What Each WCHA Team Needs in Week 23

I thought that I’d take a quick pass at what each team needs this weekend.  Before I jump in, let me note who plays where this weekend along with the three most likely results.

  • Bemidji at Ferris: Split 50%, Bemidji sweep 37%, Ferris sweep 8%
  • Tech at Mankato: Split 39%, Mankato sweep 31%, Tech sweep 25%
  • Lake at Northern: Northern sweep 48%, split 45%, Northern win+tie 7%
  • BG at Anchorage: BG sweep 94%, BG win+tie 4%, split 2%
  • Fairbanks at Huntsville: Alaska sweep 51%, split 42%, Alaska win+tie 7%.  (UAH sweep .01%)

Now the obvious here is always this: win your games and don’t worry about tiebreakers.  However, every team can’t sweep.

  1. Mankato needs to sweep Tech.  This ensures them possession of the McNaughton Cup, and it means that they can take their foot off of the gas a little next weekend, get some guys some rest, etc.  While it may seem a little silly to worry too much about positioning here — Mankato or Tech will get one of Huntsville, Lake, or Anchorage, none of which have taken a point off of the Mavericks or Huskies this season — the players and the fans surely care.  Sweeping Tech finishes things, and the model says that happens 31% of the time.
  2. Tech simply needs to take points off of Mankato to push to another weekend.  Simply put, the Mavs have a much easier slate next weekend in their home-and-home with the Wildcats than the Mavs do in going into the Sanford Center.  Points this weekend pushes it to another round, and my model says that the Huskies win the McNaughton 61% of the time.
  3. Bowling Green simply needs two points in any of their final eight games to snag third regardless of what either Bemidji or Northern do the rest of the way.  That seems like an easy task, even though they’re in the 49th right now to face the Seawolves, because they come home to face UAH, which has been a pretty easy win for a home squad.  In fact, in 10,000 runs of my model, BG gets two points 10,000 times.  They just want to remove all doubt.  A terrible weekend against Northern cost them a shot at the McNaughton, but the gulf between them and the teams below them makes this a pretty easy task.  Pick up a win tonight and you have three games to work on things.
  4. Bemidji State and Northern Michigan need wins, period.  The three-way tiebreaker between Bemidji, Northern, and Ferris is a complicated one, but this result is pretty simple: Northern must win to keep pace with / get ahead of Bemidji, and Bemidji must simply keep pace.  As I noted on Wednesday, Bemidji sweeping Ferris pretty much puts Ferris in sixth.  Bemidji has to want that, because that takes one team out of the race for home ice and ensures that Northern can’t pull ahead.  If the Beavers can’t go for the road sweep, they at least want the split and for the Lakers to hold up their end of the bargain.  Bemidji gets as many or more points than Northern 98% of the time in my model, but they have to go and get them.  Bemidji gets points 63% of the times in my model, so they’re doing okay.
  5. Northern needs help for home ice, but they’re in a crappy position.  Sure, they have two points on Ferris, but they lose the A tiebreaker to Bemidji.  They have to hope that they get more points than Bemidji does this weekend and hope that Ferris doesn’t draw even in the process.  Sweeping the Lakers in Marquette really, really helps them here, because they come out of the weekend 12-10-4 (28) and no fewer than two points ahead of Ferris and no worse than even with Bemidji.  Simply put, beating Lake is easier this weekend than beating Tech next weekend, the early-season results notwithstanding.  A Wildcat sweep and a split in Big Rapids should leave everyone happy.  My model says that happens about 24% of the time.
  6. Ferris State needs points.  Sweeping Bemidji pushes them past the Beavers, and they have to hope that Lake takes points off of the Wildcats.   A strong weekend in net by senior captain CJ Motte gives the Bulldogs hope that this won’t be the last time they see him at the Ewigleben Ice Arena.  Obviously, their best hope is to sweep the Beavers and have the Lakers sweep the Wildcats (0 of 10000 runs in the model), but it’s more likely that they get the sweep and the Lakers the split (3.72%).
  7. Alaska needs a time machine.
  8. Huntsville needs three points to send it to tiebreakers — where they’ll win — and four points to win it outright.  Their goal this weekend is to hearken back to earlier home weekends where they swept the other team from the 49th and then Northern Michigan.  If that teams shows up this weekend, the Chargers — who are banged up over already thin depth — can relax a little next weekend and focus on the parts of their game that make them effective against much more skilled opponents.  But since the numbers don’t favor the Chargers, they need a to just keep pace or pull ahead of Lake Superior.  The model says that happens 70% of the time.
  9. Lake Superior needs to slow the momentum of a rolling Wildcat squad.  Nothing less than a split will do.  While it’s unlikely that Anchorage will pass them (like 0.00% unlikely) this weekend, the Seawolves do have their final four at home, where they’ve had a modicum of success in 2014-15.  Given that the model says that the Seawolves pick up a win just 2% of the time, that aforementioned split should lock up the final playoff spot.
  10. Simply put, Anchorage has to win at least once and UAH and LSSU have to be swept.  While the model says that Anchorage can pass both teams above them about 2.5% of the time, that only happens because they have the Governors Cup to play for next weekend, a series where they get a win (and the cup) pretty much every time out.  (Note to self: make sure that’s right.)  This happens 0.64% of the time.  Believe, Seawolves fans.

