On 2015-16 Games 83, 86, 91, and 93

As a note: I number all 140 games based on a simple formula:

  • Game start in GMT.
  • If two or more games start at the same time in GMT, the game further to the east gets listed first.

I could probably do this by the order (that makes no sense) in which the games are listed on USCHO’s week-by-week results, or I could do it series-by-series.  This is the way that I’ve chosen to do it the last three seasons.

In “Re-thinking the Goal Differential Bonus“, I was responding to a criticism of the wise Tim Braun of Tech Hockey Guide, who was wondering why Mankato’s destruction of Lake State netted them more points than the Huskies picking up three points against the Mavericks.  It’s a fair question!  Let’s do the math.

As a starting point: the current main constant in BELOW calculations, generally referred to as K, is 40.  The multiplier of the goal-differential is 10.

Starting points:

  • Game 83 BELOWs: Minnesota State 1698, Michigan Tech 1580.
  • Game 83 Expected Values: MSU .664, MTU .336.
  • Game 83 Results: MSU .500, MTU .500.

Again from calculating BELOW, we take the difference between the expected result and the actual result and use that to calculate a new BELOW.

For Mankato: BELOW 83,7 = 1698 + (40 + 10*0) * (.500-.664) = 1691.

To deconstruct that:

  1. We start with Mankato’s BELOW coming into the game.
  2. We calculate our volatility factor by adding the base constant (40) to the goal multiplier (10) by the goal differential (0).
  3. We calculate the final factor by comparing the real result to the expected one.  A positive value here means that the team outperformed the results.

Multiply and add and you’ll see that Mankato loses 7 BELOW points by tying with Tech.  The two teams are indeed pretty far apart in BELOW, but a tie just reverts them to the mean a bit.  Is that enough?  We’ll consider that below.

Consider the range of possible outcomes for Mankato’s BELOW on Game 83:

  1. Mankato wins by three or more goals: +24
  2. Mankato wins by two goals: +20
  3. Mankato wins in regulation by a goal: +17
  4. Mankato wins in overtime: +4
  5. Mankato tie: -7
  6. Mankato loses in overtime: -21
  7. Mankato loses by one goal in regulation: -33
  8. Mankato loses by two goals: -40
  9. Mankato loses by three or more goals: -46

Because the difference between the two teams is significant, decisive results move the teams closer fairly significantly.  A three-goal Huskies win makes the margin 1652 to 1626 — a vastly different affair.

So with that said, the Friday result didn’t change a lot in terms of BELOW, because the expected value of each team is pretty close to the tying result (+/- .164).

What about Saturday?

  • Game 85 BELOWs: Minnesota State 1691, Michigan Tech 1587.
  • Game 85 Expected Values: MSU .647, MTU .353.
  • Game 85 Results: MSU 0.00, MTU 1.000 by two goals.

For Tech:

BELOW 84,8 = 1587 + (40 + 10*2) * (1.000-.350) = 1625.

That means that Tech, on the weekend, gained 45 BELOW points — but Mankato also lost those points.  A gap that was 118 points was now just 28.

Now you know what?  I just found an error in my spreadsheet, which makes me want to hurl my computer across the room.  I had done a sanity check that Tech’s BELOW had gone up with the result, but I hadn’t fully audited the equation.  That, Tim, is what addresses your question about the result.

So I guess I get to audit this again!  That’s what I get for making the spreadsheet on midnight shifts.

Let’s complete the exercise, though.  Now to Mankato-Lake the next weekend, Games 91 and 93:

  • Game 91 BELOWs: Minnesota State 1652, Lake Superior 1430.
  • Game 91 Expected Values: MSU .739, MTU .261.
  • Game 91 Results: MSU 1.000, LSSU 0.000 by eight goals (capped at three).

For Mankato:

BELOW 91,7 = 1652 + (40 + 10*3) * (1.000-.739) = 1671.

