THE MARKET FOR TALENT: ARE TOP DRAFT PICKS OVERPAID?

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1 THE MARKET FOR TALENT: ARE TOP DRAFT PICKS OVERPAID? Nikhil Joshi 1 May 2011 Department of Economics Stanford University Stanford, CA nrjoshi@stanford.edu Advisor: Roger Noll ABSTRACT The National Basketball Association imposes two important, and unusual, restrictions on its new employees: a draft, in which they are assigned a single employer with which they can contract with, and a pay-scale, which prescribes maximum compensation levels for up to the first four years of their careers. Using a sample of veteran players, who have gone through free-agency, I establish the value owners ascribe to a player-season in the open free-agent market. Comparing this value to player compensation, under rookie contracts, allows me to examine the surplus generated by new players for their teams. I find that the two rookie restrictions allow owners to extract significant monopsony rents from new players; the rents are highest for top draft choices, and decline steeply as the draft goes on, implying that owners are rational surplus-maximizers. Keywords: National Basketball Association, player compensation, rookie compensation, monopsony, collective bargaining, NBA draft, NBA rookie pay-scale 1 I would like to thank Professor Noll not only for his guidance and insights in this project, but for his invaluable service as an advisor throughout my Stanford career. I am very grateful for his time and energy. I thank Professor Rothwell for his help at the outset of this project, and Professor Hanson for allowing me to present my findings and receive feedback at the SIEPR Sports Economic Policy Forum.

2 May 2011 Nikhil Joshi 2 Contents 1 Introduction 2 Literature Review 3 Background: The Collective Bargaining Agreement 4 The Compensation Equation 4.1 The Data 4.2 The Parameters of the Model 4.3 Specification Issues 4.4 Results 5 Surplus Value 5.1 The Data 5.2 Calculating Surplus Value 5.3 Formal test: relationship between surplus and draft order 5.4 Discussion 6 Conclusion 7 Appendix References

3 May 2011 Nikhil Joshi 3 1 Introduction The market for talent in the National Basketball Association is an interesting and highly unusual one. Prospective employees are subject to intense and endless scrutiny by fans, media and teams, before they even become eligible to join the league. After they become eligible, they are, in a draft, assigned one possible employer. Then, they are signed to contracts that run into the millions of dollars, the bulk of which is guaranteed no matter what happens on the court. And once they do start playing, their performance is easily measurable through dozens of statistics, carefully parsed by fans and expert commentators, and televised live around the world. If, the argument goes, a high-stakes, high-visibility labor market, like the one for NBA rookies, can t properly predict performance and assign pay, then there s little hope for the more mundane labor markets faced by most new workers, like the markets for new investment bankers or computer engineers, where the stakes are less high and performance far less observable. But two important features of the market for rookies in the NBA get in the way of a rational and consistent relationship between pay and performance - the NBA draft and the rookie pay scale, both established in the Collective Bargaining Agreement (CBA) between the owners and the National Basketball Player s Association (NBPA). Per the terms of the CBA, rookies must enter the league through a draft, which restricts their ability to market their services to only the team that selects them, and forecloses competition amongst teams for new players. The pay scale then sets maximum salaries for each pick in the first round of the draft. These two features, negotiated between the veteran players who control the NBPA and league officials representing the owners,

4 May 2011 Nikhil Joshi 4 effectively allow veterans and owners to let the brunt of the league s monopsony rent extraction fall on rookies, who don t have a seat at the negotiating table. In this paper, I investigate how monopsony rents vary by draft order in the NBA. This allows me to answer two questions: (1) are rookies overpaid, and (2) are owners rational and consistent in the way that they value, draft and sign rookies. To determine the answers to these questions, I calculate the surplus value of every player in the draft, over the four years during which the drafting team holds the exclusive rights to a rookie. This analysis is done by establishing the performance value of each playerseason the value owners ascribe to a certain level of on-court production in the free agent market, estimated from a sample of veteran players who have been through free agency. While even performance value doesn t fully capture the marginal revenue product of a player free agent salaries are still subject to the salary cap and the collective monopsony power of the league s thirty owners it does come closer than rookie pay. Subtracting compensation from performance value yields the surplus value of a player-season. Surplus value is the difference between what an owner pays a new player, under the terms of a rookie contract, and the unfettered market value of that player s level of production, on the open free agent market. I find that surplus value is reliably positive throughout the draft, likely because rookie contracts are negotiated within the bounds of the two significant constraints mentioned previously: the NBA Draft, and the rookie salary scale. All new players, whether they are widely-acclaimed lottery picks, or anonymous late second-round choices, are subject to some degree of monopsony exploitation by the owners.

5 May 2011 Nikhil Joshi 5 Once the sign of surplus value has been established, it is valuable to investigate its relationship with draft order. If owners are rational and consistent in their drafting strategies, surplus value should decline over the course of the draft, with the first pick the most valuable, and sixtieth pick the least valuable, in terms of surplus. But recent research (Thaler and Massey 2010) suggests that this may not be true, and that judgment and decision-making pathologies outweigh the market incentives facing owners, leading surplus value to peak well after the first pick. I find that, in the NBA, the market is efficient there is a strong, significant, and negative relationship between draft position and surplus value in all regions of the draft. The relationship, though significant throughout, is especially strong amongst top picks, in the lottery round (picks 1-14). 2 Literature Review The sports economics literature faces two initial questions. Is there any value in studying professional sports labor markets beyond satisfying the curiosities of sports fans? Can findings from these labor markets be extrapolated to more relevant labor markets found in the real world? Kahn (2000) says that professional sports can serve as a valuable laboratory for studying the economics of labor markets. They offer several distinct advantages, to the empirical economist, over traditional labor markets: professional sports leagues have retained extensive data on player performance and compensation, and the number of employees is small enough so that significant information is available for each employee. Sports labor markets are an ideal laboratory for the testing of monopsony effects, says Kahn (2000), because in most cases, professional sports leagues are the only

