I like this idea but I think the poster is focusing on the terrible teams from the major conferences. I took your idea and did some modifications. Since there are 79 total teams in the Power 4 + Big East I decided that any team with a Massey rating of 80 or lower is considered an "awful" team. With that criteria, the following is a list of awful team:
81 BYU
82 Missouri
---- BOTTOM 25% ----
83 Boston College
84 Penn St
93 Georgia
94 St John's
---- BOTTOM 20% ----
95 Wisconsin
101 Purdue
103 Wake Forest
105 Arkansas
107 Depaul
108 UCF
111 SMU
114 Northwestern
---- BOTTOM 10% ---
115 Rutgers
116 Arizona State
118 Georgetown
119 Butler
122 Pittsburgh
139 Providence
155 Houston
244 Xavier
This makes up 22 of the 79 teams (aka the bottom 28%). Thinking in terms of a bell curve, I think that is a little too many teams in the "awful" category, so I broke it up into percentiles. To me, the bottom 10% seems like a more reasonable metric.
Edit: I colored each team by conference.