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Pairwise and Bracketology 2013 Edition

  • Thread starter Thread starter Priceless
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Re: Pairwise and Bracketology 2013 Edition

Patman,

Interesting... but I'm not sure that I agree with the numbers. I'm not implying that the tool is wrong so maybe it is the choice for determining win probabilities (CHODR). Look at AH. Here are the numbers for the 3 teams that must win AH in order to get in:

UCONN: 25.34%
Mercyhurst: 19%
Canisius: 22.95%

Given that Canisius play Niagara first while Mercyhurst plays UCONN, does anyone really see how Canisius' chances are better than Mercyhurst? Mercyhurst can get in without having to even play Niagara. Canisius needs to win 2 games against one team that is a lot better than they are and a 2nd that is also better. How in the world do they end up at 22.95% chance while Mercyhurst's is only 19%? I'm surprised that Niagara's chances of winning AH are only 32.71%.

Admittedly, Canisius is on a little run though. Does the probability model weight recent games more highly than others?
 
jmhusker said:
Patman,

Interesting... but I'm not sure that I agree with the numbers. I'm not implying that the tool is wrong so maybe it is the choice for determining win probabilities (CHODR). Look at AH. Here are the numbers for the 3 teams that must win AH in order to get in:

UCONN: 25.34%
Mercyhurst: 19%
Canisius: 22.95%

Given that Canisius play Niagara first while Mercyhurst plays UCONN, does anyone really see how Canisius' chances are better than Mercyhurst? Mercyhurst can get in without having to even play Niagara. Canisius needs to win 2 games against one team that is a lot better than they are and a 2nd that is also better. How in the world do they end up at 22.95% chance while Mercyhurst's is only 19%? I'm surprised that Niagara's chances of winning AH are only 32.71%.

Admittedly, Canisius is on a little run though. Does the probability model weight recent games more highly than others?
Click to expand...

Here's the thing with the score model, niagara was ranked fairly low.

I suppose its a matter of "how does a team "win"... Is there a reason their goal totals haven't separated, does it happen that some teams have knack of bellying over?

---

I once simulated entire NHL seasons because at the time I was proposing a three conference system to add insularity (for the benefit of rivalry and sport interest)... I found the reverse, teams modeled as a great team would from run to run do miserable as a result of random variation. Now granted that is more B|A than A|B.

Bottom line, I suspect if you look at the scores Niagara are winning a lot of 1-2 goal games and not so much putting up a 6 or 7 spot.

I haven't looked at the schedule. I don't know.

That being said, I have a few more exotic forms I'd like to try out in the future.

---

Edit: ok, out of conf is bad and when they lose they've gotten lit up... That makes some sense to me
 
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Re: Pairwise and Bracketology 2013 Edition

RHamilton calculated probabilities using KRACH weighting. He posted the probability of RPI making the tourney with that weighting (20.95%) on the RPI thread.
 
Re: Pairwise and Bracketology 2013 Edition

jmhusker said:
Patman,

Interesting... but I'm not sure that I agree with the numbers. I'm not implying that the tool is wrong so maybe it is the choice for determining win probabilities (CHODR). Look at AH. Here are the numbers for the 3 teams that must win AH in order to get in:

UCONN: 25.34%
Mercyhurst: 19%
Canisius: 22.95%

Given that Canisius play Niagara first while Mercyhurst plays UCONN, does anyone really see how Canisius' chances are better than Mercyhurst? Mercyhurst can get in without having to even play Niagara. Canisius needs to win 2 games against one team that is a lot better than they are and a 2nd that is also better. How in the world do they end up at 22.95% chance while Mercyhurst's is only 19%? I'm surprised that Niagara's chances of winning AH are only 32.71%.

Admittedly, Canisius is on a little run though. Does the probability model weight recent games more highly than others?
Click to expand...

