Are sunk costs irrelevant? Evidence from playing time in the National Basketball Association.
Leeds, Daniel M. ; Leeds, Michael A. ; Motomura, Akira 等
I. INTRODUCTION
"Sunk costs are irrelevant," is a common mantra of price
theory, but our students seldom believe this claim--and for good reason.
Political and corporate leaders alike appeal to sunk costs to justify
future policies. The "escalation effect," which Borland, Lee,
and Macdonald (2011) define as, "commitment to a previous decision
despite the expected marginal benefit of that commitment being less than
expected marginal cost," has become a key element of behavioral
economics, dating back to seminal work by Thaler (1980) and Tversky and
Kahneman (1981), and of economic experiments (e.g., Khan, Salter, and
Sharp 2000).
Most evidence regarding the relevance of sunk costs stems from
anecdotes or artificial experiments. We provide a real-world test of the
escalation effect by estimating the impact of draft position,
particularly lottery and first round status, on playing time in the
National Basketball Association (NBA). Whether a team maximizes wins or
profits, it should give the most playing time to its most productive
players regardless of how they were acquired. (1) However, sports
commentators constantly report that teams are committed to specific
players because they had used high draft choices or paid high prices to
obtain them, a classic application of the escalation effect.
The abundance of data on productivity and playing time allows us to
test whether teams give first-round draft picks or lottery picks more
playing time than other players after accounting for performance. We
build on earlier studies of playing time in the NBA by Staw and Hoang
(1995) and by Camerer and Weber (1999) (hereafter "CW") by
employing data and techniques that have only recently been widely used.
Our estimation builds on Staw and Hoang and on CW in three ways.
First, our more recent data avoid possible problems of heterogeneity.
Second, we have access to variables that better measure playing time and
player productivity, its main determinant. Third, and most importantly,
we focus more on the transition between discrete states--lottery versus
nonlottery and first versus second round--than on the precise order of
draft picks. This shift of focus leads us to use regression
discontinuity (RD) analysis. RD enables us to avoid omitted variable
bias and thus to discuss causality when evaluating how crossing such
thresholds as the lottery or the first-round of the draft affects
playing time.
The next section of this article briefly reviews the literature on
sunk costs, with particular attention to Staw and Hoang (1995) and CW.
The third section shows that our data are consistent with those used by
previous studies by applying CW's framework and variables to our
data. Section IV explains the relevance of regression discontinuity and
presents the empirical model. Section V addresses several potential
threats to the validity of our RD estimates. The sixth section presents
and discusses our results. The seventh section concludes.
II. THE BEHAVIORAL ECONOMICS OF SUNK COSTS
Standard neoclassical theory claims that sunk costs have no bearing
on current choices because they affect neither marginal benefit nor
marginal cost. However, Thaler (1980) and Tversky and Kahneman (1981)
cite psychology studies dating back to the 1950s showing that subjects
consider previous expenditures of money or effort when making decisions.
Their findings thus contradict the core neoclassical assumption that
agents behave rationally.
Despite the controversy over sunk costs and their centrality to the
neoclassical-behavioral debate, there is little rigorous empirical
analysis of their role in decision-making. One of the few tests comes
from Staw and Hoang (1995). Using data for players drafted in the first
two rounds of the 1980-1986 NBA drafts, (2) they regress playing time
per season on draft position, performance measures, and such control
variables as race and nationality conditional on players' years of
experience.
Staw and Hoang create three indices for performance: scoring,
toughness, and quickness. They also include indicator variables for
whether a player was a guard or was injured during the season in
question. To test whether teams are less committed to players whom they
did not draft, they add an indicator variable for players who had been
traded. They include draft position linearly; the first player selected
takes a value of one, the second player a value of two, and so on. Staw
and Hoang find that players with lower draft numbers (picked earlier)
get more playing time but that the impact falls as NBA experience rises.
Because they do not provide standard errors or t-statistics, we cannot
tell whether their coefficients are significantly different from one
another or from zero.
CW build on Staw and Hoang in several ways. For our purposes, the
most important addition is an indicator variable for first-round status.
This allows them to test for a discrete jump in playing time as one
moves from second-round choices to first-round choices. They also
control for performance in both the current and previous seasons and
unbundle Staw and Hoang's performance indices.
CW use data from the first two rounds of the 1986-1991 drafts. Like
Staw and Hoang, they find that draft position has a strong impact on
playing time early in a player's career but that the impact
declines over time. They find no discontinuous impact of the round in
which a player was selected.
Borland, Lee, and Macdonald (2011) find limited evidence of an
escalation effect in Australian Football. Controlling for performance,
they find that draft position has a small impact on games played and on
tenure with a team. However, the impact is not consistently significant
and does not behave consistently over a player's career.
III. EXTENSION OF PREVIOUS RESULTS
To compare our results with those of previous studies, we must
first determine whether any differences stem from our using different
data, different variables, or different techniques. To isolate the
source of any differences, we proceed in three stages. First, we attempt
to replicate CW's results using more recent data. Finding no
significant differences from their results, we then replace some of the
original variables with new metrics from our data set. This yields
results that are largely the same but differ in a few crucial ways. In
Section IV, we apply RD techniques to the new data set. The remainder of
this section details the first two steps of this process.
A. Reproducing Camerer and Weber's Results
Our data set comes from BasketballReference.com (2008-2012). It
includes all 409 players who were drafted by NBA teams between 1995 and
2005, signed an NBA contract, and played at least 500 minutes in at
least one season. (3) It contains performance data for the first 5 years
of players' careers.
