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SUPERSTARS
IN
THE NBA: ECONOMIC VALUE AND POLICY
Jerry A.
Hausman
Gregory K. Leonard
95-2
Sept. 1994
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
SUPERSTARS
IN
THE NBA: ECONOMIC VALUE AND POLICY
Jerry A.
Gregory
95-2
Hausman
K.
Leonard
Sept. 1994
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
MAR 2
9 1995
LIBRARIES
95-2
SUPERSTARS IN THE NBA: ECONOMIC VALUE AND POLICY
Hausman, MIT
Gregory K. Leonard, Cambridge Economics
Jerry A.
ABSTRACT
Two
competing arguments have been put forward regarding the extraordinary fan interest in
sports leagues. The first argument is based on the concept of "superstars," asserting that fan
interest is generated by the desire to see great players exhibit their skills. The second
argument, called "competitive balance," is defined as the condition that prevails when the
disparity between the best and worst teams in a league is not too great. We investigate the
effects of superstars on fan interest and the revenues of NBA teams. In particular, we
analyze the impact superstars have on attendance and television ratings and show that, in
addition to the effect they have on their own teams, superstars exert a tremendous positive
on other teams. The NBA and NFL have adopted salary cap policies
problems caused by the superstar externalities and maintain competitive balance.
externality
demonstrate that a salary cap
is
typically not the economically efficient
way
show
that the league should
impose a tax on superstar
salaries.
We
show
We
to achieve the
goals of competitive balance and the financial viability of small market teams.
distortionary than the salary cap.
to avoid the
Instead,
we
that the tax is less
Preliminary
Please
Do Not Quote
September 1994
Superstars
in
NBA: Economic Value and
the
Jerry A.
Gregory
Policy
1
Hausman, MIT
Leonard, Cambridge Economics
K.
Introduction
L
The major US
sports leagues are extremely popular with
billion to attend live professional sporting events
and
television advertisers
Two competing
reach viewers of televised sporting events.
is
skills.
in
loosely defined as the condition that prevails
league
is
not too great.
"Parity"
is
when
the part of the league's fans.
ratings,
and
outcome
of every
is
is
The
first
generated by the desire to see
called "competitive balance," has
2
is
the disparity between the best and worst teams
in
another word that
is
and
over $2.5 billion to
"Competitive balance"
labor
Leagues argue that competitive balance
balance, the argument goes, the
interest
The second argument, based on what
been put forward by sports leagues engaged
who spend
approximately $1.5
interest in sports leagues.
based on the concept of "superstars," asserting that fan
great players exhibit their
who spend
(but not necessarily mutually exclusive)
arguments have been put forward regarding the extraordinary fan
argument
consumers
is
antitrust disputes.
commonly used
vital to
game
to describe this condition.
a sport league's success.
is
in
a
With competitive
doubt, creating excitement and interest on
This excitement and interest translates into increased attendance, television
sports paraphenalia purchases,
all
of
which increase the revenues
Without competitive balance, the sports leagues claim
that fan interest will
existence of low revenue teams, or even the entire league.
In
of the league's teams.
wane, jeopordizing the
the labor and antirust disputes, the leagues
station WCN and the Chicago Bulls in their antitrust suit
The issues in this paper are not directly related to the issues in
the lawsuit. All views expressed are ours and not necessarily those of WCN and the Bulls. We thank Peter
Diamond for helpful discussions and Tomomi Kumagai, Karen Hull, and Ling Zhang for excellent research
1
The authors consulted
for
Chicago television
against the National Basketball Association.
assistance.
2
See, e.g., the recently litigated "McNeil" case.
have argued that league-instituted
restrictions
on player movement, such
agency, and the teams' ability to compete with each other, such as
and
as the draft
limits
territorial restrictions, are
on
free
simply ways
to maintain competitive balance.
The National Basketball Association (NBA)
As recently as the
attendance, and
however, the
late 1970's,
interest
little
NBA
is
currently the
had serious
model
difficulties
from the national television networks. 3
In
for a successful sports league.
with drug scandals, declining
1983, one year prior to the
ascension of David Stern to commissioner, an innovative collective bargaining agreement was reached by
NBA
the
and the
salary cap,
The agreement contained, among other
Players' Association.
and a guarantee from the teams
The resurgence of the
NBA
that the players
would receive
provisions, a drug policy, a
at least
53%
of gross revenues.
has frequently been attributed to the collective bargaining agreement with
provisions for improving competitive balance.
enact league policies similar to those of the
its
Indeed, the other sports leagues have recently begun to
NBA.
For instance, the National Football League (NFL) has
recently adopted a salary cap system.
70's
The collective bargaining agreement was not the only important
NBA
event to occur
1979, Larry Bird and Magic Johnson entered the
NBA
after
and early
80's.
In
NCAA
the 1979
Championship game, which
each other
in
in history.
Starting from that season, a succession of
Michael Jordan,
who
entered the
sport well-suited for the
wear headgear, only
development
five players are
addition, although basketball
The advantage
that
superstars have
had
NBA
NBA
in
is
in
NBA
is still
on the
floor at
the late
having played against
the highest rated college basketball
superstars
1984, to Shaquille O'Neal,
of superstars.
in
emerged-from
who
entered
in
Bird
and Magic
1992.
a team game, individual players can
players have over players from other sports
make
is
to the action.
The
last
game
do not
In
demonstrated by the success
NBA
obtaining endorsements.
of the
1980
NBA championship series was televised on tape delay at 1:30
NBA Finals, where each game was shown in prime time.
Contrast this treatment to the 1993
is
spectacular individual plays.
Recent developments suggest that superstars are more important than competitive balance.
3
to
Basketball
Players are highly visible to fans because they
any one time, and fans are close
game
1
pm.
The
a
1993
NBA
which featured Michael Jordan, averaged a 17.9 Nielsen
Finals,
television rating (meaning that
an estimated 17.9% of television households watched each game on average). The 1994
however, averaged only a 12.2 rating despite the presence of the
largest Nielsen market.
to
be contenders
for the
Although the
NBA
NBA was
New
NBA
Finals,
York Knicks, a team playing
in
the
well-balanced that season, with a number of teams thought
championship, Michael Jordan had retired and Larry Bird and Magic Johnson
were long since gone.
Thus, the superstar theory suggests
was orchestrating
NBA's
changes
structural
was due
revival
emergence
as a powerful alternative
Indeed, given the emergence of superstars
balance theory.
the
itself
of superstars.
in
the
way
seems quite plausible
superstars, regardless of competitive balance.
the revenues of
NBA
television ratings
teams.
and show
In particular,
We
we
NBA
at
the
to the competitive
same time
the league office
the league operated, a natural question to ask
to competitive balance, as
It
the
in
argument
is
is
whether
frequently asserted, or, alternatively, to the
that fans are
more
likely to
watch
investigate the effect of superstars
NBA games
on fan
with
interest
and
analyze the impact superstars have on attendence and
that, in addition to the effect
they have on their
own
teams, superstars exert a
tremendous positive externality on other teams.
We also
demonstrate that a superstar exerts a positive externality within his
commentators frequently discuss how true superstars "make the players around them
own
team.
better."
We
characterize this superstar effect as a form of increasing returns to scale or a positive externality.
effect
is
somewhat
poor substitute
different than the superstar effect
for superstar quality
analyzed by Rosen (1981).
Sports
This
There, average quality
is
a
and a few superstars can serve many consumers. Thus, superstars
receive large compensation and "produce" most of the good.
of the production technology, as described above.
Here,
we
are focussing on a different aspect
With the two types of
superstars, paying salaries to players equal to their marginal
externalities generated
by
revenue product could lead teams, especially
small market teams, into financial difficulties.
The
externalities
NBA
and NFL have adopted salary cap policies
and maintain competitive balance.
We
to avoid the
problems caused by the superstar
demonstrate that a salary cap
is
typically not the
economically
efficient
market teams.
the tax
is
way
Instead,
to achieve the goals of competitive balance
we show
less distortionary
The success
player salaries.
In
of the
should impose a tax on superstar
that the league
Draft,
NBA
over the
last
15 years has been
NBA
the 1991-1992 season, the average
amounts than the average
in
We
show
that
When
he retired
was about $3
accompanied by
player
a substantial increase in
was paid approximately
$1 million,
Superstar players, of course, are paid even
the early 1980's.
player.
Jordan's salary from the Chicago Bulls
1993-1994 season, Michael
prior to the
million per season and his professional earnings,
including endorsements, totalled about $35 million.
superstars, like Larry
salaries.
and Competitive Balance
about three times the average salary
greater
financial viability of small
than the salary cap.
