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.