Bemidji-Northern-Ferris tiebreaker going into Week 23

Hello, USCHO fans!  Jack and Shane asked me to run scenarios for them.  I’ve already tweeted about this a little, but without applying probability to it, I just wanted to do the math and show what happens with the Bemidji-Northern-Ferris tiebreaker, which is the really fun one left at this point (depending on how Tech and Mankato go this weekend).

I’m going to assume that you’ve read my extended look at the WCHA’s tiebreakers for 2014-15 and know what I’m talking about when I say “the C tiebreaker”.  If not, I suggest reading the first paragraph and then the six bullet points (and not the other 1700 words that follow).

To recap one of the later sections, these things are true:

Bemidji State and Northern Michigan both sit tied for fourth at 10-10-4 (24 points).  Ferris is two points behind them at 11-13-0.  Ferris has the potential for winning a B tiebreaker, as they have one more conference win at this point.

Let’s ignore the chances that ties get involved here and just say that there are wins and losses here.  Here are the remaining games for each team:

  • Bemidji State: @ Ferris State, v Minnesota State
  • Ferris State: v Bemidji State, @ Lake Superior
  • Northern Michigan : v Lake Superior, home-and-home with Michigan Tech

Later, I quote the tiebreakers, but the important things here are these:

A tiebreaker: this only comes into play between Bemidji and Northern, and Bemidji wins the comparison.

B tiebreaker: currently Ferris has 11 conference wins to 10 for Bemidji and Northern.  Of course, they also have the handicap of three more losses where they got no points.

C tiebreaker: Bemidji and Ferris have yet to play this weekend, and Ferris and Northern push to the D tiebreaker.

D tiebreaker: Here are the records against the top three seeds:

  • MSU: BSU 0.000 (with two games left); FSU 0.000; NMU 0.250 — Northern wins all comparisons
  • MTU: BSU 0.000; FSU 0.000; NMU 0.750 — Northern wins all comparisons
  • BGSU: BSU 0.375; FSU 0.250; NMU 0.625 — Northern wins all comparisons

So in other words:

  • Ferris: To get level with Bemidji and/or Northern and win home ice, Ferris has to get the B tiebreaker in their favor, which generally means that they need to keep winning.  Ties are better than losses, but here, a win-loss split is better than a two-tie split.
  • Northern: They just have to hope that they’re not tied with Bemidji alone.  If they are tied with Bemidji and Ferris, they have to hope that Ferris has tied some games along the way and keeps from passing them in conference wins and have split with the Beavers.  If it’s Northern and Ferris alone, they again have to hope that Ferris doesn’t have more conference wins.  I’m not sure that I can concoct a scenario where things get to the D tiebreaker, although I’m going to try below.
  • Bemidji: They’re in the catbird’s seat here: they have the tiebreaker over Northern, a points advantage on Ferris, and two games against Ferris.  Bemidji is much better at home than on the road (9-4-2 v. 3-10-2), so they have to be gunning for things.