Even though it was a huge win, Mankato was so much of a lock that it barely moved the needle.  Again, compare that result to Game 83: +24 there vs. just +19 here.

  • Game 93 BELOWs: Minnesota State 1652, Lake Superior 1430.
  • Game 93 Expected Values: MSU .777, MTU .233.
  • Game 93 Results: MSU 1.000, LSSU .000 by four goals (capped at three).

For Mankato:

BELOW 93,7 = 1671 + (40 + 10*3) * (1.000-.777) = 1686.

That’s also worth noting: because the Friday result said, “Wow, the Mavs are way better than the Lakers,” the marginal improvement on Saturday was smaller.

So on the Mankato @ Tech weekend, the Huskies picked up 45 points; on the Lake @ Mankato weekend, the Mavericks picked up just 34.  Improving in BELOW is as much or more of a matter as who you beat as it is by how much, but it’s also a cumulative, relative measure of value.

Mankato’s high BELOW this year is 1744, and they have eight weeks above 1700 (and a ninth at 1698), so bringing that down will take more than just one good weekend for the home side in Houghton.

I hope that this answers some questions.  Hopefully this is the only error in my spreadsheet.

Lastly, on the topic of goal differentials: what if I nix the multiplier completely?  That weekend goes +36 for the Huskies (remember, there are lots of other games in there), while the Mavericks pick up +19.  As to whether a marginal multiplier is “right”, I’d have to do something like error minimization between the actual and expected results.  That’s … a lot more math, and I’d have to be diving into Minitab or Matlab to make that work.

Re-thinking the Goal Differential Bonus

Tim Braun pointed out something on USCHO’s Fan Forum that I hadn’t fully considered:

Is it just me or does it seem strange that MTU gains 25 points for taking 3 points from a superior BELOW team, but that same team gains 43 for sweeping an inferior team?

Other than the way MSU did it against LSSU, I don’t think anyone would be more impressed with MSU’s sweep of LSSU than MTU’s 3 points vs MSU?

He’s right.  In thinking about it, a goal-differential of 3 seems to be decisive.  Limiting things to a goal differential of 2 would leave me going into the box scores to seeing if there’s an empty-net goal that makes it a wider margin.  Even if there’s an ENG in a 3-goal game, the game was already pretty decisive.

Going forward: I’m capping the goal-differential bonus at three goals, regardless of outcome.  I explain my reasons why below after looking at the data.  When I re-calculate BELOW going forward based on results alone, this cap will have an effect.  BELOW gains/losses in the first list of ten games will be adjusted appropriately, and as such the ratings will change slightly.

How often are there three-goal margins?

I decided to look into how many times a goal margin exceeded three goals in the 2015-16 WCHA.  We would presume that these wide margins would come in games where BELOW was ranking one team well above the other, with the better team getting the big win.

Let’s look at the data.  Matchups in bold are situations where a wide margin benefits the lower BELOW team; matchups in italics are big road victories.

  1. Game 1: Michigan Tech (1654) beats Ferris State (1481) by a 5-1 margin.
  2. Game 13: Alabama-Huntsville (1391) beats Lake Superior (1389) by a 5-0 margin.
  3. Game 32: Alaska-Anchorage (1450) upsets Ferris State (1566) by a 5-0 margin.
  4. Game 49: Minnesota State (1708) beats Alaska-Anchorage (1481) by a 6-2 margin.
  5. Game 66: Michigan Tech (1551) beats Lake Superior (1490) by a 6-2 margin.
  6. Game 80: Bemidji State (1520) beats Alaska-Anchorage (1458) by a 5-1 margin.
  7. Game 89: Bowling Green (1645) beats Alaska-Anchorage (1430) by a 6-2 margin.
  8. Game 90: Bowling Green (1661) beats Alaska-Anchorage (1414) by a 6-2 margin.
  9. Game 91: Minnesota State (1670) beats Lake Superior (1472) by an 8-0 margin.
  10. Game 93: Minnesota State (1687) beats Lake Superior (1455) by a 5-0 margin.

