Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

[TonyTheTiger20]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

Conference tournament odds: https://www.bcinterruption.com/bosto...n-four-bracket

Interestingly, BC is the most likely team to win its conference tournament, but Hockey East is also by far the most likely conference to boot Minnesota from the tournament.

[Quiet Riot]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

Conference tournament odds: https://www.bcinterruption.com/bosto...n-four-bracket

Interestingly, BC is the most likely team to win its conference tournament, but Hockey East is also by far the most likely conference to boot Minnesota from the tournament.

wow is my head spinning. I was just thinking...when I was in high school I would always hound the smart nerdy kids. had I known that I'd be on this board 38 years later reading all of this stuff I surely would have studied harder in math. WOW.

some figure it and some build it

[TonyTheTiger20]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

wow is my head spinning. I was just thinking...when I was in high school I would always hound the smart nerdy kids. had I known that I'd be on this board 38 years later reading all of this stuff I surely would have studied harder in math. WOW.

some figure it and some build it

Ha cheers

[TonyTheTiger20]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

Our last bracketology before Selection Sunday (we'll have one after the last championship game) plus an in-depth look at what each team's options are:

https://www.bcinterruption.com/bosto...son-colgate-bc

[hockeydad23]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

Does anyone think there is any chance St. Anselm gets an at-large bid to the tournament? If they did, wouldn't it almost certainly cost the Gophers their spot?

If it happens, Wisconsin might beat them by 15?

[robertearle]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

Does anyone think there is any chance St. Anselm gets an at-large bid to the tournament? If they did, wouldn't it almost certainly cost the Gophers their spot?

If it happens, Wisconsin might beat them by 15?

Bus/plane rules, I assume, would apply. BC would beat them by 20.

(There's a guy - Phil - who does a call-and-answer with the crowd at Badger games: "One ... Two ... Three... We Want More", for whatever the appropriate number is for goals scored. If the count gets high enough, he switches to multiples: "Two ... Four ... Six" etc. Back when I was just out of school, I was at a Wisconsin men's game against the University of Windsor, just across the bridge from Detroit. "Five ... Ten... Fifteen... Twenty..." We ... really didn't want any more. 20-0 final score.)

[TonyTheTiger20]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

Does anyone think there is any chance St. Anselm gets an at-large bid to the tournament? If they did, wouldn't it almost certainly cost the Gophers their spot?

If it happens, Wisconsin might beat them by 15?

I think there's a non-zero chance, but I think it's pretty close to zero. They're on the bubble as it is. If they were undefeated, the committee would have had a much tougher decision to make. But as it is, I don't expect them to make it.

They wouldn't play Wisconsin though -- they'd stay east and Ohio State would go to Madison.

I don't think they'd lose by 15... they're roughly similar to or maybe slightly better than Holy Cross. Holy Cross beat Harvard, so I mean at least they wouldn't get completely embarrassed lol. But they would lose handily.

[ne7minder]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

I admit to not really paying any attention to the rating systems but something struck me looking at them just now & I wanted to ask. It seems to me that there is usually a couple of big differences between them, particularly KRACH and the other two. Is this year odd in that they seem very similar or was I just not paying attention in the past & think there were significant differences?

[ARM]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

I admit to not really paying any attention to the rating systems but something struck me looking at them just now & I wanted to ask. It seems to me that there is usually a couple of big differences between them, particularly KRACH and the other two. Is this year odd in that they seem very similar or was I just not paying attention in the past & think there were significant differences?

I think that there have been more notable differences in some past seasons. Particularly in a year where three WCHA teams would be in the top five, ratings like Rutter and KRACH would show those teams collectively as doing better than the PairWise would.

Even this season, you can find rankings where Minnesota comes out higher than Cornell, such as the WCHODR rankings, that have been around for quite a while:
http://it.stlawu.edu/~chodr/wchodr/current.html

[TonyTheTiger20]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

I think that there have been more notable differences in some past seasons. Particularly in a year where three WCHA teams would be in the top five, ratings like Rutter and KRACH would show those teams collectively as doing better than the PairWise would.

