Pairwise and Bracketology 2013 Edition

[PaulG]

Re: Pairwise and Bracketology 2013 Edition

The thing is, it cleaned up a bit of an issue that was seen in the past. From the USCHO article covering this when it was only a proposed change:


The old way could lead to a situation where Team 1 went 5-2 against common opponents, where they played the worst team in a conference 4 times, going 4-0, and 1-2 against the top team in that conference. Team 2 ended up 4-2 against the same two teams, but went 3-2 against the top team in the conference and 1-0 against the worst team. Under the old method, Team 1 wins the common opponent comparison .7143 to .6667. Under the new system, team 2 would win the COp comparison 1.6 to 1.333 (1 point each for undefeated against the worst team, with Team 2 getting .6 for the 3-2 record against the top team and Team 1 only getting .333 for their 1-2 record)

Wow, perfectly clear now. I think the old method was MUCH better. Factor in SOS to the old method if you want to improve it ... but method 2 is just plain silly. By totally ignoring games when one team has all the wins or losses is ridiculous. There is no way records of 1-0 and 4-0 should be the same weight. The faults in the new system are much higher than the faults in the old.

 

[Numbers]

Re: Pairwise and Bracketology 2013 Edition

Wow, perfectly clear now. I think the old method was MUCH better. Factor in SOS to the old method if you want to improve it ... but method 2 is just plain silly. By totally ignoring games when one team has all the wins or losses is ridiculous. There is no way records of 1-0 and 4-0 should be the same weight. The faults in the new system are much higher than the faults in the old.

Easy enough to say that, Paul. But, what if someone were 3-0 versus Robert Morris? Is that worth 3 times as much as 1-0 versus UND?

I believe it's more correct to say that it is difficult to make the ComOpp part do what you want it to do.

 

[Numbers]

Re: Pairwise and Bracketology 2013 Edition

Which, by the way, brings up this for discussion:

Disclaimer first: The current PWR follows the current RPI rankings pretty closely. As for the tourney field, only BC (+3), and Dartmouth (+3) are more than 2 spots off of their RPI rank. (I am ignoring that Providence wins the 4-way tie in the HE). Only BC and Lowell would be in the wrong bands (compared to if they simply used RPI), and only RPI (the school) would be out of the field, replaced by Omaha.

Now, that being said, what would everyone think of this:
To calculate each comparison:
RPI = 2 pts + tiebreak
TUC = 1 pt
ComOpp = 1pt
H2H = 1 pt unless the teams played more than 2 games and there was a sweep (then = 2pts)

My reasoning: First, if the RPI is doing what you want it to do, you should only override it in extreme circumstances. Hence, 2 points.
Second, in a long season, when you play someone is often more important than who is better, hence the change in the calculation for H2H.

Comments?

Doing this on the present calculation (from the calculator here http://www.elynah.com/tbrw/2013/cgi-bin/rankings.cgi) without being able to implement the h2h sweep, leaves all the rankings going by RPI.

Is their something better yet?

I think it unlikely the committee ever goes to KRACH, so I don't count that. How about, "Whenever RPI with within 1%, then look at other criteria?"

 

[Priceless]

Re: Pairwise and Bracketology 2013 Edition

I would say no only because the current formula for RPI is flawed. Fix that and we can look at tweaking the pairwise a little.

Edit: I'm on my Kindle so I won't be expanding that answer for a while but it is cool that my Kindle offered up "pairwise" as an option. Guess it knows me well.

 

[Numbers]

Re: Pairwise and Bracketology 2013 Edition

I would say no only because the current formula for RPI is flawed. Fix that and we can look at tweaking the pairwise a little.

Priceless,
I agree. RPI is totally flawed. That's why I wrote "Assuming the RPI does what you want it to." It doesn't. Those %ages are arbitrary. I don't know how they were chosen, but I suspect that somehow they were chosen to approximate the results of the Bradley-Terry method. Obviously, it doesn't do that all the time either.

My question is really about: Excluding using Bradley-Terry, because they won't (too hard to explain, even if it's perhaps easier to calculate on a computer than the PWR), how can we get the best system - so we get the best teams?

 

[Priceless]

Re: Pairwise and Bracketology 2013 Edition

Oh great...here come the KRACH-heads

 

[Happy]

Re: Pairwise and Bracketology 2013 Edition

Priceless,
I agree. RPI is totally flawed. That's why I wrote "Assuming the RPI does what you want it to." It doesn't. Those %ages are arbitrary. I don't know how they were chosen, but I suspect that somehow they were chosen to approximate the results of the Bradley-Terry method. Obviously, it doesn't do that all the time either.

My question is really about: Excluding using Bradley-Terry, because they won't (too hard to explain, even if it's perhaps easier to calculate on a computer than the PWR), how can we get the best system - so we get the best teams?

aren't your really arguing about the bottom best teams? After all, the really good teams will all be in the tourney any way, and often at that point it is luck as to wether they get an easy or hard regional.