So of those 10 matchups, only one — Anchorage going into Big Rapids and shutting the Bulldog down 5-0 — was what you’d term an upset.  The Huntsville win over Lake State was surprising, but you’ll always get one outlier in a season’s worth of games. (Given that UAH has won just four games to-date, I’d call that an outlier.  Please give me a minute to pull myself together.)

The road rout by Tech over Lake State isn’t a big shock, as the Taffy Abel isn’t a huge home-ice advantage, and the trip across the UP is one of the shorter ones in the WCHA.  The big Bemidji win in Alaska was, as we’ve noted, indicative of a big turn for the Beavers as 2016 has started.

In light of the above, it makes sense that goal-differential should be capped.  As such, I have a nice IF statement in my table: if the goal differential is greater than 3, the goal differential bonus is capped as if the margin were only 3.

What about margins of three goals — how many are two-goal games that became three-goal games?

For completeness, the below 3-goal games had empty-net goals that padded their outcome:

  1. Game 19: Ferris State v. Minnesota State.
  2. Game 41: Bemidji State @ Alabama-Huntsville (and it wasn’t even the final goal; the Beavers later scored 5×5).
  3. Game 44: Bemidji State @ Alabama-Huntsville.
  4. Game 46: Michigan Tech @ Alaska.
  5. Game 64: Bowling Green @ Bemidji State (ENG SHG to boot).
  6. Game 68: Alabama-Huntsville @ Minnesota State.
  7. Game 97: Michigan Tech @ Bowling Green.

Games 3, 12, 22, 26, 31, 74, 76, and 84 have “true” three-goal wins, or eight of the 15 wins.

To recap:

  1. 25 WCHA games through 98 played have margins of three goals or higher.
  2. 10 of those games have margins greater than three goals.  For purposes of calculating BELOW, they will be treated as if they were three-goal victories.
  3. Of those ten games, only one can truly be considered an upset, while another was a 50-50 matchup.  As such, three goals is where we draw the line.
  4. Of the 15 remaining games, eight were three-goal margins unaffected by empty-net goals.
  5. Of the remaining seven games, six ended in empty-net goals.
  6. That last game is when Huntsville gave up an ENG with :43 left and then another goal with :08 left and the goalie in the net.  Ladies and gentlemen, your 2015-16 UAH Chargers.

We may re-visit this three-goal cap in the offseason, but I’m willing to bet that we’ll see similar data from the previous two seasons.

2015-16 Week 18 Prediction: Alabama-Huntsville at Alaska-Anchorage

Alabama-Huntsville sweeps, keeping slim playoffs alive: 14.00%

Alabama-Huntsville gets three points, Seawolves edge past Alaska: 13.91%

Teams split, Seawolves pull into tie for 7th with Lake Superior: 33.32%

Alaska-Anchorage gets three points, pulls clear into 7th: 17.39%

Alaska-Anchorage sweeps, pulls into three-way tie for fifth with Bemidji State and Northern Michigan: 21.37%

This series is just as interesting as the one for first.

2015-16 Week 17 BELOW Ratings

TeamW17 BELOWRank (Last)StandingsW16 -> W17W1 -> W17
0-UAH132110 (10)10th0-79
1-UAA13999 (7)8th (tie)-34-17
2-UAF14088 (9)8th (tie)0-115
3-BSU15376 (4)5th (tie)-15+3
4-BGSU16782 (2)2nd+34+103
5-FSU15385 (6)3rd (tie)+15+57
6-LSSU14427 (8)7th-43+19
7-MSU17131 (1)1st+43+25
8-MTU16253 (3)3rd (tie)0-29
9-NMU15394 (5)5th (tie)0+32

No huge changes from last week’s results, and I don’t think that the numbers are telling us anything that we didn’t already know.  Look for predictions for Tech-BG and UAH-UAA later this week.

The Case for Alternate League Points Systems

I’m working on a long post about tiebreakers that are likely to be in play this season.  But I want to stop and look at something else: two proposals for alternate point systems.

