Is the sports media color-blind?
Berri, David J. ; Van Gilder, Jennifer ; Fenn, Aju J. 等
Introduction
Scoop Jackson of ESPN.com says that he often tells the following
story when he is asked to speak at a high school or college: (1)
I ask everyone to tell me how many black professional basketball
players they know. Depending on the size of the room, 90 percent of the
time, the students say they can name most of the players in the NBA.
There are roughly 350 players in the League, about 85 percent of
them black.
We usually round to about 300--therefore, the students claim to
know for a fact that there are 300 professional basketball players.
Then I ask them to name 300 black sportswriters.
The room always gets eerily quiet. Beyond mortuary.
Michael Wilbon's name comes up, Stephen A.'s, "that
black man with the beard who's on 'SportsReporters' a
lot" gets mentioned (for the record, William C. Rhoden), and, if
they're seriously official with their sports journalist knowledge,
Phil Taylor and Ralph Wiley will get nods.
Past that, more silence.
Then I make a point.
"Do you know why you can't name 300 black
sportswriters?" I say to them. "Because 300 of us don't
exist."
The room becomes less quiet. Mumbling. Private conversations break
out.
Then I make the point: "Which means you all have a better
chance to make it to the NBA than you do doing what I do for a
living."
The scarcity of black sports writers leads to an interesting
research question. As Jackson notes, most of the players in the NBA are
black. But most of the sports writers--who determine many of the
post-season awards--are white. (2) So one might wonder, does race play a
role in the voting for these awards?
The nature of this role is difficult to predict. It could be that
white voters would discriminate against black players. In this case,
black players would get fewer votes than their performance might
indicate. Then again, there is a sentiment that blacks are simply better
at basketball. If this sentiment was shared by many white voters, then
blacks might get more votes than their performance would suggest.
The issue of the impact of race on worker evaluations is not a new
subject for researchers in economics. The perpetual gap between the
wages paid to whites and members of other ethnic groups has led
researchers to question whether or not such differences are due to
discrimination. The standard methodology followed in these studies
involves regressing a decision variable--such as wages or employment - -
upon measures of productivity and race.
There are two issues with these studies. First, how does one
measure productivity? In most industries, measures of worker
productivity are scarce. Hence, economists have studied racial
discrimination for decades in the context of professional sports.
Professional team sports provide one with a plethora of productivity and
decision measures. Such abundance--as we will note--presents its own
challenges.
Going beyond the issue of productivity measurement, we will also
highlight the issue of how one measures race. Traditionally studies have
utilized a simple dummy variable to measure race. In addition to this
traditional approach, we also provide a continuous measure of race.
Consequently, we show that how one measures race also presents
additional challenges.
These challenges will impact what we report with respect to our
study of bias among sportswriters. Additionally, we think these
challenges also lead one to reconsider previous studies of racial
discrimination inside and outside of professional sports. (3)
The decision to be examined
Although studies of professional basketball have examined the role
of race in the determination of employment (4) and playing time, (5)
most frequently researchers have focused upon player wages. (6) The
study of wages is problematic because a firm's wage offer is a
function of the employer's expectation of future productivity. This
is a factor that cannot be measured with precision at the time the
contract is signed. As noted, the finding of racial bias depends
crucially upon a researcher controlling for worker productivity. If past
productivity does not equal future output, the findings reported from
studies of player wages may be questionable at best. Hanssen and
Anderson (1999) suggested an alternative approach. These authors, in an
examination of racial bias in professional baseball, examined the
fan's voting for starting players in Major League Baseball's
mid-season All-Star game. The advantage of this approach is that voting
patterns are not generally a statement about future performance, but
rather votes are offered in response to both past and present player
characteristics. Unfortunately, a difficulty with fan voting is that
votes do not typically need to be justified to any other person.
Consequently, as noted by Hanssen and Anderson, fans can vote for a
player for any number of reasons, a fact that may hamper the researchers
attempt to quantify the determinants of the voting pattern.
In contrast, honors bestowed by members of the media are generally
attacked and defended by other members of the press. (7) The need to
justify one's choices may lead people to more often base their
votes on factors that can be quantified; or, at the very least
explained. Consequently, the link between the objective measures of
worker productivity and media's voting pattern may be stronger than
the link between worker productivity and wages, employment, or the fans
voting for the All-Star game.
Following this argument, this inquiry will focus on the
media's selection of the National Basketball Association's
(NBA) Most Valuable Player (MVP) award. Beyond following the work of
Hanssen and Anderson (1999), the study of the NBA's MVP award also
allows us to examine a decision where--as noted in the discussion of
Scoop Jackson's observation--the decision-makers are generally
white while the people evaluated are generally black.
The voting for this award is conducted in the following fashion.
Each member of the voting media lists five players on his/her ballot.
The first person listed receives 10 voting points, the second is worth 7
points, 5 points are awarded for third, with 3 and 1 point awarded for
fourth and fifth places, respectively. The player with the most points
is given the award. (8)
Voting points will serve as our dependent variable in this study.
Our purpose is to understand the role of race in these voting point
totals. In order to understand that role, we need to first measure each
player's productivity.