6 May 2011 Nikhil Joshi 6 employers of players in their sport. In one of the first papers written on the subject, Scully (1974) seeks to measure the economic loss to players that results from the reserve clause, which gives the team owner the exclusive option to renew a contract. He finds significant exploitation of monopsony power over a career, average players receive 20% of their marginal revenue products. But determining the extent of monopsony exploitation in professional sports is dependent upon accurately finding the marginal revenue product of a player, which is not an easy task. Player performance is the most obvious of the determinants of marginal revenue product the players that produce on the field and help their teams win should, logically, be generating revenue for their owners. Scully (1974) establishes the groundwork for this area of the literature by basing his calculation of marginal revenue product of a player on assumptions of how a player s individual performance alters team results. Scully does not use the individual player as the unit of analysis because of the difficulty of comparing hitters, who play every day, with pitchers, who rest for several days in between starts, through the use of attendance data. Other factors, including draft order and superstar status, have been used to help explain variation in player compensation and contribute to an understanding of marginal revenue product. Staw and Hoang (1995) were the first to establish the sunk cost effect in testing to see if there were, after controlling for performance, any lingering effects of draft order. They find that, ceteris paribus, draft order does impact minutes played, seasons played, and likelihood of being traded. Camerer and Weber (1999) re-examined Staw and Hoang s data, and found that though their basic findings were correct, they had exaggerated the duration and magnitude of the sunk cost bias. By including player

7 May 2011 Nikhil Joshi 7 popularity and pre-draft scouting reports, Camerer and Weber found that there were other relevant non-draft factors that do correlate with draft order, and impact the playing time, season survival, and trade rates of players. The literature does not converge on a strong understanding of the effect of draft-order on player value. Star power would appear to have a strong link to marginal revenue product, but the literature does not firmly establish this relationship. Schmidt and Brook (2004) find no relationship between all-star votes and gate revenue in a linear model, but do find a positive correlation between the two in a double-lagged model. Several individual superstar dummies (for players of unusual popularity, like Michael Jordan) did have statistically significant correlations with gate revenue. But the effect of star power was dwarfed by the importance of winning the authors found that a team would need 370,000 all-star votes to generate the revenue it receives from one win. Camerer and Weber (1999) find that star power has some relevance. When they include the pricing of player trading cards as an explanatory variable in their test of the sunk-cost effect of draft order, they find that the magnitude of the sunk-cost effect is smaller than is established by Staw and Hoang (1995); this means that player popularity does have some effect on compensation. Just as with the sunk-cost effect, the literature has not converged around a single understanding of the effect of star power on marginal revenue product. Finding the value of players in professional sports is ultimately dependent on the driving factors of consumer demand for the professional sports product. Schmidt and Brooks (2004) set out to find the effect of competitive balance on consumer demand. They assume that demand is determined by team performance, franchise characteristics and market characteristics. Of these factors, team performance is found to be most

8 May 2011 Nikhil Joshi 8 valuable in explaining revenue, and by extension demand. Scully (1974) reached a similar conclusion thirty years prior to Schmidt and Brooks he found that revenues are related to individual performance primarily through its effect on team standings. The lesson from the literature here is clear: winning determines consumer demand. I examine monopsony exploitation of rookies in the NBA by using replacement cost as a proxy for marginal revenue product. Thaler and Massey (2010) use this technique in an examination of rookie compensation in the NFL: they define replacement cost as the cost of obtaining the equivalent value that a young player provides with a veteran. This cost, termed performance value, is found by estimating a compensation equation for a sample of veteran players, who have had their wages set in the free agent market. It is important to note that performance value is not marginal revenue product even in the relatively open market of free agency, monopsony effects (through the salary cap, and the limited number of teams in a league) limit wages. Thaler and Massey find that in the NFL, performance value declines with draft order, but not as steeply as compensation they find that surplus value, the difference between performance value and compensation, is highest not at the top of the draft, but at the end of the first round. Citing various judgment and decision-making pathologies, they say that owners systematically overvalue the top picks in the draft, and because arbitrage is impossible (early picks are given to the least successful teams, and can t be sold short ) the market has converged on an inefficient equilibrium. I find that data from the NBA does not support Thaler and Massey s conclusion that surplus value peaks after the early picks in the draft. Because individual performance is much easier to observe in basketball all players share the court at the same time, and

9 May 2011 Nikhil Joshi 9 perform much more similar functions high-quality performance data that is easily comparable across player position is readily available. This performance data has less noise, and presumably less bias, than similar NFL data. Thaler and Massey are forced to use categorical data (separating players into five categories based on number of games started), which offers much less detail than continuous performance data. It is also important to note that there are differences in the way the two leagues operate notably, the NBA, unlike the NFL, has set a pay scale for rookies. 3 Background: NBA Salary Rules Three features of the CBA that currently governs the relationship between players and owners in the NBA are relevant to the analysis in this paper. First, the CBA establishes a soft salary cap that exerts broad downward pressure on player pay league-wide. For the season, the salary cap is set at $58,044,000 per team. The cap also sets maximum salaries for veterans, based on number of years of service. There are a number of notable exceptions to the cap: most importantly the midlevel exception, bi-annual exception, Larry Bird exception, and Early Bird exception, all of which allow owners to exceed the cap by signing players under certain conditions. If, after using these exceptions, a team s payroll exceeds luxury tax levels (in , $70,307,000), then the owner must pay a tax to the league, which is re-distributed to nontax paying teams. For the season, 11 of the NBA s 30 teams paid a luxury tax, with the Los Angeles Lakers leading the league with a $21.42 million tax bill. The ownership group in the NBA is diverse owners range from Russian oligarchs (Mikahil Prohorov of the New Jersey Nets), to small partnerships (Atlanta

