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Division I Rutter Rankings for 2012-2013

Re: Division I Rutter Rankings for 2012-2013

When I click through to the graph from your webpage, I get last season's graph (2011-12). Is there a graph for this season?
 
Re: Division I Rutter Rankings for 2012-2013

greenmtngirl said:
When I click through to the graph from your webpage, I get last season's graph (2011-12). Is there a graph for this season?
Click to expand...

OnMAA is correct, the plot is for the 2012-2013 season. I can never find all the year changes I need to make the first time through. Thanks for pointing that out. It has now been corrected.
 
Re: Division I Rutter Rankings for 2012-2013

For games played through November 18, 2012

Code: 
	Team		Rating
1 	Minnesota 	3.0004 	
2 	Cornell 	1.6827 
3 	Clarkson 	1.4901 
4 	Mercyhurst 	1.4659 	
5 	Ohio State 	1.2943 	
6 	Boston Unive. 	1.1949 	
7 	North Dakota 	1.1689 	
8 	Harvard 	0.9978 	
9 	Boston College 	0.9654 	
10 	Minnesota Dul. 	0.7612
 
Re: Division I Rutter Rankings for 2012-2013

For games played through November 25, 2012

Code: 
  	Team 	        Rating 	
1 	Minnesota 	2.9527 	
2 	Cornell 	1.5074 	
3 	Clarkson 	1.4930 
4 	Harvard 	1.4339 	
5 	Mercyhurst 	1.4043 
6 	North Dakota 	1.2413 
7 	Boston Univ. 	1.2109 	
8 	Ohio State 	1.0278 
9 	Boston College 	0.9837 	
10 	Wisconsin 	0.6967
 
Re: Division I Rutter Rankings for 2012-2013

LakersFan said:
For games played through November 25, 2012

Code: 
  	Team 	        Rating 	
1 	Minnesota 	2.9527
Click to expand...
Did this come down because of other teams' performances or because the Gophers beat up a lower-ranked team this past weekend (or a combination of both)?
 
Re: Division I Rutter Rankings for 2012-2013

CrazyDave said:
Did this come down because of other teams' performances or because the Gophers beat up a lower-ranked team this past weekend (or a combination of both)?
Click to expand...
I would guess the former. In a decent mathematical model, a team should not be hurt by winning. If you look back to November 11, Minnesota was even higher then. Ohio State is the second-best team Minnesota has played according to Rutter after UND, so Buckeye losses to teams they haven't played will weaken the Gophers' ranking.
 
Re: Division I Rutter Rankings for 2012-2013

Even if they have dipped under 3, Minnies number is almost double that of it's nearest pursuer. That is mathematically a humongous outlier.

Spread between 1 and 2 at each end tends to be 0.5 or less, so a spread of 1.45 is out of the norm.
To illustrate, in D1, the top two are +2.95 and +1.50 while at the other end the numbers are -2.05 and -1.43.
In D3, the equivalent numbers are +2.66 and +2.39 at the top and -2.34 and -1.90 at the bottom.

I'm sure Lakersfan has all the stats on that.
 
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Re: Division I Rutter Rankings for 2012-2013

CrazyDave said:
Did this come down because of other teams' performances or because the Gophers beat up a lower-ranked team this past weekend (or a combination of both)?
Click to expand...

ARM is correct. Under my model, winning a game never lowers your rating. For example, if Minnesota defeated Lindenwood, neither rating would change. The probability that UM defeats LU is 99.99997% (to keep things simple, assume a tie is not a possible outcome). Under those conditions, since that result is almost guaranteed under the model, the ratings would only increase (or decrease, in the case of LU) .0001 or less, which for practical purposes is no change.

If the teams UM beats lose, then UM ratings will decrease because those previous wins are now less impressive. Since my model does not take into account when the game is played, every time I generate ratings the model essential assumes all the games were played simultaneously. For example, the wins over St. Cloud State has become less impressive as SCS rating decreases (from Oct 19 onward), therefore the UM rating will not be as high as it was prior to Oct. 19.

Now, UM has not lost or tied a game. Under some models, that would result in UM having an infinite rating, since that is the way (mathematically) to guarantee a victory against every other team. This tends to break the model (computers have trouble with infinity), so I constrain the rating by using a prior distribution. The prior is based on last years rating, which for UM was 1.88. That means that if UM played and defeated only top 10 teams every game, the maximum rating would be about 3.88 (this assumes a standard deviation of 1, and 3.88 is two standard deviations away). As you can see, they are not near that value, since they have played a wide range of opponents in terms of quality. That means 2.95 is a high as the model needs to push UM's rating up to balance the likelihood of not losing the games against the opponents they have played vs. the likelihood of the team improving two+ points in terms of rating.
 