Measurements of worker productivity in the National Basketball
Association
Unlike most industries, the world of sports offers a wealth of
worker productivity data. Such wealth, though, presents a different
challenge. Which measure should the researcher employ?
Is the Sports Media Color-Blind?
Berri, Brook, and Schmidt (2007) describe two plausible performance
indices for NBA players. (9)
First, one can turn to the NBA efficiency measure PRODnba,
described in equation (1).
[PROD.sub.nba] = (PTS + TREB + STL + BLK + AST)-(TO + FGMS + FTMS)
(1) where PTS = points scored, TREB = total rebounds, STL = steals, BLK
= blocked shots, AST = assists, TO = turnovers, FGMS = field goals
missed, and FTMS = free throws missed.
The NBAs efficiency index is quite similar to Dave Heeran's
TENDEX system (10) and Robert Bellotti's Points Created model. (11)
An apparent problem with these models is that no attempt is made to
ascertain the relative value of each statistic. For example, the above
model argues that a missed field goal is equal in value to a missed free
throw. Given the point value associated with each action, such an
assertion seems difficult to justify.
In addition to the arbitrary nature of the measure, Berri and
Schmidt (2010) note an additional problem: (12)
Imagine a player who takes twelve shots from two-point range. If he
makes four shots, his NBA Efficiency will rise by eight. The eight
misses, though, will cause his value to decline by eight. So a
player breaks-even with respect to NBA Efficiency by converting on
33% of his shots from two-point range. From three-point range, a
player only needs to makes 25% of his shots to break-even. Most NBA
players can exceed these thresholds. Therefore, the more shots most
NBA players take the higher will be his NBA Efficiency total. As a
consequence, players who take a large number of shots tend to
dominate the player rankings produced by this measure.
Berri and Bradbury (2009) also note that NBA Efficiency only
explains about 32% of the variation in teams wins. (13) So NBA
Efficiency is simply not an accurate measure of each player's
contribution to outcomes on the court. However, as Berri et al. (2007)
observe, this model does seem to be consistent with player
evaluation--as expressed via free agent salaries--in the NBA.
In contrast, the Wins Produced model explains approximately 95% of
the variation in team wins. As detailed in Berri (2008), (14) this model
begins by estimating the relationship between an NBA team's
offensive and defensive efficiency and the number of regular season
wins. (15) This estimation indicates that wins in the NBA are determined
by a team's ability to gain possession of the ball from its
opponent without its opponent scoring and the ability to turn
possessions efficiently into points. In other words, a player primarily
impacts wins by gaining and keeping possession of the ball (i.e.,
rebounds, steals, and turnovers) and shooting efficiently (from the
field and free throw line).
In contrast to the NBA Efficiency model, the Wins Produced model
indicates that inefficient scorers do not have much impact on team wins.
Consequently, if we wish to measure how a player impacts wins, the Wins
Produced model would be the preferred measure. However--as Berri et al.
(2007) report--the Wins Produced model (relative to NBA Efficiency) is
not as consistent with the evaluation of players by decision-makers in
the NBA. Furthermore, we will demonstrate that the choice of performance
measure impacts the evaluation of the link between race and the
evaluation of players (as measured via the media's voting for
league MVP).
Measuring Race
Before we get to that issue, though, we need to discuss how one
measures race. Studies of race frequently consider a simple dummy
variable. A few studies, though, have attempted a different approach.
For example, Fort and Gill (2000)--in a study of baseball
cards--utilized a questionnaire to ascertain "how black" a
person appeared. Such an approach provided a continuous measure of race.
Robst, VanGilder, Coates, and Berri (2011)--in a study of the NBA
free agent market--also employed a continuous measure. But unlike Fort
and Gill (2000), this study built upon a literature examining the role
colorism--or intraracial discrimination--plays in understanding
disparities across populations. (16)
Such studies require a research measure of a person's skin
tone. For our study, we employ an objective measure. Specifically we
will employ a measure called the RGB color score, which is derived from
a model in which red, green, and blue are combined in various ways to
reproduce other colors. This model is referred to as an additive model
in which the combination of these three primary colors in differing
amounts produce the full range of colors. This measurement is calculated
using Adobe Photoshop, which is commonly used by photographers to
measure and adjust skin tones in pictures.
The color in the RGB color model can be described numerically by
indicating how much of each of the red, green, and blue color is
included. Each of the primary colors can vary from the minimum amount
(no color) to the maximum amount (full intensity). The color values in
Adobe Photoshop CS3 Extended are reported in a range between 0 and 255.
Full intensity red would be reported as 255, 0, 0. A white image would
be reported with high values (closer to 255) for red, green, and blue. A
black image would be reported with low values (closer to 0) for red,
green, and blue (Wright, 2006).
All images are from the NBA website. Using an image leveling tool
of Photoshop, the players' photos are normalized to eliminate bias
due to camera or photograph differences. The RGB values are observed
from three facial areas, the forehead, right cheek, and left cheek of
each sample point. The R's, G's, and B's for each area
are averaged to eliminate significant variation of color over different
sections of the face. Summing the average R, G, and B for the three
areas yields a value between 0 and 765 (255 + 255 + 255). A smaller RGB
score is indicative of a darker colored player, and a higher score
suggests a lighter skinned player.