For purposes of calculating BELOW, I take note of overtime results, both ties and decisions.  I thought that I’d look to see if I could determine some better approaches to league points calculations that might drive league coaches to different decision points.

I want to propose two systems:

  • 3-point.  Regulation wins get three points, overtime wins get two points, and getting to overtime (tie or loss) gets one point.
  • 4-point.  Regulation wins get four points, overtime wins three, ties two, and overtime losses one.

Now, I’m of two minds about this.  The 3-point system encourages teams to go for the extra point in overtime, as there is no penalty for losing.  But the 4-point system might encourage winning in regulation and lessens the idea of “carry it to overtime and we’ll see if we can get the extra point”, because the value of winning in 60:00 is now 4x the value of just making it to OT.

This next table is the 2015-16 WCHA standings with 2-point, 3-point, and 4-point systems.

TeamW-OTW-T-OTL-L2*W + T3*W + 2*OTW + 1*(T+OTL)4*W + 3*OTW + 2*T + 1*OTL
Minnesota State12-0-5-0-3294158
Bowling Green9-2-4-1-2263651
Michigan Tech9-1-2-0-6223143
Ferris State7-2-4-2-5223144
Northern Michigan6-1-4-2-5182637
Bemidji State6-1-4-1-8182536
Lake Superior5-1-4-1-7162232

You can see that there’s not a ton of change in the standings regardless of system.  It may not matter too much, but I’m for anything that encourages a decisive result without radically changing the shape of the game (3×3, shootouts).

No More Week 17 Predictions

While those of you in the UP may laugh at what screws up roads here in Huntsville, it’s getting bad and I’m probably going to have to head in to work early.  All of the prep for that kept me from finishing predictions for this week.  I’ve mainly figured out that my tool isn’t up to the task, so I’m going to be regrouping this week (which I thankfully have off from work!).

The matchups are Ferris State at Bemidji State and Lake Superior at Minnesota State.  If you want to eyeball it from the Week 16 ratings and the work that I did on the BGSU-UAA series, you can expect that the FSU-BSU series would converge around a split, while the LSSU-MSU series models a lot like that BGSU-UAA series give or take a few percentage points.

I’ll be back at you next week.

2015-16 Week 17 Prediction: Alaska-Anchorage at Bowling Green

These predictions take into account the BELOW calculations from earlier today, so read that post if you haven’t yet.  I mused in that post about changing my weighting factors, and I’ve done that here: the K constant is now 40, with a 10x goal-differential multiplier (which I can’t use here anyway).

I know that I’ve written about this before, but let’s look at how the whole prediction calculation set works:

  1. We start with BELOW rankings for each team in the game after each team’s previous game.  Here, we have UAA at 1466 and BGSU at 1647 (again, different than the earlier rankings because of the constant changes).
  2. Calculated an Expected Value (EV) of the matchup.  In this case, BGSU’s EV is .739, which is pretty high — essentially, you can expect that they’ll get a favorable result about three times in four.
  3. I calculate bands around the possible results, which I’ll show in a table below.  First I establish a center point that is skewed in favor of the team with the better EV; then I set values for ties, overtime results, and regulation results based on that center point and the overtime trends of the league.
  4. I use a random number generator that picks a value between 0.000 and 1.000.  That value is slotted into the bands above, and a result is found.
  5. I then take the result — regulation, overtime, or tie — and re-calculate BELOW for each team.
  6. I repeat steps 1-5 above, and additionally, I tabulate the results.

All calculations are run 10,000 times.

Week 16 BELOW14661647
EV Game 89.261.739
Center Point0.381
UAA Wins0.0000.244
UAA OT Wins0.2450.284
BGSU OT Wins0.4770.517
BGSU Wins0.5181.000

As you can see, UAA gets a win about 28.4% of the time, while BGSU gets one about 52.3% of the time.  Indeed, my 10,000 calculations of this series give UAA a win or an overtime win in 28.34% of the Game 89 results.

