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

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

TonyTheTiger20 said:
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.
Click to expand...
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 ... :D
 
Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

ARM said:
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 ... :D
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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.
 
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ne7minder said:
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?
Click to expand...

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.
 
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.
 
robertearle said:
(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.
Click to expand...
It's better RPI to the 5th digit. I can expand it when I get home and let you know what it is.
 
Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

TonyTheTiger20 said:
It's better RPI to the 5th digit. I can expand it when I get home and let you know what it is.
Click to expand...

After I posted, I noticed that the full comparison chart is working; last time I looked - maybe a month ago or so, it wasn't. Colgate wins Common Opponents 11.167 — 10.750 (records of 24-2-0 — 26-2-1). But yeah, even with that, if Clarkson had a better RPI, they'd win... unless somebody decided the margin on COp was 'more significant' than a 5th digit of RPI.

(Edit: looking again at their color scheme, they actually show the RPI is a 'tie', and appear to indeed be awarding the pair to Colgate on COp.)

Fortunately, they're gonna settle in on the ice. It may take multiple OTs, however...
 
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Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

robertearle said:
After I posted, I noticed that the full comparison chart is working; last time I looked - maybe a month ago or so, it wasn't. Colgate wins Common Opponents 11.167 — 10.750 (records of 24-2-0 — 26-2-1). But yeah, even with that, if Clarkson had a better RPI, they'd win... unless somebody decided the margin on COp was 'more significant' than a 5th digit of RPI.

(Edit: looking again at their color scheme, they actually show the RPI is a 'tie', and appear to indeed be awarding the pair to Colgate on COp.)

Fortunately, they're gonna settle in on the ice. It may take multiple OTs, however...
Click to expand...

No overtimes necessary.
 
Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

D2D said:
27.42%. So you're telling me there's a chance?
Click to expand...

Would love to see the numbers for the WCHA FF. I am guessing they would not have been better.
Look at it this way, that is better than a 1 in 4 chance.
 
D2D said:
I forgot the Gophers' chances of winning the WCHA Tournament were just 1 in 10. A far cry from the 7 in 10 of BC winning Hockey East's.
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Yes indeed -- that's why they play the games...

By the way, I was telling myself that I would be more surprised to see Mercyhurst beat Clarkson than I would be too see BC win the whole thing... And the numbers support that. KRACH gives BC a 15.56% chance to win the whole thing, and Mercyhurst a 12.56% shot to beat Clarkson.
 
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