In addition to employing the actual RGB score, we also constructed
three dummy variables: Dark, Medium, and Light. Dark is equal to 1 if a
player is black and has an RGB score that is 300 or lower. Medium is
equal to 1 if a player is black and has an RGB score between 301 and
350. Light is equal to 1 if a player is black and has an RGB score that
is 351 or higher. The omitted or reference category is comprised of
non-black players. Finally, the simple dummy variable Race is defined as
1 for black players and 0 for white.
Modeling Voting for the NBA's Most Valuable Player Award
We now have two options with respect to the measurement of player
productivity and we have three approaches to the measurement of race. To
complete our model, we need to consider a few additional explanatory
variables.
The MVP award has been granted since 1956. Historically, the award
has been dominated by front-court performers, specifically centers. Of
the 49 awards granted, only Bob Cousy, Oscar Robertson, Magic Johnson,
Michael Jordan, Allen Iverson, Steve Nash, Kobe Bryant, and Derrick Rose
won the award while playing primarily in the back-court. Consequently,
it is possible that a player's position matters, but how this
matters is unclear. Again, historically this award went to big men.
However, in the years we examine (1996 to 2012), guards have won the
award seven times and traditional big men (i.e., power forwards and
centers) have won the award seven times. Thus, it is unclear if position
will matter across our sample. Nevertheless, to capture this effect, we
employ two dummy variables. DBIG is equal to one if a player is a center
or power forward. DGUARD is equal to one if a player is a point guard or
shooting guard.
The relationship between the media and the player can also be
important. We would expect several factors to impact this relationship.
First, more experienced players should be better known by the media, so
we expect a player's age to positively impact votes received.
Additionally, market size should also matter. (16) Teams in larger
markets tend to get more media exposure than teams playing in smaller
cities. Consequently, market size could also matter. (17)
There are two more issues that may impact the media's vote.
First is whether or not a player has won in the past. The impact of past
awards is not easy to predict. On the one hand, it could be that members
of the media wish to spread this award around. On the other hand, it
could that members of the media favor past award winners. To ascertain
which is true, a variable has been added to measure the impact of
winning this award in the past five years. (18)
Finally, it is possible the media's perceptions of a player is
impacted by the quality of the team employing the player. Specifically,
players from better teams, measured via team wins (TMWINS), should
elicit more votes from a media focused on identifying winners and
losers.
Given our list of independent variables, our model of voting points
is described by equation (2).
[VP.sub.n] = [[beta].sub.0] + [[beta].sub.1]RACE +
[[beta].sub.2]AGE + [[beta].sub.3]TMWINS + [[beta].sub.4]MARKET +
[[beta].sub.4]DBIG + [[beta].sub.5]DGUARD + [[beta].sub.6]PMVP5 +
[[beta].sub.6]PROD + [e.sub.i](2)
Where RACE = simply dummy variable, RGB variable, or three dummies
(Dark, Medium, Light)
TMWINS = Team Wins
MARKET = Population of city where team is located
DBIG = Dummy variable, big man (center or power forward)
DGUARD = Dummy variable, guard (points guard or shooting guard)
PMVP5 = Past MVP's won, weighted for last five years
PROD = NBA Efficiency or Wins Produced
Empirical Findings
To estimate equation (2) we began by collecting data across 17
seasons, beginning with the 1995-96 campaign and ending with 2011-12. We
wished to consider all players who may have been seriously considered
for the MVP award; if a player received consideration for the All-NBA
team, he was included in our sample. In all, our sample consisted of 736
player observations, with 273 of these observations having a value of VP
greater than zero.
Table 1 reports for this sample values of the descriptive
statistics tabulated for the dependent and independent variables listed
in equation (2) and additional statistics employed to measure the
performance of an individual NBA player.
Following convention, most of the player statistics employed are
tabulated on a pergame basis. The specific statistics employed follow
from the literature and include points scored, total rebounds, steals,
assists, blocked shots, turnover percentage, (19) adjusted field goal
percentage, (20) and free throw percentage. Additionally, we also will
consider each player's per-game performance according to the NBA
efficiency measure ([PROD.sub.NBA]) and Wins Produced ([PROD.sub.WP]).
With respect to the latter, the average player in our sample produces
0.12 wins per game. Over an 82 games season, such a performance is
equivalent to nearly 9.6 wins. We should also note that the average
player in our sample is 27.4 years old and comes from a winning team.
Finally, with respect to the issue of race, 84% of our sample is black
and the average player has a RGB score of 363.71.
With data in hand, we next turn to the estimation of our model. As
noted, we considered all players who received consideration for the
All-NBA team. Only 273 of these players, though, also received
consideration for the MVP award. Given the nature of our dependent
variable, we estimated equation (2) as a TOBIT model. The results are
reported in Table 2. (21)
We consider six different formulations of equation (2). Three
utilize NBA Efficiency as the measure of performance while three employ
Wins Produced. Across all six formulations the story, with respect to
race, team performance, and player performance, is similar when we
consider statistical significance. A player is more likely to be an MVP
if he is darker in skin tone, plays for a winner, and is a productive
player. The impact of age, market size, and position depends on how we
specifically formulate the model.