Because I can’t calculate a goal-differential from this method — I have some ideas of how I could fake one in, but I need more data — the BELOW changes are purely based on the W-OTW-T-OTL-L result.  Here’s what happens:

UAA Win14961617
UAA OT Win14861627
BGSU OT Win14661647
BGSU Win14561657

Note that the OTW bonus is 0.750, which is very close to BGSU’s BELOW.  As a result, BELOW says that BGSU should only gain points if it wins in regulation; winning in OT just treads water, while any other result says that the gap between Anchorage and Bowling Green wasn’t as wide as we thought.  Conversely, anything that’s a tie or better is a net gain for UAA.

Now, this is all very well and nice, right?  Sure, you and I could sit down over a beer and predict this one: UAA comes out with a win about one in four, a tie somewhere in between, and a BGSU win at least 50% of the time.  Duh, right?

The value of BELOW comes in that you can play, “What-if?”  What if UAA were underrated by BELOW and they pulled off a resounding regulation win?  Well, BELOW would narrow the gap from 181 points to just 121.  Remember, the win expectation grows with the gap, so cutting that by 1/3 is huge.

Let’s consider a situation where UAA wins on Thursday night.  Again, that happens in 2,834 of our 10,000 cases.  How does that affect things for Friday night?

UAA Results# Results

UAA wins 2,432 on Thursday night.  Its winning percentage on Friday night after taking into account Thursday night’s result is 28.7%.  It’s not a big increase, but it is one.

It’s probably easiest to see the results in one last table.

UAA RecordProbabilityResultProbabilityBGSU Record
7-8-36.43%Win + Tie14.38%10-3-5
7-9-230.74%Win + Loss30.74%10-4-4
6-8-41.64%Tie + Tie1.64%9-3-6
6-9-314.38%Loss + Tie6.43%9-4-5

With BG three points behind Mankato in the table, they stand a pretty good shot of getting the result that they want to have.  Even then, it’s just two-in-five.

I’ll come back on Friday with predictions for the other two games.

Week 16 BELOW

2015-16 Week 16 BELOW Rankings

TeamWeek 16 BELOWWeek 16 RkWeek 15-16 DeltaWk 10 to Wk 16
BELOW is an Elo-inspired ranking for WCHA member teams. This is the ranking set after Week 16 (games ending 2016-01-17). Constants have been adjusted slightly, which explains the changes in rankings from last week.

A couple of notes:

  1.  I’ve changed the constants for the post-game Elo-style calculation to induce a little volatility to the ranking.  Teams can get a theoretical 40 point increase per contest (in a world where the bad team has a BELOW of 1).  This is larger than previous weeks.  Why increase it?  I wanted to increase the signal of any given win, as this is very much a one-goal, often-overtime league.  Teams that win — and preferably win big — deserve a bonus.
  2. Speaking of OT: of the 88 WCHA games that have been played, 24 of them have gone to the extra five minutes, a stunning 27.3%. In fact, there have already been as many OT games in 2015-16 as 2014-15, and there are 52 games left to play.  If that rate continues, we’ll see 38 overtime games.
  3. Because of the OT glut, I only give OTW a 0.75 rating rather than a full 1.00.  (This is actually above where I once was at 0.60.)  This means that Alaska’s big win in Marquette on Friday — ask Nanooks fans how much they love the Berry Events Center — was only a bump of (40+5*(1 goal))*(0.75-.347), or an increase of 18 BELOW points instead of 29 with a one-goal, regulation win.
  4. I’m considering increasing the goal-differential multiplier, which is currently at 5x the differential.  I’m not sure that it much matters, but I’ll consider it.

It’s important to remember the calculation that’s being made here.  Let’s go back to that Alaska-Northern Michigan result.

