204 R.E. McCormick, R.D. Tollison J. of Economic Behavior Org. 44 2001 201–219
Table 1 Summary statistics
Variable n
Mean Median
S.D. Minimum
value Maximum
value Home attendance
184 464714
456628 136944
160537 1066505
Ticket price 157
11.37 11.00
2.59 7.00
18.50 Ratio of number of white
to number of black players 184
0.407 0.321
0.320 2.25
Ratio of total minutes played by whites to total
minutes played by blacks 184
0.351 0.252
0.325 2.24
Number of all-stars 184
1.011 1
0.986 4
individual owners to pay each player the value of his marginal product. We believe that the institutions of the NBA reveal just such a pattern over the time period at issue.
First, there is a draft of players out of the college ranks each year.
7
This draft allocates the signing rights for each player chosen to one team for 1 year, thus eliminating any intra-league
competition during that year for incoming players. Starting with the 1976–1977 season and carrying through the 1981–1982 season, the collective bargaining agreement CBA
between the league and its players association allowed for limited free agency. The team bidding away a player had to pay compensation to the player’s team, plus the existing team
had the right of first refusal matching on any new contract. The CBA that went into effect for the 1982–1983 season maintained limited free agency for players. It eliminated the
compensation clause, but retained the right of first refusal. The 1987–1988 season began a new CBA which continued restricted free agency for a player’s first 4 years in the league,
and was followed by unrestricted competition among teams for a player’s services after a player had been in the league for 4 years or two contracts.
So even if certain players today face sufficient competition to avoid being discriminated against, the institutions in place for the period of our data, 1980–1988, are sufficient to
allow for the exploitation of differences in labor supply among classes of inputs. Until the data on current salaries are available, we cannot investigate whether the wage differential
between black and white players persists in this new era of intra-league competition for veteran talent.
3. Attendance results
We accumulated data on NBA teams for eight seasons, 1980–1981 through 1987–1988, primarily from various issues of Sporting News Official NBA Guide
8
and Sporting News Official NBA Register.
9
Summary statistics on these data are reported in Table 1. Over the period of the data, the average team drew slightly less than half-a-million home fans
7
Colleges supply the overwhelming bulk of players; occasionally, a foreigner or high school athlete is drafted.
8
NBA Guide, 1980–1981 to 1987–1988. The Sporting News, St. Louis.
9
We identified the race of each player by examination of his picture in the NBA register. NBA register, 1980–81 to 1987–88. The Sporting News, St. Louis.
R.E. McCormick, R.D. Tollison J. of Economic Behavior Org. 44 2001 201–219 205
for the season. This amounts to 11,334 fans per game. The average ticket price was US 11.37, generating slightly more than US 5 million in gate receipts per year for regular
season games.
10
There were about two and a half black players for each white player on the average team.
11
But black players play almost three times as many minutes as whites on average. There are 13 cases out of a possible 184 where the number of whites is equal
to or greater than the number of blacks in a team. We note that the predominately white teams are either in Boston or the west depending upon where one places the two Dallas
entries.
We employ various techniques to investigate the relation between attendance and racial composition. First, we regress NBA home attendance on price and several other demand
variables, including the ratio of white to black players.
12
The results of estimating the home attendance equation by ordinary least squares are reported in Table 2.
13
We note several things about these results. The sport is growing in attendance over time. The first law of demand is not denied. A second NBA team in an SMSA reduces
attendance for each team in the area by about 178,000 fans per year. The presence of a National Football League NFL or National Hockey League NHL team seems to have
no impact on basketball attendance, but a major league baseball team is negatively linked to attendance. Bigger populations are associated with more attendance, but there is no link
with income. Other things the same, the number of all-stars on a team is not related to attendance.
The relation between winning and attendance is complicated by our inclusion of an in- teraction between winning and population. It has been speculated that the sensitivity of
attendance to won–lost records depends on population. The probability that a given fan will attend is a function of record, so that total attendance is the product of this probability
and the size of the market. Thus, we interact wins and population. The partial derivative of attendance with respect to winning is: ∂ attendance∂ wins = 6916 − 0.1 × population.
The mean population in this sample is 5224. Therefore, at the mean, the relation between games won and attendance is an additional 6394 fans per each additional game won over
the season. The maximum SMSA population in our database, New York, is 18,087. There- fore, the relation between winning and attendance is positive over the whole range of
the data.
10
Each team offers an array of seats and ticket prices. We chose the median ticket price as our measure. Hence, this average is an average of medians.