Two issues need to be highlighted with respect to race. First, the
traditional approach to measuring race (i.e., utilizing a simple dummy
variable) indicates that black players are favored. When we consider
skin tone, though, a more subtle story is told. Specifically,
lighter-skinned black players don't seem to benefit as much from
their race as darker-skinned black players. This can be highlighted by
looking at the models that employ the Dark, Medium, and Light dummy
variables. Of these, only Dark is statistically significant. This would
suggest that only darker-skinned black players are favored by the sport
media.
We see another important issue when we turn to economic
significance. Consider what we see when the RGB score is used to measure
race. In Model 2b, we see a coefficient on RGB that is significant at
the 10% level. And when we turn to elasticity-- measured at the mean
value of RGB (22)--we see that a 10% change in a player's RGB score
(i.e., the player is becoming whiter)--lowers a player's voting
points by 3.4%.
In model 2e, though, we see a somewhat different story. Again, RGB
is statistically significant (now at the 1% level). The elasticity
estimate, though, indicates that a 10% increase in a player's RGB
score reduced voting points by 9.2%.
The difference between these two models is simply how we measure
performance. In model 2b we employ the NBA Efficiency model; in model 2e
we use Wins Produced. Our choice of productivity measures seems to
impact dramatically the estimated impact race has on outcomes.
Beyond the issue of race and productivity, we would also note that
these results indicate that the sports media have trouble separating a
player from his team. In other words, a player with better teammates
will receive more MVP votes than an equivalent player on a lesser team.
In addition, the NBA Efficiency model--which is a poor model of player
performance--seems to be more consistent with the sports media
evaluation (as indicated by the Pseudo R-squared). And again--regardless
of which performance metric we employ--it appears the sports media tends
to think blacker players are simply better.
One could stop at this point and be satisfied with a fairly good
story. However, there is one more approach that we could try. The
studies that have examined race and professional basketball have tended
to measure player productivity with a collection of player statistics
(as opposed to an index of performance). When we take this approach --as
noted in Table 3--part of our story changes.
The results from Table 3 suggest that the collection of box score
statistics--as opposed to employing an index--does a better job of
capturing the evaluations of the sports media. When we take this
approach, the statistical impact of race vanishes. Thus, it seems very
clear that how we measure performance impacts the story we tell with
respect to race.
Again, in most industries we don't have very clear measures of
worker performance. In sports we have many measures. What our study
suggests, though, is that the wealth of performance metrics leads to
another problem. Which measure the researcher employs could impact the
results uncovered with respect to race. Consequently, we would suggest
that researchers employing sports data to examine the topic of race
consider a variety of measures of player performance. And past studies
that have found, or not found, racial bias with models that only
considered one measure of performance (or race) might need to be
reconsidered.
Is there bias?
Our study of racial bias in the voting for the NBA's MVP award
indicates that how we measure productivity impacts our findings with
respect to race, so it not clear that racial bias exists. However, there
is evidence of a different sort of bias.
To see this, let's move beyond statistical significance and
consider the economic significance of what is reported in Table 3.
Specifically, we estimated--at the point of means--the elasticity of
voting points with respect to each statistically significant factor from
Table 3.
The results indicate that voting points are primarily driven by
points scored per game and team wins. So the key to being named MVP is
to be a scorer on a winning team.
This can be seen by just looking at the 17 winners in our sample.
Of these players, 15 were the leading scorer on their team. The lone
exception was Steve Nash, who won the award in 2005 and 2006 by being
the primary assist man on a high-scoring team. In addition, the average
team employing these players won 74.4% of their regular season games
(about 61 wins across an 82-game season) and the very worst team was the
Phoenix Suns, who won 65.9% of their games in 2005-06. In sum, if you
are not a leading scorer on a top team, you are not likely to be the MVP
of the league.
The importance of this finding can be illustrated by story of
Derrick Rose. In 200910, the Chicago Bulls won 41 games, a mark that
ranked 8th in the Eastern Conference. Derrick Rose--at 21 years of age
and in just his second season--led this team in both shot attempts from
the field and points scored per game. Across the league, though, Rose
was only 12th in points scored per game. For this effort, Rose did not
receive any consideration from the sports media for league MVP and only
15 points in voting by the sports media for the three All-NBA teams.
(24)
The next season the Chicago Bulls won 62 games, which was the best
mark in the entire league. Once again, Rose led his team in shot
attempts and points scored. Across the league, he was 7th in points
scored per game and 3rd in field goal attempts. The improvement in the
team's record and Rose's scoring was clearly noticed by the
sports media. When the season was over, the sports writers named Rose to
the All NBA first team and also named him league MVP.
Was Rose the reason this team improved? To answer this question, we
turn to Table 5. This table reports the Wins Produced for each player
the Chicago Bulls employed in 2009-10 and 2010-11. The players are
separated into three groups.
