Virginia Tech fans must be a bit on the irritated side. Last year they were a clear-cut case of getting snubbed; this year they were the highest-rated team by any metric that was not given an invitation. At the same time, a VCU team with the same number of losses (granted, two more wins) against a vastly weaker schedule was given an at-large invitation.
This is usually where I'll go into a rant about the RPI, and how the RPI's system of approximating strength of competition is inadequate. That's only half the story. In other words, Virginia Tech's RPI was errantly low poor to the fact that the RPI's formula of using opponents' record and opponents' opponents' record instead of a real solution. But, VCU's RPI was actually hurt by this as well. So, my "improved RPI" metric, which actually goes through the iterative solution such that a team's improved RPI score equals its win-loss record modified by the average "improved RPI" of its opponents (adjusted for home court), still rated Virginia Commonwealth ahead of Virginia Tech.
The bigger story here is that you can't simply take the shortcut of rating a team by some function of its win-loss record and its opponents cumulative rating. Instead, every game must be analyzed in its own merits, which is the difference between my standard or win-loss ratings and my RPI or improved RPI ratings. In the first case, a team is scored based on a game-by-game analysis of who they played and whether they won or lost. The RPI-like stats just do an ensemble schedule strength average and score the team's record against it. That's not enough to deny a top-25 team a tournament appearance (as happened to the Hokies last year), but still enough for a boneheaded selection choice.
Oddly enough, this marks the second straight year in which the most blatant snub was against a team from the ACC, not something that one would tend to expect given the purported major-conference bias of the NCAA selection process.
Minor points: Not quite sure how USC (#62 here, #67 RPI) was picked over St. Mary's or Colorado; Tennessee and UAB owe their tournament selections to the RPI's errors.
For the most part, the seedings were fairly reasonable. The most notable exception is Utah State, which had rankings of #14/#21 (my win-loss/predictive), #15 (RPI), #19 (polls) but was given a #12 seed for no apparent reason. The opposite example of overrating was UCLA, (my #38, RPI #44) which got a #7 seed.
Note: if you use any of the facts, equations, or mathematical principles introduced here, you must give me credit.