2012-13 KRACH RANKINGS - Updated 03/02 FINAL w/FINAL LPH RK

[MNHockeyFan]

SOS (Strength-Of-Schedule) is at:
http://www.bgoski.com/KRACH_SOS.htm

Interesting how the top 4 teams are members of the Lake Conference. In addition to having (getting?) to play each other twice, they choose to schedule very good teams out of conference as well. The other member, Hopkins, is at #16 so they've chosen an easier non-conference schedule.

Other top-ranked teams:

Mounds View is quite a ways down the list at #39. When it gets to sections it's probably a legitimate question whether their schedule has tested them enough, although they seem to have a knack of winning the close games.

BSM's SOS - also weak at #35 - is seriously dragged down by their games against North Suburban Conference teams. Out of conference their schedule has been pretty strong. FWIW their boys' team opted out of the North Suburban for hockey only this season, and their schedule has been very challenging, currently #6 on KRACH.

[sinbin]

The Lake conference SOS is no surprise since they play 1/3 of their season against ~Top 10 teams. Nor are BSM and MV's easy schedules surprises. The item that surprised me was the many Section 2AA teams near the top. I would expect Lake EP and Edina, but we also see Chan/Chaska, PL, and Jefferson in the Top 11. Do they really play in such a strong conference(s), or are they scheduling the big guns for non-conference play?

[Goalie-Dad]

SOS (Strength-Of-Schedule) is at:
http://www.bgoski.com/KRACH_SOS.htm

Interesting how the top 4 teams are members of the Lake Conference. In addition to having (getting?) to play each other twice, they choose to schedule very good teams out of conference as well. The other member, Hopkins, is at #16 so they've chosen an easier non-conference schedule.

Other top-ranked teams:

Mounds View is quite a ways down the list at #39. When it gets to sections it's probably a legitimate question whether their schedule has tested them enough, although they seem to have a knack of winning the close games.

BSM's SOS - also weak at #35 - is seriously dragged down by their games against North Suburban Conference teams. Out of conference their schedule has been pretty strong. FWIW their boys' team opted out of the North Suburban for hockey only this season, and their schedule has been very challenging, currently #6 on KRACH.

The SOS in girls high school is a non-factor in evaluating teams. Teams in large conferences, with weaker teams, have little or no opportunity to play teams outside of their conference and/or section. If all conferences had the same number of teams, then SOS maybe more relevant.

Secondly, looking at the MV schedule (probably the same for BSM), 18 of their 22 victories can against teams with a higher SOS ranking. This does not make sense in evaluating team strength.

[ghshockeyfan]

It's a well known fact that SOS is to some degree out of the control of teams in a conference for their conference play.

What SOS can start to tell us is a bit about non conference choices. Maybe an interesting SOS would be for NC only - just to see what teams are really stepping up and taking on top opponents when given a choice.

SOS is a big factor in deciding the ranking of teams in any sport. To say otherwise seems to indicate that an undefeated season against the worst teams in the state is just as good as an undefeated season against the very best - and I think we can logically agree these are not equal achievements.

It's unfortunate that some teams don't have as many, if any, NC chances to up their SOS. But, we can't throw out SOS as a result - IMHO, regardless of the specific sport, its gender, etc.

[Goalie-Dad]

It's a well known fact that SOS is to some degree out of the control of teams in a conference for their conference play.

What SOS can start to tell us is a bit about non conference choices. Maybe an interesting SOS would be for NC only - just to see what teams are really stepping up and taking on top opponents when given a choice.

SOS is a big factor in deciding the ranking of teams in any sport. To say otherwise seems to indicate that an undefeated season against the worst teams in the state is just as good as an undefeated season against the very best - and I think we can logically agree these are not equal achievements.

It's unfortunate that some teams don't have as many, if any, NC chances to up their SOS. But, we can't throw out SOS as a result - IMHO, regardless of the specific sport, its gender, etc.

Deciding the top teams in Girls hockey should not be based on a mathematical formula like SOS. For example Prior Lake is #8 in SOS ranking with only 4 wins this season (not picking on PL, just an example). It's a weak team with a strong schedule. Is PL that much better than MV and BSM?

[ghshockeyfan]

Deciding the top teams in Girls hockey should not be based on a mathematical formula like SOS. For example Prior Lake is #8 in SOS ranking with only 4 wins this season (not picking on PL, just an example). It's a weak team with a strong schedule. Is PL that much better than MV and BSM?

"You have to play the best to be the best..." ...I don't think that's what we are saying here alone.

