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Assessing the Relative Value of Draft Position
in the NBA Draft

By Aaron Barzilai, Ph.D.

Introduction

Success in the draft is crucial to the success of an NBA team. With their accomplishments in the last decade, the San Antonio Spurs are often cited as an example of the draftís importance. The Spurs had the good fortune to win the draft lottery in 1997, which allowed them to draft Tim Duncan. Later, they demonstrated their skill by drafting Manu Ginobili and Tony Parker with the 57th pick in 1999 and 28th in 2001.

As advanced quantitative analysis has become more prominent in the NBA generally of late, it has also become more prevalent in draft preparation. A variety of quantitative approaches to the draft have been discussed in the media. These include the Trail Blazers arrangement with Jeff Ma and ProTrade, John Hollingerís new system for rating draft-eligible players, and Ed Weilandís articles for HoopsAnalyst.com.

While these efforts aim to rate the value of players, they donít attempt to quantify the value of holding the rights to a particular pick in the draft. This is an important aspect of the draft that is relevant both on draft night and throughout the season, as many trades involve the exchange of future draft picks. It is particularly important the night of the draft lottery, but attempts to quantify the expected value of moving up to the 1st pick from the 6th pick as Portland did this year are rarely mentioned. Similarly, while there was a recognition that exchanging 2007 draft picks as part of the Eddy Curry trade aided Chicago, there was limited discussion of how much more value Chicago could expect to obtain with the 9th pick rather than the 23rd once the season concluded.

This article aims to quantify the relative value of picking in different positions in the NBA draft. This topic appears to be relatively neglected in publicly available analysis, with Kevin Peltonís interesting 2003 article serving as the primary public source of information. Kevin assessed the draft from 1995 through 2001 using his Value Over Replacement Player formula as the metric to value players. In this article, the results of the draft from 1980 through 2003 are considered, resulting in up to 24 observations for a given draft position. Additionally, multiple metrics are considered in this analysis in an attempt to develop a "metric-neutral" assessment of value, one that both a proponent of PER and a Win Shares evangelist would both be comfortable using.

Methodology

The data used in this analysis was graciously provided by Justin Kubatko of basketball-reference.com. The dataset included the draft results from 1980-2006, the advanced performance data for each player for the 1980-2007 regular seasons, and the estimated salaries for each player from 1980 through 2007. Without Justinís database of information, this analysis would not be possible.

As stated above, a key goal of this analysis was to develop an assessment that isnít overly dependent on one particular metric. To ensure the results would be meaningful to a wide audience that may prefer one advanced statistic over another, values were assessed using four statistics:

    • PER-Minutes (Season PER*Season Minutes)
    • Player Wins
    • Win Shares
    • Estimated Salary

These metrics are all defined in the basketball-reference.com glossary. PER, developed by John Hollinger, is perhaps the most widely used "advanced" NBA statistic. It is a per-minute measure of player efficiency, so it has been multiplied by minutes played to assess the cumulative value a player contributed over the course of a season in terms of PER. Player Wins and Win Shares, as reported by basketball-reference.com, are both cumulative statistics that estimate how many wins (or shares of a win) are attributable to a player over the course of a season. Estimated Salary is also considered in this analysis as it is a market assessment of the value of a player, though it is distorted by a variety of NBA Salary Cap rules (e.g. the mid-level exception, rookie salary scale).

In addition to exploring different statistics, the cumulative value of each statistic was assessed for multiple time periods. The three time periods were:

    • Career
    • First 4 Years
    • Years with Rookie Team

Evaluating a player over their entire career is probably the most straightforward and intuitive method to assess the value of a player. However, all of the value in a playerís career is not always realized by the team that drafted him. Therefore, players were also evaluated on the value generated in their first 4 seasons after the draft as well as with their rookie team. The first 4 years is a relevant time period because under the current collective bargaining agreement rookies sign a two year contract with a team option for the third and fourth year. After the fourth year, a player becomes a restricted free agent and has slightly more control over where they play. Other time periods could have been chosen, such as the minimum number of years that a talented NBA player must play for their drafting team before becoming an unrestricted free agent (5 years), but the clear definition of restricted free agency eligibility is preferred to the variability in a playerís eligibility for unrestricted free agency.