The data represent the first 11 draft classes subject to
league-mandated first-round rookie contracts. Previous studies analyzed
years that preceded the scale. First-round draft picks in the earlier
studies might therefore have engaged in protracted contract negotiations
with teams. These negotiations could themselves have been a source of
escalated commitment and of unobserved heterogeneity between first- and
second-round picks. League-mandated rookie contracts prevent such
negotiation, removing one unobservable source of commitment.
Standardized contract length eliminates another potential source of
heterogeneity among first-round draft choices.
To test whether these data yield different results from those
obtained by CW, we attempt to replicate their results with the new data.
Table 1 shows the results of this test. (4) Each column represents a
given level of experience. Controls include measures of shooting
accuracy and both positive and negative performance measures
standardized to a per-minute basis. CW use the same variables for a
player's "backup," whom they define as the alternative
player at the same position with the most minutes. (5) In the case of
guard and forward, in which two players are typically on the court at
once, they also take the alternative player with the second-most
minutes. They also use the player's expected draft position
according to guides compiled by ESPN NBA draft analyst Don Leventhal
(Leventhal 1986-1991) to predict players' abilities. Finally, they
include teams' winning percentages and indicators of whether a
player had been acquired by trade or missed time due to injury.
Although our variables closely resemble those used by CW, they are
not all identical. Because Leventhal's reports ended in 1997, we
use a similar report compiled by ESPN's current NBA draft analyst,
Chad Ford (2014). Unfortunately, Ford's reports date back only to
2001. We chose not to merge the two predictions because the two analysts
could have used different criteria to rank players. In addition, it
still would have omitted players drafted in 1998, 1999, and 2000. Using
Ford's projections limits us to using players drafted since 2001.
Because data have become more refined, we can now more precisely
identify "backup" players as shooting and point guards or
power and small forwards.
Our results are generally consistent with CW. Players with higher
(later) draft positions play less in their first 2 years, even
controlling for performance. CW obtain this result for the first 3
years. Draft round is insignificant in both studies. Among the control
variables, positive performance--especially shooting accuracy and
assists--is rewarded with more playing time, while fouls are penalized.
Players with better backups play less, whereas players with worse
backups play more. Injuries naturally reduce playing time. Players on
winning teams play less in their first year. We therefore conclude that
our data do not differ significantly from those used by CW.
B. Using New Metrics for Playing-time and Performance
In our second set of regressions, we take advantage of the fact
that finer measures of key variables are available to us than to
previous researchers. Most importantly, we account more fully for time a
player is unavailable due to injuries or suspensions (e.g., for fighting
or drug offenses). Such data are now available on the Pro Basketball
Transactions (PBT) website (2005-2011). We use these data to compute the
number of games missed for these reasons and use this to approximate a
player's maximal number of regulation minutes in each season. (6)
We then use the ratio of the actual number of minutes played to this
maximum as our dependent variable. If a player is on the court for every
possible minute of regulation time this variable equals 1; it equals 0
for a player who is on a team roster but does not play at all. In our
sample, the fraction varies from 0.127 to 0.886.
Turning to the control variables, we replace the vector of
performance variables with a single measure, wins produced per 48
minutes played (WP48). WP48 uses individual performance measures to
compute how many of a team's wins can be attributed to a given
player. For more on wins produced, see Berri, Schmidt, and Brook (2006)
and Berri (2008).
Because the physical demands of different positions and the
tendency of players at different positions to commit fouls vary, we
include indicator variables for a player's primary position. As
noted above, we can define position more finely than previous studies
could and include indicators for center, power forward, small forward,
and shooting guard. Point guard is our default category.
We replace current winning percentage with lagged winning
percentage because current winning percentage is endogenous to playing
time decisions. We also include an indicator of whether the team
qualified for the playoffs in the preceding season. We hypothesize that
teams that performed poorly in the recent past feel more invested in
high draft choices as potential franchise saviors.
Previous studies have hypothesized that teams feel less committed
to players acquired via trade rather than the draft. However, players
change teams for a variety of reasons. We therefore include an indicator
for whether a player changed teams for any reason.
A variant of the principal agent problem could also affect playing
time. Personnel decisions such as draft selection and player
transactions are typically made by upper-level management, most often by
general managers, while game-time decisions are made by coaches. Because
a coach's job depends on his team's performance, he is more
likely to respond to players' performance than to a sense of
commitment. We therefore include a dummy variable indicating whether a
team's coach is also its general manager. We expect such teams to
have a greater escalation effect than others. However, only about 6% of
our sample involves coaches with a dual role, so it might be difficult
to separate differences in escalation effects from individual fixed
effects.
Because players with prior experience are more fully developed and
can make more immediate contributions, we expect prior experience to
increase playing time, especially early in a player's career.
Because of the growing presence of international players, who frequently
come to the NBA from club teams, we use a variable listing prior
experience at the collegiate or club level. Groothuis, Hill, and Perri
(2007) show that younger entrants underperform relative to their draft
position in their first two seasons, then surpass older players from the
same draft cohort. In effect, teams picking such players accept some
short-term performance cost in hopes that greater potential will emerge.
Discrimination could also affect a team's sense of commitment.
Specifically, teams might feel less committed to minority or foreign
players. We therefore add indicators for whether a player is Black or
foreign.
We also delete several variables used by CW. As noted above, using
draft predictions significantly reduces our sample size. The lack of
degrees of freedom becomes a critical issue in the RD analysis we run in
Section IV. It is also not clear what role the prediction of one
prognosticator has on a coach's decisions. (7) For these reasons
and because the variable does not have a consistent impact in our
replication of CW's results, we drop this variable in later
regressions.
