RPI primer (brackets for dummies): Why #2/#3 Cornell may seed lower

[billhoward]

Thank you, experts, for explaining. There clearly were a number of Ivy-educated RPI-TUC dummies out there who were able to come out of the closet.

[Will]

[Q]jy3 Wrote:

this is something that i have mentioned for months but no one seems to care. things are quite tight in bunches in the rankings...no one seems to think that who gets the bids from aha and cha will change the rankings, but the two teams above doing so would add a win vs tuc for cornell. that would help things[/q]

As far as Record vs. TUCs goes, in addition to helping us, Canisius winning the AH tournament helps North Dakota; Sacred Heart winning the AH tournament helps Ohio State, Colgate, and Vermont.

[RedAR]

ok, let me chime in.

why is there a need for TUC at all? wouldn't it make more sense if wins, ties, and losses against all teams should count? wouldn't including all teams somewhat stablize the pwr (ie. brown or slut can't drop out of being a TUC).?

my guess is that it is much more computationally intensive to include all the teams, but then again, any modern desktop computer should be able to run the calculations without breaking a sweat.

what am i missing?

[Dart~Ben]

[Q]Will Wrote:
[E]ach team basically wants all its wins to come from TUCs and all its losses to come from non-TUCs.  Put more simply: wins against TUCs, good; losses to TUCs, bad.[/q]

AKA the Dartmouth method.
:-D

[Will]

That would mean a win against Colorado College would be worth the same as a win against American International.  As much as I hate the Cornell detractors using the weak schedule argument to say that Cornell isn't a real contender, I have to say that there is a real difference there.  It's not a matter of computing power.

[Liz \'05]

[Q]Will Wrote:

 As far as Record vs. TUCs goes, in addition to helping us, Canisius winning the AH tournament helps North Dakota; Sacred Heart winning the AH tournament helps Ohio State, Colgate, and Vermont.[/q]

[attempt at understanding PWR without actually looking up anything]
Which means...we're rooting for Sacred Heart, right?  Because we win comparisons with Colgate and Vermont that won't be affected by an additional TUC win on their parts; also, the better the ECAC teams are, the better we look (hence, secondary rooting for ECAC teams)?  I have no idea how North Dakota or Ohio State would fit in here...
[/attempt]

Next weekend, in the "other scores" thread that seems to have appeared every game day recently, can someone post a (consolidated) list of teams that I want to win and why?  I admit to getting all confused, but there seem to be a lot of you out there that understand it all and can create such a list fairly easily.  
 ::help::

[RedAR]

but doesn't strength of schedule take care of weighting wins against stronger teams more than weaker teams?

also, does this mean that a win against slut or brown is pretty much equivalent to a win against DU or CC?

[DeltaOne81]

[Q]Liz '05 Wrote:
Next weekend, in the "other scores" thread that seems to have appeared every game day recently, can someone post a (consolidated) list of teams that I want to win and why?  I admit to getting all confused, but there seem to be a lot of you out there that understand it all and can create such a list fairly easily.  
  [/q]
Check yesterday's "other scores" thread. JTW and I have some suggestions for next weekend at the bottom

RedAR, yes, it does, yet another flaw of the TUC category. It should probably be weighed within it. Also, to be fair, the same applies to TUC. Someone who goes 2-0 against Princeton and 0-1 against CC - and another team goes 1-0 against Princeton and 0-1-1 against CC - well, that's 2-1 versus 1-1-1 - so the former wins.

Yes, there are issues, definitely.

[Dart~Ben]

[Q]RedAR Wrote:

 but doesn't strength of schedule take care of weighting wins against stronger teams more than weaker teams?

also, does this mean that a win against slut or brown is pretty much equivalent to a win against DU or CC?[/q]

1st question: Because the RPI is a very flawed system and the committee knows this. The RPI was not designed to pick a field all on its own, merely to provide a tool for a committee to use.

2nd question: yes and no. In the case of an ECAC team, a win over DU or CC would be worth more because as a non-conference game vs. a top 15 team (as ranked by the RPI), it would be worth a bonus (of varying amount depending on whether it was home/road/neutral). But if you're talking solely about the TUC comparison, then yes, they would be the same.

[Jacob '06]

[Q]RedAR Wrote:

 but doesn't strength of schedule take care of weighting wins against stronger teams more than weaker teams?

also, does this mean that a win against slut or brown is pretty much equivalent to a win against DU or CC?[/q]

RPI weights strength of schedule, albeit poorly as most people on here believe. For the tuck category of PWR, a win against slut or brown is equivalent to a win against DU or CC if all of them are TUCs. Two different components of the comparison treat them differently. I personally would go with the KRACH only system that properly weights strength of schedule and does not have arbitrary cutoffs for comparisons.

[DeltaOne81]

[Q]Dart~Ben Wrote:
1st question: Because the RPI is a very flawed system and the committee knows this. The RPI was not designed to pick a field all on its own, merely to provide a tool for a committee to use.[/q]
Not sure about this one. I think it was designed to be the main factor, if not the only factor. Luckily, few sports use it that way, and luckily hockey is smart enough to use it even less.

[jtwcornell91]

[Q]Dart~Ben Wrote:

 [Q2]RedAR Wrote:

 but doesn't strength of schedule take care of weighting wins against stronger teams more than weaker teams?
[/Q]
1st question: Because the RPI is a very flawed system and the committee knows this. The RPI was not designed to pick a field all on its own, merely to provide a tool for a committee to use.
[/q]

Before 1996, it was used to pick the field, with the other selection criteria used as a "tiebreaker" if two teams were close in the RPI.

AFAICT the reason to have the other selection criteria is to satisfy people who say "How can my team be seeded lower when they beat good teams/beat that team/beat teams that team lost to/are on a winning streak".

[jtwcornell91]

[Q]Will Wrote:

 That would mean a win against Colorado College would be worth the same as a win against American International.  As much as I hate the Cornell detractors using the weak schedule argument to say that Cornell isn't a real contender, I have to say that there is a real difference there.  It's not a matter of computing power.[/q]

No, it would mean a win against CC and a loss to AIC would be worth the same as a loss to CC and a win against AIC.

[elliotb]

The TUC business is essentially a "weighted" winning percentage, where a game gets a weight of 1 if it's against a TUC and a weight of 0 otherwise. A natural alternative, which would eliminate the problem of teams popping in and out of TUC status would be to make the weights a continuous function of the opponent's RPI.

On the issue of KRACH...people talk about it as if it were the greatest thing since sliced bread, but it's still an estimate of the "true" rankings. Like any other estimate, it is subject to the lack of information available for comparing certain pairs of teams -- like Dartmouth and Wisconsin, as discussed in Adam Wodon's column. Since KRACH fits a statistical model, there should be variance estimates that go with things like the KRACH rating. It seems to me the variance of a team's KRACH rating would be a good measure of how volatile its position in the rankings is. Are those available anywhere?

- Elliot

[LarryW]

Elliot, this is something I've been idly (and by idly, I mean having done no actual work on) thinking about over the last few years.  I once tried to at least caluclate a covariance matrix for KRACH, but failed.  To measure a variance requires you to define the extent to which the initial knowledge is imperfect.  But, to what extent is the W-L-T(1-0-0.5) info of a given game imperfect?  20%, 10%, does it depend on the score?  There's a whole new bunch of weighting constraints to work up.

Still such a matrix would be very interesting for other reasons, it would identify the most "important" games of the season, and I'm curious how many there are and how much more important are non-conference games than intra-conference ones?