The Salary Cap, the
IL
and the
In
the
last
several years, a
number
of
emerging
Johnson of the Charlotte Hornets, have received long term contracts with
total
payments amounting to nearly $100 million.
The
collective bargaining
league to impose on each
player salaries.
the players.
team a salary cap which
In return for this
concession, the
NBA
which put the team above the
toward the cap.
a draft pick), the
full
amount
If,
and the
limits the total
guaranteed that
cap."
of the salary
Only
O'Neal's services (assuming he were a free agent),
if
amount
53%
a "base"
the team can spend on
of gross revenues
amount
would go
its
to
current
of a current player's
to enter a contract with a free agent (or
would count toward the
For instance,
Players' Association allows the
a team can enter contracts with
on the other hand, a team wants
"raiding" the rosters of other teams.
4
NBA
Also, the salary cap system has a complication:
players at salary levels
salary counts
NBA
agreement between the
cap.
the Boston Celtics
their salary offer
Thus, the cap prevents teams from
wanted
would be
to obtain Shaquille
limited by the cap.
The
Teams have recently attempted to take advantage of this complication using so-called "one year and
Under such a contract, a team signs a free agent to a contract (at a salary under the cap)
out" contracts.
which gives the player the option of
at
a
much
higher salary,
now
free
unrestricted
agency after one
by the cap.
year.
At that time, the team can resign the player
Orlando Magic's
The
meet the
ability to
NBA
Celtics' offer,
however, would not be impeded by the cap.
has argued that the salary cap and the draft are necessary to create competitive balance
since teams have revenue streams that differ according to city size
TV
generated by the NBA's national
by a team
teams.
in its local territory,
such as
Thus, teams with large local
teams with relatively small
The
quality, as
NBA
contracts are shared equally
live gate, local
territories,
and other
among
the teams, the revenues generated
TV, and local radio, are not shared with the other
such as
New
may have
York,
higher revenue streams than
draft distributes entering talent to
teams according to descending order
measured by win-loss record. Thus, players entering the
NBA
limits the ability of the high
revenue teams. Thus, the
draft
ot existing
team
are not allowed to take their
which prevents high revenue teams (which may otherwise have
Meanwhile, the
a low draft position) from buying up the most talented players entering the league.
cap
While the revenues
such as Sacramento. 5
local territories,
services to the highest bidder, a restriction
factors.
salary
revenue teams from bidding away existing talented players from the low
and
salary cap are thought to allow small city teams,
revenue streams, to obtain and retain talented players which,
in turn,
which have lower
allows them to compete on the court
with large city teams.
Economists working
for the various players' associations
irrelevant for competitive balance
positions)
do not
when applied
to
major league baseball and,
the salary cap creates a transactions cost
must be
(a
Although
until recently, the
this
NFL,
6
We
it
does not apply to the
team's payroll cannot exceed the cap).
address the question of whether the salary cap
5
Of
6
Note, however, that economic inefficiency
some
(i.e.,
the draft
argument may have certain merits
is
NBA
because
Thus, the draft
salary cap does have the potential to increase competitive balance in the
support small market teams.
course,
that the draft
because the Coase theorem implies that the endowments
affect the final allocation of players.
combined with the
have argued
NBA
and
the most economically
small city teams like Portland have generated large revenue streams.
Michael Jordan's marginal value in Chicago was
Sacramento had drafted Jordan and the salary cap
had prevented Chicago from trading for him, the result might have been a loss in efficiency. Thus, we see
that the salary cap is most likely a way to transfer wealth from the players to the owners. These points are
also discussed by Quirk and Fort (1992).
likely greater than
it
would have been
in
results.
Sacramento.
If
way
efficient
to support small
market teams
in
the
last section.
In
the next
two
sections,
we measure
the
extent of the superstar effect on league revenues and attempt to determine the relative importance of
competitive balance.
The Superstar
III.
A
Effect
on League Revenues
superstar can have an impact on the revenues of his
superstar directly increases the quality of his
attracts
more
fans.
players around
superstar
him
may have
own
team.
own team
in at least
The increased quality
Second, the superstar indirectly increases the quality of
better.
his
three ways.
First,
the
team presumably
of the
own team by making
This indirect effect can be characterized as a positive externality.
the
Third, the
a "personal appeal" that attracts fans even after controlling for his team's (increased)
quality.
A
superstar will generally increase other teams' revenues as well as his
effect of the superstar
on other teams' revenues
receive the benefit, but
a positive externality
is
do not contribute towards paying the
in
own
team's revenues.
The
the sense that the other teams
superstar's salary.
In
what follows,
we
attempt to measure the size of the effect superstars have on various sources of team revenue.
Gate Revenue
A.
We
start
by estimating the
effect of a superstar
roughly estimated by comparing the team's
home
on
his
attendance
own
in the
team's attendance.
This effect can be
season prior to the arrival of the
superstar to subsequent seasons (assuming that the quality of the other players on the team remains the
same).
7
We
other teams'
subsequently estimate the effect a superstar has on other teams' revenues by comparing the
home
attendance for games against the superstar's team to their average attendance against
other teams. In estimating the superstar effects,
7
we
focus on
two
of the
most prominent
This analysis also does not fully account for any price increases that the teams
charge.
NBA
may be
superstars
able to
in
the 1980's, Larry Bird
Larry Bird
and Michael Jordan.
had a
NBA.
his
entrance into the
per
game was approximately
50%
no longer
10,000.
during the Bird era.
sell
viewed with some degree
In
number
out and the
at
the Boston Garden after
the 1978-1979 season, a year before Bird's arrival, the average attendance
In
Boston Garden was sold out for every
about
on the attendance of Celtics games
substantial impact
second season and
Starting in Bird's
game
(capacity
about 15,000).
is
lasting until his retirement, the
Thus, attendance increased by
the 1993-1994 season, the second since Bird's retirement,
of season ticket holders
of caution,
is
These comparisons must be
declining.
however, since the Celtic teams
home games
prior to Bird's arrival
and
after his
retirement have been of very different composition, apart from Bird, than the Celtic teams during his
career.
Like Larry Bird in Boston, Michael Jordan had a huge effect on attendance at Chicago Stadium.
The
was about 6,000 per game the season before Jordan
Bulls average attendance
attendance doubled
in his first
prior to Jordan's retirement
may be due
increase
year,
and every game
to a "championship" effect since the Bulls
home games have
Scottie Pippen
ticket holders
Bulls.
If
Jordan's
we
first
Chicago Stadium sold out during the
(Chicago Stadium holds about 18,000).
seasons ending with the 1992-1993 season.
retirement,
in
who was
may be
a
continued to
In
Of
course,
were the
NBA
the 1993-1994 season, the
sell out,
but team
Dream Team member and
unwilling to give up their seats
is
in
Average
arrived.
is still
first
some
we assume
seasons
of the attendance
champions
for the three
season after Jordan's
of high quality
and indeed
still
has
an All-Star player. Also, to some extent season
anticipation that Jordan might yet return to the
conservatively estimate the Jordan attendance effect by the increase of 6,000 per
year and
six
that the incremental tickets
were sold
at
game
in
the average ticket price, Jordan
increased the Bulls' gate revenue by about $8.6 million.
The
effect of a superstar
on the gate attendance of other teams can be measured by comparing the
attendance of the superstar's road games to average road attendance.
superstar's
team draws
better
the observed superstar effect
on the road than other teams.
may
In
other words,
we
ask whether the
Because stadiums have capacity constraints,
underestimate the potential superstar
effect.
Even
so,
we
find the
observed superstar effect to be quite
large.
Several facts point to the existence of a substantial Michael Jordan effect on road attendance.
the
1989-1990 season,
but one Bulls road
ail
game was
seasons, every Bulls road
sold out.
game was
Since
sold out.
NBA
8
In
In
the 1990-1991 and 1991-1992
teams' average attendance
is
less
than
full
stadium capacity, Jordan was certainly having an effect on other teams' attendance.
We examine
more
closely the attendance data for the 1989-1990 and 1991-1992 seasons to
estimate the size of the Jordan and Bird effects on attendance and gate revenue.
of Table
for
1,
games
we
give by
NBA
team the average 1989-1990 home attendance
against other teams.
The attendance
for Bulls
for
games was higher than
In
the
games
for
first
two columns
against the Bulls and
non-Bulls games for
every team except three (Detroit, Boston, Sacramento) where stadium capacity constraints were binding
even
for
non-Bulls games.