The first is players retained for each season. This group only
consists of five players. In 2009-10, these five players combined to
produce 27.1 wins. The next season, these five combined to produce 32.7
wins. Thus, part of the team's improvement in 2010-11 can be linked
to the improved play of the player retained. And closer scrutiny reveals
that Rose was a big part of that specific story. Specifically, Rose
produced nearly five more wins in 2010-11 more than he did in 2009-10.
The team, though, improved by more than 20 wins, so the bulk of the
team's improvement cannot be linked to the playing of Rose. This
can be seen when we look at the performance of the players lost (i.e.,
employed in 2009-10 but not in 2010-11) and the players added (employed
in 2010-11 but not in 2009-10).
In all, the players lost produced fewer than 10 wins in 2009-10.
Because an average player will post a WP48 of 0.100, we can see that
only one of the players lost, Tyrus Thomas, was actually above average.
In contrast, five of the players added were above average, and these
players combined to produce more than 27.7 wins in 2010-11. (26)
Given what we see in Table 5, how did Rose win the 2011 MVP award?
The Bulls added a collection of productive players that allowed the team
to improve tremendously. In addition, Rose--the team's point
guard--increased his shot attempts and consequently increased his
scoring totals. Given what we have seen with respect to what primarily
determines the voting for the league's MVP, it is not surprising
that these two changes resulted in Rose being named league MVP. (27)
Concluding Observations
Our story began with a discussion of the role race might play in
the voting for the NBA's MVP award. As Scoop Jackson notes, most
sports writers are white while most basketball players are black. Given
this situation, one might wonder if race matters in this selection
process.
Our initial examination indicated that race might matter, but how
one measured race and productivity impacted the reported results.
Nevertheless, it did appear that the sports writers favored
darker-skinned basketball players in the voting for this award.
This result, though, was cast in doubt by our final approach to the
measurement of player performance. When we moved from an index of
performance to the employment of a basketball player statistics, the
impact of race was no longer statistically significant.
That did not mean, though, that bias vanished from the process. Our
results indicate that sports writers are clearly biased towards leading
scorers on top teams. Such results indicate that sports writers are not
particularly skilled at measuring the impact of individual players on
outcomes, and the story of Derrick Rose illustrates that finding.
Although the bias uncovered is interesting, the most important
result of this research is that studies of race need to be careful with
respect to how race and worker performance is measured. The choice the
researcher makes with respect to race and productivity seems to impact
the results uncovered. Consequently, we suggest that future studies of
race consider a variety of measures of both race and worker
productivity.
Authors' Note
The authors would like to acknowledge the participants of the 2004
Western Social Sciences Association (where an earlier version of the
paper was presented) and the 2011 Western Economic Association. We would
also like to acknowledge the assistance of two anonynous referees.
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Endnotes
(1) http://sports.espn.go.com/espn/page2/story?page=jackson/060713
(posted in 2009, accessed on March 14, 2013). Jackson goes on to quote a
study from the Associated Press Sports Editors and Richard Lapchick
(director of the Institute for Diversity and Ethics in Sports at the
University of Florida). The APSE study looked at how many black sports
editors were employed at APSE newspapers in the United States. Out of
305, the study only found four.
(2) We do not know the specific identity of these sports writers.
But following Jackson's observation, it is not a stretch to assume
that the majority are indeed white.
(3) This is not the first study to look at the voting for the
NBA's MVP award. Coleman et al. (2008) also examined this topic. In
contrast to the earlier study, this current inquiry considers a variety
of measures of both player performance and player race. As we will note,
the results of this study do depend on which measures are employed.
(4) See Hoang and Rascher (1999).
(5) See McCormick and Tollison (2001).
(6) For studies examining the relationship between wages and player
performance, see Kahn and Sherer (1988), Koch and Vander Hill (1988),
Brown, Spiro, and Keenan (1991), Jenkins (1996), Dey (1997), Hamilton
(1997), Guis and Johnson (1998), Bodvarsson and Brastow (1998, 1999),
Bodvarsson and Partridge (2001), and Eschker, Perez, and Siegler (2004),
Kahn and Shah (2005), Berri et al. (2007), and Robst, VanGilder, Coates,
and Berri (2011).
(7) To illustrate, Fred Hickman of CNN was the lone media member
not to vote Shaquille O'Neal the Most Valuable Player in the
National Basketball Association for the 1999- 2000 season. When his vote
was publicized, members of the press quickly wrote columns both
attacking and defending Hickman's choice of Allen Iverson.
(8) Data on voting points can be found at the website of Patricia
Bender and at BasketballReference.com. Because the number of voters
changes from year to year, the maximum number of voting points can also
change. Consequently our study normalizes voting points. Specifically,
the maximum number of voters was in 2006-07, where 1290 voting points
was possible. So for each observation we did the following calculation:
(1290/maximum number of votes points in season)*number of voting points
player received.
(9) Quirk and Fort (1992), Scully (1995), Jenkins (1996) and
Hanssen and Anderson (1999) have all argued that an index of performance
provides a more accurate assessment of a player's productivity.