 

[Almington]

Re: Pairwise and Bracketology 2013 Edition

Priceless,
I agree. RPI is totally flawed. That's why I wrote "Assuming the RPI does what you want it to." It doesn't. Those %ages are arbitrary. I don't know how they were chosen, but I suspect that somehow they were chosen to approximate the results of the Bradley-Terry method. Obviously, it doesn't do that all the time either.

My question is really about: Excluding using Bradley-Terry, because they won't (too hard to explain, even if it's perhaps easier to calculate on a computer than the PWR), how can we get the best system - so we get the best teams?

With conferences moving to larger NC schedules should help, the issue is that if you ever calculate the uncertainty in any of the rankings, given the small sample size for comparison between NC opponents, it's impossible to mathematically differentiate between the teams.

 

[Numbers]

Re: Pairwise and Bracketology 2013 Edition

It seems like Happy and Almington are saying the same thing:
There is no perfect way to determine the best 16 teams, because the differences are so small. I can appreciate that, and will now drop the discussion. I am sorry.

 

[purpleinnebraska]

Re: Pairwise and Bracketology 2013 Edition

aren't your really arguing about the bottom best teams? After all, the really good teams will all be in the tourney any way, and often at that point it is luck as to wether they get an easy or hard regional.

Agree completely. I think the hockey guys looked at the sort of smoke-filled room method that basketball uses, and tried to make something more "objective." And what's more objective than math, right? Of course, "math" is only as objective as the formulas you use. The cream of the crop rises under the PWR system, but just like with basketball, is there any real difference between the last 2 teams in, and the first 2 out? No, BUT WE USE MATH!!!

 

[kingdobbs]

Re: Pairwise and Bracketology 2013 Edition

Wow, perfectly clear now. I think the old method was MUCH better. Factor in SOS to the old method if you want to improve it ... but method 2 is just plain silly. By totally ignoring games when one team has all the wins or losses is ridiculous. There is no way records of 1-0 and 4-0 should be the same weight. The faults in the new system are much higher than the faults in the old.

It's an attempt to mitigate the effect of unbalanced league scheduling, in the case of comparisons involving three teams all in the same conference, and the benefit a team can accrue by playing a team in-conference three or four times a year while an out-of-conference team can only play them once or twice, usually.

Case A: St. Cloud plays UAA four times, and wins all four games. Minnesota plays UAA twice and wins both games. The two teams have a .500 record against all other COps. Old system: St. Cloud wins because they get credit for two more wins that Minnesota had NO WAY of getting. New system: neither team wins the comparison.

Case B: St. Cloud plays UAA four times in WCHA play, winning all four games. Quinnipiac plays UAA once as part of UAA's October tourney, and wins. Again, St. Cloud got three more wins that Quinnipiac had no way of getting.

 

[Almington]

Re: Pairwise and Bracketology 2013 Edition

It seems like Happy and Almington are saying the same thing:
There is no perfect way to determine the best 16 teams, because the differences are so small. I can appreciate that, and will now drop the discussion. I am sorry.

What I am saying that that their is no perfectly objective way of determining the best 16 teams, either you select those 16 teams subjectively (smoked filled rooms), or you subjectively select the criteria that objectively sorts the teams at the end of the season. Since ALL of the different mathematical ranking yield different results (even if some are more mathematically pure than others) and all view the completed games objectively you will never get a consensus agreement on the who the exact 16 best teams are.

I would rather they subjectively pick any mathematical ranking system prior to the season and stick to it than have the NCAA field determined subjectively at the end of the season by a nearly unaccountable group of people.

 

[Ralph Baer]

Re: Pairwise and Bracketology 2013 Edition

What I am saying that that their is no perfectly objective way of determining the best 16 teams, either you select those 16 teams subjectively (smoked filled rooms), or you subjectively select the criteria that objectively sorts the teams at the end of the season. Since ALL of the different mathematical ranking yield different results (even if some are more mathematically pure than others) and all view the completed games objectively you will never get a consensus agreement on the who the exact 16 best teams are.

I would rather they subjectively pick any mathematical ranking system prior to the season and stick to it than have the NCAA field determined subjectively at the end of the season by a nearly unaccountable group of people.

Agreed. The smoke-filled room has to be avoided. The current system is not perfect, but it gives a field unaffectd by human biases at the 11th hour.

 

[PaulG]

Re: Pairwise and Bracketology 2013 Edition

It's an attempt to mitigate the effect of unbalanced league scheduling, in the case of comparisons involving three teams all in the same conference, and the benefit a team can accrue by playing a team in-conference three or four times a year while an out-of-conference team can only play them once or twice, usually.

Case A: St. Cloud plays UAA four times, and wins all four games. Minnesota plays UAA twice and wins both games. The two teams have a .500 record against all other COps. Old system: St. Cloud wins because they get credit for two more wins that Minnesota had NO WAY of getting. New system: neither team wins the comparison.

Case B: St. Cloud plays UAA four times in WCHA play, winning all four games. Quinnipiac plays UAA once as part of UAA's October tourney, and wins. Again, St. Cloud got three more wins that Quinnipiac had no way of getting.

