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This list includes 30 players who averaged more than 24 points per game (1400 points minimum), but were not selected to play in the NBA All-Star Game.
There are players like World B. Free, Purvis Short, Mark Aguirre, Kiki Vandeweghe, Dale Ellis, Michael Redd and Monta Ellis that achieved this feat two times.
Stats updated until 2015-2016 regular season.

Criteria Totals
Rk Player Season Age PTS PTS G
1World B. Free1978-792528.8224478
2Tiny Archibald1971-722328.2214576
3Purvis Short1984-852728.0218678
4Dominique Wilkins1984-852527.4221781
5Kiki Vandeweghe1986-872826.9212279
6Michael Redd2006-072726.7141653
7Michael Adams1990-912826.5175266
8Carmelo Anthony2005-062126.5212280
9Kelly Tripucka1982-832326.5153658
10Pete Maravich1975-762825.9160462
11Kareem Abdul-Jabbar1977-783025.8160062
12Dale Ellis1987-882725.8193875
13Mark Aguirre1984-852525.7205580
14Calvin Murphy1977-782925.6194976
15Monta Ellis2009-102425.5163164
16Purvis Short1985-862825.5163264
17David Thompson1980-812625.5196777
18Michael Redd2005-062625.4202880
19Kevin Durant2008-092025.3187174
20Paul Pierce2000-012325.3207182
21Jack Twyman1960-612625.3199779
22Damian Lillard2015-162525.1187975
23Dale Ellis1986-872624.9204182
24Antawn Jamison2000-012424.9204482
25Geoff Petrie1972-732424.9197079
26Bob McAdoo1978-792724.8148760
27Kiki Vandeweghe1985-862724.8196279
28Mark Aguirre1982-832324.4197981
29Jeff Malone1989-902824.3182075
30Earl Monroe1967-682324.3199182
31John Drew1976-772224.2179074
32Bernard King1977-782124.2190979
33Joe Barry Carroll1982-832424.1190779
34Monta Ellis2010-112524.1192980
35World B. Free1980-812724.1156565
36Danny Granger2009-102624.1149762
37Jamal Mashburn1994-952224.1192680
Provided by View Original Table
Generated 1/31/2017.

And this is the same list, but only displaying players with 22.5+ points per game in any season that never have been selected for the NBA All-Star Game.
12 players with some of them making multiple appearances: Purvis Short 3 consecutive times between 1983 and 1986. Other players with two mentions are: Monta Ellis and Kevin Martin.
Stats updated until 2015-2016 regular season.

Rk Player Season Age Tm PTS PTS G
2Purvis Short1984-8527GSW28.0218678
3Monta Ellis2009-1024GSW25.5163164
4Purvis Short1985-8628GSW25.5163264
5Monta Ellis2010-1125GSW24.1192980
6Kevin Martin2007-0824SAC23.7144361
7John Williamson1977-7826TOT23.7177775
8Kevin Martin2010-1127HOU23.5187680
9Tony Campbell1989-9027MIN23.2190382
10Jason Richardson2005-0625GSW23.2174175
11Ron Harper1986-8723CLE22.9187482
12Eddie Johnson1984-8525KCK22.9187682
13Orlando Woolridge1984-8525CHI22.9176777
14Purvis Short1983-8426GSW22.8180379
15Darrell Griffith1984-8526UTA22.6176478
16Richard Jefferson2007-0827NJN22.6185782
17Kevin Loughery1968-6928BAL22.6180680
Provided by View Original Table
Generated 1/31/2017.