For
some teams,
the increase
doubled when. playing the
Bullets attendance almost
attendance went up by about
50% when
the attendance
was enormous. Washington
while the Indiana Pacers and
The
to the Bulls.
third
column
of Table
1
New
Jersey Nets
presents for each
Since a team's gate revenue
for
each game
not shared with the visiting team, the estimated incremental revenue accrued directly to the indicated
Thus, Washington, a team that has not had a good win-loss record
team.
additional
$250,000 due
to having the Bulls
across teams, the incremental revenue
the Bulls
is
$2.5 million.
due
8
to the Bulls
is
visit their
New
some
time, received an
stadium once a year.
estimated to be $1.6 million.
of incremental
The incremental revenue
and $2.1 million respectively.
The
in
revenue
for
Summing
Table 2 presents
other teams due to
Tables 3 and 4 present information on the Celtics' incremental attendance effects
the 1989-1990 and 1991-1992 seasons.
million
and Michael Jordan
1991-1992 season. The estimate
similar information for the
in
Bulls,
playing the Bulls.
team an estimate of the incremental revenue due
is
in
Jersey (Exit
16W) Nets were
the single "offender".
8
effects are estimated to
be $1.4
Superstar Effect on Television Ratings
B.
addition to being a draw for gate attendance, superstars
In
games, raising the television ratings of these games. Thus,
constant, television ratings are higher for
games
we
may draw
Among
featuring a superstar.
NBA game
of the telecast types are "national" in nature while the other
the factors that can be held
compare the
showing a game involving "good" teams versus showing
There are four types of telecasts through which an
two are
a
cable network, which
OTA
"local
telecast".
9
Finally, the
The NBA, acting
packages.
teams.
game might be
Such a
involved by a local cable outlet.
as agent for the
is
teams have contracts
The
NBA
can be televised.
"local."
for
national) of
First,
any other
involving a superstar.
the
Two
game could be
currently the National
outlet
NBAs
Such a broadcast
telecast locally in the territory of
is
national
one
teams
of the
OTA
and national cable
national network contracts are divided equally
its
called a
is
called a "local cable telecast".
own
local cable
is
given
first
and
local
OTA
among
packages.
the
Most
NBA
NBA game
NBA
restrict
the
manner
in
which
NBA games
choice of which games to televise and shows about 20-25 regular
weekend
within two hours of an
telecasts.
League rules prohibit the
afternoons.
TNT
is
NBC
telecast.
Thus,
NBA
telecast (local or
on
NBC
telecasts face
given second choice of games and shows about 51
Several teams, notably the Chicago Bulls and Atlanta
Hawks, have
local broadcast outlets
which are
Superstations are local channels whose signal is picked up by a third-party
and sent via sattelite to local cable systems throughout the US. Thus, Bulls games shown locally on
and Hawks games shown locally on WTBS end up being transmitted to other parts of the country.
also so-called "superstations".
carrier
OTA
has instituted a number of league rules which
NBC
is
for
both types of television distribution.
no competition from other
WCN
local
27 teams, negotiates the national
responsible for negotiating
season games per season, mostly on
9
telecast
The revenues derived from these
Each team
importance
Network Television (TNT). Third, the game might be broadcast
one of the teams involved by a
locally in the territory of
game
Second, the game might be telecast nationally on the
currently Turner
is
relative
can reach television viewers.
broadcast nationally on the NBA's national over-the-air (OTA) network, which
Broadcasting Corporation (NBC).
NBA
investigate whether, holding other factors
constant are the qualities of the teams involved, which allows us to
television ratings of
viewers to televised
regular season
games per season, mostly on Tuesday and Friday
season, a league rule
was
which
instituted
TNT. However, teams are
night as
competing
NBA
telecasts.
of
superstars
TV
on the
OTA,
national
Finals.
Thomas
teams can choose how to allocate
OTA
national cable, local
and cable
differ in
of the Pistons.
in
10
maximum
When
of 41.
to analyze the impact of
games. The data include information on a large number of
OTA, and
local cable telecasts.
is
A
In
our analysis,
the 1991-1992 season, the Bulls
the previous season's Finals.
In
the
1989-1990 season, the Detroit
Local
OTA
We
is
its
games
game may be
and the
focus on these three superstars, plus Isiah
were the defending champions, having
investigate the
way
stature as a superstar
are defined by Nielsen
its
in
which the two seasons
Designated Market Area
called a "local over-the-air telecast".
the source for
defending champions and "bad boys"
DMAs
we
locally into
the broadcast by Boston independent channel
Thomas'
the previous season's
Ratings
a team broadcasts one of
single
in
effects.
local broadcast station, the telecast
telecast
their
a league rule limits the
Bulls featured Michael Jordan, the Boston Celtics featured Larry Bird,
In
terms of superstar
2i
"
However,
1989-1990 and 1991-1992 seasons
NBA
or
given only limited protection from
telecasters.
over-the-air to a
ratings data from the
The Chicago
OTA
local
ratings of televised
defeated the Lakers
,0
locally, via either
Given the selection by NBC,
Los Angeles Lakers featured Magic Johnson.
game.
own games
were the defending champions, having defeated the Los Angeles Lakers
Pistons
NBA
use
their
on the same
is
televising a
games which can be shown
We
allowed to telecast
NBA games
TNT
is
remaining games between their local
number
prohibits superstations from telecasting
1990-1991
game. Thus,
same time TNT
cable, at the
still
Starting with the
nights.
two
local
WLVI
OTA
may not have been as
may have had appeal
December
of the
telecasts,
5,
of a local
using a
OTA
1989 Celtics-Charlotte
one by each team
in its
respective
great as the other three, but the Pistons as
as a team.
and generally encompass
10
An example
(DMA)"
a city
and
its
environs.
DMA. 12
In this case,
each with
telecasts
The
rating.
have data on 608 local
New
data, except for the
We
we
game
is
At
least
we
because
OTA
local
OTA
local
telecasts.
NBA
from each
telecast
telecasts.
have panel data (more than one game
4
For the 1991-1992 season,
team
included
is
we
played,
control for
by television programmers
because some viewers
Third,
NBA
we
may
to
day of the week, month,
OTA
the fraction of the
TNT
(or
start
be unwilling to forego sleep
TNT
or superstations
telecast that
NBA
is
the
13
each telecasting team),
game
we
include a
WGN
telecast.
Start time, in particular,
is
ratings, with "late starts" getting
considered
lower ratings
for televised basketball.
and
NBA
WTBS
To account
overlapped by the
the superstation) into the local
time of the telecast, and the rating of the
telecast.
be an important determinant of
providing viewers with an alternative
penetration of
game
control for the presence of "competing"
cablecaster
for
in
Second, because viewer availability can vary depending on when
half-hour on the telecasting station leading into the
national
one
York Knicks which had no
fixed effect for each telecasting team.'
the
1989-1990 and 1991-1992 seasons were obtained from
have data on 598
telecasts.
telecast observations in the data,
considered the observable factors which might determine the rating received by a
First,
telecast.
OTA
OTA
would represent separate
ratings data for the
For the 1989-1990 season,
Nielsen.
we
own
its
two
the
TNT
DMA.
particularly important for superstations since, for instance,
telecasts. Telecasts of
NBA games
can overlap with the local
for these
competing
OTA
telecasts,
(or superstation) telecast
telecast,
we
interact
with the cable
Controlling for channel penetration
WGN
by
is
has limited penetration into certain parts
of the country such as the northeast.
Fourth,
percentage.
we
control for the effect of the opponent's quality by including the opponent's win/loss
Finally,
we
account
for the superstar effect
by including four indicator variables
12
Or, of course, two local cable telecasts, or one local cable and one
13
The Knicks
telecast locally over
M Because the
New
MSG, which
York and Los Angeles
telecasting teams, not the
is
DMAs
DMAs.
11
OTA
that indicate
telecast.
a cable channel.
each have two teams, the fixed effects are
for the
whether the opponent's team
means
is
the Celtics, Bulls, Lakers, or Pistons respectively.' 5
of the variables used in the
The cable household
model by season.
television rating reported by Nielsen
households with televisions tuned to the game divided by the
DMA.