Re: Division I Rutter Rankings for 2012-2013

LakersFan said:
ARM is correct. Under my model, winning a game never lowers your rating. For example, if Minnesota defeated Lindenwood, neither rating would change. The probability that UM defeats LU is 99.99997% (to keep things simple, assume a tie is not a possible outcome). Under those conditions, since that result is almost guaranteed under the model, the ratings would only increase (or decrease, in the case of LU) .0001 or less, which for practical purposes is no change.

If the teams UM beats lose, then UM ratings will decrease because those previous wins are now less impressive. Since my model does not take into account when the game is played, every time I generate ratings the model essential assumes all the games were played simultaneously. For example, the wins over St. Cloud State has become less impressive as SCS rating decreases (from Oct 19 onward), therefore the UM rating will not be as high as it was prior to Oct. 19.

Now, UM has not lost or tied a game. Under some models, that would result in UM having an infinite rating, since that is the way (mathematically) to guarantee a victory against every other team. This tends to break the model (computers have trouble with infinity), so I constrain the rating by using a prior distribution. The prior is based on last years rating, which for UM was 1.88. That means that if UM played and defeated only top 10 teams every game, the maximum rating would be about 3.88 (this assumes a standard deviation of 1, and 3.88 is two standard deviations away). As you can see, they are not near that value, since they have played a wide range of opponents in terms of quality. That means 2.95 is a high as the model needs to push UM's rating up to balance the likelihood of not losing the games against the opponents they have played vs. the likelihood of the team improving two+ points in terms of rating.
Click to expand...

Thanks for that excellent mathematical explanation. Brings me back to learnings way back when in stats class.......

......Love this line...."computers have trouble with infinity"....Actually some of us have trouble with infinity as well.....Specially if those gophers keep on winning "ad infinitum". :D
 
Re: Division I Rutter Rankings for 2012-2013

OnMAA said:
Actually some of us have trouble with infinity as well.....Specially if those gophers keep on winning "ad infinitum". :D
Click to expand...
There are those that would have zero problem with that.
 
Re: Division I Rutter Rankings for 2012-2013

Eeyore said:
Zero and infinity are closely related concepts.
Click to expand...

You must mean zero chance of infinity :D
( Zero and infinity are about as far from each other as you can get ! ;) )
 
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Re: Division I Rutter Rankings for 2012-2013

This thread now resembles my lectures. 15 minutes of profound and relevent lecture followed by five minutes of jokes and puns as I half-heartedly try to get the class back on track :)
 
Re: Division I Rutter Rankings for 2012-2013

For games played through December 2, 2012

Code: 
  	Team 	      Rating 	Last Week	
1 	Minnesota 	3.01	1
2 	Harvard 	1.62	4
3 	Cornell 	1.41	2
4 	Mercyhurst 	1.37	5
5 	Boston Univ. 	1.29	7	 	
6 	Clarkson 	1.50	3
7 	North Dakota 	1.24	6	
8 	Boston College 	1.04	9 	
9 	Ohio State 	0.98 	8
10 	Wisconsin 	0.68 	10
 
Re: Division I Rutter Rankings for 2012-2013

LakersFan said:
For games played through December 2, 2012

Code: 
  	Team 	      Rating 	Last Week	
1 	Minnesota 	3.01	1
2 	Harvard 	1.62	4
3 	Cornell 	1.41	2
4 	Mercyhurst 	1.37	5
5 	Boston Univ. 	1.29	7	 	
6 	Clarkson 	1.50	3
7 	North Dakota 	1.24	6	
8 	Boston College 	1.04	9 	
9 	Ohio State 	0.98 	8
10 	Wisconsin 	0.68 	10
Click to expand...

While visiting in Erie this weekend, I was telling all my pals out there how I think Harvard is still underrated in the polls. I've had the opportunity to see all top 6 teams play in person, granted Minny was @ UNH, but Harvard was against Cornell, and of course I was there for the Mercyhurst - Clarkson series. I was suggesting that Harvard really should be ranked as high as #2 IMHO. When I told Doc Rutter this in person this weekend, he just smiled and said...."of course they should. That's where my calculation has them!"

Way to go Doc!! Keep pumping out that good math!
 
Re: Division I Rutter Rankings for 2012-2013

IceIsNice said:
While visiting in Erie this weekend, I was telling all my pals out there how I think Harvard is still underrated in the polls. I've had the opportunity to see all top 6 teams play in person, granted Minny was @ UNH, but Harvard was against Cornell, and of course I was there for the Mercyhurst - Clarkson series. I was suggesting that Harvard really should be ranked as high as #2 IMHO. When I told Doc Rutter this in person this weekend, he just smiled and said...."of course they should. That's where my calculation has them!"

Way to go Doc!! Keep pumping out that good math!
Click to expand...

Like you sold on Harvard being the top ECAC team. Rutter is designed to eventually catch up with reality, specially early in the season, and even more specially for Ivy teams that start a month later.

Notice how Minny is back in the 3+ stratosphere.
 
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