We also do not use performance measures for "backup"
players, as position has become a fluid concept. For example, a team
might not have a formal backup center, instead using power forwards as
backups; another team might have three or four listed centers who also
play power forward. This fluidity makes it hard to interpret the
variable used by CW, so we discard it.
Results of applying ordinary least squares to this new set of
variables appears in Table 2. Our results are again largely consistent
with those of CW. One important difference comes in the impact of
lottery status and draft round. While we again find that later draft
picks have less playing time, we find some evidence that, all else
equal, being a lottery pick increases playing time in years 1 and 2, and
its positive impact in year 3 borders on statistical significance. We
also find that first round draft picks, controlling for draft number,
have less playing time in years 3 and 4. Performance, as measured by
wins produced, has a strong positive effect that is significantly
greater after a player's first 2 years.
IV. USING REGRESSION DISCONTINUITY TO ESTIMATE PLAYING TIME
The possibility of discrete changes in playing time when a player
crosses the threshold of the lottery or the first round leads us to make
our third addition to previous work by altering the estimation framework
to include regression discontinuity. RD estimation is particularly
useful when crossing a specific threshold causes an agent to receive a
particular treatment. For example, exceeding 50% of the vote in an
election results in a politician's taking office or in a
union's being chosen to represent workers (DiNardo and Lee 2004 and
Lee 2008), In the most recent year of our data, going from the 15th to
the 14th draft pick causes a player to be a lottery selection and going
from the 31st pick to the 30th pick moves a player from a second-round
selection to a first-round selection.
A. The Value of Regression Discontinuity Estimation
RD is particularly valuable in this setting because it enables us
to test for a causal relationship between crossing the threshold from
lottery to nonlottery or from first to second round in the presence of
unobservable or otherwise omitted variables. (8) RD allows us to replace
a single, global estimate using the entire data set with two local
estimates using a small range of values on either side of each
threshold. RD resolves the problem posed by unobservables because over a
small bandwidth on either side of the threshold the unobservable
variables should not have a systematic impact on the dependent variable.
For example, in our setting, a player's history of injuries, and
implicit risk of future injury, is not observable to us. Globally, this
variable could systematically affect both a player's draft position
and playing time. His draft status could worsen because teams are
reluctant to select a player who might never develop due to injury, and
his actual playing time could fall if he is injured or if teams limit
his playing time to protect his health. This could lead to biased
estimates of the impact of being a lottery/nonlottery pick or a
first/second-round draft choice. However, in a small enough band, this
impact disappears, as injury risk is not likely to be systematically
different between the last player chosen in the first round and the
first player chosen in the second round. Similar logic applies to other
unobservable factors, such as players' leadership or character,
without loss of generality. If, as we discuss and test later,
players' observable characteristics do not vary discontinuously at
the cutoff for treatment, we are left to conclude that any impact we
might find on playing time is due to the treatment associated with
selection in a later section of the draft.
Two conditions must hold for RD to resolve the problem of
unobservable variables. First, the running variable (in our case, draft
position) that takes us from one side of the threshold to the other must
have a continuous impact on the dependent variable as one crosses the
threshold. Second, one must choose an appropriate bandwidth. Choosing
one draft choice on either side of the threshold is likely to leave us
with too few degrees of freedom. Expanding the bandwidth too far,
however, reduces the likelihood that the unobservables have a random
impact on the dependent variable. One thus faces a tradeoff between the
bias that comes with too big a bandwidth and the imprecision that comes
with too small a bandwidth. As a result, we present results using a
variety of bandwidths, with others available upon request, so that we
may be certain that our results are not an artifact of bandwidth
selection.
We use RD to analyze NBA teams' commitment to their lottery
picks and first-round draft choices. Like CW, we test for differences
between players taken in the first round and those taken in the second
round. We also look for differences between lottery picks and later
first-round picks. Since 1985, the NBA has used a lottery to determine
the draft order of the teams that failed to make the 16-team playoffs in
the previous season. The purpose of the lottery is to reduce the
incentive to lose games intentionally late in the season to secure a
higher draft pick. (9) Since 1994, the first three picks have been
determined by a weighted lottery that gives the team with the worst
record a 25% chance of receiving the first draft pick and the nonplayoff
team with the best record a 0.5% chance of receiving that pick. A
similar process determines the second and third overall picks. The
remaining draft picks, beginning with the fourth, are awarded in reverse
order of finish.
Commitment to first-round draft choices can arise for two reasons.
First, since the 1995 collective bargaining agreement, teams incur a
qualitatively greater financial obligation to the last player chosen in
the first round than to the first player chosen in the second round.
First-round draft picks receive 3-year guaranteed contracts with payment
set by a fixed salary scale. The rookie contracts of second-round draft
picks are subject to negotiation and are typically for 2 years at a
lower salary, often not guaranteed. Before 1995, all rookie contracts
were negotiated between team and player. Top draft picks often received
contracts with many more years of guaranteed salary. (10) Behavioral
economists would predict that greater financial obligation leads teams
to give high draft picks more playing time than their performance
merits. The 1995 collective bargaining agreement reduced rookie salaries
by 30% to 50%, which could lessen the overall sunk cost (Krautmann, von
Allmen, and Berri 2009; Rosenbaum 2003).
Second, teams are more psychologically committed to players whom
they draft in the first round, as these players are frequently
identified as future stars of the franchise. A "wasted"
first-round pick could doom a franchise to years of mediocrity. This was
the case for the Los Angeles Clippers, who for many years drafted
mediocrities over players who went on to become perennial All Stars.