10 May 2011 Nikhil Joshi 10 Spirit LLC of the Atlanta Hawks), to publicly-traded corporations (Comcast of the Philadelphia 76ers). While different owners can and do face very different financial constraints, all owners are subject to the salary cap. And every owner, no matter how wealthy, should generally prefer (ceteris paribus) less expensive players to more expensive players. Though this preference is not as strong as it is in the NFL, which has a hard cap, it is still safe to assume that owners, subject to the salary cap, internalize player compensation at similar levels. Second, the CBA sets rules for new player entry into the league, through the NBA draft. In the draft, the league s 30 teams take turns turning selecting new players over two rounds. Picks 1-14 are referred to as lottery picks, and are allocated, with order determined by a weighted random lottery, to the fourteen teams with the worst records from the previous season. Picks make up the remainder of the first round, and are allocated to the sixteen teams not given lottery picks, in order of finish in the previous season from worst to best. All picks in the first round receive a guaranteed two-year contract, with exclusive team options on the third and fourth years. Picks make up the second round, and are assigned in the same order as round 1. Second round picks do not receive guaranteed contracts. Third, the CBA sets a rookie pay scale for all picks in the first round. The pay scale, which began with the 2005 draft, sets salaries for the two guaranteed years of a first round pick s rookie contract, team options in years three and four, and the qualifying offer after the conclusion of the fourth year. Teams must pay players under a rookie contract % of the salary listed in the CBA. The salary scale does not have the same salary flexibility, especially amongst top picks, that is observable in leagues without

11 May 2011 Nikhil Joshi 11 rookie scales (such as the NFL). Dropping one draft position costs an average of $1.24 million per season for top 10 picks, $311,000 per season for picks 11-20, and $116,500 for picks (see Table A for the Draft s rookie pay scale). 4 The Compensation Equation The calculation of surplus value for a player-season, and any subsequent interpretation of that value, is dependent on the correct specification of a compensation model, and the estimation of that model. I establish the market value of a player-season by creating a model of the relationship between compensation and performance, and estimating that model with a sample of veteran players who have been through free agency. 4.1 The Data To find the market value of a player-season, I use a sample of 324 veteran players, who are in years 5-7 of their careers between Because veteran players have been through free agency, their wages have been set by the market, rather than by a single team restricted by the league s rookie pay scale. In signing free agents, owners have revealed their preferences they have shown what they are willing to pay for a certain level of production. But using veteran players to estimate the compensation equation also has a drawback; some sample bias occurs because of the survivorship effect players that have survived in the league until their fifth year surely have characteristics that differentiate them from the general player pool.

12 May 2011 Nikhil Joshi 12 Players in the sample work for a wide range of pay. As shown in Table B Panel 2, the 10 th percentile of pay is $1.5 million, while the 90 th percentile is almost $12 million. Average pay, and variance, both increase moderately with year-in-league. Average pay for all players in the sample is $6.1 million per year. Salary data, which includes salary and bonuses, is reported by USA Today in conjunction with HoopsWorld, and is not publicly verified by the league or the player s association. I measure performance using a per-minute efficiency measure, as calculated in John Hollinger s PER formula. The formula includes both positive (field goals, free throws, 3-pointers, assists, rebounds, blocks and steals), and negative (missed shots, turnovers, personal fouls) components of performance. PER is pace-adjusted, controlling for differences in pace across teams in the league. The main advantage of using PER to measure performance is that it makes it easy to compare the overall value of a playerseason, across different teams, positions, and specialties (e.g. scorer vs. rebounder). The PER metric is not, however, without deficiencies the value of defensive efforts may not be fully captured, and using a per-minute efficiency rating than a total minute statistic may bias performance data. Average PER in a given season is normalized to As shown in Table B Panel 1, in the veteran sample I use, average PER is PER in this sample increases with year-in-league, but only moderately. 4.2 The Model I use a log-linear functional form to model the relationship between compensation and performance. Logarithmic transformation of the compensation data is helpful, because it better accommodates the long right tail of NBA salaries in the sample. In

13 May 2011 Nikhil Joshi 13 modeling compensation, I control for several other factors, including position, year-inleague, missed seasons, and draft pick. For player i in year t, I estimate: (1)!"#!"#$!,! =! +!!"#$_!!,! + Π!!! + Κ!!!,! + Υ!!! + Θ!! +!!,!, where!"#$_!!,! is a linear spline of the weighted average of performance over the past four years, knotted at the 33 rd and 66 th percentiles,!!! is a vector of indicator variables for! player position (guard, forward or center),!!,! is a vector of indicator variables for yearin-league (5, 6 or 7),!!! is a vector of indicator variables for number of missed seasons in the past four years (1 or 2+), and!! is a linear spline of reverse draft order (pick 1 = 60, pick 2 = 59,, pick 60 = 1), knotted at the end of the lottery (pick 14) and at the end of round 1 (pick 30). I estimate the compensation equation twice: first without draft order, and then including draft order. I use a weighted average of past performance to account for the decline in explanatory power of long-ago seasons. Presumably, recent seasons are more important in determining pay than seasons in the more distant past. Other effects are also expected - performance in the last season of a contract should be more strongly correlated with pay, and performance in the rookie and sophomore years should be weakly correlated with pay later on. But regression analysis does not lend strong support to these hypotheses; in fact, performance is so highly correlated year to year that attempting to separate the explanatory power of different years is fruitless. Instead, I apply a uniform discount rate to past performance, regardless of year-in-league. Through sensitivity analysis to maximize adjusted R-squared, I chose a 15% discount rate for past performance. Performance enters the model in a linear spline to account for differentiated performances by top producers. Using a linear spline adds flexibility to the model, and

