This is going to be long.  UAH fans may not be interested in this at all, but I will say that we can play a spoiler role with Northern Michigan’s season in addition to what’s already been done to the Bemidji season.  The Wildcats come to the VBC this weekend, and a sweep for them puts them in the postseason, no questions asked. If UAH grabs any points at all, the Wildcats’ margin begins to shrink.  A UAH sweep would end their season.  I’m just throwing that out there.

Update: I realized that I called this best/worst and never, you know, listed that.  This came up tonight in some emails with Matt Wellens of USCHO.  He’ll present this in a different way in his column, but I wanted to clear things up here.

The only way that I know how to do best/worst is to do it systematically.  Since we’re virtually guaranteed to have tiebreakers, it is vital that we consider these first so we know what we’re dealing with.  We’re going to limit our set of tiebreakers, though: UAH won’t be considered at all, as you won’t get to the bottom of the table to finish these comparisons; and Ferris and Mankato will only have tiebreakers between them, as no one can get high enough to make it a 1/2/3 race.

Before I start, though, I gotta point this one thing: my model says that the Lakers are the team most likely to miss the playoffs, but you can also construct a scenario where they get home ice.  I crap you negative.

Let’s start.  Here’s how seeding for the WCHA tournament happens.

Seeding for the WCHA Tournament

If two or more teams have accumulated the same number of points shall be determined according to the following procedure:

A) If two or more teams are tied, and all teams tied have played four contests against one another, then the team with the most accumulated points from these head to head contests will be granted the higher seed.

B) If two or more teams are still tied (or all teams tied have not played four contests against one another) the highest seed will go to the team with the greater number of conference wins.

C) If not determined by A) or B) above, the recipient of the highest seed shall be determined by comparison of the winning percentages of the teams tied, against the remaining highest ranked WCHA team successively, until the determination is accomplished, or all WCHA contests have been considered.

In the event of multiple ties within the standings that become dependent on one another for determination, the procedure shall be applied to the highest tie first, using combined winning percentage against all teams involved in the lower tie(s) and continuing through the order if needed. If this fails to break the highest tie, the procedure shall be applied to the next highest tie (and so on if needed), using combined winning percentage against all tied teams as needed when proceeding through the standings.

D) If not determined by A), or B), or C), the recipient of the higher seed will be determined by “winning margin” during conference contests.

“Winning margin” = WCHA conference goals for minus WCHA conference goals against.

In the event of multiple ties within the standings that reach this step, the procedure shall be applied first to the highest tie in the standings. If this fails to break the highest tie, the procedure shall be applied to the next highest tie (and so on if needed) until any tie is broken and all procedures are re-started.

E) If not determined by A), or B), or C), or D), the recipient of the higher seed shall be determined by the flip of a coin.

In the event of multiple ties within the standings that reach this step, the procedure shall be applied first to the highest tie in the standings after which all procedures are re-started.

In the case of ties among three or more schools, the criteria will be used in order until a team, or teams, is separated from the top of the pack. At that point, the process will begin anew to break the “new” tie. In other words, when a three-way tie becomes a two-way tie, the two-way tie is treated as a “new” tie and the process begins with the first criterion.

Ferris State and Minnesota State: A) The teams did not play four times this season (the Mavericks won both meetings in Mankato).   B) The Mavericks currently have the edge in conference wins (19 v. 18).  C) I presume here that a tie for first will be decided head-to-head even though it doesn’t qualify for tiebreaker A).  It would be hard to get there, though: the Mavs would have to tie both games against Michigan Tech, while the Dawgs would have to split with the Lakers.

If the Mavericks win once, they get to 40 points and 20 conference wins.  That means that the Bulldogs have to sweep the Lakers.  This one will probably come down to Saturday night, and given the dominance of both teams at home, sweeps are fairly likely.  It’s probably about 60/40 that the Mavericks win the MacNaughton Cup.  No, that’s not me running a probabilistic model on it.  I’ll do that by Wednesday or so, because building that is going to take a while.

Tiebreakers for the Middle:

Alaska, Michigan Tech, Alaska-Anchorage, Bowling Green, Bemidji State, Lake Superior, and Northern Michigan are currently separated by five points, and with UAA-UAF and BSU-BGSU match-ups in play, things are bound to stay really tight.  Let’s look at the A) tiebreakers for all seven teams, starting with the Nanooks and going down the table.

Alaska: v. Michigan Tech, 2-2-0; v. Alaska-Anchorage, 1-1-0 pending this weekend’s slate; v. Bowling Green, only two games (0-1-1); v. Bemidji State, 2-1-1; v. Lake Superior, only two games (1-1-0) ; v. Northern Michigan, 2-2-0.  Unless the UAA-UAF series ends up with one team getting three or four points, the Nanooks will progress to tiebreaker B).

