This is probably not worth responding to, but the reason the "eye test" doesn't work is that no one can watch every game. You can't follow every Princeton possession all year to know how good they are, as well as Arizona, Duke and 350 other D1 teams. That's why statistics are needed.
Basic statistics are fine, but limited. That's why we have advanced statistics -- they theoretically give a more complete sense of who is better, more likely to win, etc.
But in a one-and-done tournament, it doesn't matter. Arizona would likely win the next four straight against Princeton in a seven-game series, but they don't get that luxury. You're cold for one game and the season is over.
Again, probably a waste of time, but so is life on a college basketball message board.