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This list includes the Top 50 players with the highest PER (*) in any season who were not selected to play in the NBA All-Star Game that year.
At least 800 minutes & 50 games played in the season to qualify for the list.
There are 36 different players on the list, some of them are listed 2-3 times, but nobody close to Manu Ginobili and Al Jefferson, who are the only two who appear 4 times.
Stats updated until 2015-2016 regular season.

(*) The Player Efficiency Rating (PER) is a per-minute rating developed by John Hollinger. In John's words, "The PER sums up all a player's positive accomplishments, subtracts the negative accomplishments, and returns a per-minute rating of a player's performance."
If you want to know more about PER and other advanced stats, check basketball-reference site.

Rk Player Season Age Tm MP PER G
1Kareem Abdul-Jabbar1977-7830LAL226529.262
2DeMarcus Cousins2013-1423SAC229826.171
3Hassan Whiteside2015-1626MIA212525.773
4Arvydas Sabonis1995-9631POR173524.773
5Manu Ginobili2007-0830SAS229924.374
6Hakeem Olajuwon1990-9128HOU206224.356
7Pau Gasol2006-0726MEM213324.159
8Manu Ginobili2006-0729SAS206024.175
9Enes Kanter2015-1623OKC172124.082
10Grant Hill1998-9926DET185223.950
11John Drew1977-7823ATL220323.770
12Brandan Wright2013-1426DAL107723.558
13Elton Brand2003-0424LAC267023.269
14Tim Duncan1998-9922SAS196323.250
15John Stockton1987-8825UTA284223.282
16Elton Brand2006-0727LAC307723.180
17Dan Issel1981-8233DEN247223.181
18Al Jefferson2008-0924MIN183623.150
19Hakeem Olajuwon1998-9936HOU178423.150
20Gary Payton1998-9930SEA200823.150
21Tiny Archibald1971-7223CIN327223.076
22Kevin Johnson1996-9730PHO265822.970
23Terry Cummings1982-8321SDC253122.870
24Al Jefferson2011-1227UTA207522.861
25Kevin Johnson1995-9629PHO200722.856
26Dirk Nowitzki2000-0122DAL312522.882
27Zach Randolph2006-0725POR242522.868
28Al Jefferson2013-1429CHA255322.773
29Al Jefferson2007-0823MIN291922.782
30Bob Lanier1975-7627DET236322.764
31Brook Lopez2014-1526BRK210022.772
32Andre Drummond2013-1420DET261922.681
33Zach Randolph2010-1129MEM272422.675
34Jonas Valanciunas2015-1623TOR155722.660
35Tim Duncan2011-1235SAS163422.558
36Pau Gasol2004-0524MEM179022.556
37Manu Ginobili2009-1032SAS215022.575
38Jason Kidd1998-9925PHO206022.550
39Karl-Anthony Towns2015-1620MIN262722.582
40Charles Barkley1985-8622PHI295222.480
41Elton Brand2004-0525LAC300122.481
42Clyde Drexler1994-9532TOT272822.476
43Manu Ginobili2005-0628SAS181322.465
44Alonzo Mourning1997-9827MIA193922.458
45Michael Adams1990-9128DEN234622.366
46Sam Cassell2002-0333MIL270022.378
47Clyde Lovellette1958-5929STL159922.370
48Paul Pierce2000-0123BOS312022.382
49Michael Redd2006-0727MIL203622.353
50John Stockton2000-0138UTA239722.382
Provided by View Original Table
Generated 2/2/2017.

And this is a similar list, but only including the Top 20 PER-Seasons made by players who never have been picked for any NBA All-Star Game.
There are 15 different players. Al Jefferson has 4 different seasons (between 2007-2014) and Arvydas Sabonis and Greg Monroe appear 2 times.
Stats updated until 2015-2016 regular season.

Player Season Age Tm MP PER G
Hassan Whiteside2015-1626MIA212525.773
Arvydas Sabonis1995-9631POR173524.773
Enes Kanter2015-1623OKC172124.082
Brandan Wright2013-1426DAL107723.558
Al Jefferson2008-0924MIN183623.150
Al Jefferson2011-1227UTA207522.861
Al Jefferson2013-1429CHA255322.773
Al Jefferson2007-0823MIN291922.782
Jonas Valanciunas2015-1623TOR155722.660
Karl-Anthony Towns2015-1620MIN262722.582
Darrell Armstrong1998-9930ORL150222.250
Bob Houbregs1955-5623FTW153522.070
Greg Monroe2011-1221DET208222.066
Chuck Share1954-5527MLH168522.069
Andray Blatche2012-1326BRK155521.982
Al Cervi1951-5234SYR85021.955
Derrick Favors2014-1523UTA228021.874
Andre Miller2001-0225CLE302321.881
Greg Monroe2015-1625MIL231421.879
Arvydas Sabonis1996-9732POR176221.869
Provided by View Original Table
Generated 2/2/2017.