KRACH weightings give:

Mercyhurst: 17.4%
Connecticut: 23.5%
Canisius: 13.1%
Niagara: 45.9%
 
Re: Pairwise and Bracketology 2013 Edition

goblue78 said:
KRACH weightings give:

Mercyhurst: 17.4%
Connecticut: 23.5%
Canisius: 13.1%
Niagara: 45.9%
Click to expand...
Yes this matches what I have too. I was surprised to see such a large divergence between the two models. I have a hard time seeing Canisius as pretty much even money (net) in both of their games.
 
Re: Pairwise and Bracketology 2013 Edition

So, I have a question. And, it seems like something like this comes up every year. Please help me out guys.
The current PWR is:
#1s: Quinny, Minny, Miami, BC
#2s:Yale, Lowell, NoDak, UNH
#3s: NoDame, Mankato Niagara, SCSU
#4s: Denver, WMU, Union, UWisc

Moy does his bracket:
#1s: QU > Prov; Minny > Rapids; Miami > Toledo; BC > Manchester
#2s: UNH > Manchester (host, put in first), NoDak > Prov; Lowell > Rapids; Yale > Toledo
So far, I am totally with him. Committee did the same thing last year. Minny was 8th, hosting, and NoDak ended up there as #4 overall, too. Just like this.
Then, #3s: NoDame > Manchester; Mankato > Prov; Niag > Rapids; SCSU > Toledo
#4s: DU > Manchester; WMU > Toledo; Union > Rapids; UWisc > Prov
Yields: Prov: QU (1) v UWisc (16) ; NoDak (7) v Mankato (10)
Rapids: Minny (2) v Union (15); Lowell (6) v Niagara (11)
Toledo: Miami (3) v WMU (14); Yale (5) v SCSU (12)
Manchester: BC (4) v DU (13); UNH (8) v NoDame (9)

Then, he moves WMU to Rapids, Union to Manchester, and DU to Toledo to avoid WMU v Miami and get WMU to Rapids. I have no problem with this.
Prov: QU (1) v UWisc (16) ; NoDak (7) v Mankato (10)
Rapids: Minny (2) v WMU (14); Lowell (6) v Niagara (11)
Toledo: Miami (3) v DU (13); Yale (5) v SCSU (12)
Manchester: BC (4) v Union (15); UNH (8) v NoDame (9)

Then, he swaps NoDak and Lowell (moves the #2 seeds) to avoid Mankato v NoDak; and then he does this for attendance:
NoDame to Rapids, Mankato to Manchester, Niagara to Providence.

QU (1) v UWisc (16) ; Lowell (6) v Niagara (11)
Rapids: Minny (2) v WMU (14); NoDak (7) v NoDame (9)
Toledo: Miami (3) v DU (13); Yale (5) v SCSU (12)
Manchester: BC (4) v Union (15); UNH (8) v Mankato (10)

So, here is the question:
Why, if you are going to move Mankato for "attendance" anyway, do you bother to move NoDak to avoid WCHA v WCHA?

Help, please. I often feel that Moy's bracketology is unnecessarily complicated, and this is another case of that.
 
Re: Pairwise and Bracketology 2013 Edition

Well, only Jason knows for sure, since it's what he does, but I suspect he eliminates conflicts before moving for attendance because conference conflicts are, by his lights, more "important" than attendance. I'm not sure there's any important path dependence in what he ends up with, which is a non-conflicted, maximal band integrity, maximal attendance bracket. And even there, there are plenty of tradeoffs of the last two criteria. But, 5 team rule aside, since the conflict rule is the highest priority, he gets it out of the way first, even though you could always maximize attendance and then vary from that to change conflicts. Other than "complicated," do you have an example where it would make a difference?
 
Re: Pairwise and Bracketology 2013 Edition

I like to do as few swaps as possible, as I feel that duplicates the committee's actions. That is more complicated than it has to be. I would put UND in Grand Rapids to start because as the 7 seed they are a natural pairing with #2 Minnesota.
 
