No Math: How to Do a 10-Team WCHA Playoff: Play-IN

I’ve been thinking about how to pull off a 10-team WCHA playoff with minimal perturbation to the first-round / Final 4ive.  I don’t think that a five-team or five-game playoff should be an end goal, as I like the current setup.  But if we’re going to go to an everybody-in system, I’d like to propose an alternative.

The Play-in

Seeds 1-4 get home ice.  Seeds 5-6 get certainty with their travel plans to 3/4.  Seeds 7-10 get sent to a 1/2 site with the #1 seed choosing the pairing whose winner they would play in the full first round.  But they’re only choosing this by picking who they host for a play-in game: 7-10 or 8-9.  7-10 and 8-9 play a single play-in game on neutral ice, and the winner then plays the host school (i.e., no re-seeding).  Finishing 7-10 now means that you have to win three games to make it to the Final 4ive.

Let’s look at this with how this season finished.  Ferris State, as the #1 seed, would’ve been able to pick a pair: Northern Michigan & Alabama-Huntsville or Bemidji State & Lake Superior.  Ferris State would have had until 3:00 p.m. on Sunday, March 9th to decide whom they would face in the opening round.  A play-in means that there’s even more reason to get the #1 seed, because you’ll get to handicap your best competitor.

Ferris could have taken BSU-LSSU and been pretty happy with it:  the Bulldogs did well against both teams, and they really held serve at home, so they would have felt confident in facing their opponent.  Or they could have taken the NMU-UAH pairing.  They were 3-0-1 against the Wildcats.  But maybe UAH knocks off Northern Michigan in that 7-10 play-in game!  Then Ferris would have an even easier task in its first-round series, as it’s pretty much a given that the McNaughton Cup winner can pick up two wins in three games no matter how many headstands Guerriero and Larose do.

Think about it for a second: two play-in games would be really exciting, probably as exciting as the WCHA’s final night was.  And even that would still have been exciting, as UAH was the only assured seed at #10.  Three teams (BSU, LSSU, NMU) could’ve been the 9th seed, four the 7th and 8th (UAA, BSU, LSSU, NMU in some combination).  After all, 66 of the 243 (27%) scenarios for how the final day came out would’ve had UAA in either 7th or 8th, and of course they could’ve gone as high as 5th.  If nothing else, we would’ve not heard caterwauling about how UAH made LSSU miss the playoffs by not playing them four times.

Don’t get me wrong: I like the top-8-or-go-home scheme.  I’ll like it next season if UAH is scuffling to be in the playoffs (don’t scoff or it might happen!  Wait, please scoff), too.  For a team at the bottom, I think that the push to fight and claw for getting into the top 8 means a lot — because making the playoffs is an accomplishment, not a given.  But if you’re really hell-bent on having all ten teams involved, send 7&10 and 8&9 to the venue of the #1 seed’s choosing.

What say you?  Comment below or reply to me on Twitter at @wchaplayoffs.

2014 WCHA Playoff Race: Playoff Branches

Are you ready to rumble?  Now, you would think that this would be pretty easy: five games.  But those five games can go three ways: a win for each team or a tie.  (You have to consider both teams because it factors into the standings each way.]  We will consider the scoring from the perspective of the home team as convention.

As we know, we have five games tonight.  I’m going to refer to them by Game #s, much the same way that the NHL does their games.  The WCHA plays 140 games: each team hosts 14 games over the course of the season.  As such, these are Games: #136-140.  We’ll go by the puck drop time and then by alphabetical listing by the home team to differentiate the games.  So we have:

  • Game #136: Bemidji State University (BSU) at Bowling Green State University (BGSU), puck drop 7:07 p.m. Eastern.
  • Game #137: Lake Superior State University (LSSU) at Ferris State University (FSU), puck drop 7:07 p.m. Eastern.
  • Game #138: Northern Michigan University (NMU) at The University of Alabama in Huntsville (UAH), puck drop 7:07 p.m. Central.
  • Game #139: Michigan Tech University (MTU) at Minnesota State University, Mankato, puck drop 7:07 p.m. Central.
  • Game #140: University of Alaska Anchorage (UAA) at University of Alaska (UAF), puck drop 7:07 p.m. Alaska.