14 May 2011 Nikhil Joshi 14 better captures the value of top performers. The spline is knotted at the 33 rd and 66 th percentiles, because there are not natural categories of performance in the data. I include dummy variables for two categories of missed seasons one, and two or more when players have not logged 6.09 minutes per game. The performance statistic I use, Hollinger s PER, designates players with fewer than 6.09 mpg as non-qualifiers, because they simply have not logged enough playing time to receive an efficiency rating that is comparable to players with more minutes. Non-qualifying player-seasons are accounted for through the missed seasons dummy variables. It is important to note that this variable does not differentiate between players who are injured (presumably the risk of injury is a systematic one, and has been factored into player salaries broadly) and those who do not play because of a team decision that their play is inferior however, reliable data on player injuries is not available for the sample. Draft order enters the compensation model in much the same way as performance a linear spline with two knots. This allows me to more fully capture the effects of being drafted at the top-end of the draft, in the lottery. As shown in Table B Panel 3, salary and performance do appear to vary across the three regions of the draft (lottery, picks 15-30, and second round). Lottery picks, especially, have higher compensation and performance numbers. 4.3 Specification Issues Including draft position in the compensation model is not an obvious step after controlling for performance, along with other characteristics including position, year-inleague, and missed seasons, there is no reason that draft order should still have a

15 May 2011 Nikhil Joshi 15 lingering effect on compensation for veterans who are five to seven years removed from the draft, and have signed another contract after the expiration of their rookie deals, unless teams are markedly slow to revise their beliefs. There is some debate in the literature over the extent of a sunk cost effect, in which the effects of draft order persists (Staw and Hoang 1995, Camerer and Weber 1999). Indeed, including draft order explicitly has very little impact on the compensation model. As shown in the regression results in Table C, including draft order increases the adjusted R-squared value only slightly, from 0.55 to The effect of draft, if any, comes almost entirely from its effect on performance. I test this by first estimating the extent to which draft order predicts salary, and then finding the incremental explanatory value of unpredicted performance (by including performance residuals - the difference between actual performance and performance as predicted solely through draft order): (2)!"#!"#$!,! =! + Ν!"#$_!"#$%!,! + Π!!! + Κ!!!,! + Υ!!! + Θ!! +!!,! As shown in Table D, draft order alone, along with indicator variables for position, year-in-league and missing seasons, accounts for just 32% of variation in compensation. The incremental value of adding performance that cannot be predicted from draft order is large adding performance residuals increases the adjusted r-squared to The value of including draft order, then, is to help correct for a specification error in how performance enters the compensation model. There are two possible sources for this specification error: the functional form of the compensation-performance relationship may not be log-linear, and the statistical measurement of performance (weighted average of Hollinger s PER) may not fully capture a player s on-court production.

16 May 2011 Nikhil Joshi 16 Including draft order explicitly also has the benefit of ensuring that the performance values I predict later on for new players, which are based on the compensation model estimated for veteran players, are non-biased relative to draft order. This becomes critical when I test the relationship between surplus and draft order. 4.4 Results As shown in Table C specification (2), the compensation model explains a full 57% of variation in player compensation in the sample. Performance plays a leading role in determining pay for veterans all three regions of the linear spline of performance are positive and significant. Surprisingly, the third region of performance (the top 33%, with a PER above 15.0) has the smallest of the three coefficients, and is least significant. This suggests that, even for free agents, there is not enough flexibility in pay to account for top performer. Two features of the CBA likely contribute to this lack of flexibility at the right tail of performance the salary cap, and maximum compensation limits for an individual contract based on years of service. The indicator variables included in the model for position, year-in-league, and missed seasons all have very little impact on the estimation of the compensation equation. This suggests that in the NBA, unlike in other leagues, compensation is not highly correlated with non-performance factors. Draft order also has little influence, as described in section 4.3. Curiously, the coefficient for the second region of draft order (picks 15-30) is negative, though the 95% confidence interval for the region does include zero. As shown in Figure 1, veteran compensation, sorted by draft order, varies significantly, with little obvious correlation.

