Author: Jim Dahl

It started with a good article in the Grand Forks Herald on UND’s home attendance that suggested a link to UND’s (thereby jinxed) home winning streak. A big home ice advantage did mention a home advantage, but only included home winning percentages as supporting evidence. That’s fine, you don’t expect in-depth statistical analysis in a newspaper article that: is trying to make a different point, has a limited word count, and is targeted toward a non-statistical audience.

However, USCHO then ran with the idea of a piece on home advantage, but used home winning percentage to compare “home ice advantage” across teams. Given that, This Week in the WCHA unsurprisingly found that the best teams of the past decade had the largest “advantage” and the worst teams the smallest. They were interesting statistics, but I would argue that they compared teams’ home success, not home advantage.

The problem (for those who missed my Forum post on the topic) is that home winning percentage isn’t really the same thing as home ice advantage. The advantage of home ice is not how well you do at home, but how much BETTER you do at home.

Sticking with winning as the measure for now, here’s how each WCHA team did in WCHA play at home and on the road from the 2001-02 season through the 2008-09 season.

That’s still not quite a perfect measure of home advantage, but as a comparison between performance at home vs. on the road, it’s quite a bit closer.

Anyone who wants to keep the ball rolling by writing a followup critical of this post should start with these caveats:

• To read this table as measure of home ice advantage would be to pretend that away games are neutral, whereas they instead actually include some home advantage for the opponent
• It doesn’t correct for strength-of-schedule (e.g. the measure would be distorted if a team scheduled tough opponents at home and cupcakes on the road)
• It compares only WCHA games
  • This is useful because it actually corrects a little bit for the above two. The WCHA schedule over 8 seasons is somewhat round-robin (though not perfectly so, due to the “rivals” system)
  • However, home advantage could be different when hosting non-conference foes less familiar with a team and its venue
• I’ve never actually seen anyone try to measure home advantage using win%, it’s usually measured in points scored or scoring differential. So, there may be more problems with this measure that I’m not thinking of right now.

Here’s a quick look, for UND only, at how things would change with different sets of games counted.

This seems to support one of my criticisms above of only including WCHA games — UND’s home advantage is a bit higher hosting non-conference opponents.

One additional point about this table — I was never able to come up with selection criteria that precisely matched the records cited by the USCHO and Herald articles. Focusing on ties, for example, I count 17 total home ties since 2001-02 (18 if you include the tie vs. Minnesota in 2009-10), whereas USCHO and the Herald cite 21 home ties. I compared the schedules at SiouxSports.com, FightingSioux.com, and CollegeHockeyStats.net (see useful summaries at bottom), but couldn’t figure it out. If anyone has any theories or explanations, I’d love to hear them and will cheerfully make any necessary corrections.

Resources

• A big home ice advantage – Grand Forks Herald
• This Week in the WCHA – USCHO
• UND Hockey schedules/results — SiouxSports.com
• UND Hockey schedules/results — FightingSioux.com
• UND Hockey schedules/results — CollegeHockeyStats.net
• While we were bemoaning REA atmosphere… — forum.siouxsports.com thread

Here’s what I get. Errors are mine, not KRACH’s 😉

KRACH predictions of the 2009 NCAA tournament

West    Game 1    Game 2 (Region Champ)    Game 3 (Frozen four semifinal)    Game 4 (National Champ)
1. Denver    62.08%    37.17%    15.72%    7.19%
4. Miami    37.92%    18.14%    5.72%    1.98%

2. Minn. Duluth    61.32%    30.04%    11.16%    4.52%
3. Princeton    38.68%    14.65%    4.06%    1.24%

Midwest
1. Notre Dame    90.22%    62.64%    44.31%    26.90%
4. Bemidji St    9.78%    2.00%    0.43%    0.07%

2. Northeastern    65.10%    25.83%    14.65%    6.76%
3. Cornell    34.90%    9.52%    3.95%    1.27%

Northeast
1. Boston U    78.06%    57.04%    39.36%    24.45%
4. Ohio St    21.94%    9.49%    3.72%    1.22%

2. North Dakota    51.04%    17.30%    7.98%    3.13%
3. New Hampshire    48.96%    16.17%    7.30%    2.80%

East
1. Michigan    80.52%    48.55%    23.06%    11.32%
4. Air Force    19.48%    5.24%    1.01%    0.20%

2. Yale    45.91%    20.27%    7.30%    2.73%
3. Vermont    54.09%    25.93%    10.28%    4.22%

I’ll post the spreads between these predictions and the SiouxSports community’s picks (a.k.a. the homer bias) later.

