Assuming Cal Tech goes winless, the percentage of paths through the remainder of the season that results in each team making the conference tournament are:
Redlands: 98%
PP: 89%
La Verne: 89%
Oxy: 65%
Chapman: 43%
Whittier: 12%
CMC: 3%
CLU: 2%

Of course, not all paths are equally likely, but this gives some idea about who is going to need help and how much they will need. 

Quote from: Purple Heys on April 13, 2015, 08:40:53 PM

Quote from: Richard Hamstocks on April 13, 2015, 06:33:19 PM

Quote from: Purple Heys on April 13, 2015, 06:06:39 PM
I am not a trophy for everybody type, but, I thought it would be fun to extend it...imagine a nothing to lose Cal Tech getting a playoff taste and in one parallel universe of infinite parallel universes, they upset the first place team...Not saying it ever would happen, but you can't say it can't ever happen.

I bet some of those boys at Cal Tech could write the mathematical proof to that...

This is just the (second) Borel-Cantelli lemma.

...but not to be conflated with the special case infinite monkey theorem.

No, same result: http://en.wikipedia.org/wiki/Infinite_monkey_theorem
One of the earliest instances of the use of the "monkey metaphor" is that of French mathematician Émile Borel in 1913...

Quote from: Purple Heys on April 13, 2015, 06:06:39 PM
I am not a trophy for everybody type, but, I thought it would be fun to extend it...imagine and nothing to lose Cal Tech getting a playoff taste and in one parallel universe of infinite parallel universes, they upset the first place team...Not saying it ever would happen, but you can't say it can't ever happen.

I bet some of those boys at Cal Tech could write the mathematical proof to that...

This is just the (second) Borel-Cantelli lemma. 

Quote from: CrashDavisD3 on April 13, 2015, 12:20:21 AM
I like the idea of pool play for the Round Robin phase. Incentives to be a 1 seed. Top 4 conferences records go to Conference tourney.

1,8,7,6 in Pool A

2,5,4,3 in Pool B

Everyone plays 9

And incentives to be the 6th seed! Why does Cal Tech play twice as many games as everyone else in this set up?

I was curious how the different schedules for the round robin would shake out this year with the rather strange 6 team race we are seeing this year, and if there were any clear advantages for different placings (and perhaps some arbitrage opportunities for teams to throw games based on "bracketology").  Clearly, conference schedules are now unbalanced since Chapman joined the conference.  Ultimately, I'd prefer for teams that are bubble teams for the conference tourney to all play each other, but this year, that would require a round robin of 5 games (with 1-6 all playing each other once) and that isn't in the cards.  I wasn't convinced that the set up would result in fairness this year, but it's actually not bad.  I'll assume the final weekend plays out as follows (PP sweeps, CLU sweeps, ULV wins 2, WC wins 2).  The final league standings then are a 3 way tie for first (CLU, ULV, PP in that order based on tie breakers each with 7 losses), UR in 4th with 8, CU with 9 in 5th and Oxy in 6th with 10. 
Based on this outcome, we have the following, with my metric being total conference wins over the 4 teams played in the round robin:

1. CLU vs 33 total SCIAC wins
2. ULV vs 39
3. PP vs 43
4. UR vs 38
5. CU vs 42
6. Oxy vs 46

You might think "not bad".  Clearly, this metric is somewhat arbitrary and open for conversation.  It's unlikely that in a given year, one could construct a round robin schedule such that every team has an equal value.  If a metric could be agreed on, I'd feel better about a round robin assignment of the form: consider all possible round robin schedules, choose the one that has the least variation in the chosen metric, subject to it being monotone in the ranking (finishing the "regular season" with the better record should be worth something). 
If you buy this metric, there is motivation for PP to go 1-2 vs Cal Tech, but I don't think it's terribly strong. 
The real problem here is that rather than let these teams fight it out for the final 4 spots over 4 games, it's actually done over two games.  Every one of the top 6 teams plays (exactly) two games over two of CMS, CIT or WC (who admittedly have proven to be dangerous).  This seems antithetical to what the conference tourney is set up to do, which is to let it play out on the field as much as possible. 
My proposal for this year:
1 and 2 play 3,4,5,6, 3 and 4 play 1,2,5,6, 5 and 6 play 1,2,3,4.   Oh well. 