Michigan Tech: v. Alaska-Anchorage, two games (0-1-1); v. Bowling Green, 2-1-1; v. Bemidji State, two games (0-0-2); v. Lake Superior, 2-2-0; v. Northern Michigan, 3-1-0.  The Huskies are in pretty good shape, and not just because they’re starting at 28 points.  BG has a realistic shot at catching them, but the boys from Houghton win that one.

Alaska-Anchorage: v. Bowling Green, 1-2-1; v. Bemidji State, two games (0-1-1); v. Lake Superior, 2-2-0; v. Northern Michigan, two games (1-1-0).  The Seawolves are at a disadvantage, and they really need more than two points at the Carlson Center this weekend.

Bowling Green: v. Bemidji State, meeting for the first time this weekend; v. Lake Superior, 1-3-0; v. Northern Michigan, two games (1-1-0 this past weekend).  Of the teams at 26 points, the Falcons are in the worst shape, but they do have those two points in hand over the teams behind them.

Bemidji State: v. Lake Superior, 3-1-0; v. Northern Michigan, two games (0-2-0); v. Alabama-Huntsville, just 3-1-0.  (Sorry, I had to throw that in there.)  The Beavers do have the hammer on the Lakers, and they may very well need it.

Lake Superior: v. Northern Michigan, two games (1-1-0).

To recap, for the A) tiebreakers: Alaska has one pending games with UAA; Michigan Tech has two; Alaska-Anchorage has none pending games with UAF; Bowling Green has one; Bemidji has one; Lake Superior has one.

Based on this, you can see that Michigan Tech is pretty well set pending the UAA-UAF result.  They probably get home ice with a win in Mankato, but those have been tough to come by for visiting teams (1-13-0).

Let’s move to the B) tiebreakers.  These are, of course, subject to change, but the league wins are, down the table, 13 for Alaska, 12 for Michigan Tech, 11 for Alaska-Anchorage and Bowling Green, 10 for Bemidji, 12 for Lake Superior, and 11 for Northern Michigan.

This is where you see the scenario of Lakers For Home Ice: they could sweep Ferris State, which gets them to 14-14-0 / 28.  If Mankato sweeps Tech, they’re at 12-12-4, and the teams are 2-2-0 on the season.  If Anchorage sweeps Fairbanks, that keeps Alaska at 13-11-2 but with no A) tiebreaker.  An Anchorage sweep would push the Seawolves to 13-11-4 / 30 points and third place, with the Lakers in fourth.  If the Alaska squads split, the Nanooks would be in third with three-way tie for 28 points that the Lakers win because they have more conference wins.

Bizarre.  Also, I’m getting ahead of myself.

Let’s move to C) tiebreakers, and then I’ll stop.  I’m only going to compute these against the teams with 28 or more points, as these are the most likely C) comparisons.  I’ll re-run this early Saturday morning, after the UAA-UAF game, to show where we are.  Things will be clearer, and I only have so much time to devote to this today.

Alaska: v. Minnesota State, 1-1-0 (0.500); v. Ferris State, 2-2-0 (.500); v. Michigan Tech, 2-2-0 (.500).

Michigan Tech: v. Minnesota State, 0-0-0 (games this weekend); v. Ferris State, 1-3-0 (.250).

Alaska-Anchorage: v. Minnesota State, 2-2-0 (.500); v. Ferris State, 0-2-0 (.000); v. Alaska, 1-1-0 (.500) pending this weekend’s series; v. Michigan Tech, 1-0-1 (.750).

Bowling Green: v. Minnesota State, 2-2-0 (.500); v. Ferris State, 0-1-1 (.250); v. Alaska, 1-0-1 (.750); v. Michigan Tech, 1-2-1 (.375).

Bemidji State: v. Minnesota State, 1-3-0 (.250); v. Ferris State, 1-3-0 (.250); v. Alaska, 1-2-1 (.375); v. Michigan Tech, 0-0-2 (.500).

Lake Superior: v. Minnesota State, 0-2-0 (.000); v. Ferris State, 0-2-0 (.000) pending this weekend’s games; v. Alaska, 1-1-0 (.500); v. Michigan Tech, 2-2-0 (.500).

Northern Michigan: v. Minnesota State, 1-3-0 (.250); v. Ferris State, 0-3-1 (.125); v. Alaska, 2-2-0 (.500); v. Michigan Tech, 1-3-0 (.250).

To recap: Alaska is in good shape vis-a-vis Tech; BG has an edge on Anchorage and Bemidji; the Lakers and Wildcats are in trouble.

:gasp:

I’ve already covered Mankato-Ferris, so let’s dive right into the middle.  I could spend a lot of time working on ties and such with this, but it’s probably gonna run 3,000 words.  I’ll revisit on Saturday and do W-L-T.  I promise — and if I don’t, I’ll give you your money back.

