protoKRACH

Including games of 2006 October 27:

...FIGHT!

Sorry to sound ignorant, but can you link to a description of how to read that chart? I read the KRACH background on TBRW, but maybe I'm too hungover to apply the knowledge.

Bah... my attempted explanation was getting garbled so I'll let John write it. Short version - there aren't enough games to link all teams in one ranking. Within a bubble you can rank. If two bubbles are connected by an arrow, all of the teams in the higher bubble are all ranked higher than all in the lower bubble. But you can't say anything to compare some teams. Example; we can't say whather COrnell is better or worse than Maine.

Keith's short explanation just about says it. The one thing to note is that teams in a bubble on the "higher" side of an arrow are "infinitely better" than teams in the "lower" bubble. E.g., Cornell's HHWP vs Merrimack is 1.000 at the moment.

Oh, and the two numbers adjacent to each team's abbreviation are the "group KRACH" (only valid for comparison with other teams in the same bubble) and the predicted round-robin winning percentage (RRWP) with all undefined HHWPs (e.g., Cornell vs Clarkson) treated as .500.

That's a very interesting way to present the situation. Thank you.

David Harding
That's a very interesting way to present the situation. Thank you.

Almost entirely meaningless at this point if what you want to know is who is really the better team. But in an abstract mathematical sense it's pretty cool.

Last night's results really consolidated things:

Now that most teams are in one group, we can almost quote a "traditional" KRACH. The one thing we lose in this table is that Maine's infinite rating is infinitely higher than Minnesota's, but they're both incomparable with Cornell's and Yale's. (Although if you look closely you can actually infer that from the RRWPs.)

1. Maine         (6-0-0, KRACH=∞, RRWP=.966)
2. Cornell       (2-0-0, KRACH=∞, RRWP=.957)
3. Yale          (2-0-0, KRACH=∞, RRWP=.957)
4. Minnesota     (6-1-0, KRACH=∞, RRWP=.948)
5. Mass-Amherst  (2-1-1, KRACH=27112, RRWP=.861)
6. Clarkson      (4-1-1, KRACH=15457, RRWP=.834)
7. Boston Coll   (4-1-0, KRACH=15104, RRWP=.833)
8. North Dakota  (5-3-0, KRACH=12457, RRWP=.822)
9. Michigan Tech (5-1-0, KRACH=11739, RRWP=.819)
10. Lake Superior (4-2-0, KRACH=11695, RRWP=.818)
11. Notre Dame    (5-1-0, KRACH=9243, RRWP=.804)
12. Ohio State    (2-4-0, KRACH=8849, RRWP=.802)
13. Northern Mich (4-3-1, KRACH=6696, RRWP=.784)
14. Wisconsin     (3-3-2, KRACH=6421, RRWP=.782)
15. New Hampshire (2-2-0, KRACH=4299, RRWP=.755)
16. MSU-Mankato   (2-4-0, KRACH=2152, RRWP=.707)
17. Vermont       (2-2-1, KRACH=1173, RRWP=.662)
18. St Cloud      (2-2-0, KRACH=1090, RRWP=.657)
19. Minn-Duluth   (2-2-2, KRACH=941.9, RRWP=.646)
20. Miami         (6-2-0, KRACH=635.6, RRWP=.614)
21. AK-Anchorage  (2-2-2, KRACH=565.4, RRWP=.605)
22. Denver U      (4-4-0, KRACH=551.9, RRWP=.603)
23. Michigan      (4-2-0, KRACH=480.2, RRWP=.592)
24. NE-Omaha      (3-1-2, KRACH=444.0, RRWP=.586)
25. Northeastern  (2-3-1, KRACH=360.0, RRWP=.569)
26. Boston Univ   (2-1-1, KRACH=328.9, RRWP=.562)
27. Mass-Lowell   (2-2-2, KRACH=328.3, RRWP=.562)
28. CO College    (3-4-1, KRACH=315.7, RRWP=.558)
29. RPI           (1-1-2, KRACH=292.8, RRWP=.553)
30. AK-Fairbanks  (4-1-1, KRACH=271.0, RRWP=.547)
31. Dartmouth     (1-0-0, KRACH undefined, RRWP=.509)
32. Quinnipiac    (2-2-1, KRACH=158.6, RRWP=.506)
33. Harvard       (0-1-0, KRACH undefined, RRWP=.491)
34. Colgate       (3-2-1, KRACH=123.6, RRWP=.489)
35. Union         (2-1-2, KRACH=57.46, RRWP=.438)
36. Niagara       (3-4-1, KRACH=18.10, RRWP=.362)
37. Mich State    (3-1-0, KRACH=16.62, RRWP=.356)
38. Air Force     (3-5-0, KRACH=13.19, RRWP=.339)
39. Bentley       (2-2-1, KRACH=11.17, RRWP=.327)
40. Western Mich  (2-4-0, KRACH=10.76, RRWP=.324)
41. Ferris State  (3-5-0, KRACH=7.680, RRWP=.298)
42. Bowling Green (2-3-1, KRACH=7.666, RRWP=.298)
43. Robert Morris (1-3-0, KRACH=7.223, RRWP=.293)
44. Bemidji State (0-3-1, KRACH=6.034, RRWP=.279)
45. RIT           (3-3-1, KRACH=4.056, RRWP=.247)
46. Princeton     (0-1-1, KRACH=3.724, RRWP=.241)
47. Providence    (1-4-1, KRACH=3.652, RRWP=.239)
48. St Lawrence   (2-3-0, KRACH=2.947, RRWP=.222)
49. Brown         (0-0-1, KRACH=2.313, RRWP=.203)
50. Merrimack     (1-4-1, KRACH=2.313, RRWP=.203)
51. AL-Huntsville (2-5-1, KRACH=1.608, RRWP=.176)
52. Holy Cross    (2-3-0, KRACH=1.581, RRWP=.175)
53. Sacred Heart  (2-3-1, KRACH=1.125, RRWP=.152)
54. Army          (3-2-1, KRACH=1.014, RRWP=.145)
55. Canisius      (1-6-0, KRACH=.6895, RRWP=.121)
56. Wayne State   (1-5-0, KRACH=.5535, RRWP=.109)
57. Mercyhurst (2-4-0, KRACH=.5081, RRWP=.105)
58. Connecticut   (1-5-0, KRACH=.2232, RRWP=.070)
59. American Intl (0-5-0, KRACH=0, RRWP=.017)

