The 2015 Pairwise, Bracketology and History Thread

[HarleyMC]

Re: The 2015 Pairwise, Bracketology and History Thread

First, this isn't a B1G Tourney thread; second, rather than getting is a ****ing match over whose command of statistics is better, I will respectfully disagree. If you think there is no noise, ie that there is informative content worth discriminating over, well, we disagree. And your comments about the method for calculating the MLE rather than the important question, which is whether the maximum likelihood has any particular claim on our attention show that we're discussing the problem at different levels, which is fine. I didn't mean to suggest instability in the estimation algorithm which,as you point out, can be stabilized through partitioning. I meant that there is actual noise in the estimate which makes the maximum of the likelihood not particularly compelling as a discriminator. It discriminates, sure, but in a method that is at best marginally farther from nonarbitrary than the simplest Bradley-Terry models, ie, KRACH which in turn are at best marginally better than PWR. And my point above is that discrimination has a very limited purpose: to pick a set of 16 teams in a deterministic way that (a) bears some relationship to quality and that (b) encourages, marginally, better out of conference scheduling.

Thanks for the short discussion. You are still missing major elements of my procedural hypothesis and even points of my most recent post. There's quite a bit more that I could suggest on the projected hybrid model which you may find quite interesting and favorable. Peace.

[LTsatch]

Re: The 2015 Pairwise, Bracketology and History Thread

Take it to the woodshed boys and just tell me what other teams have to win to get Yale into this thing. Most are saying Harvard, BU and RIT wins will do it.

[Patman]

Re: The 2015 Pairwise, Bracketology and History Thread

"in this world"? It's done all the time, pal. Think casuality for a change. Academically, this is a statistical nightmare and violates some of the most basic assumptions necessary to establish internal validity. If an undergrad....its probably publishable? I'm not talking at all about the model. I conduct a research study using a probability model involving gender, I run the procedures but I treat the sample without any discrimination. I challenge you to find ONE peer reviewed research journal that will publish something like this. You'll end up with a pile of rejection letters. With this system forget about statistical power because as it stands it's non-parametric.

Journal of Quantitative Analysis in Sports... if somebody were to do a SOLID comparison of methods and sensitivity and it were plopped in front my desk I'd be for it... of course I'd poke holes and tell them to revise as the nasty little snit that I am... but I do that to everybody and in the end it serves the paper better for it.

edit: btw, Im a Ph.D. in Statistics, goblue is a Ph.D. of Economics.

[Patman]

Re: The 2015 Pairwise, Bracketology and History Thread

HarleyMC: The flaw in your thoughts about this come from trying to precisely measure something that the data are too noisy to allow precise measurement of. The NCAA is well aware, for example, that it could get more precise estimates of whether Team A is better than Team B by using the scores of the games rather than just using the results of the games. They refuse to do this because it has the unfortunate side effect of teams running up scores to improve rankings. (It has a second side effect that taking a high risk strategy to win a game may lower your ratings as well.) So when you play 40 games or so, and a few of them are obvious mismatches of talent, you just can't learn that much from who wins a game. Refining the methodology for discrimination with an MLE technique doesn't help because the results themselves are unstable. But there's a fundamental issue you're missing: the teams from, say, 10-25 in any rating system just aren't that different one another. They almost can't be and have a sport anyone wants to watch. So all the NCAA wants is a system that (a) takes some set of teams that are OK; and (b) takes conference winners automatically. Any such system has to leave out teams who are statistically indistinguishable from some of the teams that are in -- but that's because those teams aren't just statistically indistinguishable; they're actually indistinguishable. You can discriminate using a model, but the model isn't stable to perturbation, as Patman said above.

One more thing. You say you need to revamp scheduling to allow better estimation: that's exactly what the NCAA is uninterested in. Conferences are what the thing is about, and the Tournament at the end is gravy. The less that is known about interconference strengths come tournament time, the happier the NCAA is.