Quote from: CrashDavisD3 on March 25, 2015, 02:15:45 AM
Only Pool A for ASC, SCIAC, SCAC, NWC

SCIAC has 3 teams at the bottom that will kill the SOS for a Pool C team from the SCIAC.

Conference wins are pretty much a wash in terms of SOS (if every team only played a balanced conference schedule, every teams SOS would be .500).
Cal Tech is 2-1 against non-conference D3 opponents (and can be at worst 2-2 depending on MIT this week), so it's really just 2 teams killing SOS.

Quote from: Teddy_Ballgame on April 20, 2014, 03:51:55 PM


Meanwhile, ULV, Redlands, and Oxy all play two on Saturday, one Sunday, and one Tuesday. They'll be left in a tough spot as their aces will only have two days rest for the final game. Case in point, Redlands will likely have to throw a fourth starter against PP's ace Miles on 4/29.

Rather the exception. The other two teams play Cal Tech. Their 3 starters can pitch the final game.

Quote from: forheavendial4999 on May 11, 2013, 08:22:54 PM

Quote from: Richard Hamstocks on May 11, 2013, 08:15:37 PM

Quote from: forheavendial4999 on May 11, 2013, 07:55:44 PM

Quote from: Richard Hamstocks on May 11, 2013, 07:32:03 PM

My usage of the word shrink is not "improper". Rather, it's quite precise. See http://en.wikipedia.org/wiki/Shrinkage_(statistics).
As for your other flippant comments, no one "schedules" Cal Tech, nor decides how many conference games they play, balanced or otherwise.

Not that I'd expect different from a use of wikipedia in a serious discussion, but it doesn't seem to fit. The first definition cited implies that there was a particular data set used for fitting, never mind whether or not it works well or not. The second definition doesn't seem to fit at all because it refers to an estimator which no one has talked about.

And then there's this. "A common idea underlying both of these meanings is the reduction in the effects of sampling variation." -- That's not what is happening here at all. A schedule is not, for statistical purposes, a sample and it is certainly not a representative sample. You're not talking about a reduction in effects of sample variation being an improvement, you're talking about it being a problem.

A more common definition of "shrink" is to make smaller...which if you move something toward .500, only applies if it was previously or would otherwise be above .500 by a greater amount, which is not necessarily true or inherent.

As for your characterization of my "flippant" comments, I just have to laugh. You seem to be implying that conference membership has no say over the makeup of their schedule, as if it's all dictated to them by the league office which for some reason sees fit to force a schedule upon school that the schools do not want.

I don't like referring to Wikipedia either, and that article is indeed poorly written (and clearly written by a Bayesian). The usage of shrink is the same as the conventional usage. To make smaller. In the sense of an estimator (in this case of how tough your schedule is) it means the variability from a particular value is being made smaller. As Bayesian estimates are always shrinkage estimators (towards the prior mean), a Bayesian would claim this is an improvement. Hence the language.
The longer your conference schedule, and the higher the overlap of non conference scheduling available, the closer your SOS is to .5 on average.
And a schedule is absolutely a sample (one can imagine all possible games a team could ever play as the population). The fact that its not a "representative" (of what?) sample, or I would say a random sample, is exactly my point about SOS.

Um...great. So are you claiming that the schedules are better than SOS represents them to be? That playing Caltech and CMS 4 times makes for that?

Seems like you're arguing two different things that lead to conclusions in opposite directions. And what's more, you seem to be arguing for its own sake, with no real purpose or conclusion to it...nothing you're arguing for that relates to the top teams in the West region.

And finally, as Ricky's post shows, what you're claiming is a problem really isn't because it's already being accounted for.

I'm saying that I don't know, and SOS isn't helping. I know that Cal Tech And CMS are bad. I don't know how good the rest of the SCIAC is. It doesn't matter to SOS either (other than the league looked good against Kean and Ithaca and Bridgewater and that's a lot of the reason SOS tends to be over .5). Maybe the national committee has this nailed down. Maybe not. I don't know what happens there. I don't see a lot of evidence supporting that they have it figured out. I don't even know what that would look like. They shipped in two teams last year, somehow they found some reason to think the west was a bad region. SOS is a primary criterion. I can't see how to use this well.

Quote from: forheavendial4999 on May 11, 2013, 07:55:44 PM

Quote from: Richard Hamstocks on May 11, 2013, 07:32:03 PM

My usage of the word shrink is not "improper". Rather, it's quite precise. See http://en.wikipedia.org/wiki/Shrinkage_(statistics).
As for your other flippant comments, no one "schedules" Cal Tech, nor decides how many conference games they play, balanced or otherwise.