17 May 2011 Nikhil Joshi 17 5 Surplus Value In an analysis of drafted players over the four years in which, for first round picks, the drafting team holds exclusive rights to their basketball services, I find the monopsony profit realized by owners for each player-season. To calculate surplus value of a rookie, I predict performance value the monetary value of a player-season in the free agent market, based on a sample of veteran player-seasons and subtract compensation, resulting in surplus. After establishing that this surplus is positive throughout the draft, I test the relationship between surplus and draft order, and find that selecting earlier in the draft reliably increases surplus value for the owner. 5.1 Data I calculate surplus value for new players, rather than veterans, so that I can find the value to the drafting team of signing a rookie. I only use the first four seasons of a rookie s career because these are the seasons to which the drafting team has exclusive rights to the player (for a first round pick). The drafting team does have some rights to the player beyond four seasons if a team exercises its fourth-year option for a first round rookie, then the player becomes a restricted free agent after the end of the fourth season. The team can then make a qualifying offer at the rookie scale amount (see Table A) after the fourth year, and then retains the right to match any other offers and retain the player. There also may be some lock-in effect after four years a player, after establishing himself in his original team s market, may have some preference for staying

18 May 2011 Nikhil Joshi 18 with his current team. For the purposes of the following analysis, I ignore these two effects. The new player dataset I use includes 1,174 player-seasons, which covers all players drafted from I retain players who drop out of the league in my sample, to avoid any survivorship bias. Performance and salary data is from the same sources as the veteran player dataset, from John Hollinger s PER formula, and USA Today/HoopsWorld reporting, respectively. As shown in Table E, a sizable portion of player-seasons in the sample do not log minutes on the court. 33% of the player-seasons are not in the league, and 8% are in the league, but not playing. Of the remaining player-seasons, most (22%) are in the bottom performance tier. 5.2 Calculating Surplus Value Surplus value is calculated by predicting performance value for player-seasons in the new player dataset, and subtracting compensation in each year, resulting in surplus for player i in year t: (3)!!,! =!!,!!!,!. The mean and standard deviation, by draft pick, of the performance value estimates, yearly compensation, and surplus value estimates are summarized in Table G. Surplus average is positive for all draft picks in the first round. In the second round, surplus is positive for all picks, except for pick 35, 44, 58 and 59, because no players in the sample that were drafted at these positions played minutes per game over the first four years of their careers.

19 May 2011 Nikhil Joshi 19 The performance value curve, compensation curve, and surplus value curve are summarized by Lowess smoothing curves in Figure 4. While the curves, which are weighted averages of the underlying data and results, must be interpreted with caution, they do suggest that not only is surplus reliably positive throughout the draft, but that it declines steadily with draft order. Plotting mean and standard deviation of surplus value by draft pick, in Figure 5, gives a more precise visual representation of the data and results. While surplus does decline, it does not do so monotonically. This is a result of variation in performance around the mean some players perform better than can be expected based on draft order, and some perform worse. 5.3 Formal test: relationship between surplus and draft order To account for the unpredictable component of performance, I estimate two different specifications of the relationship between surplus value and draft order one including performance residuals (the difference between actual performance and performance predicted solely by draft order), and one without residuals: (4)!!,! =! +!!!"! +!!!"! +!!!"!_!"# + Κ!"# + Π!"_!"#$ + Θ!"#!!"#$% +!!,!. Also included are controls for players who are no longer in the league (NIL), and playerseasons in which the player is paid but does not average 6.09 minutes per game (No_mins). Including performance residuals dramatically increases the explanatory power of the model, as shown in Table F. By including the residuals, I correct for the effect of the deviation in performance from what is predicted by draft order. With this control, there is

20 May 2011 Nikhil Joshi 20 a significant and positive relationship between surplus and reverse draft order in all regions of the draft. The relationship is especially strong in the lottery portion of the draft. The relationship is weaker in the second half of the first round picks 15 to 30 but increases in strength during the second round. It is important to consider the unique features of the second round when examining that region of the draft: second-round salaries are not subject to the rookie pay scale, and need not be guaranteed for two years. This means that, as shown in Table G, average salaries drop off and variance increases steeply between the end of the first round and the start of the second round. Of course, because second-round salaries aren t subject to the rookie scale, they can also be swiftly upwards adjusted for top performers Carlos Boozer (pick #34) and Paul Millsap (pick #47), have the highest salaries in the sample. Also, note that of 574 second-rounder player-seasons in the sample, only 195 are active and log more than 6.09 mpg. 5.4 Discussion The surplus values calculated for player-seasons within the first four years of a rookie s career have two clear and interesting implications rookies are underpaid, by a sizable margin, and owners rationally and consistently maximize surplus by choosing players with the biggest gap between performance and pay at the top of the draft. Later in the draft, this gap shrinks significantly. While the average surplus value of the top pick is $13.6 million, average surplus falls below $1 million per pick by the end of the second round.

21 May 2011 Nikhil Joshi 21 The underpayment of rookies, due to the monopsony power exercised by the owners through two mechanisms, the draft and the rookie first-round pay-scale, is dramatic. Rookies, over the first four years of their careers, are paid roughly one-quarter 2 of what they would receive in the open free-agent market. On average, surplus is significantly higher in the first round ($4,872,969) than in the second round ($1,462,137), where contracts need not follow the rookie scale, and are not guaranteed. While performance values are also much lower in round 2, this suggests that the rookie pay scale may be driving high surplus values in round 1. The extent to which surplus value falls as the draft goes on is remarkable, and serves as proof of the rationality and consistency of owners drafting strategies, contrary to recent commentary (Thaler and Massey 2010). When a control is added to correct for deviation in performance from what is predicted from draft order (this doesn t penalize owners for not responding to information about the unpredictable component of performance that they don t have), surplus rises reliably as you move up in pick order. 6 Conclusion What do Pope Benedict XVI, Leonardo DiCaprio, Sam Bradford and your car mechanic have in common? asked USA Today writer Mike Lopresti in a sports column last year. Right. None of them has even thrown a pass in an NFL game. But one of them has just been guaranteed $50 million to do it. (Hint: It s not the pope.) Seemingly the entire sports world from owners to commentators to fans has embraced the notion that rookies are vastly overpaid. 2 The median of the ratio of mean salary, by draft pick, to mean performance value, by draft pick, is 0.24.