(10) TENDEX was first formulated by Heeran in 1959. Heeran begins
with a model identical to the one currently employed by the NBA, but
then weights each player's production by both minutes played and
the average game pace his team played throughout the season being
examined.
(11) Robert Bellotti Points Created model, published in 1988, is
also quite similar. Bellotti begins with the basic TENDEX model and then
simply subtracts 50% of each player's personal fouls. Jeffrey
Jenkins (1996), in a departure from the practice of employing a
collection of individual player statistics, employed the Points Created
index in a study of racial discrimination.
(12) Berri and Schmidt (2010) note that both Game Score and Player
Efficiency Rating--two measures developed by John Hollinger--also
overvalue inefficient scorers. Both measures are also highly correlated
with NBA Efficiency.
(13) Berri and Bradbury (2010) also notes that Games Score and PER
explain only 31% and 33% of the variation in wins respectively. These
authors also note that even when team defense is incorporated into these
measures, explanatory power only rises to about 60%. In contrast, Wins
Produced explains approximately 95% of the variation in team wins.
(14) The Wins Produced model connects the player statistics to team
wins. The model explains more than 90% of team wins and allows one to
connect team outcomes to specific players. This model builds upon
earlier work (see Berri and Brook [1999], Berri [1999], and Berri and
Krautmann [2006]). The model was detailed in Berri (2008) and Berri
(2012). This model was recently updated to account for the diminishing
returns associated with defensive rebounds (detailed in Berri and
Schmidt (2006)]. For the details of this updated calculation one is
referred to Berri and Schmidt (2010) to
wagesofwins.com/wins-produced/how-to- calculatewins-produced/
(15) Offensive efficiency is calculated as points scored divided by
possessions employed. Defensive efficiency is points surrendered divided
by possessions acquired. Possessions employed (PE) is calculated as
follows: PE = FGA + 0.45*FTA + TO-ORB Possessions Acquired (PA) is
calculated as follows: PA = Opp.TO + DRB + TMRB + Opp.FGM + 0.45*Opp.FTM
(16) A sample of this literature would include Thompson and Keith
(2001), Goldsmith, Hamilton, and Darity (2006), and Gyimah-Brempong and
Price (2006).
(17) For market size we utilized--from the U.S. Census--the size of
the standard metropolitan area where each team was located. Data for
Canadian cities was found at Statistics Canada (n.d.).
(18) The approach to measuring the impact of winning an MVP award
in the past follows from Berri, Schmidt, Brook (2004). This paper
measured the impact of past titles won on an NBA's gate revenue by
including a measure equal to 20 if a team won a title last year, 19 the
year before, etc... The variable for any specific year considered the
value of all past titles won in the last 20 years. A similar approach
was taken for players who won MVP awards in the past. If the player won
last year, he was given a 5. If he won two years ago a 4, and so on. If
the player won multiple times in the past five years, the numbers were
added together (so a win in the past two years would be worth 9). We
also tried constructing a similar variable for players who won in the
last three years or won in just the past year. It appeared that
explanatory power was highest for five years. We thank two anonymous
referees for suggesting this variable.
(19) Turnovers and scoring are highly correlated. Turnover
percentage is a measure of turnovers that adjusts for this issue. The
specific calculation is as follows: 100 * (TO))/ (FGA + 0.44*FTA + TO)
(20) NBA players can attempt field goals from two and three point
range. Adjusted field goal percentage is a measure of shooting
efficiency that takes into account shooting from each distance. The
specific calculation--from basketball-reference.com--is as follows:
[Field Goals Made + 0.5*Three Point Field Goals Made] / Field Goals
Attempted.
(21) We should also note that our dependent variable is the log of
normalized voting points. In addition, robust standard errors are
employed.
(22) We utilized the marginal effects of the TOBIT analysis (as
provided by Stata) for the calculation of elasticity.
(23) This list only considers the non-dummy variables.
(24) Brandon Roy was the last player named to the All-NBA third
team and he received 87 points. Eight additional players--beyond the 15
players named to the three All-NBA teams--received more voting points
than Rose. Voting points data taken from the website of Patricia Bender.
(25) An average team will win 0.500 games in 48 minutes (the length
of a game). So therefore an average player in 48 minutes will produce
0.100 wins.
(26) One might think that Rose could have made these players
better. Of the ten players added, eight played in the NBA in 2009-10.
Had these players maintained the same per- minute performance in 2010-11
as they did in 2009-10, these players would have produced 29.0 wins in
2010-11. With the Bulls, though, these players only produced 24.6 wins.
So the veterans added actually played a bit worse with Rose as a
teammate. Such a result doesn't indicate Rose makes his teammates
less productive. But it certainly is inconsistent with the hypothesis
Rose makes his teammates better. We would add, the Bulls also added Tom
Thibodeau as head coach before the 2010-11. The Bulls improvement likely
led the media to name Thibodeau as coach of the year. But again, the
improvement seems linked to the team just adding much better players.
(27) Rose did lead the Bulls in Wins Produced in 2010-11. But in
the league, he ranked 21st. The leader--Chris Paul--produced 18.45 wins;
or more than eight wins beyond what Rose offered.