Alaska: at 28 wins with one more league win than the Huskies, the Nanooks really do control their home ice destiny.

• A sweep of the Seawolves gets them 3rd even if the Huskies sweep Mankato.
• A split sees them with home ice: the only teams that can get to 30 points are UAF, MTU, UAA, and BG.  MTU is irrelevant in this calculus, and Anchorage can’t get there if the teams split.  That leaves a comparison with BG, whom they did not play four times, so the B) tiebreaker goes to the Nanooks (14 league wins with a split).
• An Anchorage sweep keeps the Nanooks at 28 points (13-13-2).  The Seawolves will have leapfrogged into the 3/4 zone, which I’ll cover in a bit.  If Tech is swept, that gets you to a two-way tie, a comparison the Nanooks win: A) 2-2-0, B) 13-12.  If Bowling Green splits with Bemidji State, that gets them to 13-13-4.  BG and UAF would push the Huskies to fifth with the B) tiebreaker, and then the Nanooks win with the C) tiebreaker no matter who wins between FSU and MSU.  If Bemidji sweeps BG, they get to 28 points as well, but the Nanooks win the A) and B) tiebreakers.
• Best: 3rd with a sweep. Worst: 7th if they get swept, BG sweeps Bemidji, Tech gets any points in Mankato, and LSSU sweeps Ferris.  Yep, you can go from home ice to facing the lesser of Mankato and Ferris.

Michigan Tech: Also at 28 points, the Huskies also control their home ice destiny.  The Huskies have been very volatile in and out of the playoffs, but at this point, they are in, as Northern Michigan cannot get to 28 points.

• A Husky sweep in Mankato, as unlikely as that may be, would get the boys from Houghton up to 32 points, which could be matched only by the Nanooks.  As noted earlier, Alaska wins the B) tiebreaker.  They are guaranteed to have home ice with a sweep, and 3/4 is merely a matter of the Nanooks-Seawolves result.  There’s likely to be a bit of a gap between #5 and #6, so this distinction matters for more than avoiding the #1 seed in Grand Rapids.
• A Husky split in Mankato carries them to 13-11-4.  Anchorage and BG can get there.  We know that MTU loses the B) tiebreaker to the Nanooks,   Tech has an A) tiebreaker win over the Falcons.  The B) tiebreaker isn’t sufficient for MTU-UAA, and that goes to the C).  Tech would win those: both teams would be .500 against Mankato, and the Huskies are .500 against the Bulldogs, who swept the season series with the Seawolves.
• A Mankato sweep, which seems likely, keeps the Huskies at 28 points at 12-12-4.  UAA could get to 28 with a split at the Carlson Center, but they lose the tiebreaker as noted above.  A UAA sweep keeps the Nanooks at 28 points as well (and leapfrogs the Seawolves into 3rd/4th at 30 points if BG also sweeps), and if BG split with Bemidji, Tech would be 12-12-4 along with Bowling Green, and the A) tiebreaker is in effect again.  But sweeps by UAA and BGSU, combined with an MSU sweep of MTU, would push the Huskies into fifth.
• Best: 3rd if they sweep and UAF doesn’t sweep.  Worst: 7th, if they are swept, BGSU sweeps, UAA wins and ties, and LSSU sweeps.  Yep, you can go from home ice to facing the lesser of Mankato and Ferris.

Alaska-Anchorage can still jump into home ice.  It takes a road sweep of their in-state rivals.  Will that be enough?

• An UAA sweep puts them at 13-11-4 / 30 points.  Michigan Tech can still get to 32 points with a Mankato sweep.  Bowling Green can get to 13-13-4 / 30 points with a sweep of BSU.  If Tech sweeps, they get 3rd, and it’s the A) tiebreaker that gets the Falcons into fourth.  If all three schools are tied at 30, we have to go to the B) tiebreaker as Tech and UAA have only played two games; in that case, we have to to all the way to the C) tiebreaker.  All three are .500 against Mankato, and Anchorage drops out against Ferris.
• An UAA split puts them at 12-12-4 / 28 points.  UAF will be at 30 points.  Tech could get swept at Mankato, and again we’re at the C) tiebreaker.  BG could split with BSU and put us again into the situation listed above; they could also sweep the Beavers and jump to 30 points, which puts UAA on the road in two weeks.
• A winless Anchorage weekend puts them at 11-13-4 /26 points, where it gets head-hurty.  BG is already there, but if they get swept by the Beavers, the Green are at 28 points.  A split between the squads ties BSU and UAA up in points and record, so we’re to C) tiebreakers, which favors BSU if Ferris is #1 and UAA if Mankato is #1.  LSSU can also get to 26 points with a win in Big Rapids, and the Lakers win the B) tiebreaker.  Northern Michigan can leapfrog them into 27 points with a sweep here in Huntsville.
• Best: 3rd if they sweep UAF, Tech picks up only one point, and BGSU doesn’t sweep.
  
