I would like to take this opportunity to point out that as of today, the NCAA Men's Ice Hockey Tournament Committee is officially considering the following teams for their postseason tournament:
Northeastern: 11-14-3, tied for 8th in Hockey East, 30th out of 59 in RPI.
Alaska: 11-15-4, 10th place in CCHA, 31st out of 59 in RPI
Providence: 12-14-2, tied for 8th in Hockey East, 32nd out of 59 in RPI
Those are not NCAA tournament teams. I could figure that out without the help of the calculator.
Defenders of the Pairwise system will say that we're not at the end of the season, and that it's only a terrible math system one day per year, instead of a terrible math system every day of the year. It's true that the bottom end of the TUC Cliff will look different on Selection Sunday, but it won't look that different. Out of the grouping of Northeastern, Alaska, Providence, Massachusetts, RIT, Wisconsin and Michigan Tech, about half will end on the right side of the "Under Consideration" and the other half won't, and it will be those literally-below-average teams that end up determining the final makeup of the NCAA tournament..
When the PWR system was first devised by the NCAA tournament committee, the only teams they looked at were the four or five teams around the bubble for the last couple at-large bids. Everybody else was clearly in the tournament, or clearly out of the tournament. As the general public tried to reverse-engineer the process used by the committee, they came up with the formula that is currently used today. The number of teams "under consideration" was raised to any team with an RPI over .500, then to the top 25 teams in the RPI for a while, and now back to any team with an RPI over .500. This year is especially bad because with no really great teams at the top, and a few very bad teams at the bottom, the number of teams with a +.500 RPI is an unwieldy 30-ish teams.
Having more teams than necessary under consideration creates two problems. The first problem is that comparing a top team like Ferris State or even a bubble team like Ohio State or North Dakota to a team so significantly behind them in the RPI like Alaska or Providence is that it can only produce two types of information: information that is useless, or information that is flat-out incorrect. There's no point to comparing teams with such a wide disparity in RPI because we already know which team is better. The Pairwise system was created to help adjust small flaws in the RPI, not completely override it. All including those clearly-not-in-the-tournament teams does is create the possibility of a legitimate contender losing a comparison based on some flukey coincidences to a team they are clearly better than. So far, this year's table looks pretty good in terms of outlying comparisons, but there is still that possibility.
The second problem is that the current system completely devalues the purpose of comparing the records of "teams under consideration". As it stands now, a game against Ferris State or Boston College counts the exact same as a game against Alaska or Providence, even though it is quite there is a wide gap in quality between those two teams.
So what are the solutions to this? The simple solution is to go back to a hard cap of teams under consideration. I'd set the cap at 20 teams. It's still not a perfect system. No matter where you draw the line, there is still going to the major issue of the TUC Cliff with this system. At least with only 20 teams, all the teams included have at least a reasonable claim to being considered for the tournament, and the last team to be a TUC likely wouldn't be that far in terms of RPI from the 14th or 15th team in the RPI, eliminating the possibility of a crazy outlying comparison changing the tournament field.
The other, better, but also more complicated solution involves using the individual comparison categories as a way of adjusting RPIs to determine comparisons. For example, let's take one of the current tables more outlying comparisons between RPI #8 Michigan State and RPI #18 Notre Dame. Michigan State holds a fairly decisive .5436 to .5324 RPI advantage, but Notre Dame leads in TUC (12-12-3 to 11-12-4) and Common Opponents (.5972 to .5333) to win the comparison 2 to 1. A modified RPI system would say MSU has a 2.5 game advantage in terms of RPI(this is a rough estimate, and would be calculated as a percentage). Notre Dame has a half game advantage in TUC and one game advantage in common opponents. Add that up and MSU would still win the comparison with a one-game advantage in RPI.
This system eliminates the possibility of a solid advantage in RPI being outweighed by two miniscule advantages in the other comparison categories. Again, there's still the issue of which teams count in the TUC category of the comparison, but that will almost always be the case. It also has the disadvantage of making the math involved virtually impossible for the average fan to calculate or even understand. But ultimately, if the math is better, that's probably the way they should go.