David J. Berri is a professor of economics in the Department of
Economics & Finance. His research primarily examines the economics
of sports, with a specific focus on behavioral economics, worker
productivity and compensation, and competitive balance.
Jennifer Van Guilder is an assistant professor in the Business and
Economics Department where she teaches Business Statistics, Managerial
Economics, Labor Economics, and Race and Gender in the American Economy.
Her research interests include labor economics, the economics of
education, and the issues of mental health and labor market outcomes.
Aju J. Fenn is an associate professor and Gerald L. Schlessman
chair in the Department of Economics and Business. His research
interests include sports economics, environmental economics, pedagogy,
and the economics of addiction.
Table 1: Summary Statistics for Variables Employed
Variable Mean Standard Minimum Maximum
Deviation
Voting Points 77.47 231.19 0.00 1286.80
Dummy Variable, Race 0.84 0.36 0.00 1.00
RGB 363.71 108.26 168.67 637.00
Dummy Variable, Dark 0.34 0.48 0.00 1.00
Dummy Variable, Medium 0.16 0.37 0.00 1.00
Dummy Variable, Light 0.33 0.47 0.00 1.00
Age 27.39 4.13 19.00 40.00
Team Wins 47.57 10.82 12.00 72.00
Market Size 4,780,098 4,377,485 968,858 18,300,000
Dummy Variable, Big Man 0.44 0.50 0.00 1.00
Dummy Variable, Guard 0.39 0.49 0.00 1.00
Past MVP Wins, last 5 0.31 1.19 0 9
years
NBA Efficiency, per game 20.88 3.94 7.34 33.82
Wins Produced, per game 0.12 0.06 -0.09 0.30
Adjusted Field Goal 0.50 0.04 0.41 0.68
Percentage
Free Throw Percentage 0.77 0.09 0.41 0.95
Points, per game 19.24 4.71 4.56 34.18
Rebounds, per game 6.92 1.68 1.73 13.13
Steals, per game 1.22 0.44 0.27 2.76
Assists, per game 4.21 1.45 1.03 9.15
Blocked Shots, per game 0.88 0.58 -0.61 3.58
Personal Fouls, per game 2.56 0.56 0.78 4.21
Turnover Percentage 12.96 2.84 5.30 29.67
Table 2: Estimation of Equation (2)
Dependent Variable: Log of voting points for MVP award, normalized for
number of voters
Estimation Method: Censored (TOBIT)
Left censored observations: 463
Uncensored observations: 273
Robust standard errors
Years: 1995 to 2012
t-stats below each coefficient
Variable Model 2a Model 2b Model 2c
Dummy Variable, Race 0.28 ***
1.84
RGB 9.44E-04 ***
-1.93
Dummy Variable, Dark 0.47 *
2.84
Dummy Variable, Medium -0.02
-0.14
Dummy Variable, Light 0.24
1.41
Age 0.01 0.01 0.01
0.79 0.52 0.88
Team Wins 0.06 * 0.06 * 0.06 *
9.69 9.65 9.67
Market Size -1.94E-08 -1.91E-08 -2.48E-08 ***
-1.56 -1.49 -1.89
Dummy Variable, Big Man -0.66 * -0.65 * -0.62 *
-4.23 -4.13 -3.93
Dummy Variable, Guard 0.27 *** 0.29 ** 0.29 **
1.83 1.96 1.97
MVP Wins, Past 5 years 0.12 * 0.12 * 0.12 *
3.90 3.91 3.86
NBA Efficiency, per game 0.29 * 0.28 * 0.28 *
19.32 18.77 18.43
Wins Produced
Observations 736 736 736
Pseudo R-Squared 0.30 0.30 0.31
Variable Model 2d Model 2e Model 2f
Dummy Variable, Race 0.58 *
3.03
RGB -2.52E-03 *
-3.99
Dummy Variable, Dark 0.97 *
4.75
Dummy Variable, Medium 0.20
0.85
Dummy Variable, Light 0.32
1.52
Age -0.06 * -0.07 * -0.06 *
-3.32 -3.73 -3.39
Team Wins 0.06 * 0.06 * 0.06 *
8.01 7.97 8.01
Market Size -3.17E-09 -2.91E-09 -1.20E-08
-0.19 -0.17 -0.70
Dummy Variable, Big Man -0.15 -0.12 -0.06
-0.74 -0.61 -0.29
Dummy Variable, Guard 0.08 0.13 0.15
0.38 0.64 0.76
MVP Wins, Past 5 years 0.40 * 0.41 * 0.40 *
9.07 9.20 8.94
NBA Efficiency, per game
Wins Produced 8.87 * 8.93 * 8.63 *
7.07 7.11 6.97
Observations 736 736 736
Pseudo R-Squared 0.15 0.15 0.16
* - significant at the 1% level