Re: Pairwise and Bracketology 2013 Edition

Priceless said:
I like to do as few swaps as possible, as I feel that duplicates the committee's actions. That is more complicated than it has to be. I would put UND in Grand Rapids to start because as the 7 seed they are a natural pairing with #2 Minnesota.
Click to expand...

Perhaps, Priceless, but here 4 and 8 have to go together, as they did last year (Ironically, UND(4) and Minn(8)). So, if 4/8 are together, then the natural pairing for 7 is with 1.

My complaint here is the NoDak for Lowell is unnecessary, since Mankato moves anyway. Now, if you want to move the 3 seeds for attendance, and then say "Hey Lowell out east is better for attendance" I can see that. And, really, in this bracket, there is no natural draw to Providence available, so perhaps Lowell is best. But, if that is the reasoning "Say That!!" Don't move them for a bogus reason, which is what this amounts to, at least to me.

Actually, off this set of PWRs, the right bracket might be:

Prov: Q (1) v UWisc (16); Lowell (6t) v Mankato (9t)
Rapids: Minny (2) v WMU (14); NoDak (6t) v Niagara (9t)
Toledo: Miami (3) v DU (13); Yale (5) v NoDame (9t)
Manchester: UNH (4) v Union (15); BC (8) v SCSU (12)

Where we put the #1s in order, and then decide that the ties don't need to be broken, so you can shuffle them anywhere.
 
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Re: Pairwise and Bracketology 2013 Edition

FYP - you bungled BC and UNH.

Numbers said:
Prov: Q (1) v UWisc (16); Lowell (6t) v Mankato (9t)
Rapids: Minny (2) v WMU (14); NoDak (6t) v Niagara (9t)
Toledo: Miami (3) v DU (13); Yale (5) v NoDame (9t)
Manchester: BC (4) v Union (15); UNH (8) v SCSU (12)

Where we put the #1s in order, and then decide that the ties don't need to be broken, so you can shuffle them anywhere.
Click to expand...

Actually this seem smarter. You break the ties at the bands but leave ties inside the band essentially alone. That makes it clearer where movement really doesn't change bracket integrity. It is the same thing but gives the committee more freedom to slide teams.

I find the strict banding funny that switching 9 and 12 is OK but 12 and 13 is just crazy. For making bands it is like some sort of magic that the PWR is perfect. Seems to me bracket integrity is better held switching 12 and 13... This is particularly true at the band 3 to 4 line, road team either way.
 
Re: Pairwise and Bracketology 2013 Edition

JB said:
Actually this seem smarter. You break the ties at the bands but leave ties inside the band essentially alone. That makes it clearer where movement really doesn't change bracket integrity. It is the same thing but gives the committee more freedom to slide teams.

I find the strict banding funny that switching 9 and 12 is OK but 12 and 13 is just crazy. For making bands it is like some sort of magic that the PWR is perfect. Seems to me bracket integrity is better held switching 12 and 13... This is particularly true at the band 3 to 4 line, road team either way.
Click to expand...

Thanks for the fix, JB. And, your analysis is exactly what I was thinking, and why I put 9t, etc in the brackets. The more room the committee has, the better. For example, last year, UND and Minny were slotted together at St Paul, even though they just played the F5 final. I don't know how that could have changed, but that's not a good thing - even though UND/Minn is a great rivalry.

As for your comment about 12/13, I agree with that, too, except that I would say that if the committee has license to do that, then they also need do this:
Either, there is a stipulation that these 2 teams can't be in the same regional, or their needs to be an explicit explanation that the 12 is really the higher seed, but that the bracket required an adjustment. This is for the sake of the possibility that 12 and 13 meet in a regional final. The 12th overall should get last line change.
And, the same kind of thing applies if they are in different regionals, but arrive at the F4. If they play there, the 12th PWR team should have last change.

Just details, but important ones...
 