Yeah that's true, that's usually the big difference is how high those 2nd tier WCHA teams end up, although that hasn't really been the case this year. Part of that is probably due to the fact that the WCHA isn't quite as dominant as it has been in past years (or at least it didn't feel like it was).

The HUGE difference between KRACH and the other systems this year has been in how they deal with the D-I/D-II independents. Saint Anselm is 5th in PWR but 27th in KRACH (you have to look at KRACH here; USCHO doesn't properly include the independents). Given that Holy Cross was able to win a couple D-I games this year (including one over Harvard) and that Saint Anselm is a bit better than Holy Cross is, that 27th feels like it might be pretty darn accurate.

It's usually INCREDIBLY difficult to deal with low interconnectivity (like we have every year between conferences in general with so few interconference games). But with even fewer between the independents and everyone else, KRACH dealt with them, I think, exceptionally well. I think that given that knowledge, this year has really shown just how robust KRACH is as a rating system.

[ne7minder]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

ARM & T320 - THANKS.

Sorry if this has been hashed out previously but, given that none of these is perfect or even agree, how is it that NC$$ settled on PWR (or PWR-like)? Any idea?

[ARM]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

Given that Holy Cross was able to win a couple D-I games this year (including one over Harvard) and that Saint Anselm is a bit better than Holy Cross is, that 27th feels like it might be pretty darn accurate.

I think 27th is too high. Who did H.C. besides Harvard, who it also lost to by five goals? And Harvard isn't a top-20 team. H.C. was swept by Dartmouth, couldn't beat RIT, who is likely the worst (or second to Brown) full-time D-I team, but had a winning record against Saint Anselm. I think that you're giving Saint Anselm too much credit. Particularly later in the season, when the D-I teams have been toughened by better competition, the full-time D-I teams have the edge. I suppose now you'll tell me that S.A. is better because Sacred Heart split with Brown ...

[TonyTheTiger20]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

I think 27th is too high. Who did H.C. besides Harvard, who it also lost to by five goals? And Harvard isn't a top-20 team. H.C. was swept by Dartmouth, couldn't beat RIT, who is likely the worst (or second to Brown) full-time D-I team, but had a winning record against Saint Anselm. I think that you're giving Saint Anselm too much credit. Particularly later in the season, when the D-I teams have been toughened by better competition, the full-time D-I teams have the edge. I suppose now you'll tell me that S.A. is better because Sacred Heart split with Brown ...

Well mostly Saint Anselm being the best of those teams is based on them winning their regular season title haha... I mean is 27th perfect? Maybe not, but you have to admit it is *orders of magnitude* the most accurate of any of the rating systems.

EDIT: Especially given that it has them 27th with, what, 5-7 crossover games between the whole NEWHA combined? The Holy Cross win over Harvard makes a pretty big difference on its own for Saint Anselm; if Holy Cross had lost that game Saint Anselm (a team that wasn't even involved in that game lol) drops to 29th, and much closer to 30th than 28th.

[Still Eeyore]

ARM & T320 - THANKS.

Sorry if this has been hashed out previously but, given that none of these is perfect or even agree, how is it that NC$$ settled on PWR (or PWR-like)? Any idea?

It's a long story, but RPI has been used as the main rating system by the NCAA in pretty much every sport but football for decades. Back in the 90s, when men's hockey went to a system of no subjectivity in selecting the teams for the tourney, they used it as one of the main elements for the Pairwise system they came up with, along with some other badly flawed elements.

It's not entirely clear whether the NCAA committee had completely formalized what they were doing, but some folks on Hockey-l reverse engineered the outline, though it was only confirmed years later that they were correct.

Since then, people have managed to convince the NCAA that most of the other criteria were hopelessly bad, and that common opponents needed to be normalized for the number of times each opponent was played. I doubt that anyone will ever convince them to ditch RPI.

[robertearle]

Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

(I figured this belonged here, because it is of no importance in another two hours or so, but...)

Prior to today's ECAC final, Clarkson and Colgate have exactly the same QWB adjusted RPI - at least to four decimal places - .6306. They split their two games during the season, but somehow Colgate is winning the comparison; either a better 'common opponents' somehow, or a better RPI past those first four digits.