So it all comes down to ten games, here

I’m not going to go through every iteration (e.g., “Bemidji sweeps Ferris, Northern sweeps Lake, Ferris sweeps Lake”) here because I don’t have time to do this.  (I mean, it’s snowing in Alabama, and I want to go outside and play!)  But let’s consider these things, based on the above:

Bemidji sweeping Ferris fairly fixes the Bulldogs in sixth place.  The Bulldogs would be 11-15-0 (22 points), and they’d be behind the Wildcats regardless of their result against Lake Superior.  At worst, Northern sweeps Lake Superior and is 12-10-4 (28 points), which gives the Wildcats more points than the Bulldogs can get.  At best,  Lake Superior sweeps Northern and the Wildcats are 10-12-4 (24 points), and Ferris can pass them anytime then get even and have one more conference win — say, Northern splitting with Tech and the Bulldogs sweeping the Lakers.

Ferris sweeping the Beavers greatly helps the Wildcats’ chances.  Simply put, both teams play Lake Superior going down the stretch, and Bemidji is not as tough of an opponent as Tech is, especially given that the Beavers will be on the road (where, again, they’re 3-10-2, although two of those wins are in Marquette a couple of weeks ago).

Bemidji always just has to worry about keeping pace with Northern.  The only way that the Wildcats can pass the Beavers is to get more points with them, and that’s not something that happens very often in my model.  In fact, Ferris getting more points than both Bemidji and Northern happens more often (5.5% v 1.77%).  Yes, the two squads face the top two seeds on the final weekend, but Bemidji is at home for both games.

Let’s talk about ties.  The only way we get to the D tiebreakers — Northern’s favorites — are if the teams are tied in the first three, which means that they all have to finish with the same number of points and Ferris has to have taken two ties along the way to bring them level in conference wins and very likely those ties have to have come against Lake Superior, because ties with Bemidji make it harder for all teams to have equivalent numbers of points.

But here is the problem: trying to get four ties for the Bulldogs (11-13-4/26) gives the Beavers two more points (10-10-6/26) pending the results with Mankato.  If the Beavers get swept, they lose the B tiebreaker; if they get any more points, there is no tiebreaker with Ferris State.

Now you can look at Ferris and Northern and ask, “Can the Wildcats benefit from four Ferris ties?”  Yes, they can.  Again, Ferris finishing 11-13-4 means that they can go 1-3-0 themselves down the stretch.  The A tiebreaker is irrelevant; the B tiebreaker is now a wash; the C tiebreaker is still a wash; and the D is where they win.

But ask yourself this: how often does Ferris tie its final four games after not registering a tie all season>

So in short, rock-paper-scissors style if teams are tied:

  • Bemidji beats Northern
  • Ferris probably beats Northern (unless they do a lot of sister-kissing)
  • Northern just has to keep winning, because they have outpacing their peers.

Hope this helps.

2014-15 WCHA tiebreakers and their relevance

Here’s how the tiebreakers work in the WCHA.  You will regularly see me call these “the A tiebreaker” or similar.  All tiebreakers are used to compare two or more teams.  If three or more teams are involved, a tiebreaker pulls the winning team out and resets the comparison process.  More on that later.

  • A tiebreaker: a team wins the tiebreaker if they won a four-game season series.
  • B tiebreaker: a team wins the tiebreaker if they had more conference wins.
  • C tiebreaker: teams are compared based on their winning percentage in head-to-head matchups.
  • D tiebreaker: teams are compared based on their winning percentages head-to-head against teams down the standings table.
  • E tiebreaker: winning margin (goals for minus goals against) in conference contests.
  • F tiebreaker: coin flip.

Now, last year showed that it’s unlikely that we’ll pass the D tiebreaker.  Let’s see if that’s true based on where we are with everyone having played 24 league contests.

The spread

At this point, it’s Mankato-Tech 1-2 for the McNaughton Cup.  BG getting swept by Northern ended their shot at one of the top two seeds, and they’re quite clear of Bemidji and Northern in 4th — but we’ll get to that, too.

My concern here will be in the following comparisons:

  • Who wins the McNaughton, Tech or Mankato.
  • The edge case of Bemidji and BG/Northern interacting.
  • Who comes away with home ice in the Bemidji-Northern-Ferris trio.
  • Which two teams make the playoffs at the bottom of the bracket.