22 May 2011 Nikhil Joshi 22 Everyone, except of course the rookies, is clamoring to set up mechanisms to limit rookie pay. In re-negotiating the collective bargaining agreement in the NFL, the Player s Association has proposed that total rookie compensation for 2011 be reset to 2009 levels, lopping off around $200 million. The league has gone a step further, proposing a strict salary scale for all picks. 3 In the NBA, owners show no sign of removing the rookie salary scale they instituted, and have realized significant financial benefits from, in In fact, they have proposed adjusting the scale to drive rookie salaries down even further. 4 Limits on rookie pay are so popular because they are lucrative for the two parties involved in setting the limits veteran players and owners. My findings indicate that in the NBA, rookies are paid roughly one-quarter of what they would earn if their wages were set in the open free-agent market. It is clear that the owners exercise their monopsony power by colluding to mandate a new player draft and to limit compensation at each pick in that draft to great effect in the NBA. The Player s Association, presumably, acts with the hope that because owners extract significant monopsony rents from rookies, they will seek smaller rents from veterans. With the pending re-negotiation of the NFL s CBA, and the expiration of the NBA s CBA this summer, there is tremendous scope to revisit the limits that govern rookie compensation. Last year, the Supreme Court found that the NFL is not entitled to a categorical exception from Section 1 of the Sherman Act, and that the league s concerted 3 See One area of agreement in NFL labor dispute: take money from the rookies, Forbes. February 14, The league has proposed a 15% reduction in salary amounts for all first round picks, and has proposed the elimination of the provision that allows teams to exceed salary scale limits by up to 20%. See: NBA wants to carve into rookies pay, SportsBusiness Journal Daily. May 3, 2010.

23 May 2011 Nikhil Joshi 23 activities are subject to rule of reason antitrust review. 5 While the Court did say that a variety of collective decisions made by teams are likely justifiable, especially if they are essential to the very existence of the NFL s product, collusion to limit salaries of new employees through a draft and a salary scale may well be found illegal. But while the NBA s draft and salary scale are still in use, it is interesting to see whether owners rationally use these tools to maximize surplus, or whether they fall victim to judgment and decision-making pathologies. If, as suggested by Thaler and Massey, owners acting in a high-stakes easily-observable market have converged on an inefficient equilibrium, evidence of the power of decision-making pathologies grows much stronger. However, my findings strongly suggest that, in the NBA, owners are rationally maximizing surplus. Especially after controlling for the component of performance that can t be predicted by draft order, the surplus value of a rookie falls reliably as the draft goes on. The owners, it appears, have learned to astutely play the market for new talent in the NBA. Exercising their monopsony powers, they have developed two powerful limits on rookie compensation, the draft and the salary scale, and with these limits in place, have acted in a manner that maximizes the surplus they get from rookies. 5 American Needle Inc. v. National Football League et al., 130 S. Ct (2010)

24 May 2011 Nikhil Joshi 24 7 Appendix Table A NBA rookie pay scale For rookies drafted in the 2010 NBA Draft. Teams must pay players under a rookie contract at minimum 80% of the salary listed in the scale. Teams cannot, between Salary and Unlikely Bonus payments, pay players more than 120% of the listed salary. Pick 1st Year Salary 2nd Year Salary 3rd Year Option Salary 4th Year Option: % Incr. Over 3rd Year Qualifying Offer: % Incr. Over 4th Year % 30.0% % 30.5% % 31.2% % 31.9% % 32.6% % 33.4% % 34.1% % 34.8% % 35.5% % 36.2% % 36.9% % 37.6% % 38.3% % 39.1% % 39.8% % 40.5% % 41.2% % 41.9% % 42.6% % 43.3% % 44.1% % 44.8% % 45.5% % 46.2% % 46.9% % 47.6% % 48.3% % 49.0% % 50.0% % 50.0% Source: HoopsWorld. Salary amounts are in thousands.

25 May 2011 Nikhil Joshi 25 Table B Experienced-player Sample Includes players drafted who are in the league during their 5 th -7 th years, from Observations are player seasons. Panel 1: Historical Performance YIL N PER SD PER: Bottom 1/3 PER: Middle 1/3 PER: Top 1/ % 11% 10% % 11% 12% % 11% 11% Total (0,11.73) = 33% (11.73,15) = 33% (15+) = 33% Panel 2: Annualized salary and bonuses YIL N Mean SD P10 P50 P ,286,476 3,655, ,881 4,215,456 11,000, ,500,200 3,805,804 2,148,600 5,792,240 12,000, ,557,861 3,973,503 1,500,000 5,883,600 12,134,091 Total 324 6,092,014 3,844,359 1,500,000 5,324,000 11,985,120 Panel 3: Performance and compensation by draft pick Pick Order N Mean Comp SD PER SD ,882,563 4,171, ,389,744 3,241, ,245,425 2,790, Total 324 6,092,014 3,844,359 1,500,000 5,324,000

