Which players are the most versatile? Six different top 50 lists are computed. Is your favorite player on one of them? And how does Celtics rookie Kendrick Perkins fit into all this? Based on a recent Hoopsworld column by Kevin Pelton.

Kevin Pelton recently explored research by Dan Rosenbaum that suggests that the product of points per minute, rebounds per minute, and assists per minute is a strong marginal measure of a player's value. While most people are familiar with the idea of adding points, rebounds, and assists to calculate efficiency, and can even stomach the idea of putting different weights on each item, the idea of multiplying those numbers by each other may be a novel one. Yet it is a common statistical technique, especially when doing regressions: i.e., especially when trying to look for what part of performance explains value.

The easiest way to think about a product is to consider zeros. If a player never passes, he'll have zero assists, and a zero product. Similarly if he never rebounds or scores, he will again get zero marks. If all three numbers are positive, however, then doubling any one of them doubles the product. In other words, if your twin brother is the exact same player as you but just passes the ball twice as often, he will be twice as versatile.

Versatility is the key word here. Versatility means the ability to do many things well, and is the key concept being measured.

There are six natural ways to measure versatility:

1. Versatility Total
The simplest is to take each player's total points, rebounds, and assists accumulated over the entire season, and multiply them all together. This reflects the entire contribution of that player over the whole season. Players who were injured or didn't see much playing time obviously score lower than big-minute iron men.

2. Versatility Per Game
The next simplest alternative is to take each player's points per game, rebounds per game, and assists per game averages, and multiply those three numbers together. This gives players like Chris Webber and Ray Allen a fair chance to prove their worth because it levels the playing field to just those games that the player actually participated in. However, it still gives no benefit for bench players or those who saw limited action in the games they played.

3. Versatility Per Minute, or Versatility Per 40 Minutes
This measure is computed by taking each player's points per minute, rebounds per minute, and assists per minute averages, and multiplying them out. This measures how versatile a player was for a given unit of time, thus eliminating the potentially complicating factor of how many minutes each player actually played. If there are enough minutes for each player to make a statistically significant sample, then this is the best measure of the rate of versatility. In fact, this is the preferred formulation that Pelton reports Rosenbaum found to be significant. (In that article, it was expressed in terms of points, rebounds, and assists per 40 minutes, but of course that is just 40 times the versatility per minute).

4. Versatility/Turnovers Total
Assists typically come at a cost, and that cost is turnovers. The more you pass, the more you miss. Typically you could look at a player's assists/turnovers ratio to see if he is passing effectively or wildly. A ratio of 3 or more is generally considered very good. If you want to penalize those players who have high turnovers, you could replace the season assists total with the season assists/turnovers ratio. Notice that the assists/turnovers ratio doesn't depend on the interval: it is the same for the whole season, on a per game basis, and on a per minute basis. To calculate this versatility measure, you multiply the each player's total points and rebounds for the regular season by their assists/turnovers ratio. This measure now penalizes turnovers but gives more weight to player who weren't injured and who played major minutes.

5. Versatility/Turnovers Per Game
Analogously to Versatility Per Game, calculating Versatility/Turnovers Per Game involves multiplying a player's average points and rebounds per game by their assists/turnovers ratio. And again, this measure penalizes turnovers and ignores the games missed due to injury or coach's decision, but still weighs playing time heavily.

6. Versatility/Turnovers Per Minute, or Versatility/Turnovers Per 40 Minutes
Finally, this number, the product of a player's average points and rebounds per minute and their assists/turnovers ratio, measures a player's rate of versatility without regard to games or minutes played, while still penalizing turnovers.

The tables with the top 50 players by each measure are presented below. Here are some things to note:

1. Kevin Garnett is the most versatile player by any of the six measures.

2. No single player is second to Garnett by every measure. Only Tracy McGrady appears in the second slot on more than one list. The others appear at most once and are: Tim Duncan, Paul Pierce, Dirk Nowitzki, and... Kendrick Perkins.

