Rankings Players Over Last 10 Seasons

I was taking a look at the player ratings from here based on the xRAPM stat. The stats page is maintained by Jeremias Engelmann. His xRAPM combines box score statistics (the box score ratings are derived by regressing onto team points scored/allowed) and +/- for all 5-vs-5 matchups using a regularized ridge regression technique. It is a type of adjusted +/- stat that's designed to be:

1. lessy noisy than typical adjusted +/-
2. a stronger predictor for aggregate team performance

I like it for a couple reasons:

1. In principle, it captures everything of interest on the floor because it is at its root a +/- stat (so, no particular bias towards offensive players for example)
2. It separates ratings on the offensive and defensive end.
3. The results generally "make sense". Not that there are no surprises (that would be boring).

For fun, I took the stats for the last 10+ seasons (prior 10 seasons plus this season) to arrive at the "best" players over that span according to this rating. Because xRAPM is basically a per-possession rating, I decided to rank players in a slightly different manner -- what I'm calling Points Added Per Season (or PAPS). PAPS is supposed to tell us how many net points a player adds to his team, per season, relative to a "replacement-level player" (someone that can be brought in "for free", like from the D-league). Because I'm doing it per-season, the rating will benefit players who play a lot of minutes and don't miss games (in addition, of course, to being good "per-possession").

PAPS is computed very simply:

PAPS = (XRAPM + 4.0) * (Poss / 200) * (1 / #seasons)

Below are the top 15 players at each position (for some players, the true position is debatable but I chose the position that made sense to me). Note that these ratings reflect an average over all seasons. So players that have become really good in recent years, but maybe weren't so good earlier in their careers, may not rate as high as we'd expect. Kevin Durant, for example, has a superstar-level XRAPM for the last 4+ seasons as we'd expect. But in his first 2 years in the league, his XRAPM rating was sub-zero (during which time, by the way, his teams won 19 and 24 games with him playing major minutes).

Point Guards:

Code:

[size=2]
[B]    Name                  Off/100    Def/100    XRAPM       Poss      #seasons    PAPS[/B]
1   Jason Kidd            +3.0       +2.1       +5.1        102961    11          427.3
2   Chris Paul            +5.9       +0.4       +6.3        64945     8           416.6
3   Steve Nash            +6.4       -2.1       +4.3        102062    11          383.9
4   Baron Davis           +4.1       -0.3       +3.8        79789     10          311.5
5   Allen Iverson         +2.8       -0.7       +2.1        81298     8           309.2
6   Chauncey Billups      +4.7       -1.2       +3.5        89330     11          305.2
7   Steve Francis         +2.2       +0.8       +3.0        48873     6           284.7
8   Russell Westbrook     +2.7       -0.6       +2.1        45006     5           274.0
9   Deron Williams        +3.9       -2.0       +2.0        72552     8           270.3
10  Andre Miller          +2.3       -0.9       +1.4        105905    11          262.0
11  Rajon Rondo           +1.2       +1.2       +2.3        57354     7           259.2
12  Stephon Marbury       +3.4       -2.0       +1.4        59874     7           230.7
13  Gilbert Arenas        +3.5       -1.1       +2.4        70314     10          224.2
14  Derrick Rose          +2.3       -1.8       +0.5        39470     4           223.3
15  Jason Terry           +2.4       -1.9       +0.4        101542    11          204.7
[/size]

Shooting Guards:

Code:

[size=2]
[B]    Name                  Off/100    Def/100    XRAPM       Poss      #seasons    PAPS[/B]
1   Kobe Bryant           +5.0       -0.4       +4.6        114928    11          451.8
2   Dwyane Wade           +5.5       +0.2       +5.7        86118     10          418.9
3   Manu Ginobili         +4.8       +0.8       +5.6        72437     11          314.6
4   Tracy McGrady         +4.4       -0.2       +4.2        74688     10          307.5
5   Vince Carter          +2.5       +0.2       +2.7        95750     11          290.9
6   Ray Allen             +3.5       -1.4       +2.1        99551     11          276.5
7   Eddie Jones           +0.8       +1.4       +2.2        45285     6           233.9
8   Joe Johnson           +1.9       -1.2       +0.7        110247    11          233.1
9   Jason Richardson      +1.9       -1.3       +0.6        99974     11          210.2
10  Reggie Miller         +1.9       -0.6       +1.3        23515     3           208.7
11  Brandon Roy           +3.1       -1.3       +1.8        42606     6           204.8
12  James Harden          +2.8       -0.6       +2.2        26081     4           202.1
13  Doug Christie         -0.1       +1.8       +1.7        28182     5           161.9
14  Michael Redd          +3.3       -2.9       +0.4        70240     10          156.2
15  Corey Maggette        +1.2       -0.7       +0.5        73811     11          150.6
[/size]