26 May 2011 Nikhil Joshi 26 Table C Compensation Model Linear regression results for compensation in years 5-7 as a function of performance in the four prior seasons. The omitted position category is Centers, and the omitted year-inleague category is year seven. Standard deviations are shown in parentheses. Two specifications of the model are estimated. In specification (1) draft order is not included; in specification (2) draft order is included explicitly.!"#!"#$!,! =! +!!"#$_!!,! + Π!!! + Κ!!!,! + Υ!!! + Θ!! +!!,! Coefficient (1) (2) Β 1 PER < 33%ile (0.0386) (0.0385) Β 2 33%ile < PER < 66%ile (0.0376) (0.0380) Β 3 PER > 66%ile (0.0189) (0.0199) Π 1 Guards (0.0920) (0.0917) Π 2 Forwards (0.0872) (0.0868) Κ 1 Year (0.0772) (0.0763) Κ 2 Year (0.0774) (0.0765) Υ 1 Missing seasons = (0.122) (0.121) Υ 2 Missing seasons > (0.243) (0.245) Θ 1 Draft-pick: Round 2 (#31-60) ( ) Θ 2 Draft-pick: Round 1 (#15-30) ( ) Θ 3 Draft-pick: Lottery (#1-14) ( ) α Constant (0.356) (0.402) Observations Adjusted R-squared

27 May 2011 Nikhil Joshi 27 Table D Compensation Model with Performance Residuals Linear regression results for compensation in years 5-7 as a function of draft order. Performance residuals are the difference between actual performance and performance predicted by draft order. The omitted position category is Centers, and the omitted yearin-league category is year seven. Standard deviations are shown in parentheses. Two specifications of the model are estimated. In specification (1) draft order is included explicitly; in specification (2) draft order is included explicitly and performance residuals are included, to show the increment value of adding unpredicted performance to the equation.!"#!"#$!,! =! +!!"#$!,! + Ν!"#$_!"#$%!,! + Π!!! + Κ!!!,! + Υ!!! + Θ!! +!!,! Coefficient (1) (2) Ν! Performance residuals (0.0115) Π 1 Guards (0.114) (0.0929) Π 2 Forwards (0.109) (0.0884) Κ 1 Year (0.0954) (0.0777) Κ 2 Year (0.0957) (0.0779) Υ 1 Missing seasons = (0.135) (0.118) Υ 2 Missing seasons > (0.212) (0.190) Θ 1 Draft-pick: Round 2 (#31-60) ( ) (.00709) Θ 2 Draft-pick: Round 1 (#15-30) ( ) ( ) Θ 3 Draft-pick: Lottery (#1-14) (0.0113) ( ) α Constant (0.233) (0.191) Observations Adjusted R-squared

28 May 2011 Nikhil Joshi 28 Table E Drafted-player Sample Summary statistics for new players in the first four years of their careers. Includes all players drafted N = 1,174 player seasons. Panel 1: Performance Category N % Draft pick YIL NIL % Not playing 90 8% PER < % < PER < % PER > % Total % Note: performance category cut-offs are at the 33 rd and 66 th percentiles for veteran players, as shown in Table B Table F Formal test: surplus value and draft order Linear regression of the relationship between surplus value and draft-order, as specified below. Estimated for 1,174 player seasons, including all players drafted Players are within the first four years of their careers. Note: coefficients for NIL, No_mins, Perf_resid and constant are suppressed for presentation.!!,! =! +!!!"! +!!!"! +!!!"!_!"# + Κ!"# + Π!"_!"#$ + Θ!"#!!"#$% +!!,! Coefficient (1) (2) Β 1 Draft-pick: Round 2 (#31-60) 25,860 (13,601) 200,171 (6,761) Β 2 Draft-pick: Round 1 (#15-30) -82,020 98,988 (21,660) (10,289) Β 1 Draft-pick: Lottery (#1-14) 402, ,471 (32,059) (14,684) Observations Adjusted R-squared

29 May 2011 Nikhil Joshi 29 Table G Salary, performance value and surplus value by draft pick For 1,174 player-seasons. Includes all players drafted , for the first four years of their careers. Panel 1: Lottery Picks Draft Salary avg SD Perf avg SD Surplus avg SD 1 $4,837,960 $812,953 $18,404,902 $7,802,432 $13,566,943 $7,775,013 2 $4,000,218 $1,320,228 $9,577,186 $5,999,446 $5,576,967 $5,187,552 3 $3,873,317 $555,379 $10,348,983 $5,587,776 $6,475,666 $5,500,106 4 $3,339,949 $954,601 $14,066,759 $7,957,396 $10,726,810 $7,454,278 5 $2,890,044 $836,992 $10,070,593 $7,434,898 $7,180,549 $7,172,174 6 $2,739,090 $795,215 $8,308,741 $5,118,410 $5,569,650 $4,820,109 7 $2,626,812 $468,192 $9,504,417 $3,049,009 $6,877,606 $3,104,537 8 $2,288,100 $656,192 $7,058,281 $4,048,022 $4,770,182 $3,762,248 9 $2,058,060 $528,782 $8,056,590 $6,995,924 $5,998,530 $6,886, $1,581,131 $899,092 $5,677,259 $5,085,935 $4,096,128 $4,521, $1,591,581 $884,984 $5,675,392 $3,717,527 $4,083,811 $3,027, $1,491,703 $946,888 $3,700,471 $3,488,885 $2,208,768 $3,024, $1,718,001 $816,535 $4,618,982 $3,137,207 $2,900,981 $3,026, $1,826,844 $432,587 $6,114,120 $2,251,231 $4,287,277 $2,199,891 Panel 2: First Round, Picks #15-30 Draft Salary avg SD Perf avg SD Surplus avg SD 15 $1,545,873 $496,733 $3,627,121 $4,719,782 $2,081,248 $4,557, $1,327,086 $684,443 $4,092,299 $2,692,297 $2,765,213 $2,320, $1,595,653 $454,245 $6,849,582 $3,939,835 $5,253,930 $3,972, $1,215,720 $513,466 $5,604,551 $3,768,187 $4,388,831 $3,445, $1,229,877 $510,132 $4,315,611 $3,348,912 $3,085,734 $3,043, $1,273,657 $649,444 $4,506,633 $3,438,981 $3,232,976 $3,342, $1,127,245 $517,958 $5,583,553 $3,685,580 $4,456,309 $3,348, $1,001,340 $519,567 $4,082,688 $2,199,618 $3,081,348 $2,007, $1,052,230 $583,717 $6,178,441 $3,666,841 $5,126,211 $3,261, $1,084,102 $536,170 $6,637,275 $2,797,741 $5,553,173 $2,618, $947,086 $443,701 $4,048,648 $2,543,193 $3,101,562 $2,442, $955,741 $468,666 $5,859,242 $4,225,275 $4,903,501 $3,937, $968,408 $505,968 $4,792,886 $2,945,163 $3,824,478 $2,648, $898,557 $493,157 $3,930,388 $3,547,165 $3,031,830 $3,416, $706,872 $538,608 $4,352,070 $4,739,993 $3,645,198 $4,455, $802,955 $1,182,581 $5,140,621 $5,471,784 $4,337,666 $5,105,654

