Son of Engineer Bracketology

The Engineers are doing well enough on the ice and now in the PairWise Rankings that we've decided that the time is right to begin looking at the possibilities that they could make the national tournament. They're not there yet, but they are close enough to ponder the situation. The following is mostly pulled from the prologue to this exercise two years ago (when the Engineers did, in fact, end up making the tournament), slightly updated to reflect changes since then. If you know the score, feel free to skip the rest of this post.

Every week, until either the end of the ECAC Tournament or until the Engineers are no longer a viable candidate for an at-large bid, we will take a look at the PairWise Rankings (PWR) and find out where the Tute stands (I will refrain from using "RPI" to refer to the Engineers in bracketology to avoid confusion with the Ratings Percentage Index, a key component of PWR).

This is a bit of a primer to introduce you to the concept of Engineer Bracketology. It will be what I refer to as "micro-bracketology," a look at the PWR and the upcoming games as it pertains to a single team. Most national PWR observers, like Jayson Moy at USCHO, simply analyze the PWR and determine the likely makeup of the NCAA field using it. I call that "macro-bracketology." What I do is get into the nitty gritty and tell you what Engineer fans would like to see moving forward to ensure not only an at-large bid, but as high a seed as is possible in the tournament.

First, a discussion on what the PWR actually is. The PWR is comprised of four components, which will be repeatedly referred to using their common abbreviations:

RPI - The Ratings Percentage Index. This is a commonly used computer ranking used by the NCAA to determine post-season participants and rankings in a number of other sports, especially basketball. In hockey, it is a component of the PWR, and is calculated using the team's winning percentage as 21%, the team's opponents' winning percentage as 54%, and the opponents' opponents' winning percentage as the final 25%. If a win actually ends up decreasing the team's RPI due to the opponent being exceptionally weak, that game will be disregarded for purposes of calculating that team's RPI.

TUC - Record against Teams Under Consideration. Teams with an RPI over .5000 are teams under consideration for inclusion in the NCAA Tournament. These are the teams that are compared against each other in the PWR, and a team's record against these other teams is a comparison criteria. Which teams are or are not "TUCs" is often an important focus of micro-bracketology. Both teams in a given comparison must have at least 10 games against TUCs for this criteria to be used.

COp - Record against Common Opponents. Games against those teams that both sides of a comparison have played against during the season are considered in this comparison. There is no minimum for games played in this criteria. Whichever team has a better average winning percentage against each individual common opponent wins this criteria, which is a change from previous years.

H2H - Head to head. This is the simplest of the four criteria - if the teams have played each other during the season, each team gets one point for every win they picked up. Ties are disregarded in this criteria.

A single comparison might look like this:

State     -    Tech

.5673    RPI  .5787

.6364    TUC  .5769

.8000    COp  .4167

  0      H2H    0

Looking at this hypothetical comparison, Tech has a better RPI than State. That gives Tech one point in the comparison. But State has a better record against other TUCs and has a better record against teams both squads have faced during the season. That gives State one point for TUC, and one point for COp. Since State and Tech have not faced each other this season (or, alternatively, have only tied each other), State wins the comparison 2-1.

But say the teams had played each other, and Tech won. What happens then, when the comparison is a 2-2 tie? Tech would win the comparison because they won the RPI criteria, which is the tie-breaker.

That is one comparison for both of these teams. Each TUC has around 30 or so total comparisons to consider depending on the number of TUCs, given that they are compared to each of the other TUCs. There are over 375 comparisons in any PWR edition (again, depending on the number of TUCs). That's what makes micro-bracketology a daunting task - but fortunately we only have to focus on a fraction of those on any given week.

Typically (but not always) the top team in the PWR wins all comparisons with other TUCs. On the flip side, the bottom team in the PWR typically (but not always) loses all comparisons with other TUCs. The team's position in the PWR is determined by the number of comparison wins that they hold.

The PWR are NOT what the NCAA uses directly to determine the field. It is instead a ranking that mimics the process the NCAA does use - and it has never been wrong in determining the makeup of the field.

So that's the PWR in a nutshell. Now, to describe Engineer Bracketology. I'll use as an example the PWR from two years ago - both as an illustration of how this will work, and an illustration of what the PWR means about a month out from the selection of the NCAA Tournament. This comes directly from the sixth edition of  Engineer Bracketology back in 2011 - we began this exercise in January that year, since the Engineers were high in the PairWise Rankings that early.
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1. Yale
2. Boston College*
3. North Dakota*
4. Denver
5. Merrimack
6. Minnesota-Duluth
7. Union*
8. Nebraska-Omaha
9. New Hampshire
10. Michigan
11. Miami
12. Notre Dame*
13. Dartmouth
14. Rensselaer
15. Wisconsin
16. Western Michigan
17. Boston University
18. Colorado College
19. Maine
20. Minnesota
21. Ferris State
22. Princeton
23. Minnesota State
24. RIT*
25. Alaska
26. Cornell
27. St. Cloud State
28. Robert Morris
29. Alaska-Anchorage

In: Miami
Out: Western Michigan

TUCs
In: St. Cloud State
Out: Michigan State, Ohio State
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First off, of the 16 teams that would have been "in" the national tournament as of this PWR analysis, 13 were in the final field in March. Dartmouth and Wisconsin missed the tournament, while RIT failed win the Atlantic Hockey crown. All of the at-large teams were TUCs by this point, but there was room for movement. Miami, you will notice, had just re-entered the tournament field as of this update. By March, they were a #1 seed.