The McNaughton Cup

This is probably the easiest setup: Mankato has the edge by one point, and the two teams play each other two more times.

The A tiebreaker will be in play, as the Mavericks swept the Huskies earlier in the season.  If the Huskies sweep, they make the season series even and push things to the B tiebreaker.

  • If Mankato sweeps, they are 21-3-2 (44 points), and they are the regular season titlist by being five points clear going into the final weekend.
  • If Mankato wins and ties, they are 20-3-3 (43 points) while Tech is 19-5-2 (40).  Tech would have to sweep Northern while Bemidji wins at least one against the Mavs, because Mankato still wins the A tiebreaker.
  • If the teams split, Mankato is 20-4-2 (42) and Tech is 20-5-1 (41).  Mankato still gets the A tiebreaker because they went 3-1-0 on the season.  As such, Tech is going to have to get two more points on the final weekend than Mankato does.
  • If Tech wins and ties, the Huskies are 20-4-2 (42) and the Mavs are 19-4-3 (41).  Mankato still has the A tiebreaker, so they will need just one more point than the Huskies get on the final weekend.
  • If Tech sweeps, the Huskies are 21-4-1 (43) and the Mavs are 19-5-2 (40).  The A tiebreaker is now out of play.
  • Mankato would have to sweep Bemidji to get to 21 conference wins, and the Huskies would be okay as long as they got a win versus Northern. However, if the Wildcats take three points — and they did to start the seasons — both teams would be 21-5-2 on the season.
  • At that point, you go to the C tiebreaker, which is also out, and then the D, which starts with performance against teams below them.  Both teams split with BG.  Both teams would have swept Bemidji.  Mankato would win because they picked up a win against Northern.

BG is very likely to finish in third

Northern Michigan ended Bowling Green’s chances to make the McNaughton chase a three-team affair.  The Falcons can only end up tied for second in points with Michigan Tech at 39 if they win out and the Huskies lose out.  That makes Tech 19-8-1 and BG 18-7-3, and Tech wins the B tiebreaker, conference wins, as Tech and BG played just twice this season.

There is the unlikely event that the Falcons lose out and end up 14-11-3, 31 points.  Bemidji State or Northern Michigan could win out for 32 points and a shot at third.  (More on any BSU-NMU tiebreakers later.)  If either (or both) of those teams ended up with just 31 points, they’d go 3-0-1 in their final four games to finish 13-10-5, while the Falcons would be 17-7-4.  The Falcons’ edge in conference wins (and thus the B tiebreaker) won’t matter in this scenario, as the Falcons were 2-1-1 against Bemidji and 1-2-1 against Northern.  In an insane, three-way tie, BG wins with Northern in third, having lost both comparisons.

In short: BG can’t get to 2nd; they can get to 5th if they lose out and Bemidji and Northern win out; if they end up tied with 31 points, they beat Northern in the A tiebreaker but lose to Bemidji.

The race for home ice and, in consolation, realizing that they avoid the top two teams

Bemidji State and Northern Michigan both sit tied for fourth at 10-10-4 (24 points).  Ferris is two points behind them at 11-13-0.  Ferris has the potential for winning a B tiebreaker, as they have one more conference win at this point.

Let’s ignore the chances that ties get involved here and just say that there are wins and losses here.  Here are the remaining games for each team:

  • Bemidji State: @ Ferris State, v Minnesota State
  • Ferris State: v Bemidji State, @ Lake Superior
  • Northern Michigan : v Lake Superior, home-and-home with Michigan Tech

A tiebreaker: Bemidji and Ferris this upcoming weekend for the first time.  Bemidji won the season series 3-0-1 over Northern.  Ferris and Northern only played twice, splitting the series.

B tiebreaker: conference wins is pretty straightforward.  Any tie between Bemidji and Northern is very likely to result from their winning the same number of games.  Ferris will have to win one more game than either or both of the other two win, so they’re guaranteed to win the tiebreaker in that scenario.

C tiebreaker: head-to-head comes back into play again, and the only unknown is the BSU-FSU ranking.  Again, Bemidji wins over Northern and Ferris and Northern push to the D tiebreaker.