3a. That's right: by Rosenbaum's preferred formulation, Kendrick Perkins was the second-most versatile player in the league last year. The rookie that Danny Ainge drafted straight out of high school played only a total of 35 garbage minutes over the whole season. There is no way that is a significant amount or quality of minutes for him to be in the same class as these other players. By all rights, his name should be taken out of the lists for lack of sufficient data.

3b. And yet... in his 35 minutes, this young man grabbed five offensive rebounds, nine defensive rebounds, scored 22 points on 53.3 percent (8-for-15) shooting from the floor and 67 percent (6-for-9) shooting from the free throw line, and also dished out three assists. Think of his 35 minutes as a single game. 22 points, 14 rebounds, and 3 assists? Those are indeed Garnett-like numbers.

3c. Okay, enough about Perkins. Clearly his stat line should be excluded from the analysis for lack of quality data. But we can certainly say that the kid has potential. He'll be a fun player to watch next season.

4. LeBron James is higher than Carmelo Anthony on every single list, with usually a gap of at least 20 other players between them. Put the conspiracy theories to rest: by these measures, James was clearly the Rookie of the Year.

5. By the Versatility per Minute measure, Kobe Bryant is not the most versatile Laker. He's not even the second-most versatile Laker. He's third, trailing both Shaquille O'Neal and Karl Malone.

Do you notice other patterns? Feel free to email me or point them out on the Hoopsworld.com message boards, as well as discussing versatility in more depth.

