Random calculations:

States/District with the most number places on the list: 19-California, 15-New York, 10-Massachusetts, 9-Pennsylvannia, 7-New Jersey, Illinois, 6-Texas, 5-DC, North Carolina, Florida. Three states have four, eight have three, and nine have two (Unless St. Thomas is referring to Texas, in which case Texas has seven and Minnesota only has one.). Nevada, Arkansas, Mississippi, New Mexico, Idaho, West Virginia, Hawaii, Maine, Montana, South Dakota, North Dakota, Alaska and Wyoming have none.

Most per capita: 1 DC (5 with pop 671,803), 2 VT (1 with 647,064), 3 NH (2 with 1,395,231), 4 MA (10 with 6,981,974), 5 DE (1 with 1,018,396), 6 IA (3 with 3,200,517), 7 RI (1 with 1,093,734), 8 CT (3 with 3,626,205), 9 AL (4 with 5,074,296), 10 NY (15 with 19,677,151). After 11 NJ (7 with 9,261,699) and 12 PA (9 with 12,972,008) the ratio starts to drop off.

Granted, the universities aren't all of the same competitiveness. All of Alabama's (Auburn, Samford, Alabama, UAB) are in that 23-27% range. New Jersey has Princeton (82%), Rutgers (24%) and everything else sub 20%.