EXPLOITATION IN MEN’S
COLLEGE BASKETBALL
David Berri
Southern Utah University
Robert Brown
California State University, San Marcos
Dan Rascher
University of San Francisco
Andy Martinelli
Misix, Inc
Arturo Galletti
General Electric
ABSTRACT
The restrictions the NCAA places on the compensation of
athletes has led to the suspicion that at least some athletes
are being exploited (i.e., paid a wage less than the player’s
marginal revenue product). Previous research has
suggested this is true for those drafted by the NBA. We
employ data on player productivity to measure the marginal
productivity of all athletes on Division I men’s college
basketball teams from 2009-10 to 2012-13. Such a measure,
coupled with a model designed to calculate the impact wins
has on a school’s revenue allows us to measure the MRP for
more than 18,000 player observations. This measurement
indicates that thousands of college athletes are indeed
exploited by the NCAA.
One approach
[Lane, Nagel, Netz, 2012]
• The authors looked at wins data from 2001 to 2006 and
revenue data from 2001 to 2004.
• With this data the authors estimated – following the
approach introduced by Scully (1974) – a college player’s
marginal revenue product
• Such an approach allowed the authors to move beyond a
study that only examined the players drafted into the
NBA (see Brown et. al.)
• However, the Lane et. al. approach – especially with
respect to the wins model – had problems.
One approach
[Lane, Nagel, Netz, 2012]
• Dependent Variable: Team Winning Percentage
• Independent Variables:
•
•
•
•
•
•
•
•
•
•
•
•
Field goal percentage
Free Throw Percentage
Three pointers made per game
Blocked shots per game
Steals per game
Rebounds per game
Dummy for New Coach
Dummy for Coach of the Year
Won-Loss Records for “winningest” coaches
average rank of opponents (strength of schedule?)
number of games televised
team fixed effects
• Model explains 55% of winning percentage without team fixed
effects and 69% with team fixed effects.
Some problems with
[Lane, Nagel, Netz, 2012]
• Turnover, assists, and personal fouls are
excluded
• Opponent performance is poorly controlled
• Field goal percentage needs to be adjusted
for where a shot is taken
• Including blocked shots, coaching, and
televised games indicates researchers
needed to think about how to model wins in
basketball
THE SCULLY
•
•
•
(1974) APPROACH
the marginal product of a player can be
ascertained by connecting wins to player
statistics
the marginal revenue of a win can be
ascertained by connecting team revenue
to team wins
a player’s MRP = Wins * Value of Wins
PROBLEMS WITH THE SCULLY APPROACH
•
•
•
•
For Scully, players only contribute to wins via
revenue.
In sports, though, revenue is not just about wins.
For example – as Berri, Leeds, and von Allmen
note – fixed revenues confound the wins-revenue
relationship.
To illustrate, these authors estimate the
following revenue function for the NBA, MLB,
NFL, and NHL
ln(Revenueit)= a0 + a1*ln(Winsit) + a2*ln(Winsit1)+ a3*New Stadiumi + a4*ln(Stadium Capacityi)
+ eit
SUMMARY OF
MODELS
NBA AND MLB REVENUE
Different Estimates of NBA Revenue Model
Estimation Technique
Fixed Effects (no AR(1) terms)
OLS (no fixed effects, no AR(1) terms)
OLS, but with market size added to basic
model
Average percentage of
total revenue
explained
by wins in 2010-11
22.6%
26.8%
35.2%
Different Estimates of Major League Baseball Revenue Model
Estimation Technique
Fixed Effects with AR(1) terms
Fixed Effects (no AR(1) terms)
OLS (no fixed effects, no AR(1) terms)
OLS, but with market size added to basic
model
Average percentage of
total revenue
explained
by wins in 2010-11
18.0%
28.0%
83.8%
51.9%
SUMMARY OF NHL AND NFL REVENUE
MODELS
Different Estimates of National Hockey League Revenue Model
Note: NHL employs standing points and lagged standing points instead of wins.
Estimation Technique
Fixed Effects with AR(1) terms
Fixed Effects (no AR(1) terms)
OLS (no fixed effects, no AR(1) terms)
OLS, but with market size added to basic
model
Average percentage of
total revenue
explained
by wins in 2010-11
23.4%
36.7%
45.8%
48.9%
Different Estimates of National Football League Revenue Model
Estimation Technique
Fixed Effects with AR(1) terms
Fixed Effects (no AR(1) terms)
OLS (no fixed effects, no AR(1) terms)
OLS, but with market size added to basic
model
Average percentage of
total revenue explained
by wins in 2010-11
wins are not statistically
significant
wins are not statistically
significant
6.8%
6.8%
PUNCH-LINE OF VARIOUS REVENUE
MODELS