D tiebreaker: It’s pretty unlikely that we’re going to get here.  Bemidji wins the A tiebreaker over Northern, so equal runs there still pushes the Beavers ahead.  A three-way tie means that Ferris wins the B tiebreaker, and cycling back again favors the Beavers.

If Ferris and Bemidji split, the C tiebreaker is irrelevant.  But then Ferris has to win one more game than the Beavers, which means that the Mavericks sweep while the Bulldogs split with the Lakers or the Mavs and Beavers split while the Bulldogs sweep.  But then Ferris State is 13-15-0 or 14-14-0 while Bemidji is either 11-13-4 or 12-12-4, and either of those scenarios results in the Bulldogs winning the B tiebreaker.

You could negate Ferris’s advantage by having the Bulldogs tie four times, finishing them at 11-13-4.  But Bemidji could then be no more than 12-10-6 if they swept the Mavericks, and they’d be 11-11-6 if they split.  That result gets us to the D tiebreaker, as the teams played just twice, have the same conference wins, and were then tied in HTH.  Then we do the D tiebreaker:

  • MSU: Bemidji would be 1-3-0, and Ferris went 0-4-0.
  • MTU: Bemidji and Ferris were winless against the Huskies.

As you can see, the only way for Ferris to jump into 4th is for them to win one more conference game than both Bemidji and Northern.  Ferris only controls its destiny by playing the Beavers this weekend; otherwise, they are fans of Lake Superior and Michigan Tech, a position that’s surely strange in Big Rapids.

The races for last

I want to stop for a second and lament Alaska’s ineligibility.  They’d be tied for sixth with Ferris State, and that pairing of four would be more interesting than the three pack, mainly because the Nanooks are 10-12-2 and ties just make for chaos.

But the UAH-LSSU-UAA race is pretty simple.  I wrote earlier on UAHHockey.com that the Chargers need three points to get to tiebreakers and four to win outright.  They can’t get to 6th, but they can miss entirely if they win just one game (8-19-1, 17) while Anchorage wins out (8-18-2, 18) and Lake State gets at least five points (8-18-2, 18 or 7-17-4, 18).  Should all three teams end up 8-18-2, UAH ends up in 7th.  If UAH and LSSU end up tied in points, UAH wins based on their 2-1-1 season series.

LSSU then really only has UAA to worry about if they play such that they go to tiebreakers.  UAA hasn’t won in the lower 48 this year (one tie against Maine), and they’re on an 0-8-0 run.  They get Bowling Green this week in Anchorage before hosting Alaska the next, so if they’re going to make a run, this is it for them.

Tiebreakers: The teams split two meetings this year, so our concerns lie with the B and D tiebreakers.  Let’s consider the D tiebreakers first before going through the permutations on the other end.

  • MSU: both teams were winless against the Mavs.
  • MTU: both teams were winless against the Huskies.
  • BGSU: the Lakers and the Falcons split two games, while the Seawolves have yet to face BG.
  • BSU: UAA went 0-2-2, while LSSU went 2-0-0.
  • NMU: UAA went 1-3-0, while LSSU is 0-2-0 against NMU going into this weekend.

Whew.  Now let’s look at every way that these teams can end up tied.

18 points:

  • Anchorage sweeps Bowling Green (winning the D tiebreaker at that point) and then Alaska to get to 8-18-2.
  • LSSU would need five points to get to 18, which is either two wins and a tie (8-18-2) or a win and three ties (7-17-4).
  • Two LSSU wins ensures that Anchorage wins the D tiebreaker; one win ensures that Anchorage wins the B tiebreaker.

17 points:

  • Anchorage would get three wins and a tie (7-18-3).  This means that Anchorage wins the D tiebreaker, since they wouldn’t lose to the Falcons.
  • LSSU would need four points, which means they either win two games (8-19-1), a single win and two ties (7-18-3), or the insanity of four ties (6-17-5).
  • Two LSSU wins ensures the Lakers win the B tiebreaker.
  • One LSSU win and two ties sees that Anchorage wins the D tiebreaker
  • Four ties ensure that Anchorage wins the B tiebreaker.