I hacked on the simulator last night and got it supporting conditional games (e.g. winner of this game plays winner of that) and I’m glad I did — the results were pretty interesting.

Possibilities

Decked out in blacks for the Final Five, here’s the distribution of possible outcomes of the Final Five.

NOTE — unlike during the regular season, outcomes are not weighted as to their likelihood. So, instead of reading the chart “UND has a 35% chance of finishing #5 if games go as predicted by KRACH”, it should be read “35% of possible Final Five outcomes results in UND finishing #5”.

What to cheer for

A game-by-game cheering guide can be found in the “UND finishes #3” scenario in the Extreme outcomes section below. However, not all games are equally important. Here’s what seemed to matter in the simulations.

These are the minimum individual events required for a #3 finish (other things have to happen, too, but they involve combinations of outcomes)

• Notre Dame wins 1
• Alaska wins 1
• Michigan can’t win any
• Yale can’t win 2
• St. Lawrence wins 1
• UW wins 1
• Northern Michigan wins 1

Interesting tidbit — UND can lose a game and still be #4. It looks like most of those scenarios involve UND losing to UW in the title game, but there are a few others floating around out there.

Extreme outcomes

As many have speculated, UND does seem to be a lock for the tourney. Though likely outcomes seem to range from #4 to #10 in the pairwise rankings, possible finishes range from #3 to #13 (a broader range than I’ve seen speculated anywhere else). The fun thing about CHN’s You Are the Committee being out now is that you no longer have to take my word for it, I can give you the scenarios, proving that the simulator does something useful 🙂

UND finishes #3

UND finishes #3 in about .2% of possible outcomes. Given that there are about half a million possible outcomes of the remaining 19 games, that’s about 1000 different ways UND could finish #3. Here’s one of them.

Northeastern > Mass.-Lowell
Boston University > Boston College
Boston University > Northeastern

Cornell > Princeton
St. Lawrence > Yale
St. Lawrence > Cornell
Princeton > Yale

Mercyhurst > RIT
Bentley > Air Force
Bentley > Mercyhurst

Alaska > Michigan
Notre Dame > Northern Michigan
Alaska > Notre Dame
Northern Michigan > Michigan

UMD > UMN
UW > Denver
UND > UMD
UND > UW
UMD > Denver

UND finishes #13

UND finishes #13 in about .005% of possible outcomes. If my game count above was right, that’s about 25 different ways UND could finish #13. Here’s one of them.

Northeastern > Mass.-Lowell
Boston College > Boston University
Boston College > Northeastern

Princeton > Cornell
St. Lawrence > Yale
Yale > Cornell
Princeton > St. Lawrence

RIT > Mercyhurst
Air Force > Bentley
RIT > Air Force

Michigan > Alaska
Northern Michigan > Notre Dame
Northern Michigan > Michigan
Notre Dame > Alaska

UMN > UMD
Denver > UW
UMN > UND
UMN > Denver
UW > UND

What now?

• PWR thread remains hopping with a lot of people who are probably smarter than I am — head over there to discuss, pontificate, and learn
• John Whelan’s You Are The Committee (hosted at CHN) lets you test my scenarios and your own

I wasn’t sure if this post would be necessary or even useful because as the number of games becomes smaller, it becomes easier to use tools like CHN and USCHO’s PWR predictors and slack.net’s build your own rankings.

However, I found the results somewhat interesting, so with minimal fanfare, figured I might as well share them.

Look back at end-of-regular-season predictions

Most weeks since I began publishing these predictions, I pointed out the success (or occasional miss) of the previous week’s one-week prediction. Now I’m going to take a look back at the end-of-season predictions.

I’m going to declare victory and that this tool is actually a useful way to look at a team’s likely future PWR. Looking back at the charts now, with the outcomes known, they provided interesting information that really wasn’t previously obtainable through traditional analysis of close pairings.

The Sioux won 6.5 of their final 8 and ended the regular season at #8 in the PWR. Here was the prediction on Feb. 11:

The Sioux won 2.5 of their final 4 and ended the regular season at #8 in the PWR. Here was the prediction on Feb. 25:

Mar. 16 Possibilities

This chart should be taken with a big grain of salt, because it doesn’t correctly include the possibility of any matchup other than UND’s going to a 3rd game. However, since it includes the sweep and swept scenarios for each team, it probably gets the approximate ranges right, just not the distributions.