Models in the literature tend to be OLS models that do not employ
fixed effects or AR(1) terms.
If we look at baseball, we can produce a revenue model where wins are
worth about 50% of revenues if we ignore fixed effects and AR(1)
terms.
With respect to hockey we can come close to 50% with OLS models
In the NBA and NFL, though, we can never get to 50%. And in the
NFL, wins are not often statistically significant.
And in no sport do we get to 50% if we include fixed effects or AR(1)
terms
PUNCHLINE: LEAGUES TEND TO PAY THEIR PLAYERS AT
LEAST 50% OF REVENUES. BUT IT IS DIFFICULT TO GET THE
SUMMATION OF WINS TO BE EQUAL IN VALUE TO 50% OF
LEAGUE REVENUES. BERRI, LEEDS, AND VON ALLMEN
ARGUE THAT THIS IS BECAUSE THESE LEAGUES HAVE
REVENUE STREAMS NOT RELATED TO TEAM WINS (i.e.
FIXED REVENUES).
PUNCHLINE FOR NCAA STUDY
•
•
Because the NCAA has substantial
broadcasting revenues, the Scully
approach will under-estimate each
player’s MRP.
So our estimates will likely underestimate the extent of exploitation.
Measuring Marginal
Product
• Our measure of marginal product applies the
methodology laid forth in The Wages of Wins and
Berri (2008) to college basketball.
• This methodology employs the following model:
•
Winning Percentage = b1 + b2*PTS/PE – b3*Opp.PTS/PA + ei
•
•
•
PTS/PE = Offensive Efficiency
PTS/PA = Defensive Efficiency
This model argues that wins are determined by offensive efficiency and
defensive efficiency; which is the same approach advocated by John
Hollinger (2002) and Dean Oliver (2004).
By utilizing Possessions Employed and Possessions Acquired one can now
connect much of what a player does on the court to wins.
•
Possession Employed
• John Hollinger (2002) and Dean Oliver (2004) define
possessions in basketball as follows:
• Possessions Employed (PE) = FGA + x*FTA + TO – ORB
• Where
o
o
o
o
FGA: Field Goals Attempted
FTA : Free Throws Attempted
TO: Turnovers
ORB: Offensive Rebounds
• In general, the value of (x) is estimated to be around 0.45
Possessions Acquired
•
Berri (2008) defines Possession Acquired as follows:
•
Possessions Acquired (PA) = Opp.TO + DRB + TMRB + Opp.FGM + z*Opp.FTM
•
Where
o DRB : Defensive Rebounds
o TMRB: Team Rebounds (that change possession). This factor has to be
estimated [as noted in The Wages of Wins, Berri (2008), and Stumbling
on Wins].
o FGM : Field Goals Made
o FTM : Free Throws Made
• In general, the value of (z) is estimated to be around 0.45
Wins as a function of
efficiency
Dependent Variable: Team Winning Percentage
Estimated across 345 team observations from the 2011-12 season
Variable
Offensive Efficiency
Defensive Efficiency
Constant Term
Coefficient
1.757
-1.753
0.485
R-squared
0.874
Adjusted R-squared
0.874
Observations
Standard Error
0.051
0.081
0.110
t-Statistic
34.320
-21.713
4.416
345
Given the definition of the efficiency measures, the model allows us
to measure – in terms of wins – the impact of PTS, FGA, FTA, ORB, TO,
Opp.PTS, Opp.FGM, Opp.FTM, Opp.TO, DRB, and TMRB
Marginal Impact of Various
College Basketball Statistics
Player Factors
PTS
FGA
FTA
ORB
TO
DRB
STL (Steals)
Team Factors
Opp. PTS
Opp. FGM
Opp. FTM
Opp.TO-STL
TMRB
Marginal Value
0.026
-0.027
-0.012
0.027
-0.027
0.026
0.026
Marginal Value
-0.026
0.026
0.012
0.026
0.026
As we saw in the analysis of the NBA and WNBA (see Berri and Krautmann, forthcoming) – in absolute
terms – points, rebounds, field goal attempts, turnovers, and steals have essentially the
same impact on team wins
 We don’t have a value for everything in the box score. With a bit of work – as detailed in Berri (2008)
and at http://wagesofwins.com/how-to-calculate-wins-produced/ -- one can determine the value
of blocked shots, personal fouls, and assists (and the diminishing returns aspect of defensive rebounds).
The Marginal Value of College
Basketball Statistics (2010-11)
NCAA Model 2010-11
Player Variables
Three Point Field Goal Made
Two Point Field Goal Made
Free Throw Made
Missed Field Goal
Missed Free Throw
Offensive Rebounds
Defensive Rebounds
Turnovers
Steal
Opponent's Free Throws Made
Blocked Shot
Marginal Value
0.052
0.026
0.014
(0.027)
(0.012)
0.027
0.026
(0.027)
0.026
(0.014)
0.01557
Team Variables
Opponent's Three Point Field Goals Made
Opponent's Two Point Field Goals Made
Opponent's Turnovers
Team Turnover
Team Rebounds
Marginal Value
(0.052)
(0.026)
0.026
(0.027)
0.026
The above table includes everything except for assists. The value of assists
(and the diminishing returns aspect of defensive rebounds) was ascertained
and incorporated (following the methodology presented at
http://wagesofwins.com/how-to-calculate-wins-produced/)
 Simple
model assumes that team revenues
depend on wins, opponent/conference
quality, market demand measure:
 Team revenues increase with quality of
opponents