(11) Such mistakes could easily cost a coach or general manager his job.
Separate analysis of lottery picks provides a way to separate
financial commitment from psychological commitment. If teams are more
committed to lottery picks than to later first-round choices, that
commitment is likely to be psychological rather than financial. The last
lottery pick costs a team only about 5% more in salary than the first
nonlottery pick, which is a much smaller difference than that between
first-round and second-round draft picks. As lottery picks receive more
publicity than other first-round picks, fans may place much greater
expectations on them than on later choices.
Using a linear measure of draft position and dummy variable for the
round in which a player is selected effectively estimates a step
function. They therefore risk modeling a continuous, nonlinear function
as a discontinuous, linear function. This misattributes the continuous
impact of draft position to the discontinuous impact of crossing from
lottery to nonlottery status or from the first round to the second. (12)
B. RD and Local Linear Regression
RD captures causal relationships in the presence of unobservable
covariates by applying local linear regression, such as that in Equation
(1)
(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where we define [T.sub.it] as the fraction of the maximal number of
minutes played by player i in year t and [Z.sub.it] as the control
variables appearing in Table 2. Unlike previous estimates, those in
Equation (1) do not use draft position. Instead, we use a normalized
draft position, [[??].sub.i], which is centered on the transition from
the lottery to nonlottery picks or from the first round to the second.
As our results may vary based on whether we treat the cut point as the
final pick before a transition or the first pick after that transition,
we define cut points as being halfway between the two picks and use the
distance between draft position and the cut point. (13) When running
local linear regressions, we restrict [[??].sub.i] to lie within a
bandwidth h, such that -h [less than or equal to] [[??].sub.i] [less
than or equal to] h, where h varies across specifications.
We estimate two separate equations because the distance between the
last lottery pick and the last first-round pick is not the same for
every year. This occurs for several reasons, including the NBA's
expansion in 2004 (with the creation of the Charlotte Bobcats) and the
loss of draft picks by the Minnesota Timberwolves in 2001, 2002, and
2004 due to violations of the league's salary cap. Changes in the
location of the two thresholds make pooled analysis of the
discontinuities impossible, so we consider the discontinuities
separately.
We run several sets of regressions to capture different possible
manifestations of the escalation effect. We first split the data into
five subsets, each of which corresponds to the number of years a player
has been in the NBA. If draft position reflects teams'
expectations, which are updated over time rather than an escalation
effect, we would expect the impact of being a first-round draft pick or
a lottery pick to decrease over time.
We capture the impact of race and nationality on a team's
commitment to its players in two ways. We first include dummy variables
for race and for whether a player is foreign in the above equations.
(14) If discrimination based on race or nationality worsens a
team's treatment of its players, the dummy variables should have a
negative impact on playing time. We also test for how race affects
player usage by running a separate set of regressions for all Black
players. (15)
V. DATA ANALYSIS
Before presenting results, we must test whether our data can yield
valid estimates. Three important qualifications in our context are (1)
that observables trend smoothly through the cutoff for treatment, (2)
that there are no simultaneous or confounding treatments, and (3) that
players near the cutoff are randomly assigned to treatment. Imbens and
Lemieux (2008) and Lee (2008) formalize the first two conditions, while
McCrary (2008) does so for the third.
The first condition means that player characteristics show no
discrete jumps between the last lottery and first nonlottery picks, nor
between the final first-round selection and the first second-round
selection. Unfortunately, the characteristics most relevant on draft
day--those for high school, college, or club performance--were generated
by varying processes and hence not readily comparable for players from
different sources, or are unobservable (e.g., "maturity" or
"leadership").
We can test one key postdraft variable, wins produced per 48
minutes. Tests for the continuity of WP48 across the lottery and draft
rounds appear in Tables 3 and 4. We show the results for three
bandwidths, with others available on request. The key coefficient here
is for the dummy variable indicating a switch from one group to another
(lottery/nonlottery or first round/second round). This coefficient is
not significant with any bandwidth, showing that performance moves
smoothly across groups. Figures 1 and 2 illustrate the continuity of
performance across these thresholds for a bandwidth of 10 draft
positions. (16)
Neither figure shows a significant drop in performance as one
crosses the threshold.
Another potential concern is whether sample sizes are balanced on
either side of the cutoff for treatment. Differences in the number of
observations on either side of the threshold could reflect composition
bias, which would raise concerns about the validity or interpretation of
our findings. We test for such differences using a McCrary density test.
We perform the test using bandwidths ranging from 5 to 10 draft picks on
either side of the cutoff. (17)
The results of these tests appear in Table 5. For all bandwidths
shown, the coefficient on lottery status remains statistically
insignificant. Hence, composition bias does not pose a problem in the
case of lottery picks. However, there is a noticeable drop in sample
size as draft position enters the second round. The positive impact of
being selected in the first round shows that players chosen in the
second round are far less likely to be found on team rosters, raising
the possibility of composition bias. If few second-round picks make team
rosters, those who do make a team might be substantially more talented
than those who do not and may therefore be unrepresentative of
second-round picks as a whole.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
Several factors reduce our concern over this finding. First, the
lack of a discontinuity in WP48 across draft rounds means that players
in our data are comparable, even if first- and second-round picks in
general are not. Second, we are not concerned with "typical"
second-round draft choices--data by definition do not exist for unsigned
players, and applying our results to them would have no meaningful
interpretation. Finally, the focus of this article is on the treatment
of players who register meaningful playing time. The fact that we
observe unrepresentative second-round draft choices does not undermine
this study.
