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 |