Most games played against conference teams
Teams in major (stronger) conferences should
attract more revenues
 Market

Demand measure
Teams located near larger populations may have
larger fan base to attract gate and TV revenues.
 Variables:

Team Revenues = EADA data for each team



Wins = Team’s number of Wins (2010-11 season)
Major Conference = dummy variable for teams in
ACC, Big East, Big 10, Big 12, Pac 10, SEC



(ticket sales, guarantees/options, radio/TV, student
fees, government/institutional support, other)
Controls for unobservable effects of major
conferences on team revenue
MSA = population of team’s location to proxy
market demand (e.g., fan base, TV market)
Private = private school dummy controls for any
unobservable effects between private/public
schools on revenues
Revenuei = a + b1Wins + b2Major Conference +
b3MSA + b4Private School
 A few high-revenue teams skew revenue distribution:
High
= $40,887,938
Low
= $346,767
Median = $1,681,843
Mean
= $3,582,512
St.Dev. = $4,634,351



OLS on conditional means will be sensitive to outliers
OLS estimates show another Win generates $157,646
in Team Revenue
Likely overestimates impact of Wins for most teams
in our sample
 Quantile
regression estimates the conditional
median and conditional quantile functions
for the dependent variable

Robust to the presence of outliers in these data
 We
estimate the coefficient on Wins at
different parts of the conditional distribution
of the dependent variable
 Quantitative impact of Wins on Revenues -and therefore player MRP’s -- vary
considerably across teams with different
revenue producing ability
Quantiles
Coefficients from quantile regressions
0.10
0.25
0.50
0.75
0.90
$17,621
$32,986
$59,229
$112,032
$159,602
Example
Southern Utah University
California State University-Bakersfield
University of San Francisco
Utah State University
Kentucky
These values are for 2010-11. We
estimated that revenue increases
by 7% each year. So we used this
7% figure to arrive at values for
2009-10, 2011-12, and 2012-13.
 The
following website says that median FBS
scholarship is $27.9K, FCS is $22.3K, and
$32.4K for D1 w/o football (there are about
347 D1 schools with 125 FBS, 124 FCS, and 98
D1 w/o football)
usatoday30.usatoday.com/sports/college/me
nsbasketball/2011-value-of-collegescholarship.htm
 For this presentation, we used the weighted
average; which is $27,177.
 We also adjusted this value by 7% for the
other years we examined.
1.
2.
3.
Measure each player’s production of wins
(i.e. marginal product)
Multiply production of wins by the impact
wins has on team revenue (i.e. marginal
revenue product)
Compare MRP estimate to estimate of
scholarship cost. If MRP estimate is larger,
then we estimate a player is exploited.