Re: Pairwise and Bracketology 2013 Edition

There is a major flaw with weighting that has not been discussed. How do you account for injuries, illnesses or DNP for key players. Specifically in regards to Niagara which went through a long spell without Giancarlo Iuorio and other key players at the same time. As well as for the games that starting goaltender Carsen Chubak did not play due to illness or injury. Take some of those factors out and Niagara becomes a prohibitive favorite.
 
Re: Pairwise and Bracketology 2013 Edition

BC/HE said:
There is a major flaw with weighting that has not been discussed. How do you account for injuries, illnesses or DNP for key players. Specifically in regards to Niagara which went through a long spell without Giancarlo Iuorio and other key players at the same time. As well as for the games that starting goaltender Carsen Chubak did not play due to illness or injury. Take some of those factors out and Niagara becomes a prohibitive favorite.
Click to expand...

I assume here you are talking about the AHA Tournament only, and with regard to the KRACH weighted odds and the Poisson distribution odds?
 
Re: Pairwise and Bracketology 2013 Edition

BC/HE said:
There is a major flaw with weighting that has not been discussed. How do you account for injuries, illnesses or DNP for key players. Specifically in regards to Niagara which went through a long spell without Giancarlo Iuorio and other key players at the same time. As well as for the games that starting goaltender Carsen Chubak did not play due to illness or injury. Take some of those factors out and Niagara becomes a prohibitive favorite.
Click to expand...

Always true with sports... all you can hope to capture with simple models is soft trends. You couldn't possibly compute more complicated models.

There do exist changepoint models where you can try to determine the location of the break and the magnitude, should it exist. Since I tend to operate as a Bayesian I'd put a prior on location (and possibly how many) and reanalyze. However, what you dont want is all your games becoming their own value otherwise you've determined nothing. Likewise for such models predictive abilities would depend upon if you had a way to model future changes.

----

Given confusing and conflicting information we just hope that we're keying in on the right thing and in general we are picking up more signal than noise. Every model has to be read within the context of the data and the situation that produced the data.

Remember, no probability is absolute. All are built upon models (unless you're doing survey sampling and even then some still say you are using models). The results are truth, the remainder is just prediction from a model that has flattened the data.

That being said, you more likely to be generally right with a model. Just like I'll be generally right more often than others by guessing every game to end 3-2
 
Re: Pairwise and Bracketology 2013 Edition

ummmmmmmm

mookie is watching the wild-wings (heh... heh heh heh) and they said there is a concert friday at the joe and the ccha is sat/sun. soooooo, does that mean the selection show is sometime sunday evening?
 
Re: Pairwise and Bracketology 2013 Edition

mookie1995 said:
ummmmmmmm

mookie is watching the wild-wings (heh... heh heh heh) and they said there is a concert friday at the joe and the ccha is sat/sun. soooooo, does that mean the selection show is sometime sunday evening?
Click to expand...

Yes, 9:00pm which means we're all being held hostage by the prolonged existence of the CCHA being caused by a stupid Rihanna concert.
 
Re: Pairwise and Bracketology 2013 Edition

Hey all,

I ran all 393,216 outcomes similar to JimDahl, but went a step further and assigned a percent likelihood using KRACH on each individual outcome. I took a brief look, and it looks like my unweighted outcomes match up with JimDahl's

Here are KRACH weighted likelihoods for all seeds:
http://pwr.reillyhamilton.com/

Note that "seed" refers to the PWR seed (after auto-bids have been accounted for), not the PWR rank. Ties broken using RPI.

Individual breakdowns for each of the outcomes tomorrow:

WCHA 'Quarterfinal' 1:
WCHA 'Quaterfinal' 2:
if Minnesota State won:
If Wisconsin won:



I'm working on some alternate ways of analyzing the data I've generated. I hope to release a dynamic "what-if" machine after tomorrow's games when the number of outcomes is a bit more manageable and less likely to crash my webhost's database server.

EDIT: Fixed typo per lugnut92 below :)
EDIT 2: Switched domain names.
 
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