Er, I know Daylight Saving Time just ended and all, but it's still October, John.

Beeeej
Er, I know Daylight Saving Time just ended and all, but it's still October, John.

October is when the group relationships are most interesting. Everyone's KRACH is finite by late November, long before the ratings make a whole lot of sense.

Just out of curiosity, what are you using to generate those images, John?

Will
Just out of curiosity, what are you using to generate those images, John?

GraphViz, specifically the perl interface GraphViz.pm 2.02.

Err, try again...

Re: protoKRACH including games of 2006 Nov 28

Molly
Err, try again...

Re: protoKRACH including games of 2006 Nov 28

Oops, thanks.

This was mentioned on the polls thread from last week. Is RIT included in the above calculation since they're still not eligible for NCAA selection? There's an "RT" in the middle of the pack, but I don't know which team that is.

For that matter, is there a canonical listing of abbrev->school anywhere?

Kyle

Yeah, RIT is included because I haven't bothered to remove them from the list.

krose
For that matter, is there a canonical listing of abbrev->school anywhere?

What, are they not obvious?

They're my standard 2-letter abbreviations, so you can find them all in the team list at:

[slack.net]

Good to see who's at the top and bottom of this. On the flipside, one result next Friday could give everbody except AIC a finite KRACH.

Hopefully everyone besides us and AIT have a finite KRACH by Tuesday night...

KeithK
Hopefully everyone besides us and AIT have a finite KRACH by Tuesday night...

Well, Yale won't.

jtwcornell91

KeithK
Hopefully everyone besides us and AIT have a finite KRACH by Tuesday night...

Well, Yale won't.

Details, details....

KeithK
Hopefully everyone besides us and AIT have a finite KRACH by Tuesday night...