Additionally, the value a player delivered to their rookie team over the course of their career was calculated. This was hypothesized to be a more accurate assessment of value obtained through the draft as it measures the value a player delivered for their rookie team on the court. The rookie team is used rather than drafting team to account for draft day trades (e.g. Kobe Bryant, Vince Carter). The on-court value captures a significant fraction of a playerís total value to a team, but when a player leaves a team he can add value through a trade or freeing up salary cap space. Ideally both components would be considered, but the logistics of assessing this "departure" value is both complicated and ambiguous in the case of multi-player trades.

Each drafted playerís value (2,698 players) was determined based on these 12 metrics (4 statistics for three time periods). In practice, estimated salary was considered to be meaningful only over the time frame of a career due to the correlation of salary with draft position early in a playerís career, leaving 10 metrics for consideration. The relative value of each player compared to the top draft choice of their draft was then calculated for each of the metrics. By assessing relative value instead of absolute value, variations in the league over time are addressed in general, such as changes in scoring or salary as well as the 1998-99 lockout-shortened season. However, these variations are not completely accounted for as playerís careers are of varying length.

Results & Discussion

Figure 1 illustrates a sample result for one of the 10 metrics, Career PER-Minutes. The figure plots the average value of each draft position relative to the first pick, and includes the 95% confidence interval for each point. The sizable confidence intervals indicate that there is a fair bit of variability in the value of drafting in a given position from year to year. This is likely the result of a number of factors, particularly the strength of a draft, the accuracy of conventional wisdom, and the skill of the general managers responsible for making the selection. It is interesting to see that the second pick has yielded less value on average, in terms of Career PER-Minutes, than the third, fourth, and fifth pick, though this difference is not statistically significant.

A clear trend of exponential decay is evident in Figure 1 despite the confidence intervals. The best fit exponential curve, also illustrated in the figure, is expressed as

(1)

The quality of the fit is quite good as measured by R2, the coefficient of determination. R2 represents the proportion of the variation in the data that is accounted for by the model.

For this metric, the exponential curve fits the data quite well with an R2 of 0.87, indicating that 87% of the change in relative value as draft position increases is explained by the model.

Figure 2 shows the data and best fit exponential curve for 4 Year PER-Minutes. Again, the second pick has yielded less value than the third on average using this metric. The best fit curve for is given by 4 Year PER-Minutes

(2)

and has an R2 of 0.91. The results for 4 Year PER-Minutes are slightly better than those for Career PER-Minutes, with smaller confidence intervals and an improved fit. However, Figure 3 illustrates that the two estimates of value are quite similar, as expected given the similar coefficients.

Figure 1: Relative value of Career PER-Minutes vs. Draft Pick

 

Figure 2: Relative value of 4 Year PER-Minutes vs. Draft Pick

Figure 3: Comparison of Career and 4 Year PER-Minutes relative value

Figure 4 shows the data and best fit exponential curve for Rookie Team PER-Minutes. The data exhibits a much larger degree of variability for the rookie team time frame than for either the career or 4 year time frame. The best fit exponential curve is a much poorer fit with an R2 of 0.64 and a curve that indicates the second pick has a higher value than the first. There appear to be significant outliers in the data with much higher values than would be expected from a draft position. This is likely a result of players in these positions having exceptionally long careers with their rookie teams.

The results shown in Figures 1 to 4 are typical for the other statistics, with the rookie team data showing more variability and less plausible results than the career or 4 year data. As a result, the remaining analysis focused on the career and 4 year time frames. Curves for all time frames for Player Wins, Win Shares, and Estimated Salary, along with a comparison for the two time frames for each statistic are shown in the Appendix.

Figures 5 and 6 illustrate the similarity of estimates of value using different statistics for a given time frame. The results for PER-Minutes and Win Shares are strikingly similar, with Player Wins indicating more value for later draft picks than the aforementioned metrics and Estimated Salary less value for later picks. The two Player Wins metrics have the lowest R2 of the seven metrics of interest with a value of 0.77 for Career Player Wins and 0.81 for 4 Year Player Wins, while Career Estimated Salary has the second highest R2 with a value of 0.89. Table 1 summarizes the best fit lines and R2 for the seven metrics of interest.