• Is there a way for UAA to miss the playoffs?!  Yes.  1) UAF sweeps UAA.  2) BSU and BG split.  3) Ferris becomes #1 AND Lake picks up a game, which means a Tech sweep of Mankato (or one point for the Mavs, but come on, I’m at 2350 words and two hours at this point). 4) NMU sweeps UAH.  Another way that Matt figured out: UAA gets swept (26 pts), NMU sweeps (27), BSU wins-and-ties (27), and LSSU gets at least three points.  That puts them in ninth.  They are a team that can go from home ice to homework.

As people keep saying on USCHO, win some games and the numbers won’t matter.

Bowling Green: Can they get home ice?  Can they miss?

• Home ice: they need to sweep BSU for 13-11-4 / 30 points.  If UAF and/or MTU split with their foes this weekend, that creates a tie at 30.  If it’s two-way, Tech wins in an A) tiebreaker, and UAF would win the B) tiebreaker.  If both Tech and Fairbanks get swept, the Falcons are tied for 3rd with the Seawolves, and BG wins the A) tiebreaker.
• Splitsville means that the Falcons (12-12-4 / 28) need some help.  They need UAA and MSU to sweep to keep the Huskies and Nanooks at 28 points: the Seawolves would jump to 30 points, and it’s no less than a three-way tie.  It could be a four-way tie if LSSU swept Ferris.  Madness!  How does this shake out? A) tiebreakers don’t work because UAF and BGSU played just once.  With B) tiebreakers, LSU would be at 14-14-0, UAF 13-13-2, BGSU 12-12-4, MTU 12-12-4.  If LSSU doesn’t sweep Ferris and this is a three-way tie, UAF gets fourth, and Tech wins the A) tiebreaker.
• If Bemidji sweeps the Falcons, they finish 11-13-4 / 26 points.  Alaska, Tech, and Bemidji would all be at 28 points or higher.  LSSU could be at 28 points with a sweep of Ferris.  Northern Michigan could leapfrog the Falcons with a sweep of UAH.  Yep, the Falcons can still miss the playoffs.  But if the Beavers sweep them and the Lakers split in Big Rapids, the Falcons win the A) comparison.  If you’re a Falcons fan, you’re rooting for Ferris and UAH to win a game at minimum so you’re in the playoffs no matter what you do.
• Best:  BG sweeps, and either Tech or Alaska has a 0-1 point weekend.
• Worst: 9th, if they’re swept, NMU (27) and LSSU (28) sweep, and UAA picks up any points.  If the Seawolves are swept, they win the A) tiebreaker over the Falcons.

Bemidji State:

• They can get to 12-12-4 / 28 points with a sweep of BG.  There will be at least one team with more points than them: Tech can get swept, but you can’t distribute four points between two teams at 28 and 26 and keep them both under 28.  Bemidji’s push for 4th: the B) tiebreaker comes into play, and Alaska is going to win that.  Beavers, your bid for home ice ended around 9:45 p.m. on Friday night.  My ROFLCopter goes WUB WUB WUB.  But to finish the thought: if UAF and UAA split, UAA is 12-12-4 with Bemidji, and the Beavers are hoping that FSU is #1; if UAF and MTU are swept, UAF gets 4th and BSU fifth, as the Beavers would get the C) tiebreaker regardless of FSU or MSU being #1.  Also, LSSU can get into this, too, and they’d win the B) tiebreaker.
• [Update]: Jack Hittinger of the Bemidji Pioneer asked me to consider the following: 1) BSU sweeps BG 2) UAF sweeps UAA 3) Mankato sweeps Tech.  That puts BSU and MTU at 12-12-4 / 28.  The A) tiebreaker doesn’t meet the four-game criteria, and the B) tiebreaker is irrelevant with the matching records.  For the C) tiebreaker: in this scenario, Mankato would be the #1 seed at 21 league wins, so the Beavers get the #4 seed unless the Lakers sweep Ferris and get into 28 points at 14-14-0.
• If they split with BG, they get to 11-13-4 / 26 points.  MTU, UAF, and BGSU would all have at minimum 28 points.  If UAA takes points off of the Nanooks, they’re above 26 points as well.  LSSU can get to 26 points with at least one win in Big Rapids, but BGSU wins the A) tiebreaker.  Could BSU miss out altogether?  Well, LSSU could pick up three or more points in Big Rapids to get to 27+, and NMU could sweep UAH and get to 27.  If UAH picked a tie off of the Wildcats, NMU wins the B) tiebreaker.
• If BGSU sweeps the Beavers, they’re at 10-14-4 and need a lot of help.  They’d need Lake Superior to get swept so that A) tiebreaker comes into effect, and they’d need UAH to take all four points off of the Wildcats.  Why?  If BSU, LSSU, and NMU are all tied at 24 points, the A) tiebreaker can’t be used since the teams didn’t all play four games against each other.  At that point, the B) tiebreaker ends the Beavers’ season.
• Best: 4th, if they sweep, Fairbanks sweeps, and Mankato sweeps.  It doesn’t make what LSSU does because the Beaers have the A) tiebreaker at 3-1-0.
• Worst, 9th, if they are sweep (24), NMU sweeps (27), and LSSU gets any points at all (25-28).