Finally, the selection of players into treatment must be
effectively random. It is possible that general managers seriously
consider tradeoffs between the mean and variance of players'
expected productivity at the cutoff between the first and second
rounds--that players with imprecisely estimated performance would not
receive guaranteed contracts over players with more stable expectations.
Such ex ante expectations, however, would not necessarily determine the
number of minutes that they play. While general managers select players
based on observable characteristics and on team needs, it is unlikely
that these decisions would result in large systematic trends in
treatment when pooled over many drafts.
VI. RESULTS
Tables 6 and 7 test for discontinuities in each of a player's
first 5 years in the NBA. Table 6 tests for discontinuity associated
with being a lottery pick, while Table 7 shows the impact of being a
first-round draft choice. Figures 3-6 illustrate the fitted curves for
local linear regressions for lottery picks and first-round draft picks
in their first and fifth years, using bandwidths of 10 draft picks.
Regressions using higher-order terms for draft order are not shown
here, as coefficients on higher-order terms are consistently
statistically insignificant.
Tables 6 and 7 show no evidence of an escalation effect. Lottery
picks and first-round draft choices receive no more playing time because
of their draft status, as coefficients on the respective dummy variables
are seldom significant. The few significant coefficients are uniformly
negative, indicating that being a lottery or first-round pick negatively
affects playing time. This unexpected effect could be the result of a
small sample size, which allows a few poor high draft picks or good low
draft picks to affect the results.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
Table 8 shows a complete set of RD results for players with 3 years
of experience, estimated over a bandwidth of 10 draft selections. (18)
These results show that additional covariates greatly improve the fit of
the regression--much of it from adding our performance measure, WP48,
the only consistently statistically significant variable. A
player's position often has a statistically significant impact on
playing time, but no one position coefficient is significant across all
specifications. (19) Surprisingly, Black players received more playing
time than White or Asian players in most specifications, holding
performance constant.
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
VII. CONCLUSIONS AND FURTHER RESEARCH
We find no evidence that NBA teams exhibit discontinuous commitment
to players drafted in the first round or in the lottery over those
drafted later. Players drafted in the above positions receive no more
playing time--and, in some situations, receive less playing time--than
other players. This finding contradicts the conclusions of Staw and
Hoang's seminal paper. It also moves farther along the path
suggested by CW, suggesting, if anything, a de-escalation effect.
While our main focus is on the possible discontinuity associated
with lottery picks or first-round draft choices, we also find no general
effect of draft position on playing time when controlling for
performance. The coefficient on normalized draft order is significant in
about half of our specifications. This contrasts with the impact of
WP48, which has a strong, positive impact in all specifications.
We see three reasons why our findings differ. First, the two
previous studies use global linear models. As Angrist and Pischke (2008)
point out, global linear specifications can identify nonexistent
discontinuities. Using a local linear RD framework avoids this.
Second, we use a broader and more accurate measure of
performance--wins produced per 48 minutes--than do the other studies. As
performance is the single most important determinant of playing time and
may include different types of contributions at each position, correctly
specifying performance is vital for any study of playing time.
Finally, we more precisely account for playing time lost to
exogenous factors such as injury. The ratio of a player's actual
playing time to his maximum possible playing time more accurately
captures the team's use of the player.
Our findings thus show that teams clearly prize performance over
draft order. This suggests, in turn, that neoclassical theory explains
NBA teams' behavior better than behavioral theory does. To the
extent that the NBA serves as a laboratory in which superior data allow
us to draw conclusions about "real world'' behavior, we
may make a similar inference about firm behavior in general.
ABBREVIATIONS
CW: Camerer and Weber
NBA: National Basketball Association
RD: Regression Discontinuity
doi: 10.1111/ecin.12190
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(1.) Some argue that wins and profits are themselves linked. See,
for example Berri, Schmidt, and Brook (2004).
(2.) At that point, the draft lasted seven rounds. In 1988, the
draft was reduced to three rounds, and in 1989 to the present two
rounds.
(3.) A total of 107 draftees either never signed or had missing
data in each of their first five seasons, while another 122 failed to
reach 500 minutes in all of their first five seasons.
(4.) We refer to CW's basic model, corresponding to their
Table 4.
(5.) In the case of a reserve, this would be the starting player.
(6.) We ignore the small number of additional minutes generated by
overtime periods. A player who participated in 20 overtime periods (an
extremely high number) would see his maximum total minutes increase by
approximately 2.5%. This simplification is therefore unlikely to
qualitatively impact our results.
(7.) These predictions are available to teams and should therefore
be factored into draft decisions, or may reflect an outsider's
perception of NBA teams' evaluations.
(8.) Angrist and Pischke (2008) suggest that one possible set of
omitted variables is a polynomial in the continuous variable (here draft
number), which could transform a discrete change into a continuous one.
(9.) For more on the rationale behind a lottery, see Taylor and
Trogdon (2002), Soebbig and Mason (2009), and Price, Soebbing, Berri,
and Humphreys (2010).
(10.) The change in the CBA was effectively an attempt to save
teams from themselves after Glenn Robinson Jr. signed a 10-year
guaranteed $68 million contract with the Milwaukee Bucks in 1994.
(11.) For example, the Clippers chose Lorenzen Wright instead of
Kobe Bryant and Michael Olowokandi instead of Dirk Nowitzki. Neither
Wright nor Olowokandi played in an All Star game. Bryant has been to 15
All-Star Games and won the 2007-2008 Most Valuable Player Award.
Nowitzki has been to 11 All-Star Games and won the 2006-2007 Most
Valuable Player Award.
