There's another way to look at Princeton as an at large candidate, showing that sometimes it doesn't have to be as complicated as the ordinary process makes it. Simply look at the ranks of teams Princeton beat, tied, and lost to. Here's looking at it that way:
Wins: Teams ranked 77, 86, 132, 133, 154, 165, 180, 222, 225, 288
Ties: Teams ranked 46, 130, 138
Losses: Teams ranked 2, 41, 66, 136
Do these suggest that Princeton is a #31 team? Or do they suggest Princeton is somewhere in the range from 45 (where a tie was their best result) to 140 (where a loss was their worst result)? Sometimes, it may help to use a simple "smell" test.