Kentucky 2009-10 Wins Produced
John Wall*
7.38
DeMarcus Cousins*
7.30
Patrick Patterson
6.81
Eric Bledsoe*
3.17
Daniel Orton*
2.20
DeAndre Liggins
1.60
Darius Miller
1.53
Perry Stevenson
1.40
Ramon Harris
1.30
Darnell Dodson
0.81
Josh Harrellson
0.32
Jon Hood
0.19
Mark Krebs
-0.30
Totals
33.71
Team Wins
35
Estimated Scholarship Cost: $25,392
Estimated Value of Win: $149,161
* - one-and-done player
MRP
Exploitation
$1,101,297 $1,075,904
$1,088,398 $1,063,006
$1,016,050
$990,658
$473,306
$447,914
$327,954
$302,562
$238,851
$213,458
$228,318
$202,926
$209,467
$184,075
$193,625
$168,232
$121,130
$95,738
$47,048
$21,655
$27,981
$2,589
-$45,348
-$70,741
$5,028,076 $4,697,977
Kentucky has had ten one-anddone players in the past four years.
It is interesting to see how many
wins (and revenue) these players
have produced relative to the cost
of their one-year education.
Kentucky 2010-11 Wins Produced
MRP
Exploitation
Josh Harrellson
7.81
$1,246,578 $1,219,408
Darius Miller
5.31
$846,760
$819,590
DeAndre Liggins
4.27
$681,039
$653,869
Terrence Jones*
4.26
$680,667
$653,498
Doron Lamb
4.08
$650,412
$623,243
Brandon Knight*
3.41
$543,746
$516,576
Eloy Vargas
1.28
$204,709
$177,539
Jon Hood
0.15
$24,519
-$2,651
Stacey Poole
-0.01
-$2,116
-$29,286
Jarrod Polson
-0.13
-$20,673
-$47,843
Totals
30.42
$4,855,640 $4,583,943
Team Wins
29
Estimated Scholarship Cost: $27,170
Estimated Value of Win: $159,602
* - one-and-done player
Kentucky 2011-12
Wins Produced
MRP
Exploitation
Anthony Davis*
12.96
$2,213,591 $2,184,519
Michael Kidd-Gilchrist*
6.22
$1,061,431 $1,032,360
Terrence Jones
5.42
$925,250
$896,178
Darius Miller
4.06
$693,894
$664,822
Doron Lamb
4.03
$688,311
$659,240
Marquis Teague*
3.73
$637,264
$608,192
Kyle Wiltjer
1.07
$182,927
$153,855
Eloy Vargas
0.42
$71,984
$42,912
Twany Beckham
0.20
$34,727
$5,656
Brian Long
0.03
$5,886
-$23,186
Sam Malone
-0.08
-$13,218
-$42,289
Jarrod Polson
-0.09
-$15,447
-$44,519
Totals
37.98
$6,486,600 $6,137,741
Team Wins
38
Estimated Scholarship Cost: $29,072
Estimated Value of Win: $170,774
* - one-and-done player
Kentucky 2012-13 Wins Produced
MRP
Exploitation
Nerlens Noel*
6.29
$1,150,125 $1,119,019
Willie Cauley-Stein
3.40
$621,297
$590,190
Alex Poythress
3.36
$613,641
$582,535
Julius Mays
3.24
$592,090
$560,983
Archie Goodwin*
1.74
$318,409
$287,303
Jarrod Polson
1.70
$311,415
$280,309
Ryan Harrow
1.55
$283,042
$251,936
Kyle Wiltjer
1.54
$282,154
$251,047
Jon Hood
0.72
$131,456
$100,350
Twany Beckham
0.04
$6,927
-$24,180
Sam Malone
0.01
$2,155
-$28,951
Brian Long
-0.05
-$8,569
-$39,676
Tod Lanter
-0.09
-$16,420
-$47,526
Totals
23.47
$4,287,724 $3,883,337
Team Wins
21
Estimated Scholarship Cost: $31,107
Estimated Value of Win: $182,728
* - one-and-done player