Thus, the rating
is
the left-hand-side variable,
rating
R
of team
i;
i's
bounded between zero and one.
we
game
j,
conditional on X
E(Rg\X
that vary across
i;
and
,
team and game,
a,
;j
FO
is
a cumulative distribution function.
parameters
in specification (1)
TV
defined as the number of cable
number
of cable
TV households
in the
order to account for this characteristic of
In
a,
16
(D
= F(Xy{l + a,)
)
9 ai
-
In
total
is
specify the following functional form for the expectation of the television
telecast of
where X are the variables
Table 5 gives the
is
the fixed effect for telecasting team
what follows, we assume the
7
logit cdf.'
We
i,
and
estimate the
using quasi-maximum likelihood where the likelihood for an observation
is
specified as the Bernoulli likelihood
L, = [F(Xyfi
+ a )]*>
The quasi-maximum likelihood estimates (QMLE)
expectation
(1) is
correctly specified even
variance-covariance matrix of the
'
5
Of
effect) that
QMLE
if
of
-
[1
(3
and the
a, are consistent as
the Bernoulli specification
estimates
is
long as the conditional
(2) is incorrect.'
estimated maintaining only
first
8
might be present
after controlling for win/loss
17
The use
of the normal cdf leads, of course, to similar results.
18
There
no
is
incidental parameters
fixed while the
number
more
(e.g.,
details regarding this
approach.
problem with fixed effects here because the number
team is assumed to go to infinity.
of observations per
12
a Celtics
percentage.
See Papke and Wooldridge (1993)
for
The asymptotic
moment assumptions
course, the superstar effect cannot be identified separately from any team effect
,6
assumed
(2)
F(Xft + a^-**
of
teams
is
(1)
without any additional second
moment
assumptions.
The 1989-1990 Local
a.
For reasons discussed further below,
we have
data.
The estimated
surprising result
coefficient
is
we
OTA
Results
estimate separate models for the two seasons for which
1989-1990 season are provided
coefficients for the
in
the relative unimportance of the opponent's win/loss percentage.
on win/loss percentage
only 0.047 and a
is
t-test
mean
of the data, a rating increase of only
2% would
were playing against an opponent with a 0.750 win/loss record instead
The
coefficients
on the superstar team
dummy
increase), while the Michael Jordan
Magic Johnson has the
largest effect
The other variables
commonly
held
in
in
the sports
on
TV
We
find that Isiah
ratings, raising
Late starts
Telecasts in
December
do not have very precisely estimated impacts on
that Saturday
is
The 1991-1992
Thomas
on
zero.
ratings.
the telecasting team
and
The
and they are
large
has only a small effect on ratings
ratings
by
24% and 21%
respectively.
them by 31%.' 9
do poorly
November
relative to earlier starts, with a 7-7:30 start
(the
opening month of the season) receive
receive the lowest ratings.
ratings,
although the result
The day
for
of the
Saturday
is
week
variables
consistent with
a poor night for television ratings generally and sports telecasts in particular.
b.
19
effect
is
it
0.250 win/loss record.
variables are estimated to be positive
and Larry Bird increase
industry.
the highest ratings, while telecasts in
view
of a
if
little
that
the model generally have an impact on ratings consistent with the beliefs
receiving the best ratings on average.
the
result
One
The estimated
superstar effects, on the other hand, are quite important determinants of ratings.
estimated with a high degree of precision.
(8%
6.
does not reject the hypothesis
Thus, controlling for superstar effects, the quality of the opponent appears to have
For instance, at the
Table
OTA
The 1991-1992 Local
OTA
results are given in Table 7.
These estimates of percentage increase
in rating
the underlying data.
13
Results
In
some ways,
these results are similar to the
are calculated from the estimated coefficients and
1989-1990
results.
The 7-7:30
among
time again receives the highest ratings
start
telecasts receive higher ratings than other
months, and Saturday
is
start
times,
November
not a particularly strong night for
Also, the opponent's winning percentage again has a small and imprecisely estimated impact on
ratings.
ratings.
However, the estimated
The
results.
much
Bulls with Michael Jordan
On
1989-1990 season.
effect in the
are
superstar
now
it
effects differ substantially
increase ratings by
smaller than their 1989-1990 effects (5% each).
was usually
in great
from those
45%, which
is
in
the 1989-1990
even higher than the Bulls
the other hand, the 1991-1992 effects for the Celtics and the Lakers
Johnson had retired and Larry Bird played
play,
team
in
The explanation
only 45 of 82 games
pain and with lessened effectiveness.
1991-1992 season essentially without
in
the 1991-1992 season.
that
Magic
When
he did
is
Thus, the Celtics and Lakers played the
which reduced
their superstars,
for the difference
their viability as television
attractions.
The 1989-1990
results
and the
1991-1992
Bulls
result suggest the
The comparison between the
superstar effect, controlling for the quality of the opponent.
two seasons provides even more evidence
that superstars
that the estimated superstar effect applies to the local
Since a team's local
crucially
TV revenues
on season average
have a substantial
OTA
ratings of
are not shared with the other teams
ratings,
presence of a powerful
effect
on
ratings.
teams other than the
20
,
results for the
We
note
superstar's.
and television revenues depend
teams with superstars produce a large positive externality
for
teams
without superstars.
2.
When
Local Cable Ratings
a team telecasts locally into
sports network), the telecast
distribution
December
20
is
by SportsChannel
6,
its
DMA
using a local cable network
called a "local cable" telecast.
New
England
(a
regional sports network)
1989 Celtics-Knicks game. As with
Aside from a payment of
6%
to the
An example
NBA
local
instance, a regional
of a local cable telecast
is
the
the Boston area of the
OTA, we obtained from Nielsen
league office.
14
in
(for
ratings data for
1989-1990 and 1991-1992 seasons. For the 1989-1990 season, we have 583
local cable telecasts in the
we have 654
observations, while for the 1991-1992 season,
NBA
teams appear
the local cable dataset.
in
As with the
local
according to equation
day
of
week, month,
OTA
The
(1).
model, the conditional expectation
local
OTA
cable rating
8.
is
specified
specification includes fixed effects for the telecasting teams; variables for
Note
Means
in
the
1989-1990 season).
regional sports networks are typically on an upper
tier
on
One
NBA
telecasts;
of the variables used in the
average rating of a local cable telecast
that the
(2.9% versus 6.2%
telecast
for the local
time, and rating of the lead-in program; controls for competing
start
Table
in
seventeen of the 27
for
21
opponent's winning percentage; and the superstar effect variables.
model are given
Data
observations.
is
well below that of a
reason for the lower rating
is
that
local cable systems, requiring subscribers to
pay
an extra fee to receive the service.
The 1989-1990 Local Cable Results
a.
The
results of the
from the local
OTA
1989-1990
In contrast to
results.
model, given
local cable
the local
by the win/loss percentage, leads to higher
OTA
in
Table
The estimated
effect of
to increase the rating
by 17%.
ratings for a local cable telecast.
much
less
is
important here than
in
estimated Bulls/Jordan effect has a relatively large magnitude, leading to a
results for the
the local
20%
OTA
1991-1992
30%. However,
opponent's win/loss percentage
21
Only
the
increase in rating.
local cable
model are given
in
Table 10.
As with the 1989-1990
season, of the superstar effects, only the Bulls/Jordan effect has a sizable magnitude.
increase ratings by
model.
On
The 1991-1992 Local Cable Results
b.
The
important ways
model, a higher quality opponent, as measured
increasing the opponent's win/loss percentage from 0.250 to 0.750
the other hand, the superstar effects are
9, differ in several
Some NBA teams do
is
the effect
is
estimated somewhat imprecisely.
The Bulls/Jordan
The
coefficient
on the
estimated to be only half as large as the 1989-1990 coefficient.
not have a local cable contract and thus
15
do not have
local cable telecasts.
more support
Nevertheless, these results provide
The difference between the
audiences of the cable and
OTA
of cable rating than
more important determinant
OTA
OTA
and cable
Many
telecasts.
conclusion that the quality of the opponent
for the
of the
OTA
of a superstar than the
a
rating.
results
may be due
to differences in the potential
cable telecast viewers have to pay for the service.
they are likely to be viewers with stronger preferences for
swayed by the appearance
is
more
NBA
casual
Such viewers may be
basketball.
NBA
viewers
who
Thus,
less
constitute a large fraction
telecast audience.
Although the superstar externality
revenues typically
make up a much
smaller with regard to local cable ratings, local cable
is
smaller share of total local
Thus, the large externality demonstrated by the
OTA
TV revenue
than local
have a large
results will
effect
OTA
when
revenues.
22
overall local
TV
revenues are considered.
TNT
3.