Now, anyone who’s been following this fun WCHA playoff run (USCHO, knows that the final tally of this season will come down to Game #140.  Will Anchorage stay in the playoffs?  Will either school bump teams out for home ice?  All of these things were possible from my perspective starting this post before Friday’s games — I needed the time to set everything up!

There are 243 ways that this whole sordid mess can be sorted out tonight.  Yes, 243: three possible outcomes for each of the five home teams is 3 * 3 * 3 * 3 * 3 = 243.  Yeah, this breakdown seemed a lot more fun when it was 2 * 2 * 2 * 2 * 2 = 32.

I’ve attached a PDF an Excel spreadsheet at the end of this post.  It’s the clearest way to present the situation, because there are branches off of the root of “Saturday’s games that have not been played”.  Let’s look at how this might work:

Winners: BGSU, FSU, UAH, MSU, UAF.

That is one of 243 overall branches, and it’s also one of 81 branches where the Falcons start the night off with a win.  If they tie or lose, you can throw those 81 winning branches away and focus on the branches that have their root with the result of the Beavers-Falcons matchup.

I think that you can see where this is going: when 9:30 p.m. Eastern rolls around, we’ll be from 243 branches down to just 27: the NMU-UAH result, the MTU-MSU result, and the UAA-UAF result.  An hour later, it’ll be down to just three.

But I wanted to do the hard work for you so that you could look things over yourself.  Print this out, or look at it in your browser — you’ll be able to follow this.  Just read it left to right.  The labels will work with you to help you narrow things down pretty quickly.  By the time the first games are over, you’ll be down to just one of the pages.

Let’s use that BGSU, FSU, UAH, MSU, UAF result again, which is #243 in the table.  That gets us the following table:

Seed Team Record Points
1 Minnesota State 21-7-0 42
2 Ferris State 20-6-2 42
3 Alaska 15-11-2 32
4 Bowling Green 13-11-4 30
5 Michigan Tech 12-12-4 28
6 Alaska-Anchorage 11-13-4 26
7 Northern Michigan 12-15-1 25
8 Bemidji State 10-14-4 24 1
  Lake Superior 12-16-0 24
  Alabama-Huntsville 3-25-1 7

BSU wins the A) tiebreaker, 3-1-0 in head-to-head play with the Lakers

Now, the PDF doesn’t have that listed tabularly, but it does give you a 1-10 listing of the teams.  You can follow the tiebreakers and standings yourself from my post over on earlier this week, but in short: A) if (all of) you played four times, it’s the head-to-head record(s); B) Conference wins; C) Winning percentage against teams from the top to the bottom of the table.

What we know here on Saturday afternoon:

  • UAH will be 10th.
  • UAF will be 3rd.

That’s it.  That’s what’s so awesome about this!

Check out the PDF.  I hope that this makes for an enjoyable companion to your Saturday night scoreboard watching!  I have audited it reasonably extensively, but it is entirely possible that I missed something.  If so, you have my apologies.  I felt that we needed a different way to visualize this information, and that was my aim.

2014 Playoff Branches 0

2014 WCHA Playoff Race: Probabilities Predict Standings

Sometimes, the obvious stuff doesn’t occur to you right away.   The probabilistic model could be extended: take the most likely scenario and use that to predict the final standings!   Gosh.

That means:

  1. BG and BSU split.
  2. FSU sweeps LSSU.
  3. NMU sweeps UAH.
  4. MSU and MTU split.
  5. UAA and UAF split.

That gives you the following:

Seed Team Record Points
1 Ferris State 20-6-2 42
2 Minnesota State 20-8-0 40
3 Alaska 14-12-2 30 1
4 Michigan Tech 13-11-4 30
5 Bowling Green 12-12-4 28 2
6 Alaska-Anchorage 12-12-4 28
7 Northern Michigan 13-14-1 27
8 Bemidji State 11-13-4 26
  Lake Superior 12-16-0 24
  Alabama-Huntsville 2-25-1 3

1 A) The teams went 2-2-0 this year, and B) the Nanooks have one more conference win.

A) The Falcons were 2-1-1 against the Seawolves this season.

Our bracket would be:

  • #8 Bemidji State at #1 Ferris State
  • #7 Northern Michigan at #2 Minnesota State
  • #6 Alaska-Anchorage at #3 Alaska
  • #5 Bowling Green at #4 Michigan Tech

The Alaska Plan ended up not becoming a reality, but here it is in all its splendor.  Oh my.