Instead, people are looking at SOS ranking in conjunction with the performance of teams to see who "play(ed) the best" teams and evaluating how they actually performed.

The actual ranking is here:
http://www.bgoski.com/KRACH_OA.htm

In fact, for this ranking system, we calculate SOS AFTER the teams are ranked based on their performance against their schedule.

Then, once a ranking is calculated based on their results (and not on who they played alone), we can retrospectively look back and say - on average, how strong were the opponents for team X?

That's what this is:
http://www.bgoski.com/KRACH_SOS.htm

More information about KRACH is at:

From a related thread:

http://www.ushsho.com/forums/viewtopic. ... ht=#605192

I'll be curious to see how KRACH computer ranking compares against some of the others mentioned here (Minnhock's PS2, USHSHO, MyHockeyRankings). KRACH is probably as "pure" as any algorithm in that it doesn't even care about score differential. That's why I prefer it. No additional human intervention.

Interestingly, it is supposed to give you odds on a game taking place. A team with a "10" rating value is considered the average team in the state regardless of Class designation. A team with, for example, a "100" rating is a 10:1 favorite over the average team. Similarly, you can compare any two teams based on their ratings.

SOS is just an average of opponents rankings played as of now.

http://www.ushsho.com/forums/viewtopic.php?t=29709

Most Recent Ranking Links NOTE THESE ARE BOYS RANKINGS LINKS:
==========================================
OVERALL:
http://www.bgoski.com/b/KRACH_OA.htm
CLASS AA:
http://www.bgoski.com/b/KRACH_AA.htm
CLASS A:
http://www.bgoski.com/b/KRACH_A.htm
SECTION:
http://www.bgoski.com/b/KRACH_SEC.htm
SOS (Strength-Of-Schedule) is at:
http://www.bgoski.com/b/KRACH_SOS.htm
==========================================

Added info. is at:
http://www.bgoski.com
And more info. on the girls forum at:
http://www.ushsho.com/forums/viewtopic.php?t=29597
http://www.ushsho.com/forums/viewtopic.php?t=27320

Here's the real details about KRACH:
http://www.mscs.dal.ca/~butler/krachexp.htm

And, our friends at USCHO speak to KRACH vs other options (yep, 7+ years ago):
http://www.uscho.com/2005/03/17/lets-get-kraching/

In addition to their ongoing rankings for both genders at both levels:
http://www.uscho.com/rankings/
http://www.uscho.com/rankings/krach/d-i-men/
http://www.uscho.com/rankings/krach/d-i-women/
http://www.uscho.com/rankings/krach/d-iii-men/
http://www.uscho.com/rankings/krach/d-ii-iii-men/
http://www.uscho.com/rankings/krach/d-iii-women/

Basic Explanation
KRACH — or “Ken’s Ratings for American College Hockey” — is the implementation for college hockey of a sophisticated mathematical model known as the Bradley-Terry rating system, first applied to college hockey by a statistician named Ken Butler.

This method is based on a statistical technique called logistic regression, in essence meaning that teams’ ratings are determined directly from their won-loss records against one another. A key feature of KRACH is that strength of schedule is calculated directly from the ratings themselves, meaning that KRACH, unlike many ratings (including RPI) cannot easily be distorted by teams with strong records against weak opposition.

The ratings are on an odds scale, so if Team A’s KRACH rating is three times as large as Team B’s, Team A would be expected to amass a winning percentage of .750 and Team B a winning percentage of .250 if it played each other enough times. The correct ratings are defined such that the "expected" winning percentage for a team in the games it’s already played is equal to its "actual" winning percentage.

An alternative definition of a team’s KRACH rating is as the product of its Winning Ratio (winning percentage divided by one minus winning percentage) with the weighted average of its opponents’ KRACH ratings. (The definition of the weighting factor makes this equivalent to the first definition of the KRACH ratings.) In addition to KRACH and RRWP, the table above lists each team’s Winning Percentage, Winning Ratio and Strength of Schedule (the aforementioned weighted average of their opponents’ KRACH ratings).


KRACH is provided for entertainment purposes only and is not used in any official way, nor is it endorsed by USCHO.com.

From the Hub:
http://www.mngirlshockeyhub.com/page/sh ... h-rankings
http://www.bgoski.com

About KRACH:
=================
KRACH is short for “Ken's Rating for American College Hockey.” Ken is Ken Butler, a statistician, and the mathematical model he used is known as the Bradley-Terry Rating System. The system and its details are well documented in great mathematical detail online (see KRACH explanation at Ken Butler's homepage).