Across these four seasons, Kentucky players
received an estimated $1.355 million in
scholarships.
These players produced 125.6 wins worth
$20.658 million.
So these players were “underpaid” by $19.303
million.
10 of these players were “one-and-done”. These
players
◦ produced 54.4 wins, or 43.3% of the total wins produced
◦ these wins were worth $8.92 million
◦ these players received scholarships worth an estimated
$278,167
◦ So these players were underpaid by $8.6 million
WP40 = Wins
Produced per
40 minutes.
Exploitation By Class: 2009-10 to 2012-13
Observations
MRP
Scholarships
Exploitation
Wins
Produced
Freshmen
4,906
$301,450,686
$138,434,702
$163,015,984
3,221
0.079
Sophomores
4,292
$456,474,971
$121,127,535
$335,347,436
5,036
0.099
Juniors
4,826
$592,154,171
$136,142,287
$456,011,884
7,120
0.108
Seniors
3,995
$591,255,244
$112,541,069
$478,714,176
7,251
0.116
18,019
$1,941,335,073
$508,245,593
$1,433,089,479
22,628
0.103
Class
Totals
Exploitation Rates by Class: 2009-10 to 2012-13
Class
Number Exploited Exploitation Rates
Freshmen
1,875
38.22%
Sophomores
2,218
51.68%
Juniors
2,820
58.43%
Seniors
2,620
65.58%
Totals
9,533
52.91%
WP40
Should average
about 0.100.
Overall, we estimate
MRP to be $1.94 billion
and scholarships to
be $0.51 billion.
Top Conference Other Conferences
All Players
Observations
4000
14019
18019
Wins Produced
6,082
16,546
22,628
WP40
0.121
0.097
0.103
MRP
$967,823,623
$973,511,450
$1,941,335,073
Scholarship
$112,807,671
$395,437,922
$508,245,593
Exploitation
$855,015,952
$578,073,527
$1,433,089,479
Exploited
2748
6785
9533
Exploitation Rate
68.7%
48.4%
52.9%
Top Conference = ACC, Big 10, Big 12, Big East, SEC, Pac 10/12


In our sample we have 440 players who played all
four years (progressed from freshmen to
seniors).
Of these 440…
◦ 98 played in top conferences. Of these, 90.8 %
generated more revenue than they were “paid” across all
four years.
◦ For the 342 in the non-top conferences, 64.9%
generated more revenue than they were paid across all
four years.
◦ For all 440 players, 70.7% generated more revenue than
they were paid across all four years.
◦ On average, these players generated $559K across four
years and received scholarships worth an estimated
$113K.
Conclusion
• The data tabulated for men’s college basketball players
allows us to measure each player’s marginal product
• Revenue data allows us to ascertain the value of a win.
• With this information in hand, we can measure MRP.
These estimates, though, only focus on wins. So the
estimates should be thought of as too small.
• That being said…
• Exploitation rates appear to increase the longer a player
is in school. This reflects the fact that
o older players are more productive per minute
o older players play more minutes
• 70% of players who stay all four years are estimated to
be exploited. This rate is over 90% if the player is in a
major conference
Future Research
• We hope to add additional revenue data.
• Player productivity also exists back to 200001.
• Beyond adding more to our revenue and
wins model, we could also investigate how
the salary of coaches relates to the rate of
exploitation on a team.