2014 WCHA Playoff Race: The Final First-Order and Probabilistic Models

Welcome to the new blog, everyone!  It was unfair to have this take over for much longer, and I have longer-term plans on it, anyway.  New blog, new Twitter handle, same nerd.

Here are the final predicted standings from the first-order model:

Team Record Points
1 Minnesota State 21-7-0 42
2 Ferris State 20-6-2 42 1
3 Alaska 14-12-2 30 
4 Bowling Green 12-12-4 28 2
5 Alaska-Anchorage 12-12-4 28
6 Michigan Tech 12-12-4 28
7 Northern Michigan 13-14-1 27
8 Bemidji State 11-13-4 26
9 Lake Superior 12-16-0 26
10 Alabama-Huntsville 2-25-1 3

1 The MacNaughton Cup would be awarded to both teams, but for seeding purposes, the B) tiebreaker goes to the Mavericks, who have  one more WCHA win.

The three-way log-jam at 12-12-4 is broken by the C) tiebreaker, given that all three schools did not play the other two squads four times.  They all have 12 wins, so you have to go to winning percentage down the table.  Against the Mavericks, the Huskies have the worst performance (.000), while the other two were .500.  At the next level, the Falcons went .250 against the Bulldogs, better than the winless Seawolves.

I call this a first-order model because it uses KRACH to create an expected value parameter that is then used to make a reasoned prediction.  It’s effective, to be sure, but it’s pretty simplistic.  As such, it’s been wrong this year on a number of occasions.  There are some limitations to the model, and let’s just look at where we work in Week 17:

Team Record Points
1 Ferris State 20-0-8 48
2 Minnesota State 16-10-2 34
3 Bowling Green 13-9-6 32 
4 Alaska-Anchorage 13-11-4 30
5 Northern Michigan 13-13-2 28
6 Lake Superior 13-13-2 28
7 Bemidji State 11-11-6 28
8 Alaska 11-14-3 25
9 Michigan Tech 9-12-7 25
10 Alabama-Huntsville 2-25-1 3

Yes, the team that the model currently expects to be #3 was in 8th, and the #9 team, Michigan Tech, is now very likely to be in the home ice race, too.

Clearly, in-season modeling is hard.  Hockey teams aren’t single numbers.  Just this past weekend, the expected value model said that Alaska would only take one point.  They, uh, swept Ferris.

Oh, and the first predictive model I had said that they had nearly no chance of this.  But I can make my model better, and I have.

Screen Shot 2014-03-06 at 6.24.48 PM

We’ve gotten somewhere!  Here’s the source of my problem: I was under-estimating UAH’s chances at winning at Bemidji.  I famously said that UAH had a 1.6% chance of winning, but you know, I was underestimating them.  Also, I had too much room for teams to get ties.

Now the model does the following:

  1. The standard deviation range goes in the right direction.  If the teams are rather unequally yoked, the SD needs to be larger (squashing the bell curve down); when you’re near 2.000 points, you have a smaller SD.  Why?  You don’t need to widen the spread as much to give the unequal teams a chance to have all possible results.  After all, UAH gets points about 1/9 of the time, and you have to account for that properly.
  2. There is a weighted standings component.  It doesn’t have an “if this happens, these are the results with the tiebreakers applied” yet, but that’s planned for the summer.  No, doing an average of the 10,000 runs will give you the estimated number of wins, and that should be a good proxy for the tiebreakers.

Screen Shot 2014-03-06 at 6.25.11 PM

As you can see, the FSU-MSU thing really is a tossup: 55 comparisons in 10,000 results are all that separate them. Also, in nearly every scenario, equal points favors the Mavericks.  (The alternate scenario: MSU ties MTU twice.)

Bemidji State fans are unlikely to be happy with me here, but losing to UAH really hurt their KRACH.  (It breaks my heart.)  It’s reasonable to think that LSSU and NMU can pick up points (see above), and it’s hard for BSU to pick up more than a point, on average.  They’re on the road against a good team that is very good at home.

(About that: there is no home-ice bonus.  I need to study that NCAA-wide to figure out how to best model that.  I have an idea, but I didn’t want to enter more noise into the system that I already have with an unproven model.

I’ll run this again on Saturday to see where we are in the finals.  I also have a nice toy coming for you on Saturday.  #branches