Not that I'd expect different from a use of wikipedia in a serious discussion, but it doesn't seem to fit. The first definition cited implies that there was a particular data set used for fitting, never mind whether or not it works well or not. The second definition doesn't seem to fit at all because it refers to an estimator which no one has talked about.

And then there's this. "A common idea underlying both of these meanings is the reduction in the effects of sampling variation." -- That's not what is happening here at all. A schedule is not, for statistical purposes, a sample and it is certainly not a representative sample. You're not talking about a reduction in effects of sample variation being an improvement, you're talking about it being a problem.

A more common definition of "shrink" is to make smaller...which if you move something toward .500, only applies if it was previously or would otherwise be above .500 by a greater amount, which is not necessarily true or inherent.

As for your characterization of my "flippant" comments, I just have to laugh. You seem to be implying that conference membership has no say over the makeup of their schedule, as if it's all dictated to them by the league office which for some reason sees fit to force a schedule upon school that the schools do not want.

I don't like referring to Wikipedia either, and that article is indeed poorly written (and clearly written by a Bayesian). The usage of shrink is the same as the conventional usage. To make smaller. In the sense of an estimator (in this case of how tough your schedule is) it means the variability from a particular value is being made smaller. As Bayesian estimates are always shrinkage estimators (towards the prior mean), a Bayesian would claim this is an improvement. Hence the language.
The longer your conference schedule, and the higher the overlap of non conference scheduling available, the closer your SOS is to .5 on average.
And a schedule is absolutely a sample (one can imagine all possible games a team could ever play as the population). The fact that its not a "representative" (of what?) sample, or I would say a random sample, is exactly my point about SOS.

Quote from: forheavendial4999 on May 11, 2013, 07:37:18 PM
So Richard, let's play a game.

You tell me, without considering SOS but considering the other primary selection criteria, who Pomona-Pitzer should be considered ahead of for a Pool C bid from among the following teams:

Washington, Oswego State, MIT, ECSU, Ramapo, Neumann, Amherst, Johns Hopkins, Christopher Newport.

The 7 Pool C bids (Marietta lost so they'll steal one now) that remain "up for grabs" will likely be given to teams in this group. So give me your case for them in the top 7, using primary criteria other than SOS -- which someone help me here if I leave something out, is head-to-head, results against regionally ranked, results against common regional opponents.

I'll decline. I'm not convinced PP should be given a pool C bid. I don't know enough about those teams to make an informed decision. Luckily, I don't have to. It's a hard problem. I've only ever argued against the claim that they clearly aren't deserving because of their SOS (one that you've essentially made).
To say that the NCAA did the west region a favor by giving Trinity a pool C with a low SOS isn't consistent with your earlier arguments. They were a 34 win team. Your claim is that you are deserving if you offset your low SOS with a high WP. That's Trinity in a nutshell. You can't have it both ways.

Quote from: forheavendial4999 on May 11, 2013, 07:11:24 PM

Quote from: Richard Hamstocks on May 11, 2013, 06:36:45 PM

Fact: playing the same opponents shrinks your SOS towards 1/2.

Not a fact. In the cases of Caltech and CMS, it probably results in those opponents hurting you less than they would otherwise. "Shrink" is an improper term as it assumes that otherwise your SOS would have been over .500.

The greater the proportion of your schedule is comprised of conference play, the less possible variability in your SOS. If you only play a balanced conference schedule, your SOS is .5. This is the problem in the west and why SOS can't be used so freely.

So then don't play as many conference games, or don't play a balanced conference schedule. Wow, I'm a genius.

West region teams have "moderated" SOS, more so than other regions. For pool C candidates, moderate=lower.
The reason that cal tech still hurts you is the use of unweighted averages and unbalanced schedules. You can do the calculation to see that scheduling cal tech still brings down your SOS.

You mean scheduling a bad team hurts your SOS? How unfair!
(snip)

I'm not asking for them to be excused for their schedule, I'm saying that SOS doesn't measure what you think it measures. Therefore, I'm asking that you excuse them for their SOS, because they play in the west.

The last two years, the team with the lowest SOS to get a Pool C bid was from the West. Given this fact, I'm not sure what the complaint is. It seems as if the committee is giving the West special treatment (for whatever reason, this one or another one).