When TNT
telecasts
Ratings
throughout the country. Since
"national" cable network
TNT
is
and
TNT
its
game,
it
are available for
is
the 25
in
up
to
reaches about
60%
via satellite to local cable systems
of cable
TV
households,
telecasts are thus considered "national."
DMAs
with
NBA
50 TNT regular season
The
total
number
is
considered a
Unlike regional sports networks,
Data on
teams were obtained from Nielsen.
telecasts.
it
TNT
For each
cable
DMA,
of observations in the
ratings
TNT
1035.
As with the
expectation of the
local
TNT
OTA
rating.
and cable models, we use equation
However, the
TNT model
respect to the included right-hand-side variables.
22
game
sends the
typically available to basic cable subscribers without an additional fee.
household ratings
dataset
NBA
an
The exceptions are the
Angeles Lakers,
who
have an
New
York Knicks,
In
differs
(1)
to specify the conditional
from the local television models with
addition to the day of week, month,
who do
not have a local
exceptionally lucrative local cable package.
16
OTA
start
time, and
package, and the Los
game
telecasts are local
OTA
will prefer to
watch
competing telecast to consider
WCN
and cable
same time TNT
locally at the
many viewers
telecast variable
23
With regard
were required.
additional variables
competing
NBA
competing
superstar variables, the
is
is
their local
for
DMAs
whether the
of the
that
should be higher than
(greater than 0.600),
For each
TNT
game,
one "medium" team,
when
when
we
in
the
TNT
DMA's team was
part of a
Table
gives the
The
in
dummy
televising a
might be lower since
may
prefer to
of
watch the Bulls play on
specification.
involved
TNT
TNT
The
doubleheader.
the
in
We
they are quite disparate.
an indicator variable
the
an indicator variable
TNT game. The TNT
indicator variable
is
is
likely
included
third set of additional variables controls
TNT game. The
first
rating
is
competitive balance
in
the
game
characterized each team as having a "high"
or "low"
(below 0.400) winning percentage.
for
each
possibility.
The
resulting indicator
dummy
variable.
of the variables used in the analysis.
given
in
Table 12, demonstrate that the winning percentage variables do not
rating suggested
by the competitive balance theory. The "high, high" case, where
definition of the superstar effect variables
were one
in
First,
the specification, with the "high, high" case the excluded
superstar effect variables are
respectively
is
determined whether the game involved two "low" teams, one "low" team and
means
results,
have the impact on
DMA
DMA
the teams' winning percentages are high and similar, interest
etc., creating
were included
The TNT
Viewers
"medium" (between 0.400 and 0.600),
variables
1 1
in that
two teams playing than elsewhere. Second, an
TNT game was
argument suggests
23
game, TNT's rating
winning percentages of the two teams involved
for the
most important
the team associated with a
If
a superstation telecast.
included to account for whether the
the
telecasts, the
team over the two teams playing on TNT. The other type
Three additional controls are included
in
NBA
two teams playing on TNT. 24
rather than the
higher
competing
to
telecasts.
televising a
defined somewhat differently and several
is
dummy
variables set to
is
slightly different for the
one
if
TNT
model.
Here, the
the Celtics, Bulls, Lakers, or Pistons,
two teams playing in the TNT game. In the local OTA and cable models, the
one only if the team opposing the local team was one of the above teams.
of the
variables are set to
24
Competition between superstation telecasts and TNT occurring on the same night has been banned
1989-1990 season by a league rule which prohibits superstations from telecasting an game the
same night that TNT telecasts a game.
since the
17
Games
the winning percentages of both teams are above 0.600 does not even yield the highest rating.
where the teams are both
same type and
of the
average than games where there
tremendous
on the
effect
TNT
is
13%, while Larry Bird has a 32%
quite large, raising
TNT's
the 1989-1990 season,
rating
we
a disparity between the teams.
Isaiah
rating.
effect
do not have higher
are thus "competitive,"
Thomas has
Superstars,
on the other hand, have a
the smallest effect, raising the
25%
and Michael Jordan has a
by 48%. With superstars appearing
estimate that superstars accounted for over
TNT
rating
Magic Johnson's
effect.
30
of the 51
19%
of total
in
on
ratings
TNT
TNT
by
effect
is
telecasts during
regular season
gross ratings points.
With TNT, superstars again exert a
NBA
split
is
amount
equally
among
of advertising
the
NBA
TNT
revenue
large positive externality.
The
teams.
size of the rights fee
can generate, which
The
rights fee paid
depends
deliver
on TNT. Thus, when the presence of Michael Jordan produces higher
benefit
even though the Bulls are paying
NBC
4.
NBC
NBA games
on
NBC
for the
TNT
ratings
NBA games
ratings, all
NBA
can
teams
his salary.
OTA
network of the NBA.
We
have Nielsen data on the ratings of
1990-1991 through the 1992-1993 seasons.
in
to the
Ratings
currently the national
than the data used
less rich
each
is
TNT
general upon the
in
depends upon the
in turn
by
TNT model
the
in
the sense that
telecast, not the ratings separately for a set of
we
Unfortunately, the data here are
have only the overall national rating
DMAs. However,
it
is still
for
possible to estimate
superstar effects with reasonable precision.
During the three seasons
afternoons.
Thus,
we
variables.
NBA
again
rules prohibit
employ
In particular,
(college basketball)
for
which
any other
we
NBA
have data,
control for start time, day of
Tournament
two seasons when Bird was
still
telecast
(1),
NBA
on
NBC
telecasts.
but with a smaller set of right-hand-side
week, month, and season; the presence of
telecasts;
and superstar
playing),
and the Lakers (during the
18
games primarily on weekend
from competing with the
telecasts
the specification given by equation
we
NBC
NCAA
effects for the Bulls, the Celtics (during the
first
when Johnson was
still
first
season
playing).
25
The means
The
large effect
results for
on
of the variables are given
NBC
are given
ratings, increasing the
Johnson were also strong draws
in
in
Table 13.
Table 14. As
NBC
in
the previous models, the Bulls/Jordan have a
by 36%. The Celtics with Bird and the Lakers with
rating
for viewers, increasing the
indicator variables for the Celtics
and Lakers are included
NBC
rating
seasons
for the
36% and 19%
by
when
Bird
respectively.
and Johnson are no
longer playing, their estimated coefficients are small and not statistically significant from zero, which
somewhat
by the Celtics and Lakers.
surprising given the nationwide following received
on television
further demonstrates the strong superstar effects
The Value of Michael Jordan
C.
We now
NBA
estimate the value of Michael Jordan to
teams are gate receipts,
of the
NBA
down
into regular season
that licenses
NBA
start
TV
NBA
teams other than the Chicago Bulls by
TV
contracts, national
paraphenalia).
26
Four of the largest sources of revenue
contracts,
The revenues from gate
and playoff components.
data from the 1991-1992 season.
We
local
We
Table 15 provides a
NBA
and
receipts
and television can broken
summary
of the results.
Section
In
III.A.,
we
estimated the
incremental 1991-1992 regular season gate revenue due to Jordan to be $2.5 million.
full
capacity for each game.
attendance of playoff games. Accordingly,
A
Its
we
Thus,
is
it
team's local television revenue derives from
ratings
26
NCAA
basketball telecasts
and thus were dropped from the
playoffs,
unlikely that Jordan has any effect on
its
contracts with local
NBA
OTA
and cable
were not found
telecasters.
office negotiates with the national
networks. Both local and national contracts are based on the advertising revenue that
Regular season
During the
estimate Jordan's effect on playoff gate revenue to be zero.
national television revenue derives from the contracts the
25
Properties (the branch
base our estimate of Michael Jordan's value on
with Jordan's effect on gate receipt revenue.
arenas are typically at
Thus, this result
ratings.
estimating the incremental revenue he generates for those teams.
for
is
NBA Teams
Other
to
If
to
is
expected to be
be an important determinant of
NBC
analysis.
Another impotant source of revenue
concessions, and luxury boxes during games.
is
"in
We
arena" revenues, which result from sales of novelties,
have no data on
19
"in arena"
revenues.
The amount
generated by the telecasts of the games.
viewers generated by the telecasts.
per viewer delivered by
and
local cable
number
OTA
local
models can be used
the regular season.
to the
its
28
Assuming
We
27
have developed
and
is
To
much
We
The econometric
number
OTA
revenues
is
calculate incremental revenue for
of the total rights fees paid
revenue per viewer delivered
to estimate the increased
NBA
TNT and NBC
by
for
number
season revenue due to Jordan.
teams from
are
due
TNT and NBC. As we
resulting
we
TV does
its
revenue
find that, for
cable
total local
not generate any
TNT and NBC, we
to the regular season
We
due
to
must
first
estimate
how
and playoffs respectively.
then estimate the regular season
we
use the econometric results
Michael Jordan.
total
The product
of
estimated incremental regular
subtract out the 1/27 share of the incremental revenue that
TNT and NBC
was
estimates of incremental regular season revenue for other
teams were $1.1 million and $5.5 million respectively.