Versatility Total Versatility Per Game Versatility Per Minute
Rank Points * Rebounds * Assists PPG * RPG * APG PPM * RPM * APM
1 Kevin Garnett, MIN  Kevin Garnett, MIN  Kevin Garnett, MIN 
2 Paul Pierce, BOS  Tracy McGrady, ORL  K. Perkins, BOS 
3 Lamar Odom, MIA  Jason Kidd, NJN  Jason Kidd, NJN 
4 LeBron James, CLE  Tim Duncan, SAS  Tim Duncan, SAS 
5 S. Marbury, NYK/PHO  Paul Pierce, BOS  Chris Webber, SAC 
6 A. Walker, DAL  Chris Webber, SAC  Tracy McGrady, ORL 
7 Tim Duncan, SAS  Baron Davis, NOR  S. O'Neal, LAL 
8 Steve Francis, HOU  S. O'Neal, LAL  Paul Pierce, BOS 
9 Tracy McGrady, ORL  Lamar Odom, MIA  Brad Miller, SAC 
10 Jason Kidd, NJN  LeBron James, CLE  Lamar Odom, MIA 
11 Sam Cassell, MIN  Elton Brand, LAC  Vlade Divac, SAC 
12 Shawn Marion, PHO  Kobe Bryant, LAL  Karl Malone, LAL 
13 Brad Miller, SAC  Allen Iverson, PHI  A. Walker, DAL 
14 Dirk Nowitzki, DAL  Brad Miller, SAC  Kobe Bryant, LAL 
15 Zach Randolph, POR  S. Marbury, NYK/PHO  Elton Brand, LAC 
16 Elton Brand, LAC  Steve Francis, HOU  Baron Davis, NOR 
17 Andre Miller, DEN  Ray Allen, SEA  Sam Cassell, MIN 
18 R. Jefferson, NJN  A. Walker, DAL  Pau Gasol, MEM 
19 Baron Davis, NOR  Vince Carter, TOR  LeBron James, CLE 
20 S. O'Neal, LAL  Dirk Nowitzki, DAL  Steve Nash, DAL 
21 J. O'Neal, IND  Sam Cassell, MIN  Ray Allen, SEA 
22 Vince Carter, TOR  Shawn Marion, PHO  Bob Sura, ATL/DET 
23 Jason Terry, ATL  G. Arenas, WAS  Andre Miller, DEN 
24 A. Kirilenko, UTH  Karl Malone, LAL  Toni Kukoc, MIL 
25 C. Anthony, DEN  J. O'Neal, IND  Kenyon Martin, NJN 
26 Joe Johnson, PHO  Zach Randolph, POR  Dirk Nowitzki, DAL 
27 Mike Bibby, SAC  A. Kirilenko, UTH  J. O'Neal, IND 
28 Kobe Bryant, LAL  Andre Miller, DEN  Vince Carter, TOR 
29 Gary Payton, LAL  R. Jefferson, NJN  S. Marbury, NYK/PHO 
30 Steve Nash, DAL  Kenyon Martin, NJN  Steve Francis, HOU 
31 J. Richardson, GSW  Steve Nash, DAL  Allen Iverson, PHI 
32 P. Stojakovic, SAC  C. Maggette, LAC  Manu Ginobili, SAS 
33 D. Stoudamire, POR  Jason Terry, ATL  G. Arenas, WAS 
34 Pau Gasol, MEM  J. Richardson, GSW  R. Strickland, ORL/TOR 
35 C. Billups, DET  C. Anthony, DEN  Carlos Boozer, CLE 
36 Vlade Divac, SAC  Ron Artest, IND  A. Kirilenko, UTH 
37 J. Crawford, CHI  Carlos Boozer, CLE  Gary Payton, LAL 
38 S. Abdur-Rahim, ATL/POR  Joe Johnson, PHO  Rodney Rogers, NJN 
39 Carlos Boozer, CLE  Pau Gasol, MEM  C. Maggette, LAC 
40 C. Maggette, LAC  Gary Payton, LAL  S. Abdur-Rahim, ATL/POR 
41 Ron Artest, IND  Mike Bibby, SAC  E. Strickland, MIL 
42 Michael Redd, MIL  C. Billups, DET  Marcus Fizer, CHI 
43 Eric Snow, PHI  J. Mashburn, NOR  Zach Randolph, POR 
44 S. Jackson, ATL  P. Stojakovic, SAC  C. Billups, DET 
45 Rashard Lewis, SEA  D. Stoudamire, POR  T.J. Ford, MIL 
46 Yao Ming, HOU  Jalen Rose, CHI/TOR  Bobby Jackson, SAC 
47 Juwan Howard, ORL  J. Crawford, CHI  J. Stackhouse, WAS 
48 Kirk Hinrich, CHI  Vlade Divac, SAC  Brent Barry, SEA 
49 L. Sprewell, MIN  Dwyane Wade, MIA  C. Anthony, DEN 
50 R. Hamilton, DET  Kirk Hinrich, CHI  Carlos Arroyo, UTH 


