary in 1980-1981) and New York (Islanders) were started. In 1974-1975
Washington and Kansas City (which moved to Colorado in 1976-1977 then to New Jersey in 19821983) were established. In 1991-1992 San Jose was established. In 1992-1993 franchises in Ottawa
and Tampa Bay were started. In 1993-1994 Anaheim and Florida were established. In 1998-1999
the Nashville Predators entered the league. In 1999-2000 a franchise in Atlanta was started. The
last expansion took place in 2000-2001, when franchises in Minnesota and Columbus were
established.
42
Upon the folding of the WHA in 1978-79, four franchises moved to the National
Hockey League, which was considered another year of expansion. Edmonton, Winnipeg (who
moved to Phoenix in the 1996-97 season), Quebec (who moved to Denver, Colorado in the 199596 season), and Hartford (who moved to North Carolina in the 1997-98 season) are all now
members of the National Hockey League.
44 The ‘original six’ as they are commonly called, are the Boston Bruins, Detroit Red
Wings, Montreal Canadians, Toronto Maple Leafs, New York Rangers, and Chicago Blackhawks.
43
Franchises were awarded for the 1967-68 season in Los Angeles, Philadelphia,
Pittsburgh, Saint Louis, Minnesota (who moved to Dallas in 1993-94), and Oakland (which
became defunct prior to the 1978-79 season, when they merged with the Minnesota franchise).
46 From “Pro Hockey and African Heritage, a Story,” available from
http://www.aaregistry.com; Internet; accessed on March 23, 2003. There are around 29 minority
hockey players in the National Hockey League (depending on the date as players can be
transferred to minor league affiliates at any time). This constitutes roughly 3.9% of the total NHL
population.
45
In this model, “normal” expansion is defined as years where only one, two, or three
teams were added to the National Hockey League.
47
As opposed to normal expansion, for the 1967-1968 season the NHL doubled in size,
going from six to twelve teams.
49 Vice President of SPS Hockey, Ben Hankinson, phone interview by author, 10 January
2003.
48
Rodney Fort and James Quirk, “Cross-Subsidization, Incentives, and Outcomes in
Professional Team Sports Leagues,” Journal of Economic Literature 33, no. 3 (1995): 1265-1300.
50