Around D-I tonight

[Al DeFlorio]

No, John, nowhere did I imply RPI is "eight times better."  You, in fact, incorrectly inferred that.  

But they clearly have a much better record, have beaten several "real" teams, and should be rated higher than UAA by any rational ranking system--and certainly not beneath them.

[jtwcornell91]

RPI has a better record against a weaker schedule, which is why we have to use some sort of model to extrapolate how they would each do if they played the same schedule.  You gave as support for "much better" the fact that UAA only has one win, which is a specious argument given all their ties.  UAA has taken a total of six points from teams of the caliber of the "real" teams RPI has beaten.  RPI has lost to the likes of Princeton (twice) and Colgate.  If you take all the results of both teams into account, it doesn't seem at all unreasonable to me that UAA's raking is slightly better than RPI's.

[Dart~Ben]

I'm of the opinion that all a team can do is win the games on the schedule. Yes, I believe a 25-9 MAAC team is more tournament worthy than a 19-15 WCHA team, especially if that 19-15 WCHA team is only .500 and about 5th place in conference play. I also believe non-conference SoS is more important than overall. You can control your non-conference SoS to some extent, you have no control over your conference schedule. If (hypothetically) Holy Cross went out and scheduled BC, Cornell, Michigan, and Minnesota among others and fared reasonably well, they shouldn't be penalized excessively for being in the MAAC.

And yes, this is a carried over from Hoops, where the mid-majors get the screw job every year due to the RPI and its inherent bias towards the power conferences.

[DeltaOne81]

I agree with Ben on this, for the most part, and actually meant to say something like that myself before it got late and I forgot :-)...

Well I don't know about his exactly numbers, I certainly feel a 16-7-1 MAAC team has done more than a 1-18-7 WCHA team, unless that WCHA team has played CC 26 times. Maybe the MAAC team hasn't played as many teams, and based on their schedule you can say they are about the same, but it's not entirely the fault of the MAAC team that they played the lesser team. As Ben said, you can only beat who you play.

On a related sidenote, the WCHA plays more in conference games (28) than any other conference, so their schedule is the most insulated, possibly leading to exagerrations in S.O.S's. I'd love the see the selection committee deny a WCHA team a seeding for the reason, the rule that was supposed to be anti-MAAC and anti-CHA.

So I guess I agree with a Dartmouth fan  ::twitch:: ... speaking of which, whaddaya say your boys come down here tomorrow, Ben, instead of waiting another whole damn week :-D.

[bigred apple]

Ben and Fred, you can only beat who you play, but you can only play who you schedule.  If the MAAC remains a ghetto of mediocrity, they should not be taken seriously as national players by objective ranking systems or subjective observers.  

Stephen F. Austin University is running away with the Southland Conference and could conceivably finish the season 29-3. When March Madness comes around should I care?

[Greg Berge]

> but you can only play who you schedule.

But you can only play who schedules you.

[Al DeFlorio]

John, we'll just have to disagree.  Your arguments above about who's strong and who isn't are based on how they're ranked in these flawed ranking systems, so you're making in effect a circular argument.

[jtwcornell91]

DeltaOne81 '03 wrote:

As Ben said, you can only beat who you play.

Yes, but you have to actually beat them.  Quinnipiac is 0-3 against a spectrum of non-conference opponents (from Maine to Lake State) and 16-4-1.  Not even considering the three non-conference losses, they're still losing to MAAC teams at a clip of 3 for every 11 wins.  Considering the MAAC's performance in non-conference games, that's not an impressive record.

On a related sidenote, the WCHA plays more in conference games (28) than any other conference, so their schedule is the most insulated, possibly leading to exagerrations in S.O.S's. I'd love the see the selection committee deny a WCHA team a seeding for the reason, the rule that was supposed to be anti-MAAC and anti-CHA.

Except that the guideline is not "insulated schedule", it's "competitive equity" based on "overall conference RPI".  Insulated schedules are the reason why strength of schedule based on opponents' winning percentage can be dragged to .500.  Considering that the WCHA has a winning record against every other conference and an overall interconference record better than all but Hockey East, insularity of schedule is more likely to hurt WCHA teams' strength of schedule.

The whole idea of proposing KRACH as an alternative to RPI is that it doesn't have this isolated-schedule-drags-your-SOS-to-.500 problem, so the committee doesn't need to have a special rule and make a subjective judgement call to overcome it.  (When it's obvious, like Quinnipiac in 1998 and 1999, this is not a big problem, but in the case of Niagara in 2000, where we knew they were not as good as their PWR implied, but still good enough to be in the running for the tournament, there was no way of quantifying the correction, and it was obvious that they would get the last at-large bid regardless of how their final few games played out.)

[jtwcornell91]

Al DeFlorio wrote:

John, we'll just have to disagree.

Nice rhetorical trick of ostensibly ending the argument peacefully and then firing a parting shot that makes me look wrong if I don't respond to it. ::rolleyes::

Your arguments above about who's strong and who isn't are based on how they're ranked in these flawed ranking systems, so you're making in effect a circular argument.