Conclusions:

• With some help, the Sioux could still be marching toward a #1 seed.
• Dropping even one game this series could put them at #10 or lower, making the WCHA Final Five games must-win to be assured a spot.
• However, even getting swept out won’t necessarily put UND out of the running; it would put them right on the edge such that other tournament outcomes could easily push the Sioux out.

Who to cheer for

In addition to just dumping the data of what games impact UND the most, I spent a minute or two on each trying to figure out why it might be important. My most interesting observation is that some are defensive plays that are important only if UND loses, when they become critical to propping up UND’s PWR.

Boston College @New Hampshire (UND averages 1.15 spots higher with a sweep)
Could flip the RPI point

AA @Denver (UND averages .98 spots higher with a sweep)
Could flip the RPI point and the COP point

Mass. Lowell @Vermont (UND averages .81 spots higher with a sweep)
Could flip the RPI point

Northern Mich. @Miami (UND averages .62 spots higher with a sweep)
NMU could become a TUC, but that just seems to solidify Notre Dame’s comparison to us by giving them the TUC point.
This is probably about making sure Miami doesn’t overtake us if the Sioux do anything other than sweep.

Brown @Yale (UND averages .48 spots higher with a sweep)
Again, this looks defensive, making sure Yale doesn’t overtake us if the Sioux don’t sweep.

More reading

Like I said in the intro, now that it’s getting easy 😉 everyone has their own predictions, so you PWR junkies can easily get your fill.

• PWR PairWise Rankings 2009 forum thread has become very active
• slack.net Build Your Own Rankings lets you supply a precise scenario of game outcomes and shows you what the PWR table will be
• CHN’s weekly PWR analysis, breakdown and comparison
• You are the committee (YATC) tools, which do both the job of slack.net’s calculator and show you the predicted seedings, should be available on CHN and USCHO after the conference tournaments end

When I started preparing this, I thought it might be the last of the season. As the number of remaining games becomes small enough, the You Are The Committee tools on USCHO and CHN start to become useful ways for you to explore the potential PWR outcomes yourself.

However, it occurs to me that the tricky thing about those tools has always been trying to figure out the impact of games not involving the team you’re studying, so I’ll probably run a few more simulations between now and selection day and post any interesting results.

This weekend’s outlook

Both the split and win curves are very stretched out this week. For either of those outcomes, UND’s fate would rest in the hands of other teams significantly more than usual.

UND loses both: 79% chance of #13-14, 98% chance of #12-15
UND splits: 50% chance of #10-11, 85% chance of #9-12 (possible outcomes range from #4-#13)
UND sweeps: 69% chance of #7-9, 92% chance of #6-10 (possible outcomes range from #3-#11)

UND’s likely PWR is given as a set of probabilities and ranges because other games’ outcomes will affect UND’s PWR. The “Who else to cheer for this weekend” section below lists, in order, the games that have the biggest impact on where UND will fall in the given ranges.

Who else to cheer for this weekend

As hinted at by nodakvindy on the forum when discussing Yale v. Princeton last week, these are the non-Sioux games that will make the biggest contributions to UND’s PWR this week.

They are focused solely on the short-term — what will maximize UND’s PWR as of next Monday (Mar 2).  Some outcomes that bump UND’s PWR upward in the short run, e.g. SCSU over Denver, may actually prove undesirable in the long-run.

Team to cheer for / how much their outcome will affect UND’s PWR this week:

AA vs Alaska (1.57 w/sweep, 1.03 w/1 win)
Princeton to lose vs Harvard/Dartmouth (1.13 lose both, .70 lose one)
SCSU vs. Denver(1.08 w/sweep, .25 w/1 win)
Ohio St vs Miami (.79 w/sweep, .58 w/1 win)
Merrimack vs UNH (.77 w/sweep, .54 w/1 win)
Maine vs Vermont (.79 w/sweep, .21 w/1 win)
UMN vs UMD (.69 w/sweep, .47 w/1 win)
Mich St vs Notre Dame (.65 w/sweep, .05 w/1 win)
Mass. Lowell vs Northeastern (.57 w/sweep, .18 w/1 win)

Season outlook

At least splitting the remaining four games is required to be in the relatively safe part of PWR. As was noted by farce poobah in the forum, “Given the likelihood that CCHA, Hockey East, and ECAC also may have upset winners, I think you have to be inside #10 to really be comfortable.”

Chat about this

There’s a good thread going on the forum discussing these forecasts. There are a lot of smart people who have gone into a lot more depth than I can in these articles, so stop by, read, chat, and ask questions.

(PWR) PairWise Rankings – 2009

For an explanation of this forecast, see previous weeks’ posts.