16 points:

  • Anchorage either finishes 3-1-0 (7-19-2) or 2-0-2 (6-18-4).  At best, they sweep the Falcons and win the D tiebreaker; at worst, they get both ties against the Falcons and sweep the Nanooks, which leads them to being Wildcat fans.
  • LSSU would need three points, which is either 1-2-1 (7-19-2) or 0-1-3 (6-18-4).
  • If the Lakers get their points via ties only, they lose the B tiebreaker.
  • If the Lakers win-and-tie, they win the tiebreakers if: 1) the Seawolves go 2-0-2 (win on B); 2) the Seawolves split with the Falcons and the Beavers edge the Wildcats in the standings.
  • The Seawolves can win if the Lakers win-and-tie and they go 3-1-0 and they save that loss for the Governor’s Cup.

15 points:

  • Anchorage finishes 2-1-1 (6-19-3) or 1-0-3 (5-18-5).
  • LSSU gets two points, either 1-3-0 (7-20-1) or 0-2-2 (6-19-3).
  • LSSU wins the B tiebreaker if they win a game or if their two-tie effort is met with a 1-0-3 effort for the Seawolves.
  • If LSSU goes 0-2-2 and UAA goes 2-1-1, the Seawolves win the D tiebreaker if they go at least 1-0-1 against the Falcons.  They could lose the same tiebreaker if their two wins come against the Nanooks or if it’s Bemidji edging Northern.

14 points:

  • LSSU ties just one of its four remaining games (6-20-2).  It won’t matter which.
  • UAA finishes either 2-2-0 (6-20-2), 1-1-2 (5-19-4), or 0-0-4 (4-18-6).
  • LSSU wins the B tiebreaker except when UAA goes 2-2-0.
  • If UAA goes 2-2-0, it wins the D tiebreaker when it sweeps the Falcons.  If it splits with the Falcons, they’re rooting for Bemidji.  If they are swept by the Falcons, LSSU wins the comparison.

13 points:

  • LSSU loses out (6-21-1).
  • UAA either goes 1-2-1 (5-20-3) or 0-1-3 (4-19-5).
  • LSSU wins the B tiebreaker.

Now, wasn’t that fun?

Week 21 Predictions

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And I’m back!  I have prettier graphs!  Well, at least this one is pretty.

The WCHA standings are ranked in three tiers: Mankato-Tech-BG, NMU-BSU-FSU, and UAH-LSSU-UAA.  This is true in the actual standings as well as the predicted ones that you’ll see below.

Here’s a legend on how to read the above graphic: the team in a bold color is on the road (with the best approximation of their colors that I can get in Excel), while the team at home is in white.  So if you look at Bemidji-Northern:

  • Bemidji wins about 1.09 times in the 10,000 runs that the model does.
  • Northern wins about 0.88 times .
  • The teams get an average of 0.04 ties.

You get this math from the ones below it, which are HM0% (the chance that the home team is swept), HM1% (the chance that they lose and tie), etc.   I’ll explain a little bit more about the math in a bit.

As you can see in the Bemidji-Northern series, a split is the most common option (40.69% of all runs), with a Bemidji sweep second (32.94%) and Northern sweeping third (22.63%).  The remainder are events where the model thinks that the schools might tie.

The math — expected values

The model I’m presenting here uses KRACH only for a way to generate an expected value of the series.  KRACH is a rigorous mathematical answer to the improper application of the transitive rule, which could be considered from a UAH perspective like so:

“Hey, Omaha is 16-7-3, eighth-best in the country winning percentage-wise with the second-toughest strength-of-schedule.  But you know what?  UAH tied them one night and lost by only a goal another night.  We’re not that bad!”  Except, you know, Tech RUTS’d UAH and has almost an inverse record to the Red Cows (7-18-3).

KRACH compares everyone to everyone with matrix mathematics that accounts for the fact that, well, everyone doesn’t play everyone.  So when teams cross over into non-conference play, it matters.  The three teams with 20-win seasons so far are Minnesota State, Michigan Tech, and Robert Morris, but the relative non-conference records of those two conferences makes a difference, as does the schedules that each of those three schools played:

  • Mankato: @Omaha 2x, H/H with Duluth, v Princeton, North Star College Cup (Minnesota, Bemidji State)
  • Tech: v Michigan 2x, @ Duluth, GLI (Michigan, Ferris State), @ Wisconsin (the split there hurts them)
  • RoMo: Lake Superior, Three Rivers Classic (Penn State, Colgate), H/H with Bowling Green

KRACH gives a numerical ranking  that can be used to do a backwards look.  If Robert Morris (103.5 in KRACH before games on 2015-02-13) played Air Force (23.82), you’d expect the Colonials to win 81.2% of the time [103.5/(103.5+23.82)].  This lines up  fairly well with reality, as the Colonials are 2-1-1 against the Falcons this season (.750), with all four contests going to overtime.