Fine, we'll look at other primary criteria. And Pomona-Pitzer and Texas Lutheran still don't measure up. George Fox was judged by your own region to not be as good as either of them, so they're really not even worth talking about.

Bottom line is Chapman has earned respect. Linfield has earned respect. George Fox won a title almost a decade ago but doesn't seem to have followed up on it that well. No one from Texas has ever done anything at the national level and the successes of the SCIAC teams pre-Chapman are well in the past. I'm not seeing a problem here with regard to nationally-contending Western teams getting shut out.

My usage of the word shrink is not "improper". Rather, it's quite precise. See http://en.wikipedia.org/wiki/Shrinkage_(statistics).
As for your other flippant comments, no one "schedules" Cal Tech, nor decides how many conference games they play, balanced or otherwise. 

Quote from: forheavendial4999 on May 11, 2013, 06:48:55 PM

Quote from: Ralph Turner on May 11, 2013, 06:36:08 PM

Quote from: forheavendial4999 on May 11, 2013, 06:11:20 PM

Quote from: Ralph Turner on May 11, 2013, 04:22:17 PM

Quote from: Richard Hamstocks on May 11, 2013, 04:09:02 PM

Quote from: forheavendial4999 on May 11, 2013, 11:18:11 AM
Nothing you said is untrue as far as the numbers. But given as you acknowledge that the hypothetical is not reality, and there are real difference between teams within the league, then I'm back to expecting the better teams to have better records. Your example also seems to dull the complaints re: Caltech, as shouldn't their SOS be artificially increased?

I offered the boundary case (what you call a hypothetical, but any example requires knowing how good teams actually are which is unknowable and thus would be a hypothetical as well) to make a point and simplify the calculations. The validity of the observation is not nullified by moving slightly in from the boundary. Diminished to some extent? Sure.  But the point remains, SOS is simply not comparable between the west region and others.
Cal tech has a real effect on SOS, the calculations aren't difficult to see that. It's not fair to talk about just removing cal tech from your schedule and recalculate your SOS, unless you recalculate OWP for your other SCIAC opponents as well. But it is still detrimental to your SOS to have to schedule them 3 or 4 times.

The isolation in the West is unique.

In 2014, Texas Lutheran will have19 potential D-3 opponents in 600 mile radius.  IF, and it is a big IF, TLU can convince Hendrix (usually very average and 599 miles away) and Millsaps (602 miiles away) to play them, you can get the OOWP on the SAA to help.

In the other parts of the country we are talking about 300 mile radii. In New England, we are talking about 150 mile radii for upwards of 50 or 60 opponents.

So what's your solution? Just cut the Western teams a break because they don't want to get on a bus?

I want the members of the National committee to know D3 so well, that they can assess what the raw number of the SOS of a  New England  teams means versus a team from the West.

What makes you think they don't?

A 25-18 Bowdoin team getting a pool C last year?

Quote from: forheavendial4999 on May 11, 2013, 06:02:29 PM

Quote from: Richard Hamstocks on May 11, 2013, 04:09:02 PM

Quote from: forheavendial4999 on May 11, 2013, 11:18:11 AM
Nothing you said is untrue as far as the numbers. But given as you acknowledge that the hypothetical is not reality, and there are real difference between teams within the league, then I'm back to expecting the better teams to have better records. Your example also seems to dull the complaints re: Caltech, as shouldn't their SOS be artificially increased?

I offered the boundary case (what you call a hypothetical, but any example requires knowing how good teams actually are which is unknowable and thus would be a hypothetical as well) to make a point and simplify the calculations. The validity of the observation is not nullified by moving slightly in from the boundary. Diminished to some extent? Sure.  But the point remains, SOS is simply not comparable between the west region and others.
Cal tech has a real effect on SOS, the calculations aren't difficult to see that. It's not fair to talk about just removing cal tech from your schedule and recalculate your SOS, unless you recalculate OWP for your other SCIAC opponents as well. But it is still detrimental to your SOS to have to schedule them 3 or 4 times.

But you're trying to have it both ways...saying that playing the same opponents brings the SOS down...but what it actually does is moderate the SOS, so teams like Caltech would actually not hurt you as much as they would otherwise. Same with CMS. I would submit that Caltech and CMS would hurt you more if there were more cross-conference play.

We do know how good teams actually are because we have these things called tournaments in the postseason. If West teams were basically climbing over each other and then dominating in the championship, then what you all are saying would make some sense.

