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February 17, 2012
Best Fit
Lineup Combinations

by Neil Paine

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On a certain level, basketball is purely a game of lineup combinations. The teamwork and chemistry required of the five-man unit lies at the very heart of the game, making it fundamentally different (and, I'd argue, better) than a sport composed mostly of one-on-one interactions like baseball. Here's what I wrote on the subject in May 2010:

"In basketball perhaps more than any other sport, the concept of team-building--creating a cohesive group that fits together and may be greater than the sum of its parts--is phenomenally important. In baseball, a sport dominated by one-on-one matchups, not a whole lot of consideration has to be made for how teammates work together; to make a great team, you basically grab the 25 best players you can, throw them together, and watch them produce. But in basketball, teammates have to work together while simultaneously 'competing' for touches & shots. Throw together a baseball lineup of nine guys who each create 100 runs, you'll probably score 900 runs; throw together a basketball lineup of five 20 PPG scorers, you probably won't score 100 PPG. There's no upper limit on the number of runs the baseball lineup can produce, but there is an upper limit to the points the basketball lineup scores, because teams are limited by a finite number of minutes in a game, and as a result, lineups are limited by a finite number of touches & shots to be allocated to the individual players."

"That's why a stat like Possession% (the percentage of team possessions a player uses while on the floor) is important in looking at how the pieces of a team fit together. A lineup of All-Stars would be interesting, but perhaps a less-talented lineup with one 26 percent usage guy, two 20 percent guys, an 18 percent guy, and a 16 percent guy would be even better if the All-Stars are not happy with the way they fit together or are unable to operate at peak efficiency in lesser roles, while the less talented lineup features players who are all at their optimal usage levels. The whole of the latter would be greater than the sum of the former's parts."

As we saw with the 2011 Miami Heat, there will be diminishing statistical returns if you throw multiple high-usage stars into the same 5-man group and ask them to share one basketball. Much like the rules of physics break down within the singularity of a black hole, the normal tradeoff between usage and efficiency breaks down under the extreme conditions of such a star-studded lineup, making predictions go haywire.

In fact, any time a player is forced to deviate significantly from his established role and/or usage pattern, it's tough to say how his efficiency will react. Some players have managed to increase their usage and their efficiency at the same time, while others find it difficult to maintain their points/possession when taking on a larger role in the offense. Weirder still, some players (including two of Miami's Big Three a year ago, LeBron James & Chris Bosh) will drop their usage but see a decline in efficiency as well. Because of these irregularities, it might be better to assemble a team whose players have to deviate from their established usage rates as little as possible, because it will be easier to predict how they will perform when tossed into a lineup together.

In the spirit of that line of thinking, I decided to construct the best hypothetical 5-man units of 2012 where no player had to increase or decrease their usage rate. In other words, I picked groups of players whose total usage adds up to 100%. I did this by selecting 5-man units at random based on Basketball Value's position designations, and keeping 11,458 unique groups whose combined usage happened to sum to 100%. This is not a complete list--obviously there are more than 11,450 possible combinations when picking groups of five from a pool of 335 players--but it does represent a good cross-section of the possible lineups out there.

For each group, I then used Dean Oliver's player Offensive and Defensive Ratings to predict composite Offensive/Defensive efficiency ratings (and therefore efficiency margins). The groups with the best margins were considered to be the best "fits":

Rk PG           SG           SF           PF           C             ORtg    DRtg    Net
----------------------------------------------------------------------------------------
 1 Paul         C. Brewer    Korver       Love         C. Andersen  118.5   100.2   18.2
 2 Rose         S. Curry     E. Davis     B. Wright    T. Chandler  116.2    99.8   16.4
 3 Ridnour      Harden       Dudley       B. Wright    Love         117.3   102.2   15.1
 4 Jack         Gee          Korver       James        T. Chandler  116.9   101.8   15.1
 5 Lucas        Dragic       R. Anderson  B. Wright    T. Chandler  115.2   100.3   15.0
 6 Chalmers     McGrady      L. James     Novak        J. Hill      114.3   100.9   13.4
 7 Burks        M. Miller    T. Young     Love         C. Andersen  113.6   100.3   13.3
 8 Paul         Lowry        Novak        McRoberts    Howard       113.4   100.1   13.2
 9 Meeks        J. Johnson   Millsap      Duncan       T. Chandler  113.1    99.8   13.2
10 Duhon        Wade         R. Anderson  P. Gasol     Ibaka        113.9   100.8   13.1
11 Dragic       Harden       L. Allen     P. Gasol     Gortat       114.2   101.1   13.0
12 Paul         T. Allen     Pietrus      P. Gasol     Brand        111.8    98.8   13.0
13 Cook         L. Williams  Leonard      James        K. Thomas    112.8    99.9   12.9
14 Curry        Harden       R. Anderson  Leuer        Mozgov       116.8   103.9   12.9
15 Paul         Kev. Martin  Pierce       Vucevic      J. Anthony   113.3   100.5   12.9
16 C. Watson    Rush         L. James     Cunningham   Pachulia     113.5   100.8   12.7
17 Paul         Childress    Durant       Leuer        Dalembert    115.5   102.8   12.7
18 Bibby        L. Williams  T. Harris    R. Anderson  T. Chandler  114.4   101.8   12.5
19 Lowry        Redick       L. James     R. Evans     Ibaka        113.7   101.2   12.5
20 Rondo        Hill         Batum        Aldridge     D. Jordan    112.7   100.2   12.4

Players who appear frequently in the top 1% of lineups might be considered to be "good fit" players, capable of working with a variety of different teammates and producing good results:

Player           Pos      #
---------------------------
LeBron James     PF/SF   21
Chris Paul       PG      15
Kevin Love       C/PF    15
Tyson Chandler   C       14
Brandan Wright   C/PF    13
Ryan Anderson    PF/SF   12
James Harden     SG      10
Kyle Korver      SF/SG   10
Chris Andersen   C/PF     9
Danilo Gallinari PF/SF    9
Derrick Rose     PG       9
Steve Novak      PF/SF    9
Lavoy Allen      PF/SF    8
Louis Williams   PG/SG    8
Nicolas Batum    SF       8
Pau Gasol        C/PF     8
Stephen Curry    PG/SG    8
Gerald Wallace   PF/SF    7
Joakim Noah      C/PF     7
Kyle Lowry       PG/SG    7
Thaddeus Young   PF/SF    7

The top of the list resembles any ranking of the best, most efficient players in the game--James, Paul, and Love are all present, for instance. However, other players might be good examples of the "fit" phenomenon: in a vacuum, Chris Andersen is no more than a solid role player, but his combination of strong defense, high efficiency, and a 15% usage rate allows him to slot in along other stars and make small but essential contributions. Andersen might be only the 43rd-most productive player in the league on a per-possession basis (using a metric based on Oliver's stats), but he might be the 10th-best "fit" player because his profile is easier to mesh with in a lineup than a higher-usage player with more star power.

Conversely, here are the worst "fit" lineups, which are generally groups of poor players who are having terrible efficiency seasons:

Rk PG           SG           SF           PF           C            ORtg    DRtg     Net
----------------------------------------------------------------------------------------
 1 Higgins      Jo. Crawford Outlaw       Samuels      Magloire     80.2   108.1   -27.9
 2 Higgins      Selby        Daniels      Gooden       Magloire     81.7   104.5   -22.8
 3 Fredette     Higgins      Daye         Vesely       Mullens      87.6   109.7   -22.1
 4 Udrih        Higgins      Aminu        Outlaw       Mullens      87.9   109.5   -21.6
 5 Telfair      Higgins      Garcia       Odom         Diaw         85.9   107.3   -21.4
 6 D. Gibson    Higgins      Daniels      S. Jackson   Samuels      85.7   106.1   -20.4
 7 K. Walker    Carroll      Prince       Daye         Hickson      89.1   109.5   -20.3
 8 Higgins      Pondexter    Daye         Speights     Samuels      85.7   105.8   -20.1
 9 K. Walker    Selby        R. Williams  Sha. WilliamsFrye         88.6   108.6   -20.1
10 Je. Pargo    Goudelock    Gr. Hill     Daye         Hickson      86.8   106.5   -19.8
11 Selby        Higgins      S. Jackson   Vesely       Brand        85.1   104.5   -19.4
12 Ja. Pargo    M. Daniels   Maggette     Daye         Vesely       85.2   104.6   -19.4
13 Selby        Terry        Outlaw       Blatche      L. Sanders   85.2   104.3   -19.1
14 S. Brown     Carroll      Wafer        Daye         Diaw         88.9   108.0   -19.0
15 Knight       Ja. Pargo    Outlaw       Blatche      Hickson      87.9   106.9   -19.0
16 Knight       Wilkins      Maggette     Blatche      Amundson     87.3   106.2   -18.9
17 Je. Pargo    Higgins      Fields       Hickson      Bogut        86.6   105.5   -18.8
18 Higgins      Stephenson   Garcia       Daye         Garnett      85.6   104.4   -18.8
19 Higgins      Telfair      Jeffries     Daye         C. Smith     86.1   104.8   -18.7
20 Higgins      DeRozan      World Peace  Forbes       Mbah a Moute 87.2   105.7   -18.5

Just as players who show up often in good lineups might be considered "good fits", here's the all-"bad fit" team:

Player              Pos      #
------------------------------
Cory Higgins        PG/SG   32
Austin Daye         PF/SF   23
Jeremy Pargo        PG/SG   23
Travis Outlaw       PF/SF   17
Josh Selby          PG/SG   15
Sebastian Telfair   PG/SG   15
Toney Douglas       PG/SG   12
Andray Blatche      C/PF    11
Boris Diaw          C/PF    11
Brandon Knight      PG/SG   11
Louis Amundson      C/PF    11
Matt Carroll        SF/SG   11
Stephen Jackson     PF/SF   11
Gary Forbes         PF/SF   10
Tristan Thompson    C/PF    10
Reggie Williams     SF/SG    9
Samardo Samuels     C/PF     8
Corey Maggette      SF       7
Jamaal Magloire     C/PF     7
Jan Vesely          C/PF     7
Jordan Crawford     PG/SG    7
Mehmet Okur         C/PF     7

The anti-Andersen, Cory Higgins is the undisputed king of "bad fit", thanks to brutal efficiency marks (77.0 ORtg, 114.3 DRtg) and a medium-usage profile (22.7 percent) that finds him frequently being the not-so-missing piece for a lineup that needs to get to 100%.

This is not to say that the construction of these lineups is an exact science (in fact, it's about as far from it as possible). Usage is not an overly effective descriptor of a player's style, meaning two players who arrive at the same usage in different ways may in reality have dramatically different impacts on a given lineup. But it is more likely that a lineup operates according to statistical prediction if its players are allowed to stay in their customary roles, and that means teams seeking greater reliability from their acquisitions should think about targeting players whose usage profiles fit in well with their existing roster.

Neil Paine is an author of Basketball Prospectus. You can contact Neil by clicking here or click here to see Neil's other articles.

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