Bottom line is... yes, the PWR is inadequate tool. KRACH is probably better... in my mind I'd love to see the "put up or shut up" and have these things be analyzed in some manner. I think KRACH would likely come out superior in the pile but as we're dealing with "small samples" the question would be how superior would it actually be.

In the end, we're talking about tools devised by athletic directors, athletic committees (coaches, whatnot), and university presidents. The lions share of whom have poor mathematical programs (this is not to call them dumb, you have to be quite intelligent to be on that level). Its going to be a system based on tangible calculations until education level can be raised via communication.

Another matter would be if we could elevate other choices based on scientific evaluation. Most organizations will bend to obvious truth so long as its really freaking obvious.

[JimDahl]

Re: The 2015 Pairwise, Bracketology and History Thread

AS FOR MINNESOTA....

I have examined all the possibilities using the Predictor on this site. My results are different than JimDahl and also, apparently, GPL.

Here is what I get, with reasoning... assuming Minnesota loses (if they win they are in, and a high #3 seed),
Any in by BU (knocks out Lowell and Providence{i think}), Harvard (knocks out Colgate), or StCloud (keeps Minnesota's RPI high because we played them twice and thus keeps us ahead of Harvard if they lose and ahead of Providence) puts Minnesota in. This is a 7/8 chance.

Now, for the other 1/8....The games in question are RIT/Mercyhurst;UND/DU;MTU/MSUM. There is no pecking order here. The results are very close in RPI. I found one scenario where the Gophers were two spots below the bubble, and Harvard qualified by leading BOTH Providence and Minnesota in the 5th decimal place of RPI.

This is what I got:
If RIT wins and MSUM wins: Gophers are in if DU does not win (means UND wins or tie)
If RIT wins and MTU wins: Gophers are in if UND does not win (means DU wins or tie)
If Mercyhurst wins and MSUM wins: Gophers are out
If Mercyhurst wins and MTU wins: Gophers are in if UND does not win (means DU wins or tie)

If someone could compare this to CHN, it would be nice....

I think that is actually the same as I got for them, but I approached it form the "what has to happen for them to miss" perspective, so sort of have to mentally invert yours.

The CHN calculator is giving different results in some of the niche scenarios which I think is confusing a lot of people.

[Numbers]

Re: The 2015 Pairwise, Bracketology and History Thread

AS FOR MINNESOTA....

I have examined all the possibilities using the Predictor on this site. My results are different than JimDahl and also, apparently, GPL.

Here is what I get, with reasoning... assuming Minnesota loses (if they win they are in, and a high #3 seed),
Any in by BU (knocks out Lowell and Providence{i think}), Harvard (knocks out Colgate), or StCloud (keeps Minnesota's RPI high because we played them twice and thus keeps us ahead of Harvard if they lose and ahead of Providence) puts Minnesota in. This is a 7/8 chance.

Now, for the other 1/8....The games in question are RIT/Mercyhurst;UND/DU;MTU/MSUM. There is no pecking order here. The results are very close in RPI. I found one scenario where the Gophers were two spots below the bubble, and Harvard qualified by leading BOTH Providence and Minnesota in the 5th decimal place of RPI.

This is what I got:
If RIT wins and MSUM wins: Gophers are in if DU does not win (means UND wins or tie)
If RIT wins and MTU wins: Gophers are in if UND does not win (means DU wins or tie)
If Mercyhurst wins and MSUM wins: Gophers are out
If Mercyhurst wins and MTU wins: Gophers are in if UND does not win (means DU wins or tie)

If someone could compare this to CHN, it would be nice....

OK.

So I did my own comparison with CHN. The only differences are that CHN puts the Gophers in with Mercyhurst/MSUM/tie and CHN puts Gophers out with RIT/MSUM/tie

And, for those interested in minutiae, in all cases that involve the following winners: Michigan/Lowell/Colgate/Miami...
If the UND/DU game ends tied the last spot in the field is decided among HU/PC/UMn and it comes down to the 5th decimal place in RPI (in other words, it won't even show in the numbers on your screen).

