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Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodies

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Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie

TonyTheTiger20 said:
Well let's be fair here -- PWR isn't supposed to be a midseason measuring stick. It's supposed to be used to compare an entire season's body of work.
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I get that any system is flawed when there are almost no data points, but the whole concept of quality wins falls apart in PWR. Haven't played any quality opponents? Fine, we'll just ignore that. Most systems try to give teams some incentive to schedule tougher. The PWR really doesn't.
 
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie

TonyTheTiger20 said:
Well let's be fair here -- PWR isn't supposed to be a midseason measuring stick. It's supposed to be used to compare an entire season's body of work. It's not perfect and KRACH is probably better (I have no idea what the formula is) . . .
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KRACH isn't a simple formula that comes down to one equation the way that RPI does. It's effectively a system of linear equations with each team having one equation with a number of variables equal to the number of games played that you solve repeated times using the coefficients generated by the previous iteration and that you keep solving until the coefficients stop changing from one solution to the next.

As always when I try to describe KRACH, that isn't really quite what happens but should give an idea of what goes on in the process. And the fact that it doesn't have a simple equation is probably one of the reasons that you'll never see the NCAA use it.

but at the end of the season they aren't really all that far apart.
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Unless you're North Dakota, in which case the differences have been quite far apart several years in a row.
 
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Eeyore said:
I expressed no opinion whatsoever in that post as to what the correct formula to use is; my opinion on that is the same as ARM's, namely something that junks RPI altogether. The flaws of RPI are in its basic concepts rather than its specific implementation. All I was trying to do was to point out that, whether it's good or bad, you can't just look at the values of the coefficients to determine what the biggest part of RPI is. You have to look at the relative differences in the values that the coefficients are multiplied against as well.
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Oh well hey you'll get no argument out of me haha
 
Eeyore said:
KRACH isn't a simple formula that comes down to one equation the way that RPI does. It's effectively a system of linear equations with each team having one equation with a number of variables equal to the number of games played that you solve repeated times using the coefficients generated by the previous iteration and that you keep solving until the coefficients stop changing from one solution to the next.

As always when I try to describe KRACH, that isn't really quite what happens but should give an idea of what goes on in the process. And the fact that it doesn't have a simple equation is probably one of the reasons that you'll never see the NCAA use it.
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I follow you... that sounds like one of the courses I took for my major actually:

MT 435 Mathematical Programming (Fall: 3)

Topics studied from linear programming include a general discussion of linear optimization models, the theory and development of the simplex algorithm, degeneracy, duality, sensitivity analysis, and the dual simplex algorithm. Integer programming problems, and the transportation and assignment problems are considered,and algorithms are developed for their resolution.
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Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie

TonyTheTiger20 said:
I follow you... that sounds like one of the courses I took for my major actually:
MT 435 Mathematical Programming (Fall: 3)
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aka "Fun with Numbers" ;)
 
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie

So when I see the legend: "*Team's RPI has been adjusted to remove negative effect from defeating weak opponent", does that mean that BC's RPI is 1.000 because they haven't played any TUC?
 
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie

OldDave said:
So when I see the legend: "*Team's RPI has been adjusted to remove negative effect from defeating weak opponent", does that mean that BC's RPI is 1.000 because they haven't played any TUC?
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I'm not sure what you're asking. The RPI page itself is all zeroes, as if it hasn't been run. But the PWR page has RPI ratings for teams and BC's is an adjusted .6847.
 
Re: Fun With Numbers '14-'15: USCHO Posters Poll, Pairwise What-Ifs, and Other Goodie

1) Boston College continues to rack up impressive scores with depleted roster but need to play better teams to deserve #1 ongoing
2) Minnesota 2-6 enjoying holding positions based on having a break in play
3) Wisconsin
4) Quinnipiac
5) Clarkson
6) Harvard
7) Boston U drops down again based on tie vs Yale--how can you be handed 19 min in PP time and still not beat an unranked opponent?!
8) Bemidji 8-10 enjoying the break to build distance versus the rest of the pack
9) UND
10) UMD
 
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