Versatility / Turnovers Total Versatility / Turnovers Per Game Versatility / Turnovers Per Minute
Rank Points * Rebounds * A/TO PPG * RPG * A/TO PPM * RPM * A/TO
1 Kevin Garnett, MIN  Kevin Garnett, MIN  Kevin Garnett, MIN 
2 Dirk Nowitzki, DAL  Tracy McGrady, ORL  Tim Duncan, SAS 
3 Brad Miller, SAC  Tim Duncan, SAS  Brad Miller, SAC 
4 Tracy McGrady, ORL  Brad Miller, SAC  Raef LaFrentz, BOS 
5 Tim Duncan, SAS  Chris Webber, SAC  Chris Webber, SAC 
6 Shawn Marion, PHO  Dirk Nowitzki, DAL  Tracy McGrady, ORL 
7 Lamar Odom, MIA  Jason Kidd, NJN  Jason Kidd, NJN 
8 A. Walker, DAL  Kobe Bryant, LAL  C. Oakley, HOU 
9 Paul Pierce, BOS  S. O'Neal, LAL  Dirk Nowitzki, DAL 
10 Jason Kidd, NJN  Elton Brand, LAC  Kobe Bryant, LAL 
11 S. Marbury, NYK/PHO  Shawn Marion, PHO  S. O'Neal, LAL 
12 Gary Payton, LAL  Baron Davis, NOR  Richie Frahm, SEA 
13 LeBron James, CLE  Lamar Odom, MIA  A. Walker, DAL 
14 Sam Cassell, MIN  A. Walker, DAL  Vlade Divac, SAC 
15 Elton Brand, LAC  M. Finley, DAL  M. Daniels, DAL 
16 Michael Redd, MIL  Ray Allen, SEA  Karl Malone, LAL 
17 P. Stojakovic, SAC  Paul Pierce, BOS  A. Daniels, SEA 
18 R. Jefferson, NJN  Carlos Boozer, CLE  Carlos Boozer, CLE 
19 S. O'Neal, LAL  LeBron James, CLE  Elton Brand, LAC 
20 M. Finley, DAL  Gary Payton, LAL  Lamar Odom, MIA 
21 J. O'Neal, IND  S. Marbury, NYK/PHO  Gary Payton, LAL 
22 Carlos Boozer, CLE  J. O'Neal, IND  Bob Sura, ATL/DET 
23 Kobe Bryant, LAL  Karl Malone, LAL  K. Perkins, BOS 
24 Mike Bibby, SAC  Michael Redd, MIL  Sam Cassell, MIN 
25 Andre Miller, DEN  Sam Cassell, MIN  J. O'Neal, IND 
26 Baron Davis, NOR  J. Mashburn, NOR  Shawn Marion, PHO 
27 D. Marshall, CHI/TOR  P. Stojakovic, SAC  Baron Davis, NOR 
28 Joe Johnson, PHO  Vince Carter, TOR  Pau Gasol, MEM 
29 Rashard Lewis, SEA  R. Jefferson, NJN  C. Laettner, WAS 
30 Steve Francis, HOU  Mike Bibby, SAC  Jabari Smith, SAC 
31 D. Stoudamire, POR  Andre Miller, DEN  Bobby Jackson, SAC 
32 Vlade Divac, SAC  D. Marshall, CHI/TOR  Ray Allen, SEA 
33 Zach Randolph, POR  Steve Francis, HOU  M. Finley, DAL 
34 A. Kirilenko, UTH  Kenyon Martin, NJN  Paul Pierce, BOS 
35 Vince Carter, TOR  Allen Iverson, PHI  Michael Redd, MIL 
36 P.J. Brown, NOR  Rashard Lewis, SEA  Andre Miller, DEN 
37 J. Richardson, GSW  A. Kirilenko, UTH  Toni Kukoc, MIL 
38 Pau Gasol, MEM  J. Richardson, GSW  Kenyon Martin, NJN 
39 Jason Terry, ATL  Joe Johnson, PHO  Steve Nash, DAL 
40 Ben Wallace, DET  Vlade Divac, SAC  Marcus Camby, DEN 
41 Eddie Jones, MIA  Pau Gasol, MEM  LeBron James, CLE 
42 Steve Nash, DAL  Steve Nash, DAL  G. Wallace, SAC 
43 C. Billups, DET  D. Stoudamire, POR  Mike Bibby, SAC 
44 S. Abdur-Rahim, ATL/POR  Zach Randolph, POR  Manu Ginobili, SAS 
45 J. Crawford, CHI  C. Billups, DET  Rodney Rogers, NJN 
46 C. Anthony, DEN  R. Wallace, ATL/DET/POR  Josh Howard, DAL 
47 L. Sprewell, MIN  C. Maggette, LAC  D. Marshall, CHI/TOR 
48 Kerry Kittles, NJN  Ben Wallace, DET  R. Strickland, ORL/TOR 
49 Eric Snow, PHI  Jason Terry, ATL  J. Mashburn, NOR 
50 C. Maggette, LAC  Eddie Jones, MIA  S. Marbury, NYK/PHO