The teams with stars represent the automatic bids. Each league has an automatic bid that goes to its tournament champion. Since those are exclusively determined on the ice, the team with the best in-conference winning percentage in each conference is assumed to be the team most likely to win the tournament.

The PWR are also the team's seeding in the tournament. PWR 1-4 are #1 seeds, PWR 5-8 are #2 seeds, PWR 9-12 among tourney teams are #3 seeds, and PWR 13-16 among tourney teams are #4 seeds. After listing the PWR, I detail the teams that entered and exited the NCAA field and then the TUC ranks in the past week.

With 16 teams in the tournament and five automatic bids, that means 11 teams in the tournament are "at-large," gaining bids despite not winning their tournament. Here's how to interpret the positioning in the PWR.

1-11: These teams are in the tournament, regardless of what happens anywhere else and whether they win their conference.
12: This team is almost certainly in the tournament - there would have to be upset tournament winners (teams that would not be in the tournament without the auto-bid) in the each of the WCHA/CCHA/ECAC/Hockey East tournaments for this team to be out.
13: Also most likely in the tournament - upsets in all but one of those conference tournaments would put this team out without an auto-bid.
14: Firmly on the bubble. Three upsets in those tournaments is unlikely, but two is possible, and would likely put this team out without an auto-bid.
15: In trouble. If there's even one team in those four conferences to gain an "upset" auto-bid, this team is likely out without an auto-bid of their own.
16: This team is in deep trouble, and could well be out. Due to the weakness of Atlantic Hockey, its conference champion is usually outside of the Top 16 of PWR and thus takes the #16 seed by default, knocking this team out. However, Niagara has been very strong this year and has been in the Top 16 for much of the last two months. If the Purple Eagles keep it up AND win the Atlantic Hockey tournament, this seed might sneak in.
17-25: These teams are also out of the tournament without the automatic bid.

OK, so now we know more about how to relate the PWR to determine the field. The next thing we do is predict the brackets. This is the focus of macro-bracketology. This prediction assumes that there are no more games to be played, and the selection is being made right then and there.

Based on the PWR above, these were my projected brackets.
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Bridgeport
1. Yale
2. Nebraska-Omaha
3. Michigan
4. RIT

Manchester
1. Boston College
2. Union
3. New Hampshire
4. Wisconsin

Green Bay
1. North Dakota
2. Minnesota-Duluth
3. Miami
4. Rensselaer

St. Louis
1. Denver
2. Merrimack
3. Notre Dame
4. Dartmouth
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Not ironically, perhaps, the Engineers did end up facing North Dakota in Green Bay when all was said and done, but they were there with Denver and Western Michigan.

There are a number of rules that go into bracketing - most notably, that regional hosts must be placed in their own regional, and that there can be no first-round matchups between teams from the same conference unless that conference has 6 or more teams in the tournament. The rest of it can often be an art, mostly focusing on the NCAA's desire to ensure as-brisk-as-possible ticket sales in each of its locations. Generally, however, bracket integrity means the #1 overall seed faces the #16 seed, the #2 overall seed faces the #15 seed, and so on.

These brackets change from week to week. From this projection in February, the only teams that ended up playing where they were listed when March arrived was Yale in Bridgeport (they were hosts), New Hampshire in Manchester (ditto) and then North Dakota and Rensselaer, which was a coincidence more than anything.

This year, the regionals are in Grand Rapids, Mich. (hosted by Michigan), Toledo, Ohio (hosted by Bowling Green), Providence, R.I. (hosted by Brown), and Manchester, N.H. (hosted by New Hampshire). As the season winds down, we can sometimes start to get a feel for where a tournament-bound team might be heading for the regionals. The Frozen Four takes place in Pittsburgh at the Consol Energy Center.

Finally, after analysis of the Engineers' PWR position and key PWR comparisons (frequently including a look at the RPI positions of teams on the Rensselaer schedule), I'll conclude with the "Engineer Cheering Section" - those games coming in the next week around the nation with some potential impact on the team's position in the PWR and which teams fans should be pulling for in those games. Not every game has equal impact, but if there's any perceived impact at all, that game will be listed. In the example edition of above, 37 different games were listed in the Cheering Section.

So there you have it - Engineer Bracketology is coming, and now you know what to expect. Watch this space shortly for our first edition.