Figure 4: Relative value of Rookie Team PER-Minutes vs. Draft Pick

 

Metric Best Fit Curve R^2
PERMinutesCareer Relative Value = 0.9711e ^ -0.05426(Draft Pick-1) 0.87
PERMinutes4Years Relative Value = 0.9072e ^ -0.05674(Draft Pick-1) 0.91
PlayerWinsCareer Relative Value =1.2129e ^ -0.05463(Draft Pick-1) 0.77
PlayerWins4Years Relative Value =1.0431e ^ -0.05601(Draft Pick-1) 0.81
WinSharesCareer Relative Value = 1.0321e ^ -0.05364(Draft Pick-1) 0.82
WinShares4Years Relative Value = 0.9172e ^ -0.05488(Draft Pick-1) 0.87
SalaryEstimatedCareer Relative Value = 0.7383e ^ -0.05847(Draft Pick-1) 0.89

Table 1: Best fit curve for the seven metrics of interest

Figure 5: Comparison of estimates of relative value of four statistics for a draft pickís career

Figure 6: Comparison of estimates of relative value of three statistics for a draft pickís first four years

 

The average of the estimates of the seven metrics of interest was calculated to form the final, metric-neutral estimate of the value of drafting with a given pick. Figure 7 illustrates the estimated value of drafting with a specified draft pick, while Table 2 lists the estimated value of the first 30 draft picks. The estimated value can also be expressed by the curve

(3)

Figure 7: Estimated value of drafting with a given draft pick

Draft Pick 1 2 3 4 5 6 7 8 9 10
Relative Value 100% 92% 87% 83% 78% 74% 70% 66% 63% 59%

Draft Pick 11 12 13 14 15 16 17 18 19 20
Relative Value 56% 53% 50% 47% 45% 42% 40% 38% 36% 34%

Draft Pick 21 22 23 24 25 26 27 28 29 30
Relative Value 32% 30% 29% 27% 26% 24% 23% 22% 21% 20%

Table 2: Estimate of relative value of the first 30 draft picks in the NBA draft

Using these results, it is now possible to say that Portland could expect to obtain a player with the 1st pick who is a 35% better player than they could have selected with the 6th pick (1.00/0.74 = 135%). Similarly, by obtaining this yearís 9th pick as part of the Eddy Curry trade, Chicago could expect to draft a player over twice as good as they would have selected with the 23rd pick (0.63/0.29 = 217%). Of course, these expectations are averages, so only time will tell the true relative value of the 2007 draft picks. Tables 3 and 4 (see Appendix) list top and median players drafted in each position for reference.

With an estimate of relative value determined, it is also possible to evaluate the distribution of salary to first round draft picks. The 2007-2008 rookie scale is posted online by the NBA Playerís Association and defines the guaranteed salary for each of this yearís first round draft picks. The first two years of their contracts are guaranteed, with team options for the 3rd and 4th years. Figure 8 illustrates the guaranteed salary of each pick relative to this yearís first pick, Greg Oden. It shows that a draft pickís salary is less than their estimated value, implying that later picks are underpaid relative to the top pick. The discrepancy is largest for the 9th pick, Joakim Noah, who would be guaranteed a contract that is 37% larger if he was paid at the same rate as Greg Oden for the value he is expected to deliver on the court. Of course, Greg Oden could make the argument that as the top pick in the draft he is expected to have a larger impact off the court on the finances of his new team, Portland, than Noah is expected to have on his new team, Chicago. However, this is both harder to quantify and outside the scope of this article.

Simply renegotiating the collective bargaining agreement so that Joakim Noahís guaranteed salary increases by 37% is unlikely to happen in the future. Since the later picks are generally underpaid relative to the top pick, these adjustments would increase the total guaranteed salary to first round draft picks. The consequence of this would be to take money from either the owners or the veteran players and shift it to the draft picks. Instead, it is far more feasible to change the rookie scale so that the total guaranteed salary of the draft picks, almost $98 million, is distributed in proportion to their estimated value. Figure 9 illustrates the results of this hypothetical change, decreasing the salary of the top 5 picks as well as the 25th through 30th while increasing the salary of the 6th through 24th picks. Again, Joakim Noah would see the largest increase as the 9th pick, but in this scenario his guaranteed salary would only increase by 13%.