Can you imagine how obnoxious @weloveuahhockey will be if the Beavers miss the playoffs?  I can!  GO FALCONS!

Lake Superior, as noted, can get home ice, but what else?

• A sweep gets the Lakers to 14-14-0 / 28 points.  While there is that convoluted set of circumstances that gets the Lakers into home ice, you have to admit that it’s pretty unlikely.  So let’s look at the rest of it: if Alaska and/or Tech pick up points off of Anchorage and Mankato respectively, it’s road life for the Lakers, who would make the playoffs at that point because NMU can only get to 27 points.  14 conference wins gives them an edge in all sorts of B) tiebreaker scenarios, and the presence of 3+ teams virtually guarantees the A) tiebreaker will not be used.  While LSSU is unlikely to host some team, two wins makes them a solid candidate for #5.  One possible scenario: UAF and UAA split, LSSU sweeps, MTU is swept; regardless of whether there’s a BGSU-BSU sweep, LSSU is going to win those comparisons.  The team has only tied once this year, and they’ve only been to overtime four times, and none since Thanksgiving.
• A split gets the Lakers to 13-15-0 / 26 points.  They could be at 26 points with either BG or Bemidji depending on how that series goes, and they’d possibly have a third at 26 if UAF sweeps UAA.  Between those four teams, an A) tiebreaker would come into play if it’s BGSU, while it would be a B) tiebreaker with BSU involved.  Note that these ties being broken are for 6th, or perhaps 7th if NMU sweeps in Huntsville.
• UAA-BGSU-LSSU: UAA is 1-2-1 against the Falcons, 2-2-0 against the Lakers; the Falcons are 1-3-0 against the Lakers.  The Lakers go 5-3-0 / 10 points in that round-robin, while the Seawolves are 3-4-1 / 7 points and the Falcons are 3-4-1 / 7 points as well.  My take, and I don’t know if this is the league’s, is that you’d do the round-robin comparison and then, once the Lakers are separated, you’d then compare UAA and BGSU, which favors the Falcons.
• UAA-BSU-LSU: the A) tiebreaker is out, as UAA and BSU played just twice.  B) is next, and it would be LSSU 13, BSU 11, UAA 11.
• If LSSU is swept, they’re in a sorry state.  They can’t hope on BSU getting swept, because again, the A) tiebreak goes to the Beavers.  They have to hope that NMU doesn’t win in Huntsville in that case.  That seems like a bad place to be hanging your heart.
• Best: 4th, if they sweep, Mankato sweeps, and one of UAA, BG, and BSU finishes with 28 points.  Not tying games is their hammer.
• Worst: 9th, if they are swept and NMU wins one night in Huntsville.

Northern Michigan:

• As noted, if the teams at 24/26 get mangled up with each other, they can leapfrog as high as 5th or 6th with a sweep of the Chargers.  They have to get a win in Huntsville to have a chance at the playoffs, and they really need to get all four points.  They don’t have any A) comparisons against the teams that could be at 26 points, but they would be at 12 conference wins, and that would be enough to beat Bemidji if they’re there.  They have to have a win and hope that LSSU is swept, and better, they need to sweep and let everyone fight it out at a point below them.
• Best: 5th, if they sweep (27), LSSU gets 0-2 points (24-26), UAA gets 0-1 points (26-27), and BSU wins-and-ties (27).
• Worst: 9th, if they are swept.

Alabama-Huntsville: Oh boy, can our boys mess some stuff up.  They may have already!

If you catch anything wrong with this, let me know!  I’m g@uahhockey.com, and there’s other places to catch me online.  This is at 3500 words, and while it’s not exhaustive, I think that it covers the subject fairly well.

[We’re now at 3920 words.]

Get ready for some math!

So I spent some time on Wednesday coming up with a probabilistic model for picking the last nine WCHA games, combining everything into a probabilistic record table, and such.  I hit some snags, so I’m not done, but I did want to present my thinking to this point.  If you don’t care anything about that, just look above and see the estimates for this weekend’s series.

