Playoff possibilities

[jtwcornell91]

TUC=Team Under Consideration for the NCAA tournament.  This is any eligible D1 team with a record of .500 or above vs eligible D1 teams, or which receives an automatic bid by winning a conference tournament (not CHA).

[ugarte]

There is no "in/out" feature of TUC. There is no such thing as a TUC until the season is over.  Teams don't get "considered" until all of the games have been played.

Our willingness to obsess over phenomena like "what would happen if the season ended today" only creates the illusion that there is an "in/out" feature. Union's season ended yesterday. Not only ARE they not a TUC, they never were.

[jtwcornell91]

Well, I don't know what you can do about the strength of a team changing as the season goes on.  After all, ECAC teams that had the misfortune to play Colgate when they were hot have an advantage over those that played them earlier, but no one complains about that.

OTOH, both the "vs TUC" criterion and the "Last 16" criterion apply a sharp cutoff which gives some funny results (e.g., a team in a conference with a play-in game might be better off not getting a bye if it lets them erase a loss from their last 16 games).  But the reasonable alternatives, which would weight some games progressively more, are likely to be opposed by the NCAA on the usual grounds of being "too complicated". ::rolleyes::

As an example, one solution I've suggested (as a further enhancement to KPWR) would be to have a record-vs-stronger-teams criterion which included all of a team's games, but weighted them by the opponent's expected winning percentage vs an average team.  So instead of having a sharp cutoff, you'd gradually go from zero weight for the worst opponents to full weight for the best opponents.

For the last 16 criterion, you could do something like having the weight of each game be 93.75% of the weight of the following one.  (This is 15/16, and is chosen so that if a team plays an infinite number of games, the total weighted number of games in this criterion will be 16.)  So the last game of a team's season would count towards this criterion as a full game. the previous one as .9375, the one before as .87890625, etc.  As an example, here's how much each of Cornell's games last year contributed to their last 16 record and how much they would contribute to this sort of progressive-games criterion.

20001104 SH 5 Cr 3 NC  0.00  0.1268
20001110 Cr 0 Un 2 EC  0.00  0.1352
20001111 Cr 3 RP 2 EC  0.00  0.1443
20001117 Ha 1 Cr 1 EC  0.00  0.1539
20001118 Bn 0 Cr 2 EC  0.00  0.1641
20001121 Me 1 Cr 1 NC  0.00  0.1751
20001125 Ck 1 Cr 2 nc  0.00  0.1867
20001126 Ni 4 Cr 3 nc  0.00  0.1992
20001201 Ya 3 Cr 4 EC  0.00  0.2125
20001202 Pn 0 Cr 3 EC  0.00  0.2266
20001227 OS 5 Cr 6 nc  0.00  0.2418
20001228 Me 2 Cr 1 nc  0.00  0.2579
20010106 Qn 2 Cr 2 NC  0.00  0.2751
20010112 Cr 3 Vt 2 EC  0.00  0.2934
20010113 Cr 1 Da 4 EC  0.00  0.3130
20010118 Cg 2 Cr 2 EC  0.00  0.3338
20010120 Cr 4 Cg 3 EC  0.00  0.3561
20010126 Ck 1 Cr 2 EC  1.00  0.3798
20010127 SL 6 Cr 3 EC  1.00  0.4051
20010202 Cr 2 Bn 1 EC  1.00  0.4321
20010203 Cr 2 Ha 1 EC  1.00  0.4610
20010209 Cr 1 Pn 4 EC  1.00  0.4917
20010210 Cr 0 Ya 1 EC  1.00  0.5245
20010216 Da 1 Cr 1 EC  1.00  0.5594
20010217 Vt 2 Cr 5 EC  1.00  0.5967
20010223 Cr 2 SL 3 EC  1.00  0.6365
20010224 Cr 0 Ck 2 EC  1.00  0.6789
20010302 RP 2 Cr 1 EC  1.00  0.7242
20010303 Un 1 Cr 2 EC  1.00  0.7725
20010309 Pn 2 Cr 3 NC  1.00  0.8240
20010310 Pn 1 Cr 2 NC  1.00  0.8789
20010316 Cr 5 Ha 2 nc  1.00  0.9375
20010317 Cr 1 SL 3 nc  1.00  1.0000

[jtwcornell91]

Yes, but the sharp cutoffs mean that looking back and changing one or two seemingly irrelevant results can have a big impact on the selection criteria if it changes who's a TUC, in effect inflating the importance of those results.

[Al DeFlorio]

Technically true, apple.  

But the point is, whether a team finishes at/above .500 vs. below .500 can have significant impact on the rankings of others--because that team goes from "counting fully" to "not counting at all" in TUC.  And what difference does it really mean for Union to be .500 or .485 in terms of the their difficulty as an opponent.  It would not be inconceivable that Cornell would have a higher ranking today (whether that's true or not in this specific case is not the point--the point is it could happen) if they had lost to Union last night.  That's the problem with TUC.  One loss more or less for borderline teams and they either influence your TUC or they don't.  If Dartmouth loses two out of three next weekend they miss TUC by a game, and our TUC record likely goes up dramatically as a result.  It's that large step-function effect (quantum leap?) that I use the term "in/out" to describe.