** - significant at the 5% level
*** - significant at the 10% level
Table 3: Estimating Equation (2) with a Collection of Player
Performance Statistics
Dependent Variable: Log of voting points for MVP award, normalized for
number of voters
Estimation Method: Censored (TOBIT)
Left censored observations: 463
Uncensored observations: 273
Robust standard errors
Years: 1995 to 2012
Variable Model 2g Model 2h Model 2i
Dummy Variable, Race 0.03
0.19
RGB -4.02E-04
-0.81
Dummy Variable, Dark 0.15
0.88
Dummy Variable, Medium -0.06
-0.35
Dummy Variable, Light -0.02
-0.08
Age 0.03 ** 0.03 *** 0.03 ***
2.03 1.87 1.79
Team Wins 0.07 * 0.07 * 0.07*
10.70 10.70 10.68
Market Size -3.20E-08 ** -3.21E-08 ** -3.47E-08 **
-2.47 -2.48 -2.56
Dummy Variable, Big Man 0.04 0.05 0.07
0.28 0.33 0.43
Dummy Variable, Guard 0.35 * 0.36 * 0.37 *
2.67 2.71 2.75
MVP Wins, Past 5 years 0.03 0.04 0.04
1.19 1.22 1.33
Adjusted Field Goal -0.24 -0.17 -0.25
Percentage
-0.17 -0.12 -0.17
Free Throw Percentage -0.04 0.02 0.07
-0.06 0.02 0.10
Points per game 0.21 * 0.21 * 0.20
12.99 12.88 12.83 *
Rebounds per game 0.17 * 0.17 * 0.17 *
4.58 4.67 4.63
Steals per game 0.23 *** 0.22 *** 0.23 ***
1.91 1.84 1.92
Assists per game 0.22* 0.22 * 0.21 *
5.66 5.77 5.07
Blocked Shots per game 0.45* 0.45 * 0.43 *
4.47 4.43 4.26
Personal Fouls per game -0.41 * -0.43 * -0.41 *
-3.77 -3.88 -3.78
Turnover Percentage 0.04 *** 0.05 ** 0.05 **
1.86 2.02 2.15
Observations 736 736 736
Pseudo R-Squared 0.35 0.35 0.35
1% level
* significant at the
** - significant at the 5% level
*** - significant at the 10% level
Table 4: The Elasticity of Statistically Significant Factors in Table 3
(23)
Variable Model 2g Model 2h Model2i
Points per game 3.97 3.95 3.93
Team Wins 3.41 3.41 3.41
Rebounds per game 1.19 1.19 1.20
Personal Fouls per game -1.06 -1.09 -1.06
Assists per game 0.93 0.93 0.88
Age 0.77 0.72 0.72
Turnover Percentage 0.57 0.61 0.66
Blocked Shots per game 0.40 0.39 0.38
Steals per game 0.28 0.27 0.28
Market Size -0.15 -0.15 -0.17
Table 5: Evaluating the Chicago Bulls in 2009-10 and 2010-11
Chicago Bulls 2009-10
Players Retained Wins WP48 *
Produced
Derrick Rose 5.4 0.090
Luol Deng 7.1 0.128
Joakim Noah 8.8 0.219
Taj Gibson 5.8 0.127
James Johnson 0.1 0.005
Summation 27.1
Players Lost Wins WP48
Produced
Kirk Hinrich 4.9 0.095
John Salmons 3.2 0.091
Tyrus Thomas 2.4 0.171
Hakim Warrick 1.0 0.089
Ronald Murray 0.5 0.036
Acie Law 0.2 0.086
Brad Miller 0.2 0.006
Chris Richard 0.2 0.041
Joe Alexander -0.1 -0.118
Aaron Gray -0.2 -0.207
Devin Brown -0.4 -0.216
Lindsey Hunter -0.6 -0.231
Jannero Pargo -1.8 -0.104
Summation
Players Lost 9.6
2009-10
Wins Produced Total 36.8
Actual 2009-10 Wins 41
Chicago Bulls 2009-10 Chicago Bulls 2010-11
Players Retained Players Retained Wins WP48
Produced
Derrick Rose Derrick Rose 10.2 0.161
Luol Deng Luol Deng 9.3 0.139
Joakim Noah Joakim Noah 8.4 0.255
Taj Gibson Taj Gibson 5.2 0.143
James Johnson James Johnson -0.3 -0.110
Summation Summation 32.7
Players Lost Players Added WinsWP48
Produced
Kirk Hinrich Ronnie Brewer 9.1 0.245
John Salmons Keith Bogans 4.4 0.146
Tyrus Thomas Carlos Boozer 4.0 0.103
Hakim Warrick Kyle Korver 3.4 0.098
Ronald Murray Omer Asik 3.2 0.155
Acie Law Kurt Thomas 2.7 0.111
Brad Miller C.J. Watson 1.0 0.042
Chris Richard Rasual Butler 0.0 0.085
Joe Alexander John Lucas -0.1 -0.268
Aaron Gray Brian Scalabrine -0.1 -0.076
Devin Brown
Lindsey Hunter
Jannero Pargo
Summation Summation
Players Lost Players Added 27.7
2009-10 2010-11
Wins Produced Total Wins Produced Total 60.4
Actual 2009-10 Wins Actual 2010-11 Wins 62
* - WP848 = Wins Produced per 48 minutes. Average WP48 is 0.100. (25)