Small Forwards:

Code:

[size=2]
[B]    Name                  Off/100    Def/100    XRAPM       Poss      #seasons    PAPS[/B]
1   LeBron James          +6.2       +1.2       +7.4        106030    10          601.7
2   Paul Pierce           +2.7       +1.1       +3.8        105700    11          376.3
3   Andre Iguodala        +0.7       +2.3       +2.9        91324     9           351.5
4   Kevin Durant          +2.7       +0.1       +2.8        60593     6           341.4
5   Metta World Peace     +0.7       +2.4       +3.1        85347     11          274.1
6   Danny Granger         +1.3       +0.1       +1.4        67007     7           257.3
7   Shane Battier         -0.1       +2.3       +2.1        90617     11          252.0
8   Luol Deng             +0.5       +1.2       +1.7        76471     9           240.3
9   Gerald Wallace        -0.2       +3.0       +2.8        71491     11          219.7
10  Carmelo Anthony       +2.1       -1.5       +0.6        94461     10          218.2
11  Hedo Turkoglu         +1.3       -0.3       +1.1        83686     11          193.2
12  Peja Stojakovic       +2.2       -1.5       +0.7        70781     9           184.6
13  Rudy Gay              -0.2       +0.1       -0.1        64362     7           181.5
14  Anthony Parker        +0.1       +0.1       +0.2        51607     6           180.0
15  Tayshaun Prince       +0.6       -0.3       +0.3        90333     11          176.2
[/size]

Power Forwards:

Code:

[size=2]
[B]    Name                  Off/100    Def/100    XRAPM       Poss      #seasons    PAPS[/B]
1   Dirk Nowitzki         +4.3       +1.9       +6.2        107618    10          548.4
2   Tim Duncan            +3.1       +5.3       +8.4        94644     11          532.0
3   Kevin Garnett         +2.8       +5.0       +7.7        99228     11          528.6
4   Pau Gasol             +2.7       +1.5       +4.2        99872     11          374.1
5   Chris Bosh            +1.7       +1.9       +3.6        91562     10          347.0
6   Andrei Kirilenko      +2.4       +3.2       +5.5        72856     10          346.5
7   Josh Smith            -0.0       +3.8       +3.7        78978     9           338.7
8   Shawn Marion          +0.5       +2.3       +2.8        107920    11          332.7
9   Blake Griffin         +2.5       +1.2       +3.8        23727     3           307.5
10  Elton Brand           +1.4       +2.3       +3.8        85830     11          304.1
11  Rasheed Wallace       +0.3       +3.4       +3.7        70344     9           301.0
12  Lamar Odom            +0.3       +2.5       +2.7        92534     11          283.3
13  LaMarcus Aldridge     +1.3       +1.1       +2.4        58912     7           268.6
14  Amare Stoudemire      +1.5       +0.6       +2.1        87192     10          265.8
15  Paul Millsap          +1.1       +2.2       +3.3        51010     7           264.4
[/size]

Centers:

Code:

[size=2]
[B]    Name                  Off/100    Def/100    XRAPM       Poss      #seasons    PAPS[/B]
1   Dwight Howard         +1.6       +4.9       +6.5        88442     9           517.1
2   Ben Wallace           -1.3       +7.3       +6.0        79827     10          400.2
3   Shaquille O'Neal      +3.6       +3.1       +6.7        61938     9           368.3
4   Marc Gasol            +0.4       +2.9       +3.3        40468     5           293.5
5   Yao Ming              +1.0       +2.8       +3.8        58434     8           284.3
6   Marcus Camby          -1.2       +5.7       +4.5        73647     11          283.3
7   Brad Miller           +1.1       +2.4       +3.5        74711     10          278.8
8   Tyson Chandler        -0.3       +3.9       +3.6        74207     11          256.5
9   Zydrunas Ilgauskas    -0.1       +2.1       +2.0        68477     9           229.8
10  Joakim Noah           +0.6       +2.6       +3.2        37454     6           223.9
11  Nene Hilario          +0.3       +3.1       +3.4        65958     11          221.6
12  Andrew Bogut          -0.6       +3.6       +2.9        50804     8           220.6
13  Samuel Dalembert      -1.9       +3.6       +1.7        70900     10          201.8
14  Jermaine O'Neal       -0.9       +3.4       +2.5        66812     11          197.6
15  Emeka Okafor          -1.3       +3.3       +2.1        58127     9           195.8
[/size]

 

Forgot to mention that I used a cutoff of 20000 possessions.

But Lin's XRAPM was +1.2, and his PAPS is 68.1.

 

The formula, in this case, would take about a page to describe.

Here's a short description of the RAPM method (from here):

[rquoter]
The last approach I have seen in public is the Regularized Adjusted Plus/Minus (RAPM) first proposed by Joe Sill and presented at the MIT Sloan Sports Analytics Conference. This approach takes advantage of a mathematical method known as Tikhonov Regularization or Ridge Regression. The method essentially adds a penalty factor to the regression for results being far away from the mean. This penalty factor, called lambda, is chosen based on cross validation, usually K-fold cross validation. The data is broken into a number of segments (folds) and 1 at a time is removed and various choices for lambda explored. The penalty factor is chosen such that maximum out-of-sample accuracy is attained. This should remove most collinearity/noise, but lose only a small amount of the validity of the measure–except, one major issue is that because all players are regressed toward league mean, players with few minutes are considered average, and to rate out really badly, a player must have had a bunch of minutes to verify that the player was indeed that bad.

Jeremias Engelmann’s site stats-for-the-nba.appspot.com contains several versions of RAPM for different purposes. He’s got 1 year RAPM for the last 5 or 6 years, a 3.x year rating that has best out-of-sample accuracy for this year, some longer term ratings, ratings for the Euroleague, and ratings for several stats (such as rebounding). The framework is all RAPM. There are a few issues, as mentioned above: the regression of rarely-used players to league mean is a big one, the lack of aging adjustment for multi-year ratings another, and not weighting multi-year ratings towards recency for best predictive power a third. APBRmetrics threads are here and here.[/rquoter]

A much lengthier writeup by Joe Sill of how regularization was used to stabilize adjusted +/- was available on the (now defunct) HoopNumbers.com website, but it can be accessed using the Way Back Machine (click here).

Engelmann's variant (which he's calling xRAPM) incorporate the previous season's box score rating and RAPM as a prior to the formula, and then stabilizes the resulting RAPM with a box score rating for the current season. He describes his approach in this thread.

 

Ratings from the 90s should be taken with a grain of salt, because he was computing "fake" RAPM due to the unavailability of actual play-by-play data. Methodology describe here.

Keep in mind, also, that his goal isn't necessarily to come up with player ratings that make the most sense to us when the players are ranked, but rather ratings that yield the best predictions of team performance.

 

So, I thought it might be interesting to compare player rankings using different metrics. So I got the players ratings according to Dave Berri's Wins Produced metric (described here) over the same years. This time, I'm ranking players according to Wins Produced Per Season (WPPS), using a 10000 minutes cutoff.