A greater disparity can be seen in the MTU-UAA matchup, where the Huskies get the sweep 100% of the time.

Mind you, I had confused the M*U with the UA* matchups this weekend (I blame the cold medicine).  But Mankato is a virtual lock to sweep UAF, too (93% of the time).

The math — distributions

Now once you get this expected value from KRACH, you can consider the results to be normally distributed, i.e. on a bell curve.  This is to say: all things told, if you know how likely Team A is to defeat Team B, you can set that as the expected value of the distribution and then run simulations on that distribution.

Now wait, you’re saying, how are these things equally distributed?  Didn’t you say that Tech was going to crush Anchorage?  Yes, I did.  Tech’s KRACH of this moment is 411.8; UAA’s is 47.44.  Tech should win 90% of the time by that.  Sorta.

See, the model says, “Okay, Tech’s going to ‘win’ 90% of the time, i.e. they’re going to get 3.6 points per weekend.”  And that expected value is what’s used.  Why?  I’ve never gotten the sense that college hockey games are independent events, which is to say that what happened on Friday night will drive what happens on Saturday night (injuries, benchings, etc.).  This may be a failing of the model — I haven’t tested it extensively, but it worked reasonably well last year. But it’s the model that I’ve chosen.

So if Tech is supposed to pick up an average of 3.0 points per weekend, rounding that up means that, on average, they sweep.  In fact, if you use breakpoints in determining what is a sweep (for the model, it’s 2.95 /4, which gets pretty close to the historic average of ties produced in WCHA games), Tech sweeps every time.

The math — standard deviation

We’ve all heard the term “outlier”.  We probably know one.  Shoot, pretty much every NHL player is an outlier in some form or fashion, a man so uniquely skilled at hockey that people pay him vast sums to do so.  But even in the NHL, some guys are simply better than others.

In statistics, this concept is variance.  Tied closely to variance is the concept of a standard deviation, which is to say how wide the distribution is.  In your standard academic exercise, 20 kids take an exam where the average is 68: 18 kids make an 80, one makes a 100, and one makes a 0 because they tried to cheat off of the kid acing the exam.

You can run this if you want, but the standard deviation is about 17 points, which is to say that the kid acing the exam was more than two standard deviations away, while the kid who cheated was four.  In statistics, the former is expected variance — there’s nothing unusual about a kid who aces an exam when the vast preponderance of the class barely passed it.  However, the latter is significant and should prod a question as to why (even though we know why in this case).

The application

In the Tech-UAA case — thanks for staying with me — the mean is shifted so close to the 4-point limit that centering a bell curve here also mean that we have to consider the width of said curve.  I set that width — the standard deviation — to the width of the mean in comparison to its distance from the edges.  As such, the closer you get to 0.0 or 4.0 expected values for the home team, the more likely a sweep will happen.

You can see this with UAH @ LSSU, which is nearly even in terms of KRACH (48.19 UAH, 43.97 LSSU).  This is why a split is most likely: the mean is very close to 2.0, and the variation is pretty wide, so the answers to to spread evenly between the center and the poles.  This is largely a pick-’em series, but the numbers say that UAH is slightly better from a comparison standpoint.

But again, that’s why they play the games.

The cascade

If you simulate all 22 remaining series — and I have — 10,000 times, you get results that look like the below.

B9sGuWHIQAA2hbf.png-large

 

It’s a shame that Alaska is ineligible, because three teams fighting for one spot would be far more desperate than three fighting for two.

My intent for the next couple of weeks is to come up with a way to set up a table that shows how many times that, say, the above order comes into play.  If I were doing this with a database and not an Excel spreadsheet, this would be simpler, but I ran out of time to do anything else.