Coming into the weekend, Alaksa’s BELOW was 1421, which is pretty bad, while Northern Michigan’s was 1531,  As a result, you’d expect that the Wildcats would win 65.3% of the time.  A Nanook upset had a pretty big impact — 18 BELOW points, as noted above — but it could have been bigger.  How much bigger?

Alaska @ Northern Michigan, 2016-10-15

Overtime win18
Regulation, one-goal win29
Two-goal win32
Three-goal win36
Four-goal win39
Five-goal win42
A table of possible results of the UAF-NMU game last Friday.

That table tells me that my goal-differential bonus is probably too small.  The last really-big WCHA win, Bemidji’s emphatic 5-1 win in Anchorage, should probably have been awarded more points.  A goal bonus of 10x would’ve had twice the bump.

Why the manipulation?  BELOW is designed to be a predictor, and we all know that teams go on runs (say hey, Beavers, who jumped 57 points in Alaska) as they get puck luck, hot goalies, team cohesion, and players back from injury.  In fact, that hot run by Bemidji indicates that they really did make a turn — that 57 point jump took the team from a .500 team to one playing .570 hockey, or stuck in the middle to a pretty good shot at finishing 4th.

So why do I call the value of BELOW as a predictor to be paramount?  Let’s take those Beavers (7-8-3), who sit with a BELOW of 1548.  Their future opponents:

  • Home v. Ferris State (8-7-3): This series is a pick-’em with the Bulldogs at 1524.  Bemidji needs at least three points to pull even with the visitors in the standings and in the A tiebreaker, as the teams split their meeting in Big Rapids.
  • Away at Lake Superior (6-6-4).  The Lakers (1450) came into Bemidji and stole three points early, and Bemidji has to return the favor.  A large BELOW advantage gives the Beavers a good shot.
  • Home v. Michigan Tech (10-6-2).  This is the Beavers’ biggest test of the year, full stop.  A sweep here is big for BELOW and the standings.
  • Home v. Huntsville (3-12-3): The Chargers are baby seals, and the Fitzg3ralds have the clubs.  200-point BELOW differentials are like .750 winning chances for the better team.
  • Away at Mankato (10-3-5): The Mavericks swept the Beavers in Bemidji, and with the regular season likely to come down to the last night (again), the Green cannot expect Mike Hastings to ride herd on the stampede.

But that’s two series where Bemidji should shine, two where they’re underdogs, and one where it’s a toss-up.  If the Beavers are what we think they were, that’s how it will go; but if they’re somehow better or worse, that changes.

Using BELOW as a random variable allows us to play, “What if?” — not only for Bemidji but for the other nine teams, all through the final 52 games.  I won’t be able to get the numbers for the rest of the season run by the weekend, but I’m hoping to complete the first predictions before January ends.

2016-01-16: BELOW, Predictions

Good morning, everyone!

Three overtime games in the WCHA made for an interesting evening, if one that many decried for being boring.  I only watched UAH-FSU, and that game was … well, something.

Of course, tight games collapse everyone to the center when it comes to BELOW.  My current calculations take into account the number of overtime games when it comes to generating the bands that the random number generator puts results into.

Here’s the summary of last night’s results:

UAH-FSU 3-3 (OT): UAH up 9 to 1352, FSU down 9 to 1508

UAF-NMU 3-2 (OT): UAF up 18 to 1439, NMU down 9 to 1508

MSU-MTU 2-2 (OT): MSU down 5 to 1686, MTU up 5 to 1607

I’ve upped the number of runs to 10,000, and the expected values of tonight’s games are as follows:


Before you look at that last column and really, truly cringe, realize that, again, these are random variables, so the chance that they’re all three going to OT is (44.09% * 44.59% * 44.35%), or only 8.7%.  Of course, the WCHA has had four nights where three or more games went OT: October 30, November 20, November 21, and last night.

I won’t have time to run the “how often does Huntsville win, Northern Michigan win in OT, and Mankato and Tech tie?”-type scenario until next week.

Enjoy tonight’s games, even though you might have to stay up a little later to watch them.