30 May 2011 Nikhil Joshi 30 Panel 3: Second Round, Picks #31-60 Draft Salary avg SD Perf avg SD Surplus avg SD 31 $387,394 $380,234 $2,774,622 $3,002,730 $2,387,228 $2,707, $458,413 $421,284 $3,092,523 $3,824,912 $2,634,110 $3,554, $678,591 $1,042,693 $4,311,680 $4,634,930 $3,633,089 $4,171, $1,614,988 $3,402,872 $4,495,140 $5,588,061 $2,880,152 $4,113, $39,900 $122,889 $0 $0 -$39,900 $122, $409,509 $759,136 $2,809,087 $4,386,762 $2,399,578 $3,817, $515,691 $981,109 $2,533,905 $3,309,997 $2,018,214 $2,821, $1,119,761 $1,059,507 $2,956,405 $2,714,241 $1,836,644 $2,485, $137,330 $263,256 $514,577 $1,707,075 $377,247 $1,548, $854,612 $2,485,179 $2,211,595 $3,168,092 $1,356,982 $3,040, $450,525 $673,751 $1,524,337 $2,134,573 $1,073,813 $1,858, $894,854 $1,530,569 $2,716,312 $3,532,695 $1,821,458 $2,843, $783,427 $962,855 $3,249,999 $3,198,761 $2,466,572 $2,692, $17,473 $78,141 $0 $0 -$17,473 $78, $845,699 $1,048,530 $3,910,968 $3,297,053 $3,065,268 $2,867, $213,934 $272,557 $855,914 $2,105,982 $641,980 $1,974, $931,668 $1,695,625 $3,818,513 $3,847,668 $2,886,845 $3,316, $98,547 $254,105 $359,844 $1,111,838 $261,298 $876, $962,906 $988,680 $4,485,017 $3,894,688 $3,522,112 $3,486, $569,483 $933,403 $2,320,406 $2,996,141 $1,750,922 $2,590, $544,206 $1,153,315 $1,214,210 $2,346,868 $670,004 $1,581, $174,419 $395,173 $880,253 $1,904,130 $705,834 $1,610, $110,486 $221,849 $345,084 $654,175 $234,597 $507, $75,164 $146,164 $523,200 $1,622,312 $448,036 $1,561, $72,412 $184,070 $302,578 $1,353,172 $230,166 $1,219, $469,164 $1,114,636 $2,359,698 $3,934,287 $1,890,535 $3,421, $72,909 $189,805 $1,042,956 $2,885,297 $970,047 $2,714, $25,795 $103,180 $0 $0 -$25,795 $103, $34,393 $119,141 $0 $0 -$34,393 $119, $190,375 $279,199 $491,283 $953,360 $300,908 $712,029

31 May 2011 Nikhil Joshi 31 Figure 1 Veteran Compensation and Draft Order Compensation plotted on draft order, for sample of 324 veteran player-seasons, with year-in-league of 5-7 years. Players in sample have gone through free agency, and are no longer working rookie contracts. All players were drafted between , and were within years 5-7 of their career between Veteran compensation by draft order Draft order Lottery Rd 1 #15-30 Rd 2

32 May 2011 Nikhil Joshi 32 Figure 2 Rookie Compensation by Draft Order Compensation plotted on draft order for all players drafted between , for the first four years of their careers. Sample includes 1,174 player-seasons from Data summarized by Lowess smoothing curve, with bandwith = 0.8. Draftee compensation, by draft order (YIL: 0-3) Draft Order bandwidth =.8

33 May 2011 Nikhil Joshi 33 Figure 3 Predicted Performance Values Performance values predicted for sample of 1,174 player-seasons, for all rookies drafted between , for the first four years of their careers. Based on compensation equation estimated for sample of veteran players, with year-in-league from 5-7, who have gone through free agency. Performance value is an estimate of what a rookie player would earn - based on performance, position and (so that values are non-biased relative to draft) draft order in the open free-agent market PER PER < < PER < 15 PER > 15

34 May 2011 Nikhil Joshi 34 Figure 4 Performance Value, Compensation and Surplus Value Performance value, surplus value and compensation data summarized by Lowess smoothing curves for a sample of 1,174 player-seasons, with year-in-league from 1-4. Curves are weighted averages of underlying data, and should be interpreted with caution.