What I’m using is an estimation that the KRACH-based expected values are normally distributed around the mean — expected value is what I’ve been doing all along.  The mean is almost always not 2.000, so the level of skew to the left and right takes the range of expected values away from 0-4 and makes them something like 0-7 for any game involving UAH, as the KRACH-based expected value for UAH games has been ~3.5.  But Bemidji can’t pick up seven points this weekend (much as they’d like to, I’m sure), so anything greater than four is, well, a sweep.

Before you black out on me: you know the bell curve we all know well?

We’re all normal when it comes to the curve. Thanks to Texas Tech for the image.

Yeah, what we’re doing is putting the bell curve between goal posts at 0.000 and 4.000, the theoretical minimum and maximum.  Any time you shift away from the center point at 2.000, the tail bit that goes outside of the goal posts automatically counts as a sweep one way or the other.  If one team is expected to sweep, the goal post will be right near the peak of the bell curve, meaning a lot of the data will be outside of the goal post.

So, you can picture moving the whole curve around by its peak with your hand.  But now we need to consider two more things: the concept of the standard deviation, and what our breakpoints will be.

I should explain these.

Breakpoints: I looked, and the WCHA has had ties around 10% of the time.  As such, I couldn’t use a standard rounding routine to make the decision whether it was a win or tie.  Instead, I’ve taken slices of data.  Instead of sweeps starting at 3.5000, they start at 3.200.  Three-point weekends happen only between 2.900 and 3.199.  Splits happen between 1.200 and 2.899 — a wide, wide swath that’s 42.5% of the entire band.  One-point weekends happen between 0.900 and 1.199, and you get swept if it comes up below 0.899.

Standard deviations: If you look at that bell curve image above, you’ll see the concept of the standard deviation.  This has to do with the spread of the data: how far the points are from the average.  I used a weighting of the standard deviation that had a wider spread in the middle — because you’d expect that a predicted split could easily go sweep with a little puck luck — than you do at the edges, because teams that are expected to sweep should have a high probability of doing so, and therefore there shouldn’t be a wide spread of the standard deviation.  The distance of the mean between the edge and the center linearly changes the standard deviation (spread).

So let’s look at the KRACH-based expected values and estimated standard deviations.

Here’s Week 23’s EVs and SDs.

You can see that Bemidji would be expected to win 3.722 points this weekend, and the spread of points is 0.392.  As you can see with the bell curve above, 68% of the points under the BSU-UAH curve fall between 3.33 and 4.114.  As all of those values are greater than 3.200, BSU should sweep 68% of the time.  But that doesn’t take account of the fact that everything on the right half of the curve is in sweep territory, so it’s 84% that’s a for-sure sweep.  Now, two standard deviations is 3.722-0.392-0.392 = 2.938, which is above the split point and below the win-and-tie point., and that covers about 98% of the data.  That’s why it’s pretty rare that UAH wins a game.

If anything, that win-and-tie thing is probably a little large.  Those 0/1/2/3/4 breakpoints are experimental, but I think that it’s realistic to say that UAH has a 2.30% chance of picking up a win this season.  UAH played teams in the 3-9 morass 18 times, and it has one win and one tie, and that’s 8.33%, which is pretty close to the pick this weekend.

Looking at the other games: we saw that the LSSU and NMU series were pretty close to the split line, and even with the wider spread (standard deviation) in the curve, the splits happen nearly 80% of the time.  As you can see, the distribution skews to the left, assuming that each of these home teams should pick up a point 90-92% of the time.  The spread may not be wide enough, because the chance that the home team sweeps is pretty darn small.  I’ll work on tweaking that.  There’s also not any sort of home-team bonus, mainly because I forgot it yesterday and haven’t thought it fully out.  It would be some sort of home W% / road W% estimation, but that’s kinda noisy, and I’ve already made this a little noisy even with 1,000 runs.

Let’s finish with the Ferris State-Alaska series.  You can see that a split is the most likely option, but the next-most isn’t Alaska picking up a point but getting swept by the Bulldogs.  That’s done because of the breakpoints trying to estimate that the tie happens around 10% of the time.  This says that it’s 22.4% chance the teams will tie one night, but that’s because the peak of the curve (expected value) is right in the break.  Now, a home-team bonus would probably bring this out of that zone.

I’m not done, but I did want to get this out there.  We’ll see if it holds water.

For those curious, I’m using NORM.INV(RAND(),mean,stdev).  The RAND() function spits out a random number, and the mean and standard deviation are from that third table.  I have that formula listed 1000 times — creating that was … fun — and the table we saw up front and just above these paragraphs sums up all of the times that 0, 1, 2, 3, and 4 points comes up in the random calculation.  That calculation is a fun nested-IF statement that does all the math for putting the calculated number into the breakpoint slots.  That took some time, and trying to create it in Google Docs nearly led me to chuck my laptop across the room, so I’m using Excel.  I’ll probably release this after the season is over because I’m not doing the model just yet and don’t want to put something half-assed out there.