UND’s PWR after this weekend

The chart below shows three forecasts for UND’s PWR as of next Monday. The forecasts show the probability distributions of UND’s PWR for each of three potential scenarios — UND’s sweeps, UND splits, and UND loses both. The probabilities are derived from KRACH-based predictions for the non-UND games.

UND loses both — 62% chance of PWR being 16-17
UND splits — 90% chance of PWR being 12-14
UND sweeps — 60% chance of PWR being 9-10

Who else to cheer for

In order of importance to UND’s PWR, here’s what to cheer for this weekend. How many of these hit or miss is a pretty indicator of where UND will fall on the above curves.

Cornell to lose swept by Rennselaer/Union (boosts UND’s PWR 1.04)
Princeton to lose swept by Brown/Yale (boosts UND’s PWR .84)
Michigan Tech (at least 1) over Minnesota-Duluth (boosts UND’s PWR .48; .64 with a sweep)
Michigan (at least 1) over Ohio State (boost UND’s PWR .50; .62 with a sweep)
Colorado College (at least 1) over Minnesota (boosts UND’s PWR .43; .50 with a sweep)
Northern Michigan (sweep) over Miami (boosts UND’s PWR .45; UND harmed .02 with a single win)
Boston College (at least 1) over New Hampshire (boosts UND’s PWR .38; .43 with a sweep)
Wisconsin (at least 1) over Denver (boosts UND’s PWR .33; .41 with a sweep)

The bye week predictions’ results were again solid — the results went slightly against the “cheer for” recommendations so UND ended up at the bottom of the expected curve (keep in mind the predictions were through Monday, pre-Beanpot finale, at which time UND’s PWR was #16).

Without further ado…

Effect on PWR of this weekend’s games

UND wins 0: 78% of being #17-#18, 98% chance of being #16-#19
UND splits: 44% of being #16, 96% chance of being #15-#17
UND sweeps: 73% of being #11-#13, 89% chance of being #10-#14

Other teams to cheer for (or against) this weekend

Mass.-Lowell sweeping Boston College gives UND an average .88 bump in PWR ranking
Providence sweeping New Hampshire gives UND an average .86 bump in PWR ranking
Michigan St. sweeping Ohio St. gives UND an average .82 bump in PWR ranking
Alaska-Anchorage sweeping Minnesota gives UND an average .77 bump in PWR ranking

And a special split cheer against:

Yale losing to RPI and Union gives UND a .79 bump

Likely PWR outcomes for regular season based on remaining UND outcomes

Winning 6 of its remaining 8 is the worst UND can do and still stand over a 50% chance of being #13 or higher in the PWR at the end of the regular season.

For frequent readers, the only surprise this weekend was the amusing groundswell of interest in my headshot.

There was no surprise in UND’s PWR, which came out right in the meaty part of the curve again — quoting Forecasting the PWR… a look ahead at SCSU, “Split: 77% chance of landing #14 or #15”. The Sioux split, and are #15.

Forecast

You might think this a boring week for predictions, given that UND doesn’t play. Quite to the contrary, it’s one of the more interesting to date.

Because UND doesn’t play, there’s only a single distribution of where UND is likely to end up. Because UND has no games, all movement through the distribution is caused entirely by other teams’ results. It’s an interesting look at how much PWR is influenced, in just a single weekend, by other teams’ movements.

#14-#15 — 62% likelihood
#13-#16 — 93% likelihood
#8 — 1/1,000,000 chance

Who else to cheer for?

Note — updated as of 2:30PM CT, Feb. 2.  List was incorrect before then.  Hat tip to Siouxweet, see comments below.

The results this week are a little wonky because of all the split series in which a team is playing two different opponents.

Denver winning 2 games (Minnesota Duluth) gives UND an average PWR ranking increase of 1.16

Minnesota winning 1 game (Wisconsin) gives UND an average PWR ranking increase of .92 (the sweep increases that to .95)

Notre Dame winning 2 games (Ohio St) gives UND an average PWR ranking increase of .92 (1 game gives just .25)

Massachusetts winning 2 games (B.C. and Mass Lowell) gives UND an average PWR ranking increase of .86

Others the Sioux want to see win: Harvard (over Yale and BU), Colgate (over Princeton), and Cornell (over Princeton)

TUC cliff quirk of the week: Maine sweeping UNH gives UND a .85 raise, but a single win harms us.  Presumably the two wins would push Maine into TUC territory.

Special Timing Note

Given the Beanpot, note that this forecast includes predictions of tonight’s games to create a predicted PWR as of next Monday, excluding that day’s games.