Okay, first of all, you still haven't said what the supposed flaw in KRACH is, other than that a team with a good record can be ranked below a team with a bad one.  Any system which accounts for strength of schedule has to to allow for this possiblity.  (In contrast, I can list the flaws in RPI: beating a bad team can hurt your rating, an extended round-robin tournament among the top three teams will lower all of their ratings, teams with good records and bad RPIs are still considered strong opponents by the strength of schedule measure.)

As far as circularity, it's true that a justification of a particular team's rating that will fit into a forum posting will only show that everything is self-consistent, but the rankings don't exist in a vacuum.  They're all determined together from all the results, and there's only one set of ratings which is consistent with everyone's results.  And I think the recursion of defining the strength of an opponent with the rankings themselves is essential if you're going to judge the strengths of opponents who themselves play vastly different schedule.  In broad strokes, if you don't believe KRACH to tell you the MAAC teams Quinnipiac plays are on average much worse than the WCHA teams UAA plays, consider the MAAC's overall non-conference records of 5-18-3 against the CHA and 2-34-4 against the other four conferences.  Those are the results that contribute strongly to the low KRACH ratings of all those MAAC teams, and thus also to a Quinnipiac team that wasn't capable of winning 4/5 of their games against them, and lost all three times they played anyone else to boot.

[Greg Berge]

I will occasionally try to follow the technical aspects of the ranking conversation until something glittery in the corner of my peripheral vision distracts me for a moment and then -- what was I saying? ::help::

But: is it true that KRACH will never penalize you for winning and never reward you for losing?  It's a value judgment (what non-trivial statement isn't?), but that should be one of the 3 basics of a ranking system:

1. Never penalize you for winning and never reward you for losing.
2. Reward you more for beating a better* team.  Penalize you more for losing to a worse* team.%
3. Eliminate as much as possible of the circularity inherent in the judgments of better and worse.

* To my untrained# logical eye there always has to be some circularity.  If there wasn't and you had an objective standard for better or worse than just chuck the whole ranking and use that. :-)

# No, you may not mention Godel numbers, John.

% Maybe.  Or maybe a loss is a loss is a loss, and the rankings should emphasize wins and ties, period.

[Al DeFlorio]

John, you always drag in the MAAC comparison, which is not the point.  The problem is, in ensuring that MAAC teams fall to the bottom, both the "new" RPI and the KRACH algorithms overrate bad teams in good conferences, which is my complaint.  The "insularity" issue has now been turned on its head in RPI.


Okay, first of all, you still haven't said what the supposed flaw in KRACH is, other than that a team with a good record can be ranked below a team with a bad one. Any system which accounts for strength of schedule has to to allow for this possiblity.


You, unfortunately, exaggerate my opinion--a typical JTW "rhetorical trick," by the way.  It's a question of degree.  The current implementations of both RPI and KRACH simply go too far in giving credit for strength of schedule.  Low-end teams in the WCHA, in particular, are overrated as a result.  


In contrast, I can list the flaws in RPI: beating a bad team can hurt your rating, an extended round-robin tournament among the top three teams will lower all of their ratings, teams with good records and bad RPIs are still considered strong opponents by the strength of schedule measure.)

Your logic flow implies--inaccurately--that I'm somehow arguing for RPI over KRACH while you're defending the honor of the latter.  Where have I ever said RPI was good?  Or better than KRACH?  This year RPI is worse than ever, IMHO.  Any algorithm that makes Michigan Tech a "team-under-consideration"--based on what they've done so far this year--has got to be flawed.  Like you, I believe KRACH is better than RPI, but, as the heading of my posting above says, I believe KRACH is flawed, too, in sweeping wretched records under a strength-of-schedule carpet.

[Al DeFlorio]

Greg wrote:

Or maybe a loss is a loss is a loss, and the rankings should emphasize wins and ties, period.

This is a point I go back and forth on, and am starting to lean toward the side expressed in your statement above, Greg.  

Barnstable High School could lose just as easily to Colorado--the College or the Avs--as to Fairfield, and it isn't clear to me that they should get more credit--or less penalty--for the former.  Either way, they're still Barnstable High School--and not competitive at any of those levels.

One would have to take into consideration the fact that team A might play 40 games and team B 30, so team A would have more chance to pile up wins and ties.

My sense is that the NCAA has recently done a variation on this for the lax tournament.  If you weren't an automatic qualifier and you didn't have a win against any of the top four or so teams, you didn't make it.  Cornell made it last year--despite losses to Princeton, Brown, and Georgetown, because it beat Syracuse.  Hofstra had no such win and was left out, to much gnashing of teeth, despite an identical record and a one-goal loss to top-seed JHU.  This approach is easier to implement, of course, in a sport with typically 12-13 game schedules rather than 30-40.

[jtwcornell91]

Greg wrote:

is it true that KRACH will never penalize you for winning and never reward you for losing?