This will be long.  I apologize.  In fact, it’s going to take two posts.  This one is the easy one!

Let’s get this over with first: here’s the methodology/model, where things stood after week 19, and where things stood after week 20, and then there’s last week.  There’s also the Google Drive spreadsheet, which you’ll want to look over if you’re of a mind to see how this progresses.

Here are the final predicted standings:

What a difference a week makes: Tech was looking to have home ice before last weekend’s sweep by Alaska; then they were on the outside looking in; now they’re in a five-way tie at 28 points!

Oh, dear God in Heaven … let’s break this tie.

1. No head-to-head comparisons can be used because the teams involved didn’t all play each other four times.
2. Conference wins puts Alaska in 3rd.
3. The team-by-team tiebreakers are on W% down the table. As such, I looked at the schedule for each of the four teams, and:
a) Everyone got 25% of their points against Ferris save Anchorage (0.000), who gets 7th as a result.
b) Of the three remaining schools, BG has the highest W% against Mankato (.500) and gets 4th.
c) Between Bemidji (.250) and Tech (.000), the Beavers have the higher ranking against the Mavs, but this is based on the premise that the Huskies don’t pick up any points in Mankato. If the Huskies pick up any points in Mankato, they’d have at least home ice and would be 3/4 with the Nanooks. But for the purpose of evaluating the predictive model as show, BSU would get 5th and MTU 6th.

About the Tech-Mankato result:  if the Huskies pick up a tie in Mankato, they don’t have more conference wins (12) than the Nanooks (13), but they have a points advantage (29 v. 28) … but … MTU does have a HTH comparison with Alaska  (season split); they’d have the same number of conference wins (13); so it comes down to W% against the Bulldogs, which has the Huskies at .500 while the Nanooks are predicted to be just .250. If Alaska sweeps Ferris (taking them to 14 league wins), we’re not having this conversation unless Tech also sweeps Mankato, and then Huskies get third — each is .500 with Ferris; MTU has the edge against Mankato —  with the Nanooks in fourth. Phew.

Chaos, man, chaos.  Best/worst to follow later this week, as this is the point that I’d said that I would do it.  However, this SQC exam beckons…

P.S. Here is the entire text from the WCHA Manual:

WCHA Tie-Breaking Procedures

For Playoff Seeding Only

In regular-season competition, each Western Collegiate Hockey Association team shall accumulate points from each WCHA contest (i.e., a contest between teams representing two WCHA member institutions played as part of the conference schedule), receiving two points for each game won in regulation time or overtime, and one point for each game tied at the conclusion of overtime. The team accumulating the greatest number of points in regular-season WCHA contests shall be the WCHA Champion. If two or more teams are tied for the Championship, they shall be consid- ered co-champions.

Seeding for the WCHA Tournament

If two or more teams have accumulated the same number of points shall be determined according to the following procedure:

A) If two or more teams are tied, and all teams tied have played four contests against one another, then the team with the most accumulated points from these head to head contests will be granted the higher seed.

B) If two or more teams are still tied (or all teams tied have not played four contests against one another) the highest seed will go to the team with the greater number of conference wins.

C) If not determined by A) or B) above, the recipient of the highest seed shall be determined by comparison of the winning percentages of the teams tied, against the remaining highest ranked WCHA team successively, until the determination is accomplished, or all WCHA contests have been considered.

In the event of multiple ties within the standings that become depen- dent on one another for determination, the procedure shall be applied to the highest tie first, using combined winning percentage against all teams involved in the lower tie(s) and continuing through the order if needed. If this fails to break the highest tie, the procedure shall be applied to the next highest tie (and so on if needed), using combined winning percentage against all tied teams as needed when proceeding through the standings.

D) If not determined by A), or B), or C), the recipient of the higher seed will be determined by “winning margin” during conference contests.

“Winning margin” = WCHA conference goals for minus WCHA conference goals against.

In the event of multiple ties within the standings that reach this step, the procedure shall be applied first to the highest tie in the standings. If this fails to break the highest tie, the procedure shall be applied to the next highest tie (and so on if needed) until any tie is broken and all procedures are re-started.

E) If not determined by A), or B), or C), or D), the recipient of the higher seed shall be determined by the flip of a coin.

In the event of multiple ties within the standings that reach this step, the procedure shall be applied first to the highest tie in the standings after which all procedures are re-started.

In the case of ties among three or more schools, the criteria will be used in order until a team, or teams, is separated from the top of the pack. At that point, the process will begin anew to break the “new” tie. In other words, when a three-way tie becomes a two-way tie, the two-way tie is treated as a “new” tie and the process begins with the first criterion.

Let’s get this over with first: here’s the methodology/model, where things stood after week 19, and where things stood after week 20.  There’s also the Google Drive spreadsheet, which you’ll want to look over if you’re of a mind to see how this progresses.