Point Guards

Code:

[size=2]
      [B] Name                   MIN      WP48    #seasons      WPPS[/B]
1      Chris  Paul           18804    0.304     8            14.9
2      Jason  Kidd           27130    0.260     11           13.4
3      Steve  Nash           25847    0.251     11           12.3
4      Rajon  Rondo          15096    0.223     7            10.0
5      Chauncey  Billups     24186    0.198     11           9.1
6      Andre  Miller         28158    0.149     11           7.9
7      Jose  Calderon        14444    0.200     8            7.5
8      Deron  Williams       19000    0.141     8            7.0
9      Jason  Terry          27105    0.134     11           6.9
10     Gary  Payton          12382    0.117     5            6.0
11     Tony  Parker          25097    0.122     11           5.8
12     Russell  Westbrook    11605    0.108     5            5.2
13     Mike  Conley          12327    0.121     6            5.2
14     Steve  Francis        13319    0.108     6            5.0
15     Stephon  Marbury      15935    0.105     7            5.0

[/size]

Shooting Guards

Code:

[size=2]
       [B]Name                   MIN      WP48    #seasons      WPPS[/B]
1      Dwyane  Wade          22845    0.223     10           10.6
2      Kobe  Bryant          29998    0.163     11           9.3
3      Manu  Ginobili        19190    0.246     11           8.9
4      Ray  Allen            26730    0.167     11           8.5
5      Brent  Barry          10325    0.231     7            7.1
6      Eddie  Jones          12579    0.151     6            6.6
7      Brandon  Roy          11561    0.155     6            6.2
8      Tracy  McGrady        19915    0.147     10           6.1
9      Jason  Richardson     25949    0.120     11           5.9
10     Vince  Carter         25569    0.121     11           5.9
11     Kevin  Martin         15593    0.149     9            5.4
12     Joe  Johnson          29526    0.094     11           5.3
13     Cuttino  Mobley       17548    0.095     7            4.9
14     Michael  Redd         18655    0.123     10           4.8
15     Jarrett  Jack         15456    0.095     8            3.8

[/size]

Small Forwards

Code:

[size=2]
       [B]Name                   MIN      WP48    #seasons      WPPS[/B]
1      LeBron  James         28397    0.261     10           15.4
2      Andre  Iguodala       24190    0.200     9            11.2
3      Shane  Battier        24188    0.198     11           9.0
4      Paul  Pierce          28050    0.167     11           8.9
5      Kevin  Durant         15505    0.160     6            8.6
6      Gerald  Wallace       21150    0.192     11           7.7
7      Josh  Childress       10409    0.238     7            7.4
8      Ronnie  Brewer        11084    0.213     7            7.0
9      Luol  Deng            20182    0.149     9            7.0
10     Rashard  Lewis        24997    0.134     11           6.3
11     Tayshaun  Prince      25110    0.133     11           6.3
12     Mike  Miller          19783    0.163     11           6.1
13     Richard  Jefferson    25431    0.125     11           6.0
14     James  Posey          16715    0.154     9            5.9
15     Anthony  Parker       13367    0.124     6            5.8

[/size]

Power Forwards

Code:

[size=2]
       [B]Name                   MIN      WP48    #seasons      WPPS[/B]
1      Kevin  Garnett        26634    0.255     11           12.8
2      Tim  Duncan           25649    0.232     11           11.3
3      Andrei  Kirilenko     19559    0.258     10           10.5
4      Pau  Gasol            26347    0.184     11           9.2
5      Dirk  Nowitzki        28404    0.147     11           7.9
6      Elton  Brand          22834    0.177     11           7.6
7      David  Lee            16878    0.169     8            7.4
8      Lamar  Odom           24356    0.155     11           7.2
9      Carlos  Boozer        21296    0.176     11           7.1
10     Chris  Bosh           24387    0.137     10           7.0
11     Paul  Millsap         13304    0.168     7            6.6
12     Josh  Smith           21228    0.120     9            5.9
13     Antonio  McDyess      13342    0.153     8            5.3
14     Donyell  Marshall     10977    0.162     7            5.3
15     Anderson  Varejao     12026    0.189     9            5.3

[/size]

Centers

Code:

[size=2]
       [B]Name                   MIN      WP48    #seasons      WPPS[/B]
1      Dwight  Howard        23451    0.255     9            13.9
2      Ben  Wallace          21892    0.261     10           11.9
3      Tyson  Chandler       19780    0.238     11           8.9
4      Marcus  Camby         18955    0.241     11           8.7
5      Al  Horford           11568    0.164     6            6.6
6      Marc  Gasol           10827    0.146     5            6.6
7      Yao  Ming             15817    0.156     8            6.4
8      Erick  Dampier        15611    0.193     10           6.3
9      P.J.  Brown           12224    0.145     6            6.2
10     Shaquille  O'Neal     16423    0.160     9            6.1
11     Jeff  Foster          12724    0.228     10           6.0
12     Samuel  Dalembert     18820    0.152     10           5.9
13     Emeka  Okafor         17205    0.149     9            5.9
14     Andrew  Bynum         10175    0.194     8            5.1
15     Brad  Miller          19414    0.125     10           5.1

[/size]

 

It occurred to me that ranking players simply by production per season might yield very similar results across different metrics since it would always benefit players who play a lot of minutes and don't miss games.

To make comparison of player metrics a little more interesting, instead here I used the per-season metric as a filter (took the top 15), and then ranked the players based on the particular per-possession or per-minute metric (thus far, XRAPM and WP48). Below, I list the top 10 players at each position using this approach. At some point, I think I'll also do the same thing with PER, NBA EFF, and any other player rating metrics I can find which look interesting.


POINT GUARDS

Top 10 XRAPM (filtered by PAPS top 15) 
     Name                PAPS    Off/100   Def/100   XRAPM
1    Chris Paul          416.6   +5.9      +0.4      +6.3
2    Jason Kidd          427.3   +3.0      +2.1      +5.1
3    Steve Nash          383.9   +6.4      -2.1      +4.3
4    Baron Davis         311.5   +4.1      -0.3      +3.8
5    Chauncey Billups    305.2   +4.7      -1.2      +3.5
6    Steve Francis       284.7   +2.2      +0.8      +3.0
7    Gilbert Arenas      224.2   +3.5      -1.1      +2.4
8    Rajon Rondo         259.2   +1.2      +1.2      +2.3
9    Allen Iverson       309.2   +2.8      -0.7      +2.1
10   Russell Westbrook   274     +2.7      -0.6      +2.1

Top 10 WP48 (filtered by WPPS top 15)
     Name               WPPS    WP48
1    Chris Paul         14.9    0.304
2    Jason Kidd         13.4    0.26
3    Steve Nash         12.3    0.251
4    Rajon Rondo        10      0.223
5    Jose Calderon      7.5     0.2
6    Chauncey Billups   9.1     0.198
7    Andre Miller       7.9     0.149
8    Deron Williams     7       0.141
9    Jason Terry        6.9     0.134
10   Tony Parker        5.8     0.122

SHOOTING GUARDS

Top 10 XRAPM (filtered by PAPS top 15) 
     Name                PAPS    Off/100   Def/100   XRAPM
1    Dwyane Wade         418.9   +5.5      +0.2      +5.7
2    Manu Ginobili       314.6   +4.8      +0.8      +5.6
3    Kobe Bryant         451.8   +5.0      -0.4      +4.6
4    Tracy McGrady       307.5   +4.4      -0.2      +4.2
5    Vince Carter        290.9   +2.5      +0.2      +2.7
6    Eddie Jones         233.9   +0.8      +1.4      +2.2
7    James Harden        202.1   +2.8      -0.6      +2.2
8    Ray Allen           276.5   +3.5      -1.4      +2.1
9    Brandon Roy         204.8   +3.1      -1.3      +1.8
10   Doug Christie       161.9   -0.1      +1.8      +1.7

Top 10 WP48 (filtered by WPPS top 15)
      Name               WPPS    WP48
 1    Manu Ginobili      8.9     0.246
 2    Brent Barry        7.1     0.231
 3    Dwyane Wade        10.6    0.223
 4    Ray Allen          8.5     0.167
 5    Kobe Bryant        9.3     0.163
 6    Brandon Roy        6.2     0.155
 7    Eddie Jones        6.6     0.151
 8    Kevin Martin       5.4     0.149
 9    Tracy McGrady      6.1     0.147
 10   Michael Redd       4.8     0.123