But that's not happening. A Texas team has never won a game in Appleton, the only California team to win games in Appleton (maybe even to make it to Appleton) Y2K is Chapman, and Linfield is usually the class up north, GF's one-off championship under their previous coach notwithstanding.

Like I said, it's not like GF and Pitzer were just victimized by their schedule. They both lost quite a few games. So you're basically asking for them to be excused both for their schedule and for their losses. Can't have it both ways. If one of them like 35-8 (or 33-7 with no conf tournament) with 3 losses to Linfield, I could understand a little more and might be a little more sympathetic. When you go 28-14 or 26-12, you're relying on fortune. Why didn't GF play the other two games they could play?

Fact: playing the same opponents shrinks your SOS towards 1/2. The greater the proportion of your schedule is comprised of conference play, the less possible variability in your SOS. If you only play a balanced conference schedule, your SOS is .5. This is the problem in the west and why SOS can't be used so freely. West region teams have "moderated" SOS, more so than other regions. For pool C candidates, moderate=lower.
The reason that cal tech still hurts you is the use of unweighted averages and unbalanced schedules. You can do the calculation to see that scheduling cal tech still brings down your SOS.

I'm already on record for being anti-conference tourney for deciding pool A bids. Fun? Yes. But a terrible use of the available information for determining the best team. But that's irrelevant here.  Even if you really believe the best team always wins their conference tournament, this only gives you an ordering within a conference. The topic at hand involves choosing pool C bids, which involves comparing teams from different regions. And I maintain that using SOS without observing these facts (primarily that you can play a tougher schedule AND have a lower SOS than another team) is a bad idea. The extreme example I proposed above had the teams with by far the toughest schedules having an SOS ranking them as having the 240th toughest schedule. 1 vs 240.

I'm not asking for them to be excused for their schedule, I'm saying that SOS doesn't measure what you think it measures. Therefore, I'm asking that you excuse them for their SOS, because they play in the west.

Quote from: forheavendial4999 on May 11, 2013, 11:18:11 AM
Nothing you said is untrue as far as the numbers. But given as you acknowledge that the hypothetical is not reality, and there are real difference between teams within the league, then I'm back to expecting the better teams to have better records. Your example also seems to dull the complaints re: Caltech, as shouldn't their SOS be artificially increased?

I offered the boundary case (what you call a hypothetical, but any example requires knowing how good teams actually are which is unknowable and thus would be a hypothetical as well) to make a point and simplify the calculations. The validity of the observation is not nullified by moving slightly in from the boundary. Diminished to some extent? Sure.  But the point remains, SOS is simply not comparable between the west region and others.
Cal tech has a real effect on SOS, the calculations aren't difficult to see that. It's not fair to talk about just removing cal tech from your schedule and recalculate your SOS, unless you recalculate OWP for your other SCIAC opponents as well. But it is still detrimental to your SOS to have to schedule them 3 or 4 times.

Quote from: forheavendial4999 on May 11, 2013, 10:26:19 AM

Quote from: Ralph Turner on May 10, 2013, 06:36:48 PM

There is so little crossover play that you cannot find an easy metric.  I once imagined a Deviation from the Mean to compare the really good SOS scores that you see in New England and the Mid-Atlantic, with the near .500 scores that we see in the West Region.  If the committee did not acknowledge how really lousy our SOS numbers are in the West and ASC/SCAC, comparable to "nationally", then we would be skunked every year.

Well if the SOS is lower (because you're not able/willing/whatever) to travel to play other power programs, isn't the obvious counterweight to win at a higher rate? If you play a weaker schedule, it seems completely reasonable to me to expect a higher winning percentage. Teams have gotten in with .800ish percentages even with wretched SOS (like 300th ish). But if you are down more like .700 and going against .650-.700 teams with much better schedules, then it just makes sense that you're usually going on lose out there.

It's kind of like a sliding scale...if you're lower in one area, you have to make up for it in another.

This assumes that strength of schedule measures, well, strength of schedule. If you took the 8 best teams and put them in a conference together on the moon with no travel budget, they all come back with SOS of .500, which puts them at 240th in the nation. By definition though, they have the toughest schedules. 
Is the west region on the moon? No.  Is the SCIAC (or NWC or anybody else) comprised of the best teams in the country? No. Is SOS really comparable across regions when you have these sparsitiy issues. I don't think so.