Holy Cross is guaranteed to be a TUC while North Dakota may or may not end up as one, perhaps missing by one game.  Should a win over Holy Cross count for more than a win over UND?  It's possible for a team playing in a conference tournament consolation game to go in or out of TUC based upon the result of that meaningless-to-them game, so a win or loss in that game could flip around the TUC rankings for teams on the bubble.  

While it's true that any individual win or loss can tip the scales in any of the ranking factors, the granularity of the others (e.g., RPI, common opponents) is much finer and you don't get the big swings that a TUC in/out change can cause.

[Al DeFlorio]

Your point about the "last 16" criterion is valid, John, but I find it less objectionable than TUC because it's something a team influences directly--by winning or losing its games.   Cornell has played hard these last games to make its "last 16" as strong as possible.
 
Also, a team's record in the "last 16" is compared directly with every other team's, whereas TUC is affected by "third party" results which will move teams you've already played in or out of TUC status, possible having significant impact on your pairwise comparisons with other teams.

[ugarte]

Interesting. I like it. Do you have a similar theory for dealing with the TUC question?

I actually think the .500 criteria, while arbitrary, is a good one - but I disagree with the Findlay rule.  Schools that are in the process of moving to D-1 should be able to upgrade their NC schedule without negative consequences.  I could see why a team wouldn't want to give up qualifying games because it would be harmful to the conference (as it will be for the ECAC since Union games don't count for TUC).

[Greg Berge]

> Interesting. I like it. Do you have a similar theory for dealing with the TUC question?

The cleanest way to get rid of TUC would be to simply get rid of it.  The concept being captured is "games against quality opponents," but this is already captured by the schedule strength metrics.

I would also vote for getting rid of L16 and anything like it attempting to capture "recent results."  I just don't think it matters -- a season is a season, period.  Or perhaps we should weigh each conference game as 93% of the one following it?  I applaud John's effort at creating a much better indicator than L16, but I still don't agree that a recent result should matter any more than an early result.

[jtwcornell91]

But accounting for strength of schedule is not quite the same thing as having a criterion which rates a team's performance against good opponents without caring about their performance against poor ones.  The vs TUC criterion, like the tiebreakers in several leagues, rewards a team more for beating a good team and losing to a bad one than the other way around.

If you really want to be fair, you should just seed the NCAAs by KRACH and be done with it.  But, presumably motivated by the usual arguments and counter-arguments about head-to-head results (How can Cornell be seeded above Dartmouth in the ECAC playoffs when they swept us?), common opponents, "who's hot", and performance in big games which figure into smoke-filled room discussions and second-guessing of seeds, they established the current selection criteria as a sort of "tie-breaker" when the differences in RPI were too small to be significant.  Then this set of criteria got transformed from a tiebreaker to the method used to rank teams in the first place.

[Greg Berge]

The KRACH isn't "fair" -- it's just another set of criteria (and one which allegedly helps mediocre teams that happen to be in good conferences).

It may be "more fair" than PWR, but even that's questionable, and it ranks us worse, so screw it anyway.

[KeithK]

If we wan to be "fair", that is to give everyone a fair chance to get in based on performace against a set of known criteria without the volatility, etc. we should go to a system like Greg mentioned the other day: bids to conference champions only.  Then there'd be no arguments about which ranking system is fair or whatever...

[ugarte]

I agree with JTW  that it is not unfair to include in the selection process biases in favor of recent success and success against better teams.  Pairwise may not be perfect, but I don't think it is horrible.  The critieria can be adjusted, however.

I like the way JTW adjusts the criteria so that games are weighted according to when they were played and agree taht it is an improvement over the arbitrary cutoff of L16.

I am in favor of including a criteria like TUC for determining how a team has done against good teams in addition to RPI, H2H, "L16", and COpp.  The Holy Cross vs. NoDak issue is an important one though, and I think a way to resolve it is something like "Record against top 25 RPI" or something like that.

[ugarte]

Oh, give it up, King of Purity.  ::rolleyes::

[jy3]

can someone explain to me one thing, though. i was wondering if anyone has a reason why the last 16 games should weigh more than the other games. why should a win over holy cross in february be worth more in L16 (though this year not in strength of schedule, etc) than a win over michigan in december?
good teams should play well in their tourney? well doesnt a win plus a shot at an autobid reward that already?
just trying to provide food for discussion. i dont really have a position either way, just curious what u all think.
 ::nut::

[jtwcornell91]

Record against top 25 RPI would have some of the same sharp cutoff problems as the current "vs TUC" criterion.  A more gradual approach would be to produce a strong teams criterion in which each opponent would be weighted by some function that went smoothly from 0 for a winless, tieless team to 1 for an unbeaten, untied team.  One possiblity is winning percentage, of course, but this has the Quinnipiac-vs-NoDak problem.  I'd propose something like weighting by the expected winning percentage vs a team with an RRWP of .500.  (I.e., a KRACH of 100, if it's normalized properly.)