SMALL FORWARDS

Top 10 XRAPM (filtered by PAPS top 15) 
     Name                PAPS    Off/100   Def/100   XRAPM
1    LeBron James        601.7   +6.2      +1.2      +7.4
2    Paul Pierce         376.3   +2.7      +1.1      +3.8
3    Metta World Peace   274.1   +0.7      +2.4      +3.1
4    Andre Iguodala      351.5   +0.7      +2.3      +2.9
5    Kevin Durant        341.4   +2.7      +0.1      +2.8
6    Gerald Wallace      219.7   -0.2      +3.0      +2.8
7    Shane Battier       252     -0.1      +2.3      +2.1
8    Luol Deng           240.3   +0.5      +1.2      +1.7
9    Danny Granger       257.3   +1.3      +0.1      +1.4
10   Hedo Turkoglu       193.2   +1.3      -0.3      +1.1

Top 10 WP48 (filtered by WPPS top 15)
     Name               WPPS    WP48
1    LeBron James       15.4    0.261
2    Josh Childress     7.4     0.238
3    Ronnie Brewer      7       0.213
4    Andre Iguodala     11.2    0.2
5    Shane Battier      9       0.198
6    Gerald Wallace     7.7     0.192
7    Paul Pierce        8.9     0.167
8    Mike Miller        6.1     0.163
9    Kevin Durant       8.6     0.16
10   James Posey        5.9     0.154

POWER FORWARD

Top 10 XRAPM (filtered by PAPS top 15) 
     Name                PAPS    Off/100   Def/100   XRAPM
1    Tim Duncan          532     +3.1      +5.3      +8.4
2    Kevin Garnett       528.6   +2.8      +5.0      +7.7
3    Dirk Nowitzki       548.4   +4.3      +1.9      +6.2
4    Andrei Kirilenko    346.5   +2.4      +3.2      +5.5
5    Pau Gasol           374.1   +2.7      +1.5      +4.2
6    Blake Griffin       307.5   +2.5      +1.2      +3.8
7    Elton Brand         304.1   +1.4      +2.3      +3.8
8    Josh Smith          338.7   +0.0      +3.8      +3.7
9    Rasheed Wallace     301     +0.3      +3.4      +3.7
10   Chris Bosh          347     +1.7      +1.9      +3.6

Top 10 WP48 (filtered by WPPS top 15)
     Name               WPPS    WP48
1    Andrei Kirilenko   10.5    0.258
2    Kevin Garnett      12.8    0.255
3    Tim Duncan         11.3    0.232
4    Anderson Varejao   5.3     0.189
5    Pau Gasol          9.2     0.184
6    Elton Brand        7.6     0.177
7    Carlos Boozer      7.1     0.176
8    David Lee          7.4     0.169
9    Paul Millsap       6.6     0.168
10   Donyell Marshall   5.3     0.162

CENTERS

Top 10 XRAPM (filtered by PAPS top 15) 
     Name                PAPS    Off/100   Def/100   XRAPM
1    Shaquille O'Neal    368.3   +3.6      +3.1      +6.7
2    Dwight Howard       517.1   +1.6      +4.9      +6.5
3    Ben Wallace         400.2   -1.3      +7.3      +6.0
4    Marcus Camby        283.3   -1.2      +5.7      +4.5
5    Yao Ming            284.3   +1.0      +2.8      +3.8
6    Tyson Chandler      256.5   -0.3      +3.9      +3.6
7    Brad Miller         278.8   +1.1      +2.4      +3.5
8    Nene Hilario        221.6   +0.3      +3.1      +3.4
9    Marc Gasol          293.5   +0.4      +2.9      +3.3
10   Joakim Noah         223.9   +0.6      +2.6      +3.2

Top 10 WP48 (filtered by WPPS top 15)
     Name               WPPS    WP48
1    Ben Wallace        11.9    0.261
2    Dwight Howard      13.9    0.255
3    Marcus Camby       8.7     0.241
4    Tyson Chandler     8.9     0.238
5    Jeff Foster        6       0.228
6    Andrew Bynum       5.1     0.194
7    Erick Dampier      6.3     0.193
8    Al Horford         6.6     0.164
9    Shaquille O'Neal   6.1     0.16
10   Yao Ming           6.4     0.156