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BEST PASSING SEASONS WITHOUT NBA ALL-STAR GAME

This list includes 34 players who averaged more than 9 assists per game in a season, but did not play in the NBA All-Star Game.
Some of them appear multiple times on the list: Kevin Johnson, Johnny Moore and Rod Strickland 4 times, and Muggsy Bogues, Deron Williams, Terry Porter, Kevin Porter and John Lucas 3 times.
Stats updated until 2015-2016 regular season.

Rk Player Season Age AST G AST
1John Stockton1987-882513.8821128
2Kevin Porter1978-792813.4821099
3Kevin Johnson1988-892212.281991
4Rajon Rondo2015-162911.772839
5Mark Jackson1996-973111.482935
6Steve Nash2010-113611.475855
7Norm Nixon1983-842811.182914
8Andre Miller2001-022510.981882
9Jason Kidd1998-992510.850539
10Muggsy Bogues1989-902510.781867
11Kevin Johnson1991-922510.778836
12John Lucas1983-843010.763673
13Deron Williams2008-092410.768725
14Mark Jackson1987-882210.682868
15Michael Adams1990-912810.566693
16Rod Strickland1997-983110.576801
17Deron Williams2007-082310.582862
18Kevin Porter1977-782710.282837
19Muggsy Bogues1993-942910.177780
20Terry Porter1987-882410.182831
Rk Player Season Age AST G AST
21Norm Van Lier1970-712310.182832
22Gary Grant1989-902410.044442
23Johnny Moore1984-852610.082816
24Doc Rivers1986-872510.082823
25Rod Strickland1998-99329.944434
26Johnny Moore1982-83249.877753
27Steve Nash2008-09349.774717
28Avery Johnson1995-96309.682789
29Ty Lawson2014-15279.675720
30Johnny Moore1981-82239.679762
31Johnny Moore1983-84259.659566
32Rod Strickland1995-96299.667640
33Reggie Theus1985-86289.682788
34Lenny Wilkens1971-72349.680766
35Terry Porter1988-89259.581770
36Kenny Anderson1994-95249.472680
37John Bagley1985-86259.478735
38John Lucas1977-78249.482768
39Scott Skiles1992-93289.478735
40Tim Hardaway1994-95289.362578
Rk Player Season Age AST G AST
41Kevin Johnson1996-97309.370653
42John Lucas1978-79259.382762
43Nate McMillan1988-89249.375696
44Damon Stoudamire1995-96229.370653
45Deron Williams2006-07229.380745
46Tiny Archibald1971-72239.276701
47Kevin Johnson1995-96299.256517
48Muggsy Bogues1991-92279.182743
49Sleepy Floyd1985-86259.182746
50Kevin Porter1980-81309.181734
51Terry Porter1989-90269.180726
52Mark Price1989-90259.173666
53Sam Cassell1999-00309.081729
54Jason Kidd1996-97239.055496
55Rod Strickland1993-94279.082740
56Nick Van Exel1999-00289.079714
57Greivis Vasquez2012-13269.078704
Provided by Basketball-Reference.com: View Original Table
Generated 1/30/2017.

And this is the same list, but only displaying players with 9+ assists per game in any season that never have been selected for the NBA All-Star Game.
There are 14 different players. Andre Miller, Ty Lawson and Greivis Vazquez are the only active players on the list. 
Stats updated until 2015-2016 regular season.

Player Season Age AST G AST
Kevin Porter1978-792813.4821099
Andre Miller2001-022510.981882
Muggsy Bogues1989-902510.781867
John Lucas1983-843010.763673
Rod Strickland1997-983110.576801
Muggsy Bogues1993-942910.177780
Gary Grant1989-902410.044442
Johnny Moore1984-852610.082816
Rod Strickland1998-99329.944434
Johnny Moore1982-83249.877753
Avery Johnson1995-96309.682789
Ty Lawson2014-15279.675720
Johnny Moore1981-82239.679762
Johnny Moore1983-84259.659566
Rod Strickland1995-96299.667640
John Bagley1985-86259.478735
John Lucas1977-78249.482768
Scott Skiles1992-93289.478735
John Lucas1978-79259.382762
Nate McMillan1988-89249.375696
Damon Stoudamire1995-96229.370653
Muggsy Bogues1991-92279.182743
Kevin Porter1980-81309.181734
Rod Strickland1993-94279.082740
Greivis Vasquez2012-13269.078704
Provided by Basketball-Reference.com: View Original Table
Generated 1/30/2017.