How will Harvard's (inevitable) loss to BC prove that they are worse than AIC? Not that I doubt it, mind you...

I thought it was a given that KRACH can't compare 2 undefeated-and-untied teams or 2 winless-and-untied teams. To quote the master:

Ken Butler
The above works perfectly well as long as every team has gained at least one point and dropped at least one: in that case, it is always possible to find a supposed "rating" for each team that is too high (expected > observed) or too low (expected < observed), and thus the correct rating for the team is somewhere between the two. For a team that has won all its games, the story is different, however. Suppose our team X is 3-0 -- 3 observed wins; the expected number of wins is the sum of 3 probabilities, each of which is less than 1, so that the expected number of wins is always less than 3. No matter how big a rating you propose for team X, you can never make the observed and expected wins equal. The same is true in reverse for a team that has lost all its games; only a rating of 0 will produce a zero expected number of wins.

Robb

KeithK
Hopefully everyone besides us and AIT have a finite KRACH by Tuesday night...

How will Harvard's (inevitable) loss to BC prove that they are worse than AIC? Not that I doubt it, mind you...

Calling jtw... what does Harvard's stunning failure to lose mean?

All the HHWPs are defined now. If you like, you could say Cornell's KRACH is infinity-squared, Yale's is infinity, and AIC's is zero.

Yale will become defined when (a) Cornell loses or (b) they lose to a team that isn't undefeated, right?

So I figured I'd abuse the protoKRACH to trty to assess the "best confwerence" (really conference ranking) argument that Ari brought up in another thread. Now that all of the HHWPs are defined, I figued I could average the HHWP for each conference and se how they rank up. In other words, if all 59 teams played H2H against every other hwo would each conference Win % stack up. Assuming that I've decoded Whelan's abbreviations correctly (I couldn't find the cross reference chart quickly and I wasn't going to check the game schedule to confirm) I came up with the following:

WCHA  .675
HEA   .608
CCHA  .583
ECAC  .545
CHA   .323
AHA   .153

So by this measzure the ECAC is still in fourth place among the conferences right now. We trail the CCHA by a bunch of points, but it's quite clear in my mind that we're in the group with the top 4, rather than in a separate middle grouping.

Onward and upward.

KeithK
Assuming that I've decoded Whelan's abbreviations correctly (I couldn't find the cross reference chart quickly and I wasn't going to check the game schedule to confirm)

On that note, would it be possible to change Harvard's abbreviation to Sk, just to avoid confusion?

Thanks.

ugarte
Yale will become defined when (a) Cornell loses or (b) they lose to a team that isn't undefeated, right?

Correct, but replace "lose" with "lose or tie". (Except of course if Cornell and Yale win all their games until they play each other again.)

KeithK
So by this measzure the ECAC is still in fourth place among the conferences right now. We trail the CCHA by a bunch of points, but it's quite clear in my mind that we're in the group with the top 4, rather than in a separate middle grouping.

Onward and upward.

Stupid numbers taking the steam out of the ECAC pride train. Talk about a kick in the KRACH. Bruhahahahahaha

Come on, John. Do you have a plane to catch or something?

ugarte
Come on, John. Do you have a plane to catch or something?

They're actually listed here - [www.collegehockeynews.com]

Avash '05

ugarte
Come on, John. Do you have a plane to catch or something?

They're actually listed here - [www.collegehockeynews.com]

Jerk.

ugarte

Avash '05

ugarte
Come on, John. Do you have a plane to catch or something?

They're actually listed here - [www.collegehockeynews.com]

Jerk.

Typical.

I love the Strength of Schedule column. It's so completely meaningless at this point. Our schedule is currently ranked #13 in the country. Wow, RIT and RMU were tough!

KeithK
I love the Strength of Schedule column. It's so completely meaningless at this point. Our schedule is currently ranked #13 in the country. Wow, RIT and RMU were tough!

It's also kind of a cheat, since the weighting factor depends on your own rating, and therefore two teams with the same schedule won't generally have the same SOS. (This sounds like a problem, but that SOS number isn't how the rating is fundamentally defined.)