Figure 8: Estimated player value and guaranteed salary of first round draft picks

in the 2007 NBA draft relative to the top pick

 

Figure 9: Actual rookie scale contracts for 2007 NBA draft picks and alternative rookie scale distributing total guaranteed salary by estimated value of draft pick

Conclusion

The right to draft with a given pick in the NBA draft is an important but often overlooked topic in basketball analytics. This article has developed an estimate of the expected value of these rights for each position in the draft. While these estimates can be a valuable tool for general managers in evaluating trade proposals that include draft picks, like all basketball analytics it cannot establish with certainty the value of those picks. The position of a team in a future draft is not known until the end of the season before that draft, and many trades involve picks multiple seasons into the future. Additionally, the strength of a future draft class is particularly hard to quantify. Finally, when valuing a pick a team might include an estimation of their skill or their trading partnerís skill in drafting players. Despite these known considerations, it is the authorís hope that the results presented here will assist teams in their evaluation of trade proposals in the future.

 

 

Acknowledgements

Special thanks to Justin Kubatko of basketball-reference.com for providing the data used in this analysis. Additionally, the feedback of Stephen Ilardi is appreciated for his contribution to this article.

About the Author

Aaron Barzilai "played" on the varsity basketball team at MIT as an undergraduate before earning his Ph.D. in Mechanical Engineering at Stanford University. He currently works as a consultant for a global consulting firm and has experience in the pharmaceutical, financial services, and online publishing industries. Aaron developed the website basketballvalue.com and would like to spend more time on basketball analytics. He can be contacted via email at webmaster@basketballvalue.com.

 

Appendix

Figure 10: Comparison of Career and 4 Year Player Wins relative value

Figure 11: Comparison of Career and 4 Year Win Shares relative value

Figure 12: Relative value of Career Player Wins vs. Draft Pick

 

Figure 13: Relative value of 4 Year Player Wins vs. Draft Pick

Figure 14: Relative value of Rookie Team Player Wins vs. Draft Pick

 

Figure 15: Relative value of Career Win Shares vs. Draft Pick

Figure 16: Relative value of 4 Year Win Shares vs. Draft Pick

 

Figure 17: Relative value of Rookie Team Win Shares vs. Draft Pick

Figure 18: Relative value of Career Salary Estimated vs. Draft Pick

 

Figure 19: Relative value of 4 Year Salary Estimated vs. Draft Pick

Figure 20: Relative value of Rookie Team Salary Estimated vs. Draft Pick

Draft Pick  Top Picks  Median Picks
1  LeBron James, Shaquille O'Neal  Glenn Robinson, Patrick Ewing
2  Steve Francis, Isiah Thomas  Wayman Tisdale, Keith Van Horn
3  Michael Jordan, Grant Hill  Kevin McHale, Charles Smith
4  Chris Bosh, Dikembe Mutombo  Lamar Odom, Byron Scott
5  Charles Barkley, Dwyane Wade  Steve Smith, LaSalle Thompson
6  Hersey Hawkins, Antoine Walker  Melvin Turpin, Trent Tucker
7  Kevin Johnson, Alvin Robertson  Quintin Dailey, Roy Tarpley
8  Vin Baker, Andre Miller  Jamal Crawford, Rex Chapman
9  Shawn Marion, Dirk Nowitzki  Rony Seikaly, Rodney Rogers
10  Paul Pierce, Jason Terry  Ed Pinckney, Lindsey Hunter
11  Kiki Vandeweghe, Reggie Miller  Gary Trent, Tyrone Hill
12  Kelly Tripucka, Mookie Blaylock  Khalid Reeves, Nick Collison
13  Karl Malone, Sleepy Floyd  Loy Vaught, Keon Clark
14  Tim Hardaway, Clyde Drexler  Fred Jones, Eric Williams
15  Gary Grant, Brent Barry  Anthony Avent, Steven Hunter
16  John Stockton, Ron Artest  Jiri Welsch, Tony Delk
17  Shawn Kemp, Larry Drew  Eric Leckner, Greg Graham
18  Vern Fleming, Mark Jackson  John Wallace, Ricky Pierce
19  Ken Norman, Jamaal Magloire  Aleksandar Pavlovic, Rob Williams
20  Larry Nance, Paul Pressey  Speedy Claxton, Jason Caffey
21  Michael Finley, Eric Murdock  Kenny Fields, Mark Bryant
22  Chris Mills, Reggie Lewis  Roy Rogers, Randolph Keys
23  Wesley Person, A.C. Green  Devean George, Stanley Roberts
24  Latrell Sprewell, Terry Porter  Felipe Lopez, Monty Williams
25  Mark Price, Jeff Ruland  Tracy Jackson, John Morton
26  Vlade Divac, Jerome Williams  Samuel Jacobsen, Sam Worthen
27  Dennis Rodman, Jamaal Tinsley  Kenny Battle, Vladimir Stepania
28  Tony Parker, Gene Banks  Corey Benjamin, Marlon Maxey
29  Eddie Johnson, Josh Howard  Toni Kukoc, Scott Hastings
30  Gilbert Arenas, Nate McMillan  Steve Burtt, Maciej Lampe