To estimate the
effect of Jordan
on
TNT and NBC
playoff revenues,
econometric models can be used to consistently estimate the increase
We
We
$1.8 million and
did for local TV,
of regular season viewers
Finally,
OTA
zero.
revenue per viewer and the increased number of viewers gives the
The
is
revenue
to Jordan during
each team can be estimated by multiplying
have relied here upon the opinions of industry participants.
NBA
due
of
roughly constant with respect
Since playoff games are not telecasted locally, local
Thus, Jordan's effect here
paid to the Bulls.
of viewers
is
of the
results of the local
by the incremental number of viewers drawn by Michael Jordan.
$0.6 million.
playoff revenue.
team an estimate
the revenue per viewer
the 1991-1992 season, Jordan's impact on total local
revenues
NBA
each
to estimate the incremental
of viewers, the value of Jordan to
per viewer delivered
for
local cable telecasts.
that, to first order,
depends upon the numbers
of advertising revenue
then apply the
27
In
same procedure
For instance, telecasts which draw
advertisers, will in general generate
which
more
for regular
due
to Jordan.
TNT and NBC
revenues.
playoff viewers
season
conservative.
telecast that
would
It
more young males, who
are highly valued by
advertising revenue.
This calculation assumes that the Bulls
is
above
that the estimated
general, the types of viewers expected to be generated by the telecast will also have an effect on
advertising revenue.
28
as that discussed
in
we assume
would have
the
same win/loss percentage without Jordan
also assumes that the teams cannot replace the "Bulls less Jordan" telecast with a
yield higher ratings.
20
We
estimate the incremental playoff revenue to other
TNT and NBC
NBA
we
consider the revenue teams receive from
which licenses
NBA
estimate the incremental
the sales of Bulls items
we
NBA
for
almost half of
due
Properties revenue
would be only
NBA
1.2 million for
we
NBA
Properties
We
to
estimate Micahel Jordan's
the part
conservatively
by assuming
that,
second highest team.
teams
is
Items associated with Bulls
Properties revenue.
as large as the sales of the
categories,
NBA
Properties.
to Michael Jordan
estimate the incremental revenue to other
Combining across the
NBA
paraphenalia such as clothing and videos.
and Michael Jordan have accounted
assumption,
teams to be $2.7 million and $1
respectively.
Finally,
of the
NBA
without Jordan,
Under
this
be $15.1 million.
total
value to other
NBA
teams to
be $40.3 million.
IV.
The Superstar
The
own
above suggest
that, in
addition to the obvious effects they have on the
teams, superstars have a substantial positive impact on the revenues of other teams
Indeed, the empirical results demonstrate that a superstar such as Michael Jordan generates
the league.
$40
and League Policy
results described
revenues of their
in
Effect
million per year in externalities to the other
share their local
any adjustment
TV and
NBA
gate revenue and national
for the possibility that
teams.
This externality arises because teams do not
TV revenues
are shared equally
among teams
some teams might generate higher viewership than
without
others.
Furthermore, the data indicate that the presence of a superstar dominates the quality of the opponent
terms of impact on local
If
each
NBA
OTA
superstar
in
television ratings (and thus revenues).
were paid
his
marginal revenue product,
many teams
in
the league,
especially those teams in small metropolitan areas (MSAs), could find their continued operations to be
unprofitable.
Also, for a given team
we
believe that increasing returns to scale (or positive externalities)
are generated by superstars, and other outstanding players, so again a salary equal to marginal revenue
product could well lead to losses
for
many teams
operations.
21
The basic idea
is
that
Michael Jordan makes
on the Chicago
other players
his direct
his total
Bulls, like
Horace Grant,
better players.
marginal contribution but also his contribution
in
still
exist for
adopted salary caps,
in
any individual
which the
of overall league revenue.
However, many teams attempt
each team
total salary bill of
NBA's
salary cap
than the current salary cap
as well as the limited
We
start
in violation of
may
exist to
account
1
j"
53%
We
new
and the NFL have
of average league revenues.
players with contracts
We now
29
1993 both the
which the
in
smaller
assume a gross
problems
MSAs.
of a single team.
We
first
consider the situation
benefit function for each team, B'(q,,
argument represents the quality of the
,h
j
We
player.
...
,
q, 2 )
where
need not assume
maximizing behavior here which may well not be consistent with actual operation of each team.
benefits
may
players.
We
The
derive from factors other than revenue.
assume
that a finite
number
of players within each quality type
30
The equilibrium
We
determined by the aggregation of the team demands.
W
costs to the
team are the
of quality types exist, indexed by
inelastic.
is
NBA
consider whether better methods
for the potential externalities/increasing returns
by analyzing the optimization problem
indexes the teams and the
NBA
the league cannot exceed a percentage
in
the salary cap limit.
revenue potential of teams
under the current salary cap.
is
to claim
well exist overall although decreasing
to alleviate the constraint of the salary cap limit, e.g., in
Portland Trail Blazers and Chicago Bulls successfully signed
claimed unsuccessfully were
may
Partly because of these reasons the
player.
Currently, the
Jordan attempts to claim not only
improving Grant while Grant attempts
marginal contribution to the Bulls, increasing returns
return will
If
k=
salaries for
and
profit
Gross
salaries paid to
1,...,K,
i
that the
its
supply
each quality type are thus
write the salary for a player of quality type k as
k.
We now
29
recast the benefit function as a function of the
antitrust laws.
The
Sherman
by the team
antitrust act in our opinion.
professional sports leagues could well argue that salary caps are legal, even absent the
unions' agreement, because the leagues claim they are single
economic enterprises. The single
which has considered the claim.
30
of players possessed
However, to the extent that
they are permitted under a nonstatutory labor exemption to the
Salary caps are violations of the
the players' unions agree to their use,
number
entity claim of the sports leagues has
This assumption seems reasonable, especially for the
Continental Basketball Association
economic
is
well below that
in
22
the
entities, not a
league of competing
been rejected by every U.S. Court
NBA, where
NBA.
the alternative
wage
in
the
in
each quality category.
Let L it
function can be written as B'(L
and maximizes
its
;
be the number of type k players employed by team
We
,,...,L,X ).
gross benefits less
assume
total
its
wage
initially that
bill
team
i
takes the salary levels
subject to the overall salary cap
B' (Li
£
-
LJ
WL
k
-
k
k
l
(M
-
order conditions are the usual
first
first
as given
amount M: 31
*£
wkLJ
(3)
order conditions for choice under a budget constraint
where here the Kuhn-Tucker conditions are imposed because a given team may not be up
salary cap
k
i=1
t-1
The
W
K
K
max
Then, the benefit
i.
against the
(we discuss second order conditions subsequently):
M
-
(1
. V) Wt , 0,
*'<w-£f.,
t -1
AT
w
"4« -o
which implies
dB?ldLk _
W
d&ldL,
W,
k
(5)
-^
dM
for
k<
>
0.
For teams that are up against the salary cap, the value of the Lagrange multiplier equals the marginal
benefit from an increase in the salary cap.
teams so that
X'
*
k'.
Note
that, in general, the
Lagrange multiplier will
Thus, economic efficiency could be improved by allowing trade,
e.g.,
differ
across
allowing
tradeable salary cap exemptions as discussed further below.
Rather than putting a cap on the overall league
31
In
imposed.
same
for
wage
bill,
another framework worth considering
second constraint which limits team size to at most twelve players should also be
However, we ignore this constraint to simplify the problem. The team size constraint is the
each team, which leads to an inefficient outcome for the same reason as the salary cap.
principle, a
23
is
the use of a redistributive tax.
A
given tax
proceeds to be distributed equally
by a
Under our assumption
tax.
demonstrate below.
