Analyzing the PairWise for Viability

[TitleIXHockey]

We know that the PairWise is ineffective with a low number of interconference games, so...

What is the threshold where it becomes viable, or how does the viability increase the more interconference games are played?

• Does every team have to have at least X number?
• Do we need an average of X interconference matchups per team for it to be viable?

How can we use this to better rank WCHA and NEWHA or anyone that plays a limited out of conference schedule - maybe some of the ivies some seasons.

 

[robertearle]

There are (currently) only three components to a Pairwise comparison: RPI, head-to-head, and common opponents.

'Common Opponents' comparison only results in a "plus one" for whichever team "wins" that component of a pairing. Likewise RPI. So if there are no head-to-head games between the two teams being compared, the only outcomes are one team is better at both 'common opponents' and RPI and wins the comparison "two to zero", or they split and the comparison is "one to one tie". And that tie is broken by whoever has the better RPI wins the comparison.

That is to say, unless the two teams have a head-to-head, whoever has the better RPI wins the comparison. Period, the end. And more "interconference games played" won't change that.

"More games" would only help those Pairwise comparisons if it added a head-to-head component to the comparison, and how many games would you have to add to get the point where there are enough head-to-heads to make a difference? Likely lots more than you have weekends available.

(One example of a head-to-head making a difference in the Pairwise this year is Duluth having swept Harvard. Right now Harvard has a SLIGHTLY better RPI, but Duluth is winning the comparison on the strength of being "plus two" in head-to-head. On the other hand, Wisconsin's head-to-head vs Quinnipiac ends up NOT being significant in their comparison, because they simply have no "common opponents". Wisconsin had a win and a tie vs Quinnipiac, and so are "plus one" head-to-head; but with no common opponents, if Quinnipiac were to end up with a better RPI, the better RPI would once again win them the comparison.)

Pretty much the only way to have the Pairwise be little more that a reproduction of the RPI list, and get more 'mixing' as a result of the comparisons (assuming such 'mixing' would be a good thing and lead to a better tournament, and I'm not at all convinced that would be the case) would be one or more additional components to a Pairwise comparison, such as the "teams under consideration" component that used to be there. And I don't have any ideas on what that might be. They got rid of "TUC" for a reason, and i don't know that anyone would want to bring it back.

If you ask me, they could pretty much do away with the Pairwise altogether, and just use RPI. (Or use KRACH, etc, instead). You'll get essentially the same tournament field anyway.

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Adding, so maybe your question should be "would more interconference play help the 'validity' of the RPI?", and the answer to that is absolutely yes.

 

[ARM]

One example of a head-to-head making a difference in the Pairwise this year is Duluth having swept Harvard. Right now Harvard has a SLIGHTLY better RPI, but Duluth is winning the comparison on the strength of being "plus two" in head-to-head.

I'm not 100 percent sure that this is how this comparison will shake out. Both teams played St. Lawrence. Harvard defeated the Saints in regulation, while UMD won over SLU in OT. Harvard will play the Saints at least once more. If an OT win counts as 2/3 of a win, are they currently tied in COp, or is Harvard ahead based on 1.000 > 0.667? The Crimson could conceivably lose the next regular-season meeting with SLU, or the teams could meet in the ECAC playoffs.

And what does a 3-on-3 OT win mean in H2H? For example, OSU has two regulation wins over UM and a regulation loss. Are the Buckeyes +2 in the H2H with the Gophers, or is the H2H edge only +1 and 1/3?

Somehow, I don't think that the powers that be think through these things when changing the rules, any more than they realize the fact that going by points percentage in league standings isn't entirely fair if one team is missing an Ohio State game while another is missing a game versus St. Thomas.

 

[robertearle]

I'm not 100 percent sure that this is how this comparison will shake out. Both teams played St. Lawrence. Harvard defeated the Saints in regulation, while UMD won over SLU in OT. Harvard will play the Saints at least once more. If an OT win counts as 2/3 of a win, are they currently tied in COp, or is Harvard ahead based on 1.000 > 0.667? The Crimson could conceivably lose the next regular-season meeting with SLU, or the teams could meet in the ECAC playoffs.

And what does a 3-on-3 OT win mean in H2H? For example, OSU has two regulation wins over UM and a regulation loss. Are the Buckeyes +2 in the H2H with the Gophers, or is the H2H edge only +1 and 1/3?

Somehow, I don't think that the powers that be think through these things when changing the rules, any more than they realize the fact that going by points percentage in league standings isn't entirely fair if one team is missing an Ohio State game while another is missing a game versus St. Thomas.

If Harvard is winning 'common opponents' and RPI, then they should be winning the Pairwise comparison; 2 to 2 tie, with RPI deciding it. But as listed by USCHO, they are not.

So one of two possibilities: either USCHO has it wrong, or OT wins are full-sized wins.

The larger point remains: this is the one and only (I think) comparison of two interconference teams where all three component are present. Except for such rare cases, Pairwise simply duplicates RPI. So why go through the contortions and - as is the case here - confusion and misunderstandings. Just use RPI.