Here are the final predicted standings:

What a difference a week makes: Tech was looking to have home ice before last weekend’s sweep by Alaska; now they’re on the outside looking in!

As a reminder: here are the tiebreakers, all with “if two or more teams …” language.  All three tiebreakers are used this week.

1. Head-to-head results if the teams have all played four games against each other.  In a three-team setup, they’d all need eight games against the other two teams to count.
2. Conference wins.
3. A comparison of winning percentages against all teams above them, team-by-team down through the table.

What happened with the model when it hit reality?

1. Alaska went into Houghton and took all four points from a team that was 7-3-3 coming into the weekend, while the Nanooks were 4-6-2.  Sports, man.
2. Bemidji upset Ferris, where they’d been expected to come away with just a tie.  That extra point may be the difference for them, even though it’s not terribly important in the model, as you can see: they jump up a spot, but mainly because Tech free-falls.
3. Anchorage stormed back from 2-0 with two-period goals and then saw Rob Gunderson stop all the overtime shots to get a point out of Friday night’s game; they then took it to BG the next night, winning 5-2.  An extra point gets them out of the morass at 28 points, one which now includes BG.

How does Tech fall so far?  As anyone knows, this is a very close-packed league.  The predicted win totals are 20, 20, 14, 12, 13, 12, 12, 13, 11, 1.  This season has been just as much about hanging on for a tie as it has been winning games.  Michigan Tech went from an expected points total of 30 to 26, and that’s enough of a difference, as you can see above.

About those tiebreakers:

1. Northern Michigan and Alaska-Anchorage played just twice this year, so conference wins breaks the tie at 29 points, and the Wildcats get 3rd.
2. Alaska, Bowing Green, and Bemidji State all have 28 points.  BG played the other schools just twice, so it falls to conference wins, which means Alaska gets 5th, and the Nanooks and Seawolves will play for the second straight weekend, this time in Anchorage.  Hoo boy.
3. To break the tie between BG and Bemidji: again, the teams played just twice, and they have the same conference record, so the comparison goes to win percentage, team-by-team.  Let’s go: Ferris is a .250 split (1-3-0 for Bemidji, 0-1-1 for BG), Mankato is a 2-2-0 for Bowling Green and 1-3-0 for Bemidji.

Lastly, let’s look at the other reason why the model is different: I made a two hand predictions.

1. I have Ferris State splitting with Alaska next weekend.  For one, the travel is hard, and it’s the first time that the Bulldogs have gone to Alaska this year.  They were in a close game against UAH one night when they were in the other far-flung league destination.  For another, Ferris is dominant in Big Rapids (10-1-1) and less so on the road (10-5-2).  Lastly, it’s unlikely that the Bulldogs are going to have their foot 100% on the pedal.  They probably cinch up the #1 spot this weekend against the other team from the 49th state.  They may want to spread minutes around and get guys healthy for the full series in two weeks.
2. The one that may prove controversial in Houghton is Mankato sweeping the Huskies in Week 24 because the Mavs are 13-1-0 at home while the Huskies are a) a bit of a mess, if you listen to their fans, and b) 5-10-2 on the road.  That point does mean that the Huskies make the playoffs, and that may not make me Mayor of Houghton, but it is a strong likelihood.  The only team to win in Mankato is BG (assuming you except the U-18 team) in a 4-3 result in early November.  The Mavs have seven league losses: three in Alaska, the 4-3 loss v. BG, a 4-1 loss at Bemidji, a 4-3 OT loss in Bowing Green, and a 5-2 loss in Marquette.  You’ll have to be good to take a point off of the purple guys at the Verizon Wireless Center.
3. I have Ferris sweeping Lake Superior State.  The seniors will want to go out winners.  This will mean a lot to the Lakers, for sure, but the Dawgs’ only home loss was to St. Lawrence early in the season.  The only team to take a point off of the Bulldogs in WCHA is Bemidji.

I have steeled myself for the hate mail from Houghton.  As always, I welcome comments, criticism, etc.  But I will make this final observation to my beloved Chargers: the model has you losing the last six games.  I believe that you could win any of them on any given night.  Pick off Lake State this weekend?  They miss the playoffs.  Bump off Bemidji?  They then get into Tiebreakersville of a different sort.  Knock off Northern at home that last weekend?  Well, two things happen then: Northern misses the first round, and two first round series would happen in Alaska.  Two.  All aboard the train to Bonkers.

We’ve been discussing this as a staff.  If you could win just one game, where would you like to win it?  We feel that winning at home would be best, but winning upsets the entire apple cart, and our #2 team behind the guys in the BlackBlue and White is Team Chaos.  But when it comes down to it, we really hate Bemidji.  If Bemidji got an early tee time because of a UAH win, well, that would be awesome, even if that win came on the road.