Seal Block: Midwest Bracketologie

Picking an NCAA bracket using basketball knowledge is as much a recipe for success as picking based on the team's mascots or school colors. To have a truly scientific and rational decision-making process, we need to delve more deeply into the essence of the competing schools. What better way to reach that quintessence than by analyzing their seals? Thus, we present the Seal Block breakdown of the Midwest Regional. Will UNC live up to its top seed, or will a sleeper rise from the lower half of the field?


OPENING ROUND

 

(16) Vermont d. (16) Lamar
Lamar, like all schools in Texas, is sure to make us know they're located in Texas. However, their very basic design doesn't match up to Vermont's old-school details, including the Pythagorean theorem, which as Shaquille O'Neal reminded us, cannot be solved.

(12) California d. (12) South Florida
USF, as we discussed in the original Seal Block series, loses serious points for its horribly inaccurate globe. The only odd thing about California's seal is that section A starts halfway through the book, a small flaw in comparison. Cal brings home the victory.

The Mathematics of Beating OSU

Another week, another titanic shift in the Pairwise rankings. As far as we're concerned, the big news is Michigan jumping up to #2 after Notre Dame's split with Ohio State. The Wolverines are tied with Northeastern for that spot, but own the comparison with the Huskies, and thus the tiebreaker. It really is a knife's edge, though. Take a look at the full chart at CHN: Michigan, Northeaster, Vermont, and Notre Dame all have 21 or 22 comparison wins over the field. Lose a game, and suddenly you're the #5 overall seed. And sometimes you don't even have to lose to have a comparison flip on you. Remember the TUC cliff?

As a refresher, the Pairwise Rankings consider four factors when comparing two teams: head-to-head record, RPI, record against common opponents, record against teams under consideration (TUCs), but you have to have played 10 TUCs for that comparison to be used.

For instance, let's consider Michigan and Miami. Head-to-head record is 2-2, so two points to each team for that. Michigan's RPI is better, so they get a point. Miami's record against common opponents is better: point, Redhawks. Miami has only played 8 TUCs, so that comparison is not used. Michigan and Miami are tied 3-3 here, and we use RPI to break the tie. Michigan takes the comparison. HOWEVA. Miami has played 8 TUCs, which are defined as the top 25 teams by RPI. They play Ohio State twice to close out the season. As OSU is currently a TUC, that would allow them to meet the 10-game requirement. If both teams win out, Miami's record against common opponents is still better and now their record against TUCs is better, flipping the comparison over to them. Maddening, I know, but that's the way the Pairwise works.

What that means is that this weekend's series against the Buckeyes is much bigger than even a regular UM/OSU brawl: It's fighting for position at the top of the Pairwise, fighting for a spot in the Grand Rapids regional against the soft underbelly of Atlantic Hockey or College Hockey America. Win, get a Miami loss, and life is looking a lot easier. If not, drop below Notre Dame and you have to fight harder to not get sent to Minneapolis.

So, what are our chances? KRACH is here to answer that. KRACH is meant to use ratios between teams' KRACH ratings to give a predicted winning percentage. For example, the expected winning percentage of a team with a KRACH of 150 playing a team with a KRACH of 50 is .750.

Michigan's expected win pct. vs. OSU = Michigan KRACH / (OSU KRACH + Michigan KRACH)

Michigan currently sports a shiny KRACH rating of 402, while OSU is up to a rather healthy 197.8. That gives Michigan an expected winning percentage of .6702. The probability of two independent events both occurring is the product of the probability of either one occurring separately (i.e., P(A and B) = P(A)*P(B)). Michigan has a 67.02% chance of winning on either night against OSU, so the probability of a sweep is 44.92%, going by KRACH. Not great odds, but I'll take 'em. OSU only has a 10.88% chance of a sweep, leaving a 44.2% chance that we split.*

Michigan's been playing decent hockey since the Bowling Green loss, while OSU has been doing weird things, like only getting a pair of ties out of four opportunities against Western and State (though they got a win againt Western in the shootout) while beating Notre Dame and almost sweeping them but for some late-period heroics by the Irish.

Meanwhile, root for Northern to upset Miami down in Oxford. We'll take any help we can get. And really pull for the Bucks when Miami comes calling.

*Odds of Michigan winning out for the rest of the season? A moderately robust 30.1%.

UPDATE: Excellent catch/clarification by Brian, reproduced here verbatim: "Miami's TUC record is actually 6-4-2, but head to head games are excluded from that category in each individual comparison, leaving Miami at 4-2-2 for the purposes of its Michigan comparison." So for the purposes of everyone not in the CCHA, Miami is a TUC.