Yes, I get all this. But, the fact remains that St. Cloud did play those games and did win. It is not fair to ignore them. If St. Cloud won 3 of 4 and Minn. won 1 of 2, St. Cloud would get credit for those extra two wins giving them .750 for that record compared to Minnesota getting .500. So, why is that a sweep discounts the wins where as non-sweeps recognize every game??? The old method was flawed but better than the new method by far!

 

[FreshFish]

Re: Pairwise and Bracketology 2013 Edition

What I am saying that that their is no perfectly objective way of determining the best 16 teams, either you select those 16 teams subjectively (smoked filled rooms), or you subjectively select the criteria that objectively sorts the teams at the end of the season. Since ALL of the different mathematical ranking yield different results (even if some are more mathematically pure than others) and all view the completed games objectively you will never get a consensus agreement on the who the exact 16 best teams are.

I would rather they subjectively pick any mathematical ranking system prior to the season and stick to it than have the NCAA field determined subjectively at the end of the season by a nearly unaccountable group of people.

The size of the field is definitely a factor, as is the size of the pool of eligible teams. Div I hockey has a relatively small pool from which to draw, which means that the "six degrees of separation" is only two or three degrees....even if my team didn't play your team this year, chances are pretty high that both teams played the same third team somewhere along the line.

Div I men's basketball has something like 350 teams or some such number; they use formulas to an extent and eventually resort to a smoke-filled room because they cannot refine their formulas over such a large pool. If you go proportional, Div I hockey has a far larger percentage of teams making the tournament than Div I basketball. While we might have 3 or 4 teams on the bubble, they'd have 15 or 20 teams on the bubble.

 

[HoosierBBall_GopherHockey]

Re: Pairwise and Bracketology 2013 Edition

Yes, I get all this. But, the fact remains that St. Cloud did play those games and did win. It is not fair to ignore them. If St. Cloud won 3 of 4 and Minn. won 1 of 2, St. Cloud would get credit for those extra two wins giving them .750 for that record compared to Minnesota getting .500. So, why is that a sweep discounts the wins where as non-sweeps recognize every game??? The old method was flawed but better than the new method by far!

Because 3 of 4 is 75% and 1 of 2 is 50%, so it is obvious that 75%>50%. How is 100%>100%? They are equal. In your hypothetical scenario, it is not fair to ignore that Minnesota was not given an opportunity to play UAA two more times. They both took care of business (i.e. swept) given their schedule.

 

[Almington]

Re: Pairwise and Bracketology 2013 Edition

The size of the field is definitely a factor, as is the size of the pool of eligible teams. Div I hockey has a relatively small pool from which to draw, which means that the "six degrees of separation" is only two or three degrees....even if my team didn't play your team this year, chances are pretty high that both teams played the same third team somewhere along the line.

Div I men's basketball has something like 350 teams or some such number; they use formulas to an extent and eventually resort to a smoke-filled room because they cannot refine their formulas over such a large pool. If you go proportional, Div I hockey has a far larger percentage of teams making the tournament than Div I basketball. While we might have 3 or 4 teams on the bubble, they'd have 15 or 20 teams on the bubble.

Except that the predictive value of one game is tiny. Again, the uncertainty is such at it's impossible to say if the 3rd place team from conference A is any better than the 4th place team from conference B. Thus, the last 25% teams in are virtually indistinguishable from the first 25% teams out regardless of how the field is chosen with any level of certainty. Any time the number of teams exceeds the number of games that is going to be the case.

 

[Almington]

Re: Pairwise and Bracketology 2013 Edition

Because 3 of 4 is 75% and 1 of 2 is 50%, so it is obvious that 75%>50%. How is 100%>100%? They are equal. In your hypothetical scenario, it is not fair to ignore that Minnesota was not given an opportunity to play UAA two more times. They both took care of business (i.e. swept) given their schedule.

By the same account, the Minnesota was not given the opportunity to lose or tie UAA in those two games.

You should have to earn both the overall and team weighted comparisons to get the COp comparison point.

 

[PaulG]

Re: Pairwise and Bracketology 2013 Edition

Because 3 of 4 is 75% and 1 of 2 is 50%, so it is obvious that 75%>50%. How is 100%>100%? They are equal. In your hypothetical scenario, it is not fair to ignore that Minnesota was not given an opportunity to play UAA two more times. They both took care of business (i.e. swept) given their schedule.

First half of season, they both play UAA once and lose...they're equal, right? Second half of season, St. Cloud goes on to win three more games whereas Minnesota wins one. St. Cloud won 100% in the second half and Minnesota won 100% ... are they still equal???

Also, in the given scenario, under the current method, Minnesota is NOT given the opportunity to play UAA two more times and they ARE PENALIZED because St. Cloud was and won the two extra games. Why is St. Cloud getting credit when they are 3-1 against 1-1 but NOT when they are 4-0 against 2-0???

 

[PaulG]

Re: Pairwise and Bracketology 2013 Edition

Didn't there used to be a L16 factor in the PWR? Is it gone?