Not sure how to calculate the %age for Minny. I would go 7/8 in (see above) + 1/8*1/2 (which I get by 6 out of 12 combos) or 93.75% in. Although I admit that is very slightly skewed high because 3 of the ties put the Gophers in and we know a tie is not as likely as either UND or DU winning. Oh, and that 93.75% is in the case of Gophers losing. So, the total %age would be 96.875% they qualify.

[Priceless]

Re: The 2015 Pairwise, Bracketology and History Thread

And, for those interested in minutiae, in all cases that involve the following winners: Michigan/Lowell/Colgate/Miami...
If the UND/DU game ends tied the last spot in the field is decided among HU/PC/UMn and it comes down to the 5th decimal place in RPI (in other words, it won't even show in the numbers on your screen).

So...you're saying it's close

[Numbers]

Re: The 2015 Pairwise, Bracketology and History Thread

I think that is actually the same as I got for them, but I approached it form the "what has to happen for them to miss" perspective, so sort of have to mentally invert yours.

The CHN calculator is giving different results in some of the niche scenarios which I think is confusing a lot of people.

I wonder why the CHN calculater is slightly different? As I wrote above, many many of the scenarios in which MN might be out come down to the 4th or 5th decimal place. There shouldn't be any rounding errors, though... I can't figure it out.

[Priceless]

Re: The 2015 Pairwise, Bracketology and History Thread

I wonder why the CHN calculater is slightly different? As I wrote above, many many of the scenarios in which MN might be out come down to the 4th or 5th decimal place. There shouldn't be any rounding errors, though... I can't figure it out.

Are the issues with a tie in the NCHC game?

[Numbers]

Re: The 2015 Pairwise, Bracketology and History Thread

Are the issues with a tie in the NCHC game?

As I wrote above, CHN gives different results for 2 scenarios where NCHC 3rd place ends in tie. However, I am not sure it's the tie itself, because the RPI calculation goes to the 5th decimal place.

[Priceless]

Re: The 2015 Pairwise, Bracketology and History Thread

As I wrote above, CHN gives different results for 2 scenarios where NCHC 3rd place ends in tie. However, I am not sure it's the tie itself, because the RPI calculation goes to the 5th decimal place.

Check the records of Denver and NoDak....is the tie reflected in their records?

[Numbers]

Re: The 2015 Pairwise, Bracketology and History Thread

Check the records of Denver and NoDak....is the tie reflected in their records?

It seems to be but there is a discrepancy between the 2 sites in the records of Denver and Lowell concerning how many ties. What do we know about that?

[Numbers]

Re: The 2015 Pairwise, Bracketology and History Thread

ATTN ED TREFZGER!!!!!!!!!!

The USCHO PWR PREDICTOR is glitching in some tie scenarios.

In the case where: Mercyhurst/Michigan/Colgate/Lowell/Miami/Mankato/tie for UND/DU are the inputted results, the records that come up on the "results page" give the ties to UND and Lowell instead of UND and DU. In fast, in this case, Lowell gets both their own win and the phantom tie added and DU gets nothing added.

[Priceless]

Re: The 2015 Pairwise, Bracketology and History Thread

ATTN ED TREFZGER!!!!!!!!!!

The USCHO PWR PREDICTOR is glitching in some tie scenarios.

In the case where: Mercyhurst/Michigan/Colgate/Lowell/Miami/Mankato/tie for UND/DU are the inputted results, the records that come up on the "results page" give the ties to UND and Lowell instead of UND and DU. In fast, in this case, Lowell gets both their own win and the phantom tie added and DU gets nothing added.

I already reported it a few days ago. I doubt it gets fixed before tonight.

[JimDahl]

Re: The 2015 Pairwise, Bracketology and History Thread

I unfortunately didn't have much time today, but here's what I bothered to write up for Minnesota, Yale, and Bowling Green.

What each at-large team needs to do to advance