HSR Bracketology

If you've been keeping a close eye on the NCAA Pairwise Rankings for college hockey, you might have noticed that, after this weekend's sweep of Lake Superior State, Michigan slid up into a tie with Notre Dame for 3rd. And if you already knew that, you're well aware of the volatility of the Pairwise. Well, after last night's Beanpot win by Boston University, there have been some additional shuffles. Notre Dame is now tied with Vermont for second (the Catamounts hold the tie-brekers), leaving us alone in fourth.

I started to think about what that means for us. The NCAA assigns the #1 seeds to their closest regional and does so in order of overall ranking. BU would go to Manchester, NH, and Vermont to Bridgeport, CT. Next up is Notre Dame. By virtue of their one place advantage in the Pairwise, the Irish are sent to Grand Rapids and Michigan is sent up to Minneapolis. Where Minnesota is hosting. At a TOTALLY NEUTRAL SITE that's 7.5 miles from their home rink. (UPDATE:  They're at Mariucci this year, then at the X in 2010 and 2011. Three years in a row hosting. Un-friggin'-believable)

The Gophers aren't the same team we played in the College Hockey Showcase and beat 6-4. They've long shed that #1 ranking, and they're hanging on by a thread to the last available at-large birth in the tournament. But they're still a dangerous team and I don't want to play them on their home turf in the first round, especially if Don Lucia can get his health back in order by then (We sincerely wish you good luck with that, Coach).

Now, if Michigan were to drop down a spot or two, there's an excellent chance that we'd be sent to Grand Rapids, in keeping with the NCAA's new emphasis on keeping teams close to home to reduce travel expenses. So this could be like two years ago, when our reward for beating Michigan State in the CCHA semi-finals was a trip out to Denver and the Regional of Death. This year's Minneapolis offering doesn't project to quite that level of hellaciousness, but for selfish reasons I'd definitely rather see them in Grand Rapids.

Speaking of that Minneapolis regional, let's figure out who'd be there as things now stand.

Start with the current Pairwise and fill in according to basic bracketing. I've penciled in Air Force and Niagara as the highest-ranking teams by KRACH in the CHA and Atlantic Hockey, respectively, and thus most likely to grab their conferences' auto-bids.

1	BU	2	Vermont	3	Notre Dame	4	Michigan
8	Princeton	7	Denver	6	Cornell	5	Northeastern
9	Miami	10	Yale	11	UNH	12	Minn.-Duluth
16	Niagara	15	Air Force	14	Minnesota	13	OSU

We now assign the top seeds to their closest regional in order of overall seeding; BU to Manchester, Vermont to Bridgeport, Notre Dame to Grand Rapids, and Michigan to Minneapolis. Next, we have to ensure host insitutions are sent to that regional (New Hampshire in Manchester and Minnesota at their NEUTRAL SITE home rink in Minneapolis). UNH is a straight-up swap with Miami. We can't do the same with Minnesota, as placing OSU in the Grand Rapids regional creates an intra-conference first-round matchup with Notre Dame. OSU is bumped over to the Bridgeport regional and Air Force is sent to Grand Rapids. Final result:

Manchester		Bridgeport		Grand Rapids		Minneapolis
1	BU	2	Vermont	3	Notre Dame	4	Michigan
8	Princeton	7	Denver	6	Cornell	5	Northeastern
11	UNH	10	Yale	9	Miami	12	Minn.-Duluth
16	Niagara	13	OSU	15	Air Force	14	Minnesota

There a couple of factors still looming out there. If the NCAA were to recognize the huge gulf between Minnesota and the CHA and Atlantic Hockey champions, they might put bracket integrity ahead of avoiding an intra-conference matchup, sending OSU to Grand Rapids.

Another factor in play is the new emphasis on travel costs. Right now we have 7 teams who would be traveling more than 400 miles, meaning they get to fly (Note: It's unclear to me whether the barrier is 400 miles by road or as the crow flies): Michigan, Denver, Cornell, Northeastern, Niagara, OSU, and Air Force. Michigan can't be touched, and Denver and Air Force will have to fly no matter what. But if our emphasis on bracket integrity (and the perfection of the Pairwise) is lessened, we can save a couple of flights. If we flip Denver into Grand Rapids for Cornell, we create an intra-conference matchup with Yale, but save a flight. We could also put OSU back into Grand Rapids at the expense of putting three CCHA teams in one regional, or flip Air Force with Niagara if we don't care about potentially screwing over BU.

Lurking out there is also the issue of New Hampshire. If they slip down to a #4 seed, that will create a mandatory intra-conference matchup in the first round and will force BU to play a much better opponent than the CHA/Atlantic Hockey can provide. Conceivably, the committee could opt to send BU down to Bridgeport and force Vermont to play UNH. At least Manchester and Durham are a little farther apart than Minneapolis and Minneapolis. It would be like Michigan hosting a regional at the Joe. We'll see how this plays out.