..
The KRACH rating system is an attempt to combine the performance of each team with the strength of the opposition against which that performance was achieved, and to summarize the result as one number, a "rating", for each team. The higher the rating, the better the team.

This system accounts for strength-of-schedule (SOS) as it ranks the teams.

Teams with equal records and differing SOS can quickly be ranked as a result (i.e. team with stronger SOS is ranked higher than other teams with same record and weaker SOS).

The ratings are calculated purely from the game results (win, loss or tie), and do not use the goals scored at all. Overtime wins count as wins. Ties, for KRACH's purposes, count as half a win and half a loss.

KRACH only counts games against Minnesota State High School League opponents.
..

[ghshockeyfan]

Updated 01/27 AM

[MNHockeyFan]

Deciding the top teams in Girls hockey should not be based on a mathematical formula like SOS. For example Prior Lake is #8 in SOS ranking with only 4 wins this season (not picking on PL, just an example). It's a weak team with a strong schedule. Is PL that much better than MV and BSM?

Goalie-Dad, a team's SOS has nothing to do with how good they are. It only measures the strength of the teams they've played! SOS is purely an evaluation tool of the quality of the opposition that each team has played.

Using your Prior Lake example above, I don't think anyone has had them ranked in the Top 20 all season, nor has anyone claimed they are a better team than either MV or BSM, even though they've played a harder schedule than either of them.

P.S. You do have to give PL credit for playing such a difficult schedule, and I wouldn't be at all surprised if they've improved over the course of the season because of it.

[ghshockeyfan]

Updated 01/29 AM

[Marty]

They should not have a ranking number below the top 20 in "A" and the top 25 in "AA.

Once you get past the top 40% of the teams in each level, the balance becomes almost unsortable and mostly irrelevant.

[luckyEPDad]

They should not have a ranking number below the top 20 in "A" and the top 25 in "AA.

Once you get past the top 40% of the teams in each level, the balance becomes almost unsortable and mostly irrelevant.

The system uses an equation that derives a number that is easily sortable. The error is placing any importance in the order. Unlike LPH rankings, KRACH attempts to predict the results of a game played between any two teams. The important number in the KRACH list is the rating, not the ordinal number placed to the left of the sorted list. I don't much care that Mounds View currently has the highest KRACH rating. I am more interested in what the KRACH numbers said about last Saturday's meeting between Eden Prairie and Shakopee. I hadn't seen Shakopee play and had no idea how good they are. At the end of the second period it looked like KRACH was right, EP dominated. However, Shakopee turned it on in the third and nearly pulled off an upset.

[Cut Above]

Must not have had any girl HS fans/volunteers for mnhockeyrankings.com to compare rankings?

http://myhockeyrankings.com/rank.php?y= ... &v=851&g=0

Two Totally Different Algorithms

[ghshockeyfan]

Must not have had any girl HS fans/volunteers for mnhockeyrankings.com to compare rankings?

http://myhockeyrankings.com/rank.php?y= ... &v=851&g=0

Two Totally Different Algorithms

My guess is they just need access to the data/scores. I've provided a tool to do this to other ranking entities and would be happy to assist them in getting the info.

The whole reason I started this KRACH thing way back when was that there wasn't anything for girls. It was all about the boys. The more the better IMHO.

[ghshockeyfan]

Updated 01/30 AM

[MNHockeyFan]

I was surprised to see the huge impact that Mounds View's loss last night had on their KRACH ranking. They dropped 443 points, from 819 to 376 (-54%)! I guess this is because White Bear Lake was ranked so far below them, at #58.

At the same time I was also surprised that the impact on WBL for their win was relatively minor. They only gained 2 points, going from 10.5 to 12. 5 (+19%). Their ranking did climb 15 places, from #58 to #43.

Would appreciate hearing your explanation, ghshockeyfan, as to why a huge upset like this, so late in the season, appears to impact the losing team (the favorite) so much more than the winning team (the underdog).

[ghshockeyfan]

I was surprised to see the huge impact that Mounds View's loss last night had on their KRACH ranking. They dropped 443 points, from 819 to 376 (-54%)! I guess this is because White Bear Lake was ranked so far below them, at #58.

At the same time I was also surprised that the impact on WBL for their win was relatively minor. They only gained 2 points, going from 10.5 to 12. 5 (+19%). Their ranking did climb 15 places, from #58 to #43.

