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Defending NCAA champion Boston College has been fighting for its life in the PairWise Rankings since Feb. 21, when the Eagles lost to New Hampshire to complete a four-game winless streak. Since then, BC has won five of six to get back in the picture, but there’s still work to be done.

Let’s take a closer look at BC’s situation, and in the process discuss the PWR and what it tells us — and what it doesn’t.

Right now, the Eagles are No. 17 in the PWR, three spots off the magic 14th spot. BC is 15th in the Ratings Percentage Index at .5368, but is being hampered by a poor record against Teams Under Consideration of 6-11-3 (.3750). The immediate task for the Eagles is clear — they must beat Boston University Friday night in the Hockey East semifinals to have any chance.

Lose that game, and the national title defense ends prematurely. Win and win again Saturday and of course BC is in the field as the Hockey East tournament champion.

What about a win Friday and a loss Saturday? Obviously, upset champions in other leagues hurt BC, so the Eagles have to hope for the favorites to win this weekend. Also, BC’s situation is so tenuous that a hundred little changes can alter the PairWise, including things as seemingly-irrelevant as who wins the CCHA third-place game.

We can’t check all the scenarios — that’s literally impossible given the number of games left to be played — but let’s look at one in particular to get a sense as to what’s going on (feel free to follow along at home using the PairWise Predictor).

The first and most obvious scenario to examine is to have all the favorites (meaning the higher seeds) win every tournament game, except we’ll have BC beat BU Friday before losing to Northeastern Saturday.

What do we get? Well, there’s a three-way tie for 14th in the PWR, but Air Force is No. 13 as the Atlantic Hockey autobid, meaning that the bubble goes down to 15th in the PairWise. So two of the three teams tied for 14th will get in.

Those three teams are Minnesota, Minnesota Duluth and Boston College. Now it’s time to talk about how we display the PairWise. Notice that all three teams are listed as No. 14 — this is just how we choose to show the information on USCHO. In reality, that tie has to be broken since one of those three teams is going to be out of the NCAAs.

This has happened a number of times before, and the question is how the tie gets broken. One way to do it is to examine those three teams in a sort of mini-PairWise, looking at the head-to-head pairwise comparisons among the three and sorting out the tie that way. This is how our Bracketology generally does it, and it’s the way I think makes the most sense.

If you do that, Minnesota wins comparisons with UMD and BC, and is therefore 14th. Then UMD beats BC, and is 15th, leaving BC 16th. Notice that this is the order in which the teams are actually displayed in the PairWise Predictor — first Minnesota, then UMD, then BC. This is done on purpose, since it’s the way we believe the tie is evaluated by the selection committee.

Here’s the catch. There is nothing in the selection criteria that addresses how the committee is supposed to break ties in the PairWise. Remember that the PairWise is a model — it’s a convenient summary of the NCAA selection criteria. We know that the way we display the results in the PairWise Predictor is pretty close to what the committee actually looks at, but we don’t know for a fact how they handle details like this tiebreaking situation.

Given this situation, if I were the committee I would put Minnesota and UMD in the tournament for the reasons above. However, there is at least one alternative school of thought, which says that a tie of this sort should be broken only by looking at the Ratings Percentage Index and not at the actual head-to-head comparisons among the teams.

If you do that, BC (RPI of .5374) gets in, as does Minnesota (RPI of .5325). UMD (RPI of .5304) is left out. Thus BC’s fate is tied to the tiebreaker process.

I would argue that the most consistent way of breaking ties is the first way, which is how the PairWise displays the information. The whole PairWise is used for selecting teams, not just the RPI. To my way of thinking, it doesn’t make sense to throw out the PWR as a whole when breaking ties and just use the RPI — if the RPI is good enough there, why not everywhere else?

But the fact of the matter is that this assumption has never been battle-tested. There have been ties on the bubble in the past, but the two systems of tiebreaking have always agreed on who got into the NCAAs, so we’ve never actually had an opportunity to validate either tiebreaking method by looking at what the committee actually did.

This year could change that. Given the unusual volatility of the PairWise this season, we could easily see a situation just like this one, in which the tiebreaking philosophies differ. If that happens, we’ll learn something new about how the committee operates.