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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

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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.

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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.

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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.

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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

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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

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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(Revenue it )= a 0 + a 1 *ln(Wins it ) + a 2 *ln(Wins it- 1 )+ a 3 *New Stadium i + a 4 *ln(Stadium Capacity i ) + e it

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SUMMARY OF NBA AND MLB REVENUE MODELS

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SUMMARY OF NHL AND NFL REVENUE MODELS

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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).

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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 under- estimate the extent of exploitation.

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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 = b 1 + b 2 *PTS/PE – b 3 *Opp.PTS/PA + e i 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.

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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 FGA: Field Goals Attempted o FTA : Free Throws Attempted o TO: Turnovers o ORB: Offensive Rebounds In general, the value of (x) is estimated to be around 0.45

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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

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Wins as a function of efficiency 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

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Marginal Impact of Various College Basketball Statistics 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 valuehttp://wagesofwins.com/how-to-calculate-wins-produced/ of blocked shots, personal fouls, and assists (and the diminishing returns aspect of defensive rebounds).

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The Marginal Value of College Basketball Statistics (2010-11) 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/)http://wagesofwins.com/how-to-calculate-wins-produced/

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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.

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Variables: Team Revenues = EADA data for each team (ticket sales, guarantees/options, radio/TV, student fees, government/institutional support, other) 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 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

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Revenue i = + 1 Wins + 2 Major Conference + 3 MSA + 4 Private School A few high-revenue teams skew revenue distribution: 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 High=$40,887,938 Low=$346,767 Median=$1,681,843 Mean=$3,582,512 St.Dev.=$4,634,351

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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

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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.

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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-college- scholarship.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.

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1. Measure each player’s production of wins (i.e. marginal product) 2. Multiply production of wins by the impact wins has on team revenue (i.e. marginal revenue product) 3. Compare MRP estimate to estimate of scholarship cost. If MRP estimate is larger, then we estimate a player is exploited.

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Kentucky has had ten one-and- done 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.

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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

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WP40 = Wins Produced per 40 minutes. Should average about 0.100. Overall, we estimate MRP to be $1.94 billion and scholarships to be $0.51 billion.

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Top Conference = ACC, Big 10, Big 12, Big East, SEC, Pac 10/12

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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.

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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

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Future Research We hope to add additional revenue data. Player productivity also exists back to 2000- 01. 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.

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