NBA
1
vector
W
=
{W
is
that in (4), the
LK)
(I,
(1
+
(7)
-
no
*)Wk
and
+
(1
The
as given.
note the similarity between conditions
order conditions
is
t}
-
|f
dLk
We
players should result
in
all
player salaries with the
redistribution
among
first
Lagrange multipliers
X'
which
distortion should result,
is
we
to
x)£*,H; Lk
k =
The
teams along
(6)
order conditions for this problem are
=
(4).
all
only a small overall distortion caused
the tax situation, the optimization problem faced by the team
In
wage
against
The lump sum
of totally inelastic supply,
maxt B
again taking the
32
the teams.
among
with the relatively inelastic supply of
would be assessed
rate, x,
K
1
(7)
crucial difference
between the two
vary across the teams, while
in (7),
sets of
first
the tax rate t
constant across teams.
A
social planner
wishing to maximize the sum of the teams' benefit functions would allocate
players across teams so that the marginal benefit of each player type
condition
is
achieved
the player allocation
in
is
equation
(7),
since
all
was equalized
teams face the same tax
Pareto efficient under the tax.
Further,
rate
across teams.
and wage
levels,
This
implying that
by the Second Theorem of Welfare
Economics, the allocation of player types could be decentralized through the use of the proper choice of
and wages
A
{Wk }.
comparison of
specific salary caps
(i.e.,
constant across teams.
32
We
t
first
order conditions
(4)
and
(7)
reveals that
one could construct
a different cap for each team) which reaches the
same outcome
a set of team-
as a tax
which
Likewise, one could construct a set of team-specific tax levels which reaches the
do not impose a "zero
profit" constraint so that
24
any
tax rate can be imposed.
is
same
(inefficient)
outcome
as a salary cap
which
is
constant across teams.
Thus, a (constant across teams) tax has smaller distortionary effects on the allocation of player
quality across teams than a (constant across teams) salary cap.
cap.
Although a salary cap system where the caps
efficiency of the tax system, such a system
hand,
is
differ
For this reason, a tax
across teams could be constructed to match the
would be very
difficult to
implement. The
tax,
on the other
quite simple to implement.
Another way
distorting result
is if
in
which the current
NBA
salary cap system can be
changed
the teams are permitted to trade their salary cap allocations.
implication of equation
(4)
is
that the
Lagrange multipliers
X'
and
to reach a similar
from teams buying and selling salary cap amounts
to trade exist
from the usual rationing result that allowing trade
X' will differ for all
34
However,
its
applications to salary
mechanisms
in
teams
and
i
j,
in
Thus, potential gains
among themselves."
in ration tickets
non-
An immediate
general, so that the value of a marginal change in the salary cap differs across teams.
welfare.
preferred to a salary
is
This result follows
typically leads to gains in
sports leagues appears not to
consumer
have been
noticed.
Furthermore, an
fulfill
initial
allocation of salary cap
the redistributive goal toward teams
in
small
amounts which are equal across teams serves
MSAs which
the leagues claim
is
important.
to
Indeed, an
equal allocation of salary cap amounts with trade allowed would be a similar redistributive framework as
equal sharing of national network
TV
revenues which the NBA, NFL, and
MLB
Furthermore, the results would be the same as the tax situation so no distortion
would occur
to the extent that the player supply function
Equations
and
(3)
also be considered.
(4)
In this
are analyzed in a
This
see e.g.
34
outcome
Hahn
Note
not improve
is
assumed
to
undertake.
among
be totally
player selection
inelastic.
one period context. However, additional seasons could
context teams could well be allowed to "bank" salary cap amounts.
team were below the salary cap
33
is
all
in
a given year,
it
could either
sell its
Thus,
if
a
allocation to another team or save
similar to trading of pollution permits in the environmental
economics
literature,
(1989).
when income distribution is accounted for in a second
consumer welfare, e.g. Guesnerie and Roberts (1984).
that
25
best situation, allowing trade
need
the allocation for use in a subsequent year.
various rationing programs used
in
35
Again, "banking" allocations has been successfully using
the energy field over the past
two decades. The
possibility of
in
banking
salary cap credits or trading credits in this year for credits to be used in a subsequent year might well be
more acceptable
to a team's fans, given the similarity to trading players for future years' draft picks.
However, the tradeable
of the salary
i.e.,
the difference between
far
we
of players
the
is
W and the overall distortionary
inelastic,
we
same choices about player
quality and output with
W and tax
k-
(inelastic)
1,...,K}
x.
These demands are the
given
W and
T.
is
team
result of
i's
is
W as given.
nondistorting
and without the
demand
in
that the supply
the sense that teams
redistributive tax.
sum
i's
Let
wage
objective function with respect
of the teams'
demands equal
L,(W{Ux))
=LS
the
(8)
i«i
L, is
the vector consisting of the supply of players
in
each quality type.
This condition can be totally differentiated with respect to
A
consider
supply of players:
£
35
now
for players of quality type k given
maximizing team
Equilibrium requires that the
We
Under our assumption
effect of a tax.
can show that the imposition of a tax
Li(WO +t)) be the vector where the k* element
where
M\
amounts occurred.
have examined a team's choices taking the salary vector
the determination of
to {L ik ,
unconstrained aggregate salary payments
of the overall cap, before trading of salary allocations
So
vector
M and the
is
the players union hired an economist, they might well use this information in bargaining over the
if
amount
make
The value
cap allocations which are traded can be used to estimate the amount that the salary cap
costing the players,
Thus,
salary cap system does have an important potential drawback.
rate of interest (perhaps zero)
would need
to
W and t to yield
be established.
26
27
£
dL, (J^O+t)) [4^(1 +t) +
Wdz]
=
<
9)
(-1
So long as each matrix dL
Thus, equation
(9)
f
is
negative semidefinite, the
sum
of the dl_
is
;
also negative semidefinite.
35
implies that
dWtf +t)
+
Wdt
=
°r
(10)
Wd-Q
dW
1+x
Equation (10) demonstrates that the salary levels change to perfectly offset the tax so that the cost to the
teams of each quality
level
remains constant. Thus, player demands remain the same and consequently
team output remains the same. The tax
To sum
is
therefore nondistortionary.
up, an analysis of a team's optimization problem demonstrates that a tax system dominates
the current (non-tradeable) salary cap system.
solution to the tax can result.
current salary cap situation.
inelastic player
If
made
tradeable, a similar
Thus, either a tax system or a system of tradeable permits
is
better than the
Indeed, an analysis of the equilibrium conditions under the assumption of
supply demonstrates that a tax
is
nondistorting.
Conclusion
V.
We
have demonstrated
that superstars like
teams that employ them, but also to other teams
important than a competitive opponent
and
the salary cap allocations are
strife
36
surrounding salary caps
in
in
in
Michael Jordan are extremely valuable, not only to the
the league.
Indeed, superstars appear to
terms of attracting television viewers.
In
more
the recent controversy
owner-player negotiations, the positive externality that superstars
The negative semidefinite condition will typically be satisfied so long as the maximum of the
is at an interior point where the usual second order conditions for a maximum hold
benefit function
27
who
net
true.
play for large market teams have on small market teams has been overlooked.
teams provide a subsidy to the small market teams
The NFL and
NBA
have salary caps
when
in place,
can be a very inefficient method
for
a sense, the large market
they pay the superstar's salary.
supposedly to help small market teams.
associations for Major League Baseball and the National
cap as part of any collective bargaining agreement.
In
Hockey League have
In this
paper,
helping small market teams.
allocation of players so that players are prevented from
moving
to
we
A
The player
refused to accept a salary
have demonstrated
that a salary
cap creates distortions
in
cap
the
teams where they would be most
valuable.
We
show
that a tax applied to
would allow small teams
Thus,
we
conclude
to receive a
that a tax
is
team player payrolls would cause very
lump sum
distribution
distortion
which would help them
superior to a salary cap for sports leagues.
28
little
to
and yet
remain viable.
References
Guesnerie, R. and K. Roberts (1984), "Effective Policy Tools and Quantity Controls,'' Econometrica 52, 5986.
Papke,
L
and
J.
Wooldridge (1993), "Econometric Methods
Application to 401
and
Quirk,
J.
Rosen,
S. (1981),
(k)
R. Fort (1992),
Plan Participation Rates,"
Pay
for Fractional
NBER
Response Variables With an
Technical Working Paper No. 147.
Dirt, Princeton University Press, Princeton, NJ.
"The Economics of Superstars," American Economic Review 71,
29
5,
845-858.
Table
1
Paid Attendance and Incremental Revenue
Bulls vs.
Other Opponents
'89-'90 Season
vs. Bulls
Average Attendance:
Incremental Revenue:
vs.
16,325
Other Opponents
13,852
$1,564,176
Table 2
Paid Attendance and Incremental Revenue
Bulls vs .Other Opponents
'91-*92 season
vs. Bulls
Average Attendance:
Incremental Revenue:
vs.