(12.) For a detailed analysis, see Angrist and Pischke (2008).
(13.) In 2005 the cut point associated with lottery status is 16.5.
The last lottery pick is assigned a value of -0.5, the previous pick is
assigned a value of -1.5, and so on. The first nonlottery pick is
assigned a value of 0.5, the next pick is assigned a value of 1.5, and
so on.
(14.) A player is foreign if he was neither born nor raised in
North America and did not attend college in the United States. Hence
Canadian players such as Steve Nash are not classified as foreign.
Players were classified as Black based on photographic evidence found
online.
(15.) Regressions for White and foreign-born players are not shown
because of small sample size.
(16.) Graphs for other bandwidths show similar results.
(17.) Results for other bandwidths were consistent with those shown
and are available on request. For more on the McCrary density test, see
McCrary (2008) and Lee and Lemieux (2010).
(18.) Results for each of players' first 5 years in the league
using bandwidths from 5 to 10 draft picks are available upon request.
(19.) Results for centers were always negative, conditional on
being statistically significant. Results for other positions varied in
both sign and magnitude based on bandwidth, year, and cut point.
DANIEL M. LEEDS, MICHAEL A. LEEDS and AKIRA MOTOMURA *
* We thank Jeffrey Borland and Eva Marikova Leeds for their helpful
comments and suggestions, and Katy Ascanio, Charles Maneikis, Katrina
Harkins, and Emily Helming for their research assistance.
([dagger]) Previous versions of this paper were presented at the
Western Economic Association International Annual Meetings in Portland,
OR, CERGE-EI in Prague, the Eastern Economic Association Meetings in
Boston, MA, and the Conference Honoring Joel Mokyr in Evanston, IL.
Leeds: Education Research Consultant, Division of Accountability
Services, Michigan Department of Education, Lansing, MI 48933. Phone
517-241-4356, Fax 517-3351186, E-mail
[email protected]
Leeds: Professor, Department of Economics, Temple University,
Philadelphia, PA. 19122. Phone 215-204-8880, Fax 215-204-5698, E-mail
[email protected]
Motomura: Associate Professor, Department of Economics, Stonehill
College. Easton, MA 02357. Phone 508-565-1149, Fax 508-565-1444, E-mail
[email protected]
TABLE 1
Applying Camerer and Weber's Variables to New Data (a)
Variable First Year Second Year
Plays center or -66.88 (0.56) 89.90 (0.59)
forward
Field goal 2640.09 *** (4.22) 1929.18 ** (2.29)
percentage
Three-point field 410.84 (1.29) 401.04 (1.01)
goal percentage
Free throw 474.05 (1.45) 1176.67 ** (2.33)
percentage
Points per minute 428.13 (0.86) 959.07 (1.32)
Rebounds per minute 407.08 (0.49) 989.47 (0.91)
Blocks per minute 196.33 (0.09) 1729.95 (0.57)
Assists per minute 4092.57 *** (3.10) 7111.23 *** (4.21)
Steals per minute -1603.73 (0.65) 1248.27 (0.32)
Personal fouls per -3682.88 *** (3.21) -2110.50 (1.41)
minute
Turnovers per minute -2732.20 (1.45) -3715.72 (1.19)
Injured during season -367.99 *** (3.72) -309.53 *** (2.86)
Acquired via trade 562.00 (0.64) -561.78 * (1.83)
Team win percentage -1112.46 *** (3.64) -490.50 (1.29)
Draft position -10.58 ** (2.03) -14.01 ** (2.12)
Backup field goal -1874.04 * (1.70) -2680.10 *** (2.69)
percentage
Backup free throw -423.68 (0.83) -631.44 (1.13)
percentage
Backup three-point 60.19(0.17) 259.43 (0.60)
percentage
Backup points per -704.85 (1.54) 106.62 (0.20)
minute
Backup rebounds per 920.82 (0.99) 245.16 (0.32)
minute
Backup blocks per -2796.07(1.10) 78.78 (0.03)
minute
Backup assists per -792.96 (0.62) -1440.45 (0.99)
minute
Backup steals per 2689.47 (0.88) 2828.93 (0.87)
minute
Backup personal fouls 2959.68 * (1.73) 5464.86 *** (2.63)
per minute
Backup turnovers per 359.47 (0.12) -2860.29 (0.90)
minute
Draft position x -4.94 (0.25) 21.49 ** (2.18)
trade
Belief -5.47 ** (2.30) -4.90 (1.64)
First round 16.38(0.10) -3.52 (0.02)
Intercept 1895.06 ** (2.51) 985.70 (1.07)
N 215 186
Adjusted [R.sup.2] 0.572 0.524
Variable Third Year Fourth Year
Plays center or 308.59(1.64) 97.89 (0.45)
forward
Field goal 2294.50 ** (2.07) 3370.04 *** (2.84)
percentage
Three-point field 383.95 (0.94) 295.37 (0.53)
goal percentage
Free throw 7676.42 *** (3.27) 881.34 * (1.91)
percentage
Points per minute 1383.13 * (1.79) 312.82 (0.45)
Rebounds per minute -2004.09 (1.55) -1581.14 (1.15)
Blocks per minute 5861.10 * (1.75) 793.27 (0.19)
Assists per minute 2742.25 * (1.79) 580.84 (0.31)
Steals per minute 234.73 (0.05) 1546.05 (0.22)
Personal fouls per -4975.01 *** (2.94) -10060.56 *** (3.52)
minute
Turnovers per minute 1428.72 (0.33) 406.14 (0.09)
Injured during season -289.75 ** (2.16) -472.43 ** (2.31)
Acquired via trade -336.70 (1.32) -28.31 (0.10)
Team win percentage -496.53 (1.25) 623.76 (1.34)
Draft position -2.43 (0.30) -5.43 (0.60)
Backup field goal -410.74 (0.41) -1202.97 (0.87)
percentage
Backup free throw -463.92 (0.73) -1082.95 (1.45)
percentage
Backup three-point 206.12 (0.46) -306.12 (0.53)
percentage
Backup points per 168.74 (0.25) -82.44 (0.13)
minute
Backup rebounds per 608.46 (0.49) -1259.11 (0.93)
minute
Backup blocks per -1652.50 (0.57) -2081.78 (0.53)
minute
Backup assists per -1377.28 (0.80) -1407.60 (0.74)
minute
Backup steals per -248.22 (0.07) -2490.58 (0.51)
minute
Backup personal fouls 4019.45 * (1.79) 3246.29 (1.38)
per minute
Backup turnovers per -530.65 (0.14) 2086.10 (0.88)
minute
Draft position x 0.29 (0.03) -13.93 (0.96)
trade
Belief -13.87 *** (3.41) -5.33 (1.21)
First round 24.66 (0.11) 0.49 (0.00)
Intercept -24.53 (0.02) 2294.23 * (1.70)
N 155 105
Adjusted [R.sup.2] 0.549 0.489
Note: t-statistics in parentheses.
