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