16,840
Other
O p ponents
13,481
$2,5
1 1
,794
1
Table 3
Paid Attendance and Incremental Revenue
Celtics vs. Other Opponents
'89-'90 Season
vs. Bulls
Average Attendance:
Incremental Revenue:
vs.
16,066
Other Opponents
13,942
$ 1 ,406,63
Table 4
Paid Attendance and Incremental Revenue
Celtics vs .Other
Opponents
•91-'92 season
vs. Bulls
Average Attendance:
Incremental Revenue:
vs.
Other Opponents
13,591
16,652
$2,130,123
1
Table 5
Means
of the Variables in the Local
OTA
Data
1989-1990
1991-1992
Variable
Season
Season
Rating
0.062
0.066
Opponents Winning Percentage
0.508
0.53
Bulls/Jordan
0.049
0.059
Celtics/Bird
0.051
0.043
Lakers/Johnson
0.056
0.061
Pistons/Thomas
0.051
0.044
Superstar Effects
Number of Observations
6
1
608
1
Table 6
1989-1990 Local OTA Results
Quasi-Maximum Likelihood Estimation
of Specification (1)
Coefficient Estimate
(Standard Error)
Variable
Opponents Winning Percentage
0.047
(0.089)
0.245
Bulls/Jordan
Superstar Effects
(0.052)
0.209
Celtics/Bird
(0.073)
Lakers/Johnson
0.295
(0.072)
Pistons/Thomas
0.084
(0.067)
Chi-Square
199.999
Statistic:
DF:
22
< 0.001
P- Value:
Notes:
(1) Also included in the specification are the following:
Fixed effects for telecasting teams;
dummy
variables for start times, months, and
days of week; a lead-in rating variable, and an
(2)
Chi-Square
statistic is for the
for telecasting
teams are zero.
Wald
NBA telecast competition variable.
test that all the coefficients
except fixed effects
1
Table 7
OTA Results
1991-1992 Local
Quasi-Maximum
Likelihood Estimation of Specification (1)
Coefficient Estimate
(Standard Error)
Variable
Opponents Winning Percentage
0.092
(0.095)
Bulls/Jordan
Superstar Effects
0.426
(0.057)
0.055
Celtics/Bird
(0.057)
Lakers/Johnson
0.063
(0.058)
Pistons/Thomas
0.110
(0.071)
Chi-Square
27
Statistic:
.
1
1
< 0.001
P- Value:
Notes:
1
22
DF:
(1)
Also included
in the specification are the
Fixed effects for telecasting teams;
following:
dummy
variables for start times, months, and
days of week; a lead-in rating variable, and an
(2)
Chi-Square
statistic is for the
for telecasting teams are zero.
Wald
NBA telecast competition variable.
test that all the coefficients
except fixed effects
Table 8
Means
of the Variables in the Local Cable Data
Variable
1989-1990
1991-1992
Season
Season
Rating
0.029
0.036
Opponents Winning Percentage
0.474
0.496
Bulls/Jordan
0.036
0.026
Celtics/Bird
0.043
0.041
Lakers/Johnson
0.027
0.029
Pistons/Thomas
0.039
0.037
583
654
Superstar Effects
Number of Observations
1
Table 9
1989-90 Local Cable Results
Quasi-Maximum Likelihood Estimation
of Specification (1)
Coefficient Estimate
Variable
(Standard Error)
Opponents Winning Percentage
0.320
(0.117)
0.197
Bulls/Jordan
Superstar Effects
(0.120)
0.028
Celtics/Bird
(0.119)
0.016
Lakers/Johnson
(0.156)
0.109
Pistons/Thomas
(0.089)
Chi-Square
Statistic:
1
1
< 0,001
P- Value:
Notes:
06.5
22
DF:
(
1
)
Also included
in the specification arc the following:
Fixed effects for telecasting teams;
dummy
variables for start times, months, and
days of week; a lead-in rating variable, and an
(2)
Chi-Square
statistic is for the
for telecasting teams are zero.
Wald
NBA telecast competition variable.
test that all the coefficients
except fixed effects
Table 10
1991-92 Local Cable Results
Quasi-Maximum Likelihood Estimation
of Specification (1)
Coefficient Estimate
(Standard Error)
Variable
Opponents Winning Percentage
0.
1
56
(0.145)
0.283
Bulls/Jordan
Superstar Effects
(0.184)
0.040
Celtics/Bird
(0.143)
Lakers/Johnson
0.053
(0.141)
Pistons/Thomas
0.065
(0.121)
Chi-Square
96.984
Statistic:
22
DF:
< 0.001
P- Value:
Notes:
(1)
Also included
in the specification are the
Fixed effects for telecasting teams;
following:
dummy variables for start
days of week; a lead-in rating variable, and an
(2)
Chi-Square
statistic is for the
for telecasting teams are zero.
Wald
times, months, and
NBA telecast competition variable.
test that all the coefficients
except fixed effects
Table 11
Summary
of the 1989-1990
TNT Data
Variable
Variable
0.016
Rating
Superstar Effects
Bulls/Jordan
0.188
Celtics/Bird
0.196
Lakers/Johnson
0.194
Pistons/Thomas
0.204
Winning Percentages Both Over 0.6
0.304
One Over 0.6, Another Between
One Over 0.6, Another Below
0.4 and 0.6
0.4
Both Between 0.4 and 0.6
One Between 0.4 and
Both Below 0.4
Observations
Mean
0.6,
0.333
0.023
0.1
Another Below 0.4
57
0.117
0.023
1035
Table 12
1989-1990
TNT Results
Quasi-Maximum Likelihood Estimation
of Specification (1)
Coefficient Estimate
(Standard Error)
Variable
Superstar Effects
0.226
Bulls/Jordan
(0.047)
0.288
Celtics/Bird
(0.044)
Lakers/Johnson
0.400
(0.055)
Pistons/Thomas
0.127
(0.048)
Winning Percentages
Both Over 0.6
One Over 0.6, Another Between
0.4 and 0.6
-0.008
(0.048)
One Over 0.6, Another Below 0.4
0.013
(0.135)
Both Between 0.4 and 0.6
-0.072
(0.068)
One Between
0.4 and 0.6, Another
Below 0.4
0.035
(0.072)
Both Below 0.4
0.073
(0.142)
Chi-Squre
476.881
Statistic:
24
< 0.001
DF:
P-Value:
Notes:
(1)
Also included
in the specification are the following:
Fixed Effects for
DMAs; dummy
variables for start times, months, days of week and
double headers; a lead-in rating variable and
(2)
Chi-Square
statistic is for the
DMAs are zero.
Wald
NBA telecast competition variables.
test that all the coefficients
except fixed effects for
Table 13
Summary
of the
NBC Data
Variable
Variable
0.045
Rating
Superstar Effects
Observations
Mean
Bulls/Jordan
0.309
Celtics/Bird
0.176
Lakers/Johnson
0.103
Pistons/Thomas
0.088
6X
MIT LIBRARIES
Table 14
3 9080 00922 6116
1990-1993 NBC Results
Quasi-Maximum Likelihood Estimation of Specification
(1)
Coefficient Estimate
(Standard Error)
Variable
Superstar Effects
0.327
Bulls/Jordan
(0.054)
0.324
Celtics/Bird
(0.076)
0.185
Lakers/Johnson
(0.070)
0.109
Pistons/Thomas
(0.082)
Chi-Square
Statistic:
DF:
11
< 0.001
P-Value:
Notes:
674.628
(1)
Dummy variables for seasons and days of week and an NCAA tournament
competition variable are also included in the specification.
(2) Chi-Square
statistic is for the
Wald
test that all the coefficients are zero.
Table 15
Incremental Revenue
For Other
NBA Teams Due to
Michael Jordan
Revenue Source
Incremental Revenue
Standard Error
Regular Season
Gate
Local
$2.5
OTA Television
Local Cable Television
(TNT)
Television (NBC)
National Cable Television
National
OTA
$1.8
0.3
$0.6
0.4
$1.1
0.2
$5.3
1.1
SI 1.3
Total
Playoffs
Gate
Local
$0.0
OTA Television
Local Cable Television
(TNT)
Television (NBC)
National Cable Television
National
Total
NBA Properties
Total
OTA
$0.0
$0.0
$2.7
0.5
$11.2
2.3
SI 3.9
S15.1
$40.3
Date Due
":'
DUE FtB
1
i
1999
Lib-26-67