A RE‐EXAMINATION OF PRODUCTION FUNCTIONS AND EFFICIENCY ESTIMATES FOR THE NATIONAL BASKETBALL ASSOCIATION
| DOI | http://doi.org/10.1111/j.1467-9485.2008.00443.x |
| Date | 01 February 2008 |
| Author | Young Hoon Lee,David Berri |
| Published date | 01 February 2008 |
A RE-EXAMINATION OF PRODUCTION
FUNCTIONS AND EFFICIENCY
ESTIMATES FOR THE NATIONAL
BASKETBALL ASSOCIATION
Young Hoon Lee
n
and David Berri
nn
Abstract
This paper seeks to re-examine the issue of estimating team efficiency for sports
teams via an application of data from the National Basketball Association. This
paper argues that the inputs the coaches allocate are the players the team employs.
Therefore, this paper employs a measure of playing talent in modeling team
production. Unlike previous studies, which only employed one measure of playing
talent, we employ measures of guards, small forwards and big men in a study of
basketball. This paper also argues that the time-varying stochastic frontier models
with the identical temporal pattern assumption such as Lee and Schmidt and
Battese and Coelli cannot be used in the analysis of team efficiency in sports. The
evidence we present shows by hypothesis test that this argument holds.
I Intro ductio n
Beginning with the seminal work of Scully (1974), there have been numerous
empirical studies of production functions and sporting team efficiency.
1
This
work begins with the elements of a standard production function, which is
typically defined as the relationship between output and inputs. In the sports
economics literature, output has been traditionally defined as the number of
wins the team accumulates. Inputs have been defined as some measure of the
playing talents a team employs, typically measured via a variety of player
performance measures. Team efficiency is determined by how well a coach
transforms the given playing talent into a winning performance.
Two recent studies moved beyond looking at player statistics as the input
variables and focused attention upon the player’s themselves. For example, Fizel
and D’itri (1996) and Dawson et al. (2000a, b) used player talent indices as an
n
Sogang University
nn
California State University-Bakersfield
1
See Dawson et al. (2000a, b), Fizel and D’itri (1996), Gustafson et al. (1997), Haas (2003),
Hadley, Poitras, Ruggiero and Knowles (2000), Hofler and Payne (1997), Porter and Scully
(1982), Ruggiero et al. (1996), Zak et al. (1979). A good review of the literature is offered by
Dawson et al. (2000b) and Lee (2005).
Scottish Journal of Political Economy, Vol. 55, No. 1, February 2008
r2008 The Authors
Journal compilation r2008 Scottish Economic Society. Published by Blackwell Publishing Ltd,
9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA, 02148, USA
51
input variable in their analyses of team or coach efficiency. Specifically, Fizel
and D’itri employed the Hoop Scoop talent index as a measure of playing input
in college basketball. Dawson et al. (2000a, b) focused on player value, via a
weighted sum of player variables, calculated before the season in question. In
other words, it is the level of talent that exists before the season in question
begins that is connected to team wins in the regular season.
Dawson, Dobson and Gerrard also argued that coaches have both a direct
and indirect impact on team winning performance. Specifically, coaches have a
direct impact when they make the decision to play or not play a particular
player. The authors argue that most empirical works in the literature ignored the
indirect effect, or the ability of the coach to train and motivate players so that
performance on the court improves. That is, coaches are not only seeking to
maximize wins given a certain amount of playing inputs, but also seek to
improve the quality of inputs employed. Estimation of the indirect effect would
require ex ante input variables that excludes the performance-enhancing impact
of coaches.
In this paper, we seek to improve upon the approach offered by Dawson et al.
(2000a, b) in a study of technical efficiency in professional basketball. Both Fizel
and D’itri (1996) and Dawson et al. (2000a, b) only included one measure of
playing talent. Like these studies, we argue in favor of employing an index of
playing talent in a properly specified production function. Unlike these studies,
though, we will also construct such an index for three player positions employed
in the National Basketball Association (NBA). Specifically, although centers
and power forwards play similar roles, the production characteristics of these
players differ from guards and small forwards. In other words, they are different
kinds of workers. Consequently, a well-defined production function in basket-
ball needs to include different measures for each type of worker employed.
2
Beyond improving the specification of the production function, there is also
contribution we seek to add in the econometric literature examining team
production in sports. Dawson et al. (2000a, b) are perhaps the first papers to use
a panel data model with a stochastic frontier approach, which these authors
applied to a study of the English Premier League. Specifically, Dawson et al.
(2000a) were the first to attempt to estimate the temporal variation in technical
efficiency of a sports team by using the time-varying stochastic production
function models of Cornwell, Schmidt and Sickles (1990, CSS), Battese and
Coelli (1992, BC) and Lee and Schmidt (1993, LS). Dawson et al. (2000a) found
that the temporal structure of efficiency and the estimation procedures of the
time-varying stochastic frontier models produce different results. However, we
argue that because the average value of the winning percentage is always 0.500 in
2
A further advantage of employing a measure of playing talent can be seen if one considers
the issue of cost minimization. The condition of cost minimization requires that a combination
of inputs be chosen where the isocost curve is tangent to the isoquant curve. With player
statistics such as rebounds and turnovers, we do not have input prices, hence it is difficult to
measure costs. With playing talent measures, though, we can calculate input price data simply
by dividing players’ salary by the measure employed. Therefore, our approach can allow for the
estimation of allocative efficiency as well.
YOUNG HOON LEE AND DAVID BERRI52
r2008 The Authors
Journal compilation r2008 Scottish Economic Society
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