Table 3: Sample of top and median players drafted with a given pick based on 4 Year PER-Minutes

 

Draft Pick  Top Picks  Median Picks
1  Hakeem Olajuwon, Shaquille O'Neal  Glenn Robinson, Larry Johnson
2  Gary Payton, Jason Kidd  Wayman Tisdale, Marcus Camby
3  Michael Jordan, Dominique Wilkins  Sean Elliott, Pau Gasol
4  Dikembe Mutombo, Stephon Marbury  Jamal Mashburn, Lamar Odom
5  Charles Barkley, Kevin Garnett  Jason Richardson, LaPhonso Ellis
6  Hersey Hawkins, Antoine Walker  Joe Kleine, Felton Spencer
7  Chris Mullin, Kevin Johnson  Lorenzen Wright, George McCloud
8  Detlef Schrempf, Tom Chambers  Jamal Crawford, Andrew Toney
9  Otis Thorpe, Dirk Nowitzki  Stacey Augmon, Cliff Levingston
10  Horace Grant, Eddie Jones  Willie Anderson, Johnny Dawkins
11  Reggie Miller, Kevin Willis  John Salley, Will Perdue
12  Mookie Blaylock, Mugsy Bogues  Vladimir Radmanovic, Vitaly Potapenko
13  Karl Malone, Kobe Bryant  Richard Jefferson, Bryant Stith
14  Clyde Drexler, Tim Hardaway  Luke Ridnour, Wes Matthews
15  Steve Nash, Dell Curry  Anthony Avent, Todd Lichti
16  John Stockton, Dana Barros  Jon Sundvold, Bill Wennington
17  Shawn Kemp, Doug Christie  Victor Alexander, Eric Leckner
18  Mark Jackson, Joe Dumars  David West, Jason Collins
19  Rod Strickland, Ken Norman  Billy Thompson, Aleksandar Pavlovic
20  Larry Nance, Zydrunas Ilgauskas  Jason Caffey, Sam Vincent
21  Michael Finley, Ricky Davis  Boris Diaw, James Robinson
22  Reggie Lewis, Scott Skiles  Randolph Keys, Mark McNamara
23  A.C. Green, Wesley Person  Devean George, Anthony Bonner
24  Terry Porter, Sam Cassell  Nenad Krstic, Brian Cook
25  Mark Price, Al Harrington  Bryan Warrick, John Thomas
26  Vlade Divac, Jerome Williams  Lance Blanks, Bill Martin
27  Dennis Rodman, Elden Campbell  Byron Houston, Brooks Thompson
28  Sherman Douglas, Tony Parker  Corey Benjamin, Marlon Maxey
29  Eddie Johnson, P.J. Brown  Travis Knight, Mark Madsen
30  Gilbert Arenas, Nate McMillan  Steve Burtt, Ed Rains

Table 4: Sample of top and median players drafted with a given pick based on Career PER-Minutes

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