(a) Dependent variable: minutes of playing time.
* Significant at the 10% level; ** significant at the 5% level;
*** significant at the 1% level.
TABLE 2
Applying New Variables to New Data11
Variable First Year Second Year
Plays center -0.0980 *** (4.25) -0.101 *** (3.62)
Plays power forward -0.062 *** (2.68) -0.062 ** (2.29)
Plays small forward -0.056 ** (2.48) -0.002 (0.84)
Plays shooting guard -0.006 (0.26) -0.023 (0.84)
Years of previous 0.011 (1.63) 0.004 (0.59)
experience
Black 0.019(0.99) 0.003 (0.12)
Foreign-born 0.071 ** (2.17) 0.031 (0.81)
Wins produced per 48 0.320 *** (7.64) 0.416 *** (7.98)
minutes
Changed teams -0.034 (1.03) -0.072 *** (3.35)
Coach is also GM 0.010 (0.33) -0.011 (0.32)
Lagged win percentage -0.281 *** (3.69) -0.269 *** (3.12)
Lagged playoff team 0.007 (0.29) 0.025 (0.91)
Draft position -0.003 *** (2.61) -0.005 *** (3.72)
First round -0.002 (0.05) -0.036 (0.99)
Lottery pick 0.134 *** (5.06) 0.091 *** (3.04)
Intercept 0.438 *** (7.33) 0.626 *** (8.10)
N 515 464
Adjusted [R.sup.2] 0.441 0.427
Variable Third Year Fourth Year
Plays center -0.071 ** (2.37) -0.068 ** (2.12)
Plays power forward -0.060 ** (2.07) -0.078 ** (2.46)
Plays small forward 0.055 * (1.83) 0.047 (1.46)
Plays shooting guard 0.004 (0.15) 0.025 (0.74)
Years of previous 0.002 (0.28) -0.003 (0.37)
experience
Black 0.004 (0.17) 0.042 (1.61)
Foreign-born 0.030 (0.17) 0.066 (1.42)
Wins produced per 48 0.761 *** (11.15) 0.545 *** (8.77)
minutes
Changed teams -0.106 *** (5.31) -0.131 *** (6.08)
Coach is also GM 0.068 * (1.87) 0.028 (0.75)
Lagged win percentage -0.152 (1.56) -0.278 ** (2.53)
Lagged playoff team 0.011 (0.39) 0.032 (1.04)
Draft position -0.006 *** (3.94) -0.007 *** (3.70)
First round -0.091 ** (2.24) -0.130 *** (2.77)
Lottery pick 0.052(1.61) -0.020 (0.56)
Intercept 0.684 *** (7.99) 0.867 *** (8.69)
N 399 352
Adjusted [R.sup.2] 0.476 0.373
Note: t-statistics in parentheses.
(a) Dependent variable: Fraction of maximal possible time played.
* Significant at the 10% level; ** significant at the 5% level;
*** significant at the 1% level.
TABLE 3
Continuity of WP48 across the Lottery
Threshold
Bandwidth Bandwidth Bandwidth
Variable = 10 = 8 = 5
Draft position 0.0001 (0.08) 0.0013 (0.52) 0.0039 (0.80)
Lottery pick 0.0062 (0.47) 0.0143 (0.94) -0.0278(1.45)
Interaction term 0.038(1.64) -0.0030 (0.92) -0.0283 *** (4.23)
Adjusted [R.sup.2] 0.0207 0.0044 0.0736
Number of 787 623 387
observations
Note: t-statistics in parentheses.
*** Significant at the 1% level.
TABLE 4
Continuity of WP48 across Draft Rounds
Bandwidth Bandwidth Bandwidth
Variable = 10 = 8 = 5
Draft position -0.0015 (0.57) -0.0058 0.54) 0.0039 (0.54)
Drafted in round 0.0070 (0.39) 0.0061 (0.30) 0.0209 (0.83)
1
Interaction term 0.0039 0.23) 0.0118 *** (2.55) -0.0021 (0.23)
Adjusted [R.sup.2] -0.0019 0.0121 -0.0103
Number of 456 354 225
observations
Note: t-statistics in parentheses.