Would appreciate hearing your explanation, ghshockeyfan, as to why a huge upset like this, so late in the season, appears to impact the losing team (the favorite) so much more than the winning team (the underdog).

The losing team had far more to lose than the winning team to gain in an upset from the KRACH perspective.

Why? Because, as I understand it, KRACH takes WBLs best prior loss and turns that into a win. So, let's just say they lost to a team ranked 45 before last night. Beating the #1 team essentially makes that #45 loss a W. Maybe I'm wrong on this, but it should make sense as to why it didn't help WBL that much if KRACH handles this in such a way.***

MV on the other hand now has their best W become a L. I don't know the best team on their schedule that they beat before, but essentially that becomes a L in KRACH's eyes so-to-speak.

This is how it was explained to me by some experts some time ago. Maybe I misinterpreted what they were saying, but in the extreme case like MV (undefeated #1), it kind of makes sense as to why this happened as it did in KRACH.

***There's a bit more detail to this but I'm going to leave it out, for now, as it could complicate the discussion and really doesn't add much value to the high-level idea.

[sinbin]

I'll throw in my $0.02. I think that KRACH looks at the ratio of wins to losses (or winning % to 1- winning %). So, if a team is 22-0-1, the W/L ratio is 45.0 (22.5/0.5). If they lose, their ratio becomes (22.5/1.5) = 15.0, so they get cut down by 67%. The actual number cited below is 54%. Then, adjust by the change in MV's SOS. Then, consider the interaction of all teams and how every team's numbers change after every game, whether they play or not (all that iterative logistic regression stuff) and I think that 54% makes sense. In fact it's only because of MV's almost perfect record and that it is so late in the season that their rating changed so dramatically (the model is highly leveraged based winning %/fewest losses). It may not make perfect sense intuitively, but that's what the mathematical model gives us.

[ghshockeyfan]

I'll throw in my $0.02. I think that KRACH looks at the ratio of wins to losses (or winning % to 1- winning %). So, if a team is 22-0-1, the W/L ratio is 45.0 (22.5/0.5). If they lose, their ratio becomes (22.5/1.5) = 15.0, so they get cut down by 67%.

Slight adjustment to the math inputs based on KRACH having a phantom tie for all teams as part of its algorithm.

With that in mind - the before WBL record for MV in KRACH is 22-0-2 => W/L Ratio is 23/1 = 23. And, similarly, after WBL record is 22-1-2 => W/L Ratio is 23/2 = 11.5 => cut down by 50% (11.5/23). from there...

The actual number cited (earlier) is 54%. Then, adjust by the change in MV's SOS. Then, consider the interaction of all teams and how every team's numbers change after every game, whether they play or not (all that iterative logistic regression stuff) and I think that 54% makes sense. In fact it's only because of MV's almost perfect record and that it is so late in the season that their rating changed so dramatically (the model is highly leveraged based winning %/fewest losses). It may not make perfect sense intuitively, but that's what the mathematical model gives us.

The "adjustment" is what gets at the final ranking value and it's not very straightforward. I tried to get at this directly with my earlier post but it may be that the math route is best understood. Some find it easier to simply think of upsets as offsetting earlier weaker losses for the winner and earler better wins for the loser. This is all part of the adjustment phase as what's above is only considering one team without comparing that to everyone else for an actual ranking value.

[ghshockeyfan]

Updated 01/31 AM

[D6 Girls Fan]

I was told there would be no math.

[sinbin]

GHS, thanks. That explains one question I always had and that is how does KRACH account for teams with 0 losses and 0 ties, since you can't divide by 0? So, it makes the calculations somewhat inaccurate based on actual records, but since this is a model anyway, once you have enough data, it doesn't impact the results as much (except for the outliers).

P.S. D6, there will be a short KRACH quiz to award bonus points for the State Tournament You Pick 'Em challenge, so please pay attention.

[ghshockeyfan]

GHS, thanks. That explains one question I always had and that is how does KRACH account for teams with 0 losses and 0 ties, since you can't divide by 0? So, it makes the calculations somewhat inaccurate based on actual records, but since this is a model anyway, once you have enough data, it doesn't impact the results as much (except for the outliers).

Yep - you got it... I could probably remove the phantom tie now as I believe everyone has at least 0.5 wins and 0.5 losses - but I'll double check and - yes - slight impact but usually not enough to change anything too much once removed.

[ghshockeyfan]

I was told there would be no math.

LOL - I actually did when I read this!

[ghshockeyfan]

Updated 02/01 AM

[ghshockeyfan]

Updated 02/02 AM