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Championship Probability Added II

Posted by Neil Paine on December 3, 2009

357AUG01020_Basketball_JCW_FileYesterday I rolled out a very primitive idea for evaluating players by logically weighting their regular-season and postseason production. In case you missed it, I put everything in terms of the typical team's championship probability, and weighted regular-season and playoff Win Shares based on how much each type of win added to the probability of winning a title. I still think the core idea is terrific, but when the smoke cleared yesterday we came out with a list that saw old-school NBAers and ABA stars dominate over modern players -- I mean, Cliff Hagan ranked ahead of Michael Jordan, for goodness' sake! What in the name of Max Zaslofsky is going on here?

David Lewin suggested we fix the problem of overvaluing the pre-expansion NBA by discounting stats from leagues with fewer teams than the modern NBA with a multiplier of x/30 (where x = the # of teams in the league that year). I liked that plan, and I also decided to throw out the ABA stats entirely; I don't have a great rationale for this, except that I'm not sure what kind of prestige the ABA's championship had next to the NBA's (that and the fact that ABA players were clearly overvalued by CPA and I didn't want to deal with them at the moment). So with that in mind, here's an amended list that looks at who added the most adjusted championship probability in NBA history:

Rank Player aCPA
1 Michael Jordan 0.3685
2 Kareem Abdul-Jabbar 0.3644
3 Magic Johnson 0.3019
4 Wilt Chamberlain 0.3014
5 Shaquille O'Neal 0.2843
6 Bill Russell 0.2587
7 Karl Malone 0.2515
8 Tim Duncan 0.2470
9 Jerry West 0.2389
10 Larry Bird 0.2320
11 John Stockton 0.2289
12 Scottie Pippen 0.2219
13 Hakeem Olajuwon 0.2196
14 Reggie Miller 0.2066
15 Kobe Bryant 0.2055
16 Charles Barkley 0.2025
17 David Robinson 0.1930
18 Horace Grant 0.1900
19 Kevin McHale 0.1895
20 John Havlicek 0.1805
21 Julius Erving 0.1684
22 Chauncey Billups 0.1676
23 Robert Parish 0.1653
24 Moses Malone 0.1649
25 Dirk Nowitzki 0.1622
26 Clyde Drexler 0.1570
27 Robert Horry 0.1535
28 Oscar Robertson 0.1527
29 Walt Frazier 0.1519
30 Jeff Hornacek 0.1476
31 Patrick Ewing 0.1453
32 Elgin Baylor 0.1411
33 Maurice Cheeks 0.1384
34 Sam Jones 0.1383
35 James Worthy 0.1351
36 Rasheed Wallace 0.1351
37 Gary Payton 0.1342
38 Bob Pettit 0.1336
39 Wes Unseld 0.1332
40 Ben Wallace 0.1321
41 Elvin Hayes 0.1312
42 Dennis Johnson 0.1265
43 Kevin Garnett 0.1247
44 Dolph Schayes 0.1240
45 Terry Porter 0.1236
46 Jason Kidd 0.1223
47 Dennis Rodman 0.1185
48 Isiah Thomas 0.1171
49 Dikembe Mutombo 0.1165
50 Chet Walker 0.1162
51 Bobby Jones 0.1160
52 Ray Allen 0.1155
53 LeBron James 0.1126
54 Sam Perkins 0.1122
55 Bob Cousy 0.1119
56 Bill Laimbeer 0.1118
57 Cliff Hagan 0.1110
58 Byron Scott 0.1107
59 Charles Oakley 0.1106
60 Bob Dandridge 0.1101
61 Bob Lanier 0.1087
62 Adrian Dantley 0.1070
63 Joe Dumars 0.1058
64 Bill Sharman 0.1052
65 Michael Cooper 0.1051
66 A.C. Green 0.1042
67 Don Nelson 0.1041
68 Manu Ginobili 0.1041
69 Gus Williams 0.1033
70 Paul Pierce 0.1033
71 Cedric Maxwell 0.1030
72 Shawn Kemp 0.1029
73 Steve Nash 0.1025
74 Kevin Johnson 0.1015
75 Dave Cowens 0.0991
76 Dan Majerle 0.0980
77 Vlade Divac 0.0980
78 Jack Sikma 0.0977
79 Frank Ramsey 0.0977
80 Buck Williams 0.0973
81 Dale Davis 0.0966
82 Derek Fisher 0.0953
83 Mark Jackson 0.0951
84 Richard Hamilton 0.0942
85 Danny Ainge 0.0937
86 Rick Barry 0.0922
87 Tom Heinsohn 0.0915
88 Sidney Moncrief 0.0897
89 Allen Iverson 0.0897
90 Hersey Hawkins 0.0895
91 Eddie Jones 0.0894
92 Steve Smith 0.0886
93 Paul Silas 0.0880
94 Tayshaun Prince 0.0875
95 Detlef Schrempf 0.0871
96 Jerome Kersey 0.0870
97 Alonzo Mourning 0.0870
98 Larry Nance 0.0867
99 P.J. Brown 0.0859
100 Shawn Marion 0.0851

12 Responses to “Championship Probability Added II”

  1. Corey V. Says:

    It's interesting that two of the top 11 (and three of the top 15) never even won a championship.