*** Significant at the 1% level.
TABLE 5
Impact of Threshold on Density
Bandwidth Lottery First Round
10 -3.5303 (0.76) 8.8348 * (1.87)
8 -3.2202 (0.60) 10.6548 ** (2.45)
5 4.1000(0.52) 13.9500 *** (3.66)
Note: t-statistics in parentheses.
* Significant at the 10% level; ** significant at the 5%
level; *** significant at the 1% level.
TABLE 6
Linear Estimate of Discontinuity across Lottery
Threshold by Years of Experience
Bandwidth Bandwidth Bandwidth
Specification = 10 = 8 = 5
Year 1 with -0.0066 (0.14) -0.0344 (0.60) -0.0856 (1.34)
covariates
Year 1 -0.0351 (0.69) -0.0633 (1.14) -0.1027 (#)
without (1.65)
covariates
Year 2 with -0.0905 * (1.84) -0.1115 * (1.92) -0.1208 (1.58)
covariates
Year 2 -0.1146 ** (2.14) -0.1332 ** (2.26) -0.1458 ** (2.00)
without
covariates
Year 3 with -0.0721 (1.33) -0.0372 (0.59) -0.0527(0.65)
covariates
Year 3 -0.0523 (0.89) -0.0251 (0.37) -0.0863(1.02)
without
covariates
Year 4 with 0.0355 (0.71) 0.0260 (0.44) 0.0517(0.70)
covariates
Year 4 0.0626(1.07) 0.0930(1.37) 0.0804 (0.88)
without
covariates
Year 5 with -0.0583(1.16) -0.0230 (0.39) -0.0002 (0.00)
co variates
Year 5 -0.0612(1.05) -0.0092(0.14) -0.0426 (0.47)
without
covariates
Note: 5-statistics in parentheses. (#) Not significant at the 10%
level because of the small sample size (n = 71).
* Significant at the 10%; ** significant at the 5% level.
TABLE 7
Linear Estimate of Discontinuity across Draft
Rounds by Years of Experience
Bandwidth Bandwidth Bandwidth
Specification = 10 = 8 = 5
Year 1 with 0.0708(1.16) 0.0270(0.41) -0.0032 (0.03)
covariates
Year 1 -0.0257 (0.40) -0.0697(1.07) -0.0748 (0.96)
without
covariates
Year 2 with 0.0176(0.30) -0.0077(0.12) -0.0572 (0.57)
covariates
Year 2 0.0016(0.02) -0.0236 (0.33) -0.0182(0.21)
without
covariates
Year 3 with -0.1057 (1.56) -0.1268 (#) -0.1046(1.05)
covariates (1.66)
Year 3 -0.0746 (0.99) -0.1139(1.42) -0.1614(1.62)
without
covariates
Year 4 with -0.0538 (0.66) -0.0102(0.11) -0.0684(0.51)
covariates
Year 4 0.0172 (0.22) -0.032 (0.38) -0.1231 (1.14)
without
covariates
Year 5 with -0.1009(1.20) -0.1635 * (1.78) -0.1308(1.06)
covariates
Year 5 -0.0275 (0.31) -0.0592 (0.62) -0.0601 (0.50)
without
covariates
Note: t-statistics in parentheses. (#) Not significant at the 10%
level because of the small sample size (n = 77).
* Significant at the 10% level.
TABLE 8
Full Set of Regressors for 3 Years of Experience and
Bandwidth = 10
Variable Lottery-1 Lottery-2
Normed draft position -0.0088(1.14) -0.0124 * (1.72)
Lottery pick -0.0523 (0.89) -0.0721 (1.33)
Drafted in first
round
Interaction term -0.0110(1.08) -0.0040 (0.42)
Shooting guard -0.031 (0.68)
Small forward 0.0054 (0.11)
Power forward -0.1052 ** (2.18)
Center -0.1332 *** (2.70)
Wins produced per 48 0.6686 *** (4.14)
minutes
Lagged winning 0.047 (0.32)
percentage
Made playoffs in -0.0056 (0.14)
previous year
Changed teams -0.0607 ** (2.07)
Black player 0.0093 (0.25)
Foreign player -0.0245 (0.41)
Years of prior 0.0076 (0.67)
experience
Coach was also 0.0654(1.12)
general manager
Constant 0.5195 *** (12.11) 0.5252 *** (5.69)
Adjusted [R.sup.2] 0.0908 0.2521
Observations 168 168
Variable Draft Round-1 Draft Round-2
Normed draft position -0.0052 (0.47) -0.0038 (0.40)
Lottery pick
Drafted in first -0.0746 (0.99) -0.1057(1.56)
round
Interaction term -0.0104 (0.77) -0.0148(1.30)
Shooting guard -0.0276 (0.56)
Small forward 0.0975 * (1.72)
Power forward 0.0180 (0.39)
Center -0.0463 (0.97)
Wins produced per 48 1.1643 *** (6.38)
minutes
Lagged winning 0.1033 (0.57)
percentage
Made playoffs in -0.0422 (0.84)
previous year
Changed teams -0.0414(1.13)
Black player 0.0686 * (1.80)
Foreign player 0.0478 (0.66)
Years of prior -0.0111 (0.79)
experience
Coach was also 0.1055 (1.55)
general manager
Constant 0.4347 *** (7.17) 0.2945 *** (2.63)
Adjusted [R.sup.2] 0.0187 0.3820
Observations 98 98
Note: t-statistics in parentheses. * Significant at the 10% level;
** significant at the 5% level; *** significant at the 1% level.
