There are numerous problems with the NCAA Tournament's selection process -- namely, that CBS turns what could be a ten-minute show to reveal the brackets into a two-hour extravaganza of commercials and Charles Barkley attempting to use technology -- and Glenn Logan at A Sea of Blue touches on some of that in a great piece, but most people who complain about the process, about the teams that were snubbed, about the teams that were included, or about the RPI are missing a far more basic point about the selection process.
It's rigged. Or at least it can be, very easily.
Here's how it works: The Selection Committee is handed a "nitty-gritty report" containing every team's RPI, record, strength of schedule, conference record, road record, and records against various categories of teams ranked by RPI. Of course, the Selection Committee isn't only considering the RPI; they're watching games (the so-called "eye test") and while they won't exactly admit to it, they do consider metrics other than the RPI, like KenPom and Sagarin. And then they're told to select the 36 best teams.
But how do you define the "36 best teams"? Well, therein lies the problem, because the Selection Committee has no guidance on that. They're told what factors they should be considering, but not what weight they should be giving to each factor.
What happens, then, is that frequently the committee can and does come up with the desired result, then makes the evidence fit the result instead of the other way around. You could see this with Vanderbilt's resume. Do you think Vanderbilt should be in the tournament? If so, you can point to the Commodores' strength of schedule (44 overall, 42 non-conference), two quality wins against the RPI top 50, seven wins against the RPI top 100, or their generally high rankings from advanced metrics that account for victory margin.
If you didn't think Vanderbilt should have been in the tournament, you could point to their 2-7 record against the RPI top 50, their 3-9 record in road games, or their three losses to teams outside the RPI top 100.
Tulsa? The argument against the Golden Hurricane was that they had three "bad" losses -- two to Memphis, including a particularly ugly showing in the American tournament, and one at home to Oral Roberts -- and that their strength of schedule wasn't anything special, and that advanced metrics like KenPom aren't sold on them. The argument for them, though, was that they had four wins against the RPI top 50 -- including a win at SMU, the only home game the Mustangs lost all season -- and they went 6-5 in road games. (On further review, the Golden Hurricane's case for a bid was much stronger than the people complaining about it made it out to be.)
St. Mary's? Proponents could point to a pair of top 50 wins, a solid RPI, and good standing in advanced metrics; detractors could point out that both of their quality wins came against Gonzaga (and if you didn't think much of the Zags, who cares if St. Mary's beat them twice?) Detractors could also point to their SOS rating of 163. South Carolina proponents could point to an 8-5 record against the top 100 and a win at Texas A&M; detractors could point out that that was their only notable win (and also, strength of schedule, particularly non-conference.) St. Bonaventure could point to three quality wins, two over St. Joseph's and one at Dayton, and an 8-5 road record; detractors could point to their anemic KenPom numbers and awful losses to Duquesne and La Salle.
The point is that depending on what you want to emphasize, you can reach an entirely different set of results. But at the end of the day, most people who complain about the process aren't really complaining about the process itself but the results that it reaches, because the process can create almost any result that it wants to create and justify it later. Most of the perennial complaints come from either homers (e.g. Garnet and Black Attack) or from the usual crowd who think that the process is biased against mid-majors (it is, but only because the committee rather consistently tends to err on the side of power conference teams and not because of any flaw in the process.)
But the basic problem is that the process can produce any result that it wants. Just be glad it's not the College Football Playoff, where being judged the fifth-best team means you don't get a shot at a national title, and you can win your conference and still not play for a national title.