  2. Anon Says:

    That's probably because Miller, Stockton, and Malone often played the team that had the guy at the top of the list. Lol

  3. DSMok1 Says:

    That list looks absolutely excellent, Neil. Great work.

  4. Mike G Says:

    "we can multiply RS Win Shares by .0004 and playoff Win Shares by .0063"

    Does this mean a PO WS is worth 16 times a RS WS?

    That may explain how Robert Horry added more 'championship probability' than Oscar Robertson.

  5. Neil Paine Says:

    Yes, that and the fact that I dinged players pretty harshly for playing at a time when the league had <30 teams.

  6. David Lewin Says:

    Looks like a pretty good list though. I thought it might be too harsh on old timers, but it looks about right.

  7. Mike G Says:

    You shouldn't ding playoff WS in earlier eras, should you? Or at least, not at the same proportion as RS games? Each PO win was 1/8 of the way to a title, in Russell's day. If a title is worth (9/30) .30 as much as now, but an PO win is 2.0 times, then a 1960 PO WS might be worth .60 as much as in 2010?

  8. AnacondaHL Says:

    In your calculations, did you adjust for years that didn't have 82 games, or 1230 league wins, in the season? Or for shorter playoffs? You only explicitly mentioned adjusting for having more or less teams in the league.

    And what was the 85 in "0.508 / 85 = 0.0063 CPA per playoff win in 2009"?

  9. Jason J Says:

    I'd like the peak season info you had on the last post added here. I think the two together gave a more comprehensive view.

  10. Neil Paine Says:

    No, I didn't even initially adjust for different league sizes, because I figured a championship is a championship. However, guys from the early days of the league were showing up obscenely high on the list. I'm not thrilled with the idea of a kludge like multiplying by x/30, but you have to admit that this list "looks" a heck of a lot better than the one yesterday. This whole idea is a lot better on paper than in execution, and it's my fault, but I'll come back to it and clean up the method someday.

    85 was the total number of playoff wins in the NBA in 2009, btw.

  11. David Lewin Says:


    I wouldn't be too discouraged with this, it looks pretty good. My one question is, did you properly account for differing number of playoff games across years?

  12. Scott Says:

    I did some more work on this a while ago. The main variable that could change from year to year (and are difficult to predict) is win distribution (the probability of team X finishing with Y wins). If we expect the 2nd best team to win about 60-65 games, a 70 win team would be far less likely to win a championship than if we expect the 2nd best team to win 50 games.

    There is also the issue that a player worth 10 wins on a 50 win team is more valuable than a player worth 25 wins on a 30 win team since the second team is not going to make the playoffs and has no chance of winning a championship. Also a the same player isn't expected to use as many possessions or play as many minutes on a better team (or play as many minutes on a terrible team). I took all of these factors into account, just to find how the impact on championships differ from the impact on wins. (For this purpose a simple statistical plus minus sufficed.) What I preferred to use was an average expected championships added above replacement based on the weighted expected distribution on wins for the NBA. In the end, it was a pretty involve set of formulas. Some discussion is in the following post:

    In the end, I came up with a table using rounded statistical pm based on SPM, Usg and MPG. I am sure you could do the same thing with wins added. This needs to be done for every season in order to see the effect. The end result would be that the best seasons weighs far more heavily. This would shoot Lebron James way ahead of Cliff Robinson. Keep in mind this assumes playoff performance can be asserted based on regular season performance. (No playoff statistics were used beyond determining championship distributions.)

    Here is my table for mean expected championships added to mean expected wins added. (Note that wins added is wins above replacement, not to be confused with replacement player. I assume that a starter's minutes are basically replaced by a reserve, whose minutes are replaced by a scrup, whose are replaced by an NBDL player.)

    -5 -0.01882
    -4 -0.01704
    -3 -0.01481
    -2 -0.01238
    -1 -0.00963
    0 -0.006
    1 -0.00037
    2 0.001511
    3 0.004367
    4 0.00811
    5 0.013328
    6 0.017616
    7 0.023498
    8 0.029744
    9 0.035451
    10 0.043908
    11 0.052041
    12 0.063664
    13 0.073888
    14 0.087118
    15 0.101152
    16 0.119303
    17 0.138155
    18 0.157056
    19 0.177604
    20 0.1988
    21 0.222828
    22 0.248568
    23 0.275004
    24 0.303676
    25 0.334224
    26 0.366949
    27 0.398595
    28 0.433916
    29 0.469887
    30 0.502555

    Let me know if you want to discuss