Yes.  I decided to actually sit down and prove that yesterday.  I'm writing it up, but I need to tighten the proof that the inverse of a particular matrix has only positive elements.  (Technically speaking, my proof only works when everyone's KRACH is already finite, but that's always true by the time we start talking about KRACH anyway.  Plus I can see in rough terms why it must be true even in pathological situations, although in some of those cases a victory will have no impact on the ratings.)

It's a value judgment (what non-trivial statement isn't?), but that should be one of the 3 basics of a ranking system:

1. Never penalize you for winning and never reward you for losing.
2. Reward you more for beating a better* team.  Penalize you more for losing to a worse* team.%
3. Eliminate as much as possible of the circularity inherent in the judgments of better and worse.

* To my untrained# logical eye there always has to be some circularity.  If there wasn't and you had an objective standard for better or worse than just chuck the whole ranking and use that. :-)

# No, you may not mention Godel numbers, John.

% Maybe.  Or maybe a loss is a loss is a loss, and the rankings should emphasize wins and ties, period.

Conditions 1 and 2 are objective, and KRACH satisfies them both.  (RPI satisfies condition 2 but not condition 1.)

The sentiment expressed in footnote % is the basis of HEAL and RHEAL, which obey 2a but not 2b.

The meaning of condition 3 is ambiguous and at odds with footnote *.

Another condition which could be added is: if you apply the rating system to teams playing a balanced round-robin schedule, you will always get the same ordering as if you used straight winning percentage.  KRACH and RPI obey this condition, but HEAL and RHEAL (and PWR) do not.

Actually, Gary Hatfield wrote a paper a few years ago where he defined a set of desirable properties for a ranking system and proved that no system could satisfy them all.  IIRC, one of those properties was that the order in which two teams are ranked should not change if neither of them plays.  Any system that uses strength of schedule is doomed to fail there.

See
http://lists.maine.edu/cgi/wa?A2=ind9903&L=Hockey-L&P=R17130&I=-3
http://lists.maine.edu/cgi/wa?A2=ind9903&L=Hockey-L&P=R17906&I=-3
for more.

FWIW, I've never heard of Gödel numbers.  I'm a physicist, not a mathematician.  (Dammit, Jim!)

[DeltaOne81]

I think effectively what Al is trying to say (before his anger gets the better of him :-) ) is that UAA is a poor team in a good conference, who would easily be poor enough to compile just as bad a record in a poorer conference, but the fact that they happen to loose to good teams, gives them a major benefit.

To make a concrete (exagerrated) example, let's say there's some heaven-given rating system that tells us that team X is ranked 50 (of 60).

Now let's put them in a 10 team conference with teams 1 -> 9 in the nation. And they compile a 1-15-2 record playing each twice (because, heck, everyone gets lucky sometimes in hockey). Now let's put them in a conference with 52->59. And in conference play they go 14-3-1 . Neither of these are unreasonable records for a #50 team in the supposed conference.

Now, when we compare situation 1 to reality, we see that the team would be ranked even higher than UAA, having played better teams. And in scenario 2, they'd be ranked even worse than QU, having played even worse teams. But these are reasonable situations for the same exact team to be in, and reasonable results for them to have.

Who you play is too important. SOS is too important, I know there's no direct weight for SOS, but obviously imbedded in KRACH. Yes, KRACH is better than RPI overall, but it still has problems.

And let me add one new aspect to this discussion... I think the only truly fair rating system would have to take winning/losing margin into account. It's all good to say that QU has an 0-3 OOC record, but they lost 2-1 to LLSU, 2-1 to NU, and 2-1 TO MAINE! It's not like they had no chance and were blown out of the water. They lost each of those games by one! Had they been totally outclassed OOC, you *might* have a point. But against a long-running #1 in the country, they were one goal shy! That deserves credit, IMNSHO.

[bigred apple]

I'm at a loss here, Al.  JTW is consistently the most humane and patient poster on this forum.  With all due respect to everyone else here, I don't think that there is a close second.  That he hasn't thrown up his hands and refused to continue to engage you in a subject on which his expertise appears to vastly outpace yours (and probably even more vastly outpaces mine - my eyes glaze over at a lot of this) is a credit to him.

I know you will accuse me of infantilizing your opinion, (and you may be right), but I have no other way to describe your opinion.  Your objection to the ranking systems appears to be no more sophisticated than "None of the statistical algorithms jibe with my preconceived notions of the meaning of a team's actual record and relative conference strength, and so they are all hopelessly flawed."  You never seriously address the possibility that the worst team in the WCHA is actually better than a middle of the pack ECAC team.

While I was typing this out I decided to read the rest of the posts, and came across your point about Barnstable High School, and it has the patina of legitimacy to it, but, as JTW has pointed out, UAA is not 0-infinity, they have 8 ties in a very good conference.  The ties count enough that it is not fair to compare them to a team that would lose to everyone, but chooses to lose to only the very best (as Fred hypothesizes on a different post).

I don't understand the nuts and bolts statistics to tell you if RPI and KRACH are internally consistent or accurate, but I can certainly tell you that JTW has much the better of this argument.

I haven't even hit "post" and I think I regret it already.