11
The nuances of the data source do not allow us to measure the racial composition of a team at every moment in time. The data are season aggregates. Hence, when players are traded or released, we do not observe the exact
composition. What we observe is the total number of white and black players that played for a given team at any time during the season.
12
We are missing ticket price data for 27 observations. This reduces the sample size from 184 to 157 when this variable is included.
13
Parameter estimates are deductively equivalent using an alternative measure of racial composition, the ratio of total minutes played by whites to total minutes played by blacks. For instance, the coefficient on this alternative
racial composition variable is 20,372, and the t ratio is 0.81. In addition, there is a potential censoring problem as home attendance may be limited by stadium capacity. In fact, the predicted home attendance from our model
exceeds stadium capacity in 10 of the 156 observations. These include three years in Boston, four in Milwaukee, two in Portland, and one in Utah. Consequently, we also estimated the attendance equation using a censored tobit
technique. The results are the same as the OLS estimates. The complete results are available on request.
206 R.E. McCormick, R.D. Tollison J. of Economic Behavior Org. 44 2001 201–219
Table 2 OLS regression estimates of NBA home attendance
Sample size: 156; F ratio: 15.95; R
2
: 0.703; dependent mean: 470,731, root M.S.E.: 81,334 Variable
Parameter estimate t Ratio
Prob |t | Intercept
297003 2.43
0.0163 1981–1982 Season dummy
− 159580
− 4.54
0.0001 1982–1983 Season dummy
− 168188
− 5.39
0.0001 1983–1984 Season dummy
− 146683
− 4.88
0.0001 1984–1985 Season dummy
− 113356
− 4.11
0.0001 1985–1986 Season dummy
− 74594
− 2.97
0.0035 1986–1987 Season dummy
− 27488
− 1.14
0.2548 Median ticket price
− 8175
− 1.71
0.0895 Stadium capacity
4.98 4.89
0.0001 Number of other NBA teams in SMSA
− 174753
− 2.89
0.0046 Number of NFL teams in SMSA
− 6292
− 0.23
0.8173 Number of M.L. baseball teams in SMSA
− 28794
− 1.37
0.1737 Number of NHL teams in SMSA
− 4658
− 0.17
0.8623 Income per capita for SMSA in 1990
− 2.46
− 0.59
0.5567 Population of SMSA in 1990
26.32 2.87
0.0047 Black percentage of population in SMSA in 1990
− 2052
− 1.71
0.0893 Total number of regular season games won
6916 6.10
0.0001 Interaction: games won times population
− 0.1
− 0.91
0.3667 Number of all-stars on team
13025 1.16
0.2463 Race of coach dummy 0 = W, 1 = B
− 22412
− 0.91
0.3664 Ratio of total number of white players to total
number of black players on team 20975
0.86 0.3909
Most importantly, we find no statistically meaningful relation between the racial com- position of the team, as measured by the ratio of the total number of white players to total
number of black players on the team, or the ratio of total minutes played by whites to to- tal minutes played by blacks, and home attendance. At least based on these data and this
specification, we find no reason to believe that NBA fans are, in general, racially biased.
14
This result is bolstered by the absence of a significant relation between the race of the head coach and attendance. Fans do not seem to care much about the race of the coach or the
players, other things the same. We use the unreported fixed effects coefficients to investigate the time-series character
of intra-city competition among teams. Starting with the 1984–1985 season, the San Diego Clippers moved without league approval to Los Angeles. The dummy coefficient for the
Lakers prior to the arrival of the Clippers in Los Angeles is 184,851 fans per season relative to the Washington Bullets, and 92,671 afterwards. The Lakers are estimated to draw 92,180
fewer fans about half as many after the Clippers arrived in town. At the same time the coefficient for the Clippers in San Diego is −30,277 and 25,013 in Los Angeles, an increase
of 55,290. The Clipper’s gain is less than the Laker’s loss, a result that may shed light on
14
The OLS results from employing a fixed-effects model across cities yields a similar outcome. For instance, the coefficient on the minutes played racial composition variable is −27,853 and the resulting t ratio is −1.14.
R.E. McCormick, R.D. Tollison J. of Economic Behavior Org. 44 2001 201–219 207
the league’s desire to control the property rights to team movement to venues where other NBA franchises are located.
15
The basic customer discrimination hypothesis does not stand up in these results. Of course, we have not shown that white fans do not prefer white players or that black fans
do not prefer black players or the reverse. Until we can observe the racial composition of those buying tickets, this issue remains open.
16
4. Local differences in racial preferences
