

Assessing the Relative Value of Draft Position
By Aaron Barzilai, Ph.D.

Metric  Best Fit Curve  R^2 
PERMinutesCareer  Relative Value = 0.9711e ^ 0.05426(Draft Pick1)  0.87 
PERMinutes4Years  Relative Value = 0.9072e ^ 0.05674(Draft Pick1)  0.91 
PlayerWinsCareer  Relative Value =1.2129e ^ 0.05463(Draft Pick1)  0.77 
PlayerWins4Years  Relative Value =1.0431e ^ 0.05601(Draft Pick1)  0.81 
WinSharesCareer  Relative Value = 1.0321e ^ 0.05364(Draft Pick1)  0.82 
WinShares4Years  Relative Value = 0.9172e ^ 0.05488(Draft Pick1)  0.87 
SalaryEstimatedCareer  Relative Value = 0.7383e ^ 0.05847(Draft Pick1)  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 pick’s career
Figure 6: Comparison of estimates of relative value of three statistics for a draft pick’s first four years
The average of the estimates of the seven metrics of interest was calculated to form the final, metricneutral 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 1^{st} pick who is a 35% better player than they could have selected with the 6^{th} pick (1.00/0.74 = 135%). Similarly, by obtaining this year’s 9^{th} 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 23^{rd} 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 20072008 rookie scale is posted online by the NBA Player’s Association and defines the guaranteed salary for each of this year’s first round draft picks. The first two years of their contracts are guaranteed, with team options for the 3^{rd} and 4^{th} years. Figure 8 illustrates the guaranteed salary of each pick relative to this year’s first pick, Greg Oden. It shows that a draft pick’s salary is less than their estimated value, implying that later picks are underpaid relative to the top pick. The discrepancy is largest for the 9^{th} 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 Noah’s 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 25^{th} through 30^{th} while increasing the salary of the 6^{th} through 24^{th} picks. Again, Joakim Noah would see the largest increase as the 9^{th} 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 partner’s skill in drafting players. Despite these known considerations, it is the author’s 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 basketballreference.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 [email protected].
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 PERMinutes
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 PERMinutes
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