The Z-Bracket: 2006 edition

Ladies and gentlemen, it's the fourth annual Z-Bracket Extravaganza and Pecan Pie Eating Contest!! Wait - where's the pecan pie? I guess the contest is off. Anyway, it's time to make a bracket, using the Z-Ratings, my application of the Bradley-Terry system of paired comparisons. This is the fourth year of the Z-Bracket - and it comes to you from a fourth different site, this year from Groton, Connecticut, homeport of USS Memphis, the submarine on which I currently serve. Connecticut? Memphis? Purely coincidence, I assure you. But I digress again. 4,757 games among 334 Division I teams have produced these ratings.

A few words about this thing at the outset: the Z-Bracket is not an attempt to predict or explain the actions of the NCAA committee. The Z-Ratings are used to select and seed the teams, independently of the ten-person cabal in Indianapolis. We will then use the NCAA's principles to establish the bracket. That having been said, sixty-five slots await.

Selecting the field

Step 1: the automatic bids.

There are still thirty-one Division I conferences, and each still gets one automatic bid to the championship. These bids go to the Ivy League regular-season champion and the tournament champions of the other thirty leagues. These teams are:

DukeAtlantic Coast2
MemphisConference USA4
GonzagaWest Coast5
IowaBig Ten10
SyracuseBig East16
KansasBig 1219
NevadaWestern Athletic34
Southern IllinoisMissouri Valley47
UNC WilmingtonColonial Athletic56
Kent StateMid-American68
San Diego StateMountain West69
XavierAtlantic 1073
Wisconsin - MilwaukeeHorizon81
IonaMetro Atlantic Athletic82
Northwestern StateSouthland87
South AlabamaSun Belt90
Murray StateOhio Valley91
PacificBig West102
MontanaBig Sky104
WinthropBig South111
PennsylvaniaIvy League120
Oral RobertsMid-Continent147
AlbanyAmerica East179
BelmontAtlantic Sun209
SouthernSouthwestern Athletic239
HamptonMid-Eastern Athletic286

Step 2: the at-large bids.

We don't need to fly ten people to Indy and put them up in a swank hotel for five days to select the at-large teams; it takes us about two minutes. This year's at-large teams are:
Ohio State7
George Washington12
North Carolina13
Boston College14
Louisiana State18
West Virginia20
Michigan State22
North Carolina State24
Texas A&M32
Wichita State36
Florida State37
Alabama - Birmingham38
Northern Iowa39
Seton Hall41
Missouri State43
Teams in italics were not selected for the actual tournament field. This year, six teams are different from the committee's selections. The teams that made the field but were left out here: Alabama (46), California (48), Bradley (51), Air Force (55), George Mason (57), and Utah State (71!).

It's important to remember that the Z-Ratings judge the totality of a team's season, without any particular regard to the stretch run or the makeup of a team at any particular time. As such, Michigan's record in the best conference in the country overcomes it's 2-7 finish; the same goes for the second halves of Louisville (5-10) and Cincinnati (6-10) in the No. 2 league. The fifth and sixth teams in the third-best conference (the ACC) are helped by the strength of their leagues. And a single first-round MVC Tournament loss doesn't kill Missouri State here.

On the flip side, the NCAA took the following: the CAA regular season co-champs; the No. 2 from the Mountain West; a mid-pack SEC team that was just short in the Z-Ratings; and three conference tournament runners-up. Cal isn't such a bad pick; Bradley is iffy, and then there's Utah State. The Aggies were 23-8, and didn't play anybody outside the WAC - the No. 10 league. This smells like a makeup bid from 2004.

Seeding the teams

If selection takes two minutes, seeding takes five, since we use the Z-Ratings we already have to produce seeds. Teams will have to be bumped up or down to satisfy the bracket, but we start with these seeds:

Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team
111Connecticut 51717Tennessee 93333Cincinnati 137349Xavier
22Duke 1818Louisiana State 3434Nevada 8150Wisconsin - Milwaukee
33Villanova 1919Kansas 3535Kentucky 8251Iona
44Memphis 2020West Virginia 3636Wichita State 8752Northwestern State
255Gonzaga 62121Georgetown 103737Florida State 149053South Alabama
66Texas 2222Michigan State 3838Alabama - Birmingham 9154Murray State
77Ohio State 2323Indiana 3939Northern Iowa 10255Pacific
88Illinois 2424North Carolina State 4040Maryland 10456Montana
399Pittsburgh 72525Arkansas 114141Seton Hall 1511157Winthrop
1010Iowa 2626Washington 4242Louisville 12058Pennsylvania
1111Florida 2727Oklahoma 4343Missouri State 13959Davidson
1212George Washington 2828Wisconsin 4444Arizona 14760Oral Roberts
41313North Carolina 82929Michigan 124745Southern Illinois 1617961Albany
1414Boston College 3030Bucknell 5646UNC Wilmington 19562Monmouth
1515UCLA 3131Marquette 6847Kent State 20963Belmont
1616Syracuse 3232Texas A&M 6948San Diego State
Rk = overall ranking by the Z-Ratings.
FR = Field ranking - the ranking of the team among the field of 65.
OR = opening round.

The four No. 1 seeds match the real bracket, but as in past years, there are other teams that warrant explanation.

George Washington as a #3. 26-2. Twenty six and two! Yes, they were in the No. 9 conference and played the No. 90 ranked schedule, but I refer you back to that record. And they are the lowest of the No. 3's.
Tennessee as a #5. The Volunteers have a couple of good nonconference opponents, but some cupcakes as well - and being the first victim on South Carolina's run to the SEC final deprived Tennessee of the chance to get a couple of wins.
North Carolina State as a #6. The Wolfpack may have closed the season with four losses, but they started 21-5, including a win over the aforementioned Colonials of George Washington.
Texas A&M as a #8. 21-8, including 10-6 in the Big XII, and a big win in the conference tournament over Colorado (who was the first team out).

Establishing the bracket

(Again this year, I'm referring to the regionals by the cities they're played in - Washington, Atlanta, Minneapolis, and Oakland.)

We again stick to the bracketing principles established by the committee. You need to know these things:

We also adhere to the bracketing procedure outlined in the championship handbook. No changes from 2005. Here we go.

Step 1: Place the No. 1 seeds, and pair the regional winners for the national semifinals.

Connecticut, the top overall team and 2004 champion, goes to the Washington regional; Duke to Atlanta; Villanova to Minneapolis, and Memphis to Oakland - same as the real bracket. The regional winners are matched such that should all the top seeds get to the Final Four (which has never happened), the overall No. 1 faces No. 4, and No. 2 plays No. 3. This gives us Washington v. Oakland, and Atlanta v. Minneapolis - not the same as the real bracket.

Step 2: Place the No. 2 seeds.

Gonzaga to Oakland; Texas to Atlanta; Ohio State to Washington; and Illinois to Minneapolis.

Step 3: Place the No. 3 seeds.

Pittsburgh to Atlanta, since we can't put them in Washington (UConn is there); Iowa to Oakland (can't place them with Ohio State or Illinois); Florida to Washington; and George Washington to Minneapolis.

Step 4: Place the No. 4 seeds.

We send defending champion North Carolina to Washington since they can't be in the Atlanta region with Duke; Boston College in Minneapolis; UCLA goes to Oakland; and Syracuse to Atlanta.

Step 5: Check for conflicts and balance in the Nos. 1 through 4 seeds.

No conflicts thus far. Balance is checked by comparing the sums of the field (1-65) rankings of the four-team groups in each region. These sums range from 32 (Washington) to 37 (Minneapolis); the balance is sound.

Step 6: Assign first and second round sites.

We assign the top 16 teams to pods in order of their overall ranking. We get this:

Philadelphia, PA: Connecticut, Villanova
Dayton, OH: Ohio State, Iowa
Greensboro, NC: Duke, North Carolina
Jacksonville, FL: Florida, George Washington
Dallas, TX: Memphis, Texas
Auburn Hills, MI: Illinois, Pittsburgh
Salt Lake City, UT: Gonzaga, Boston College
San Diego, CA: UCLA, Syracuse

Why can we put Villanova in Philadelphia, effectively in its own city? Because the Atlantic 10 is hosting the Philadelphia pod, and the Wildcats played only three games in the Wachovia Center this year.

Time to do the 13 to 16 lines. These teams, and the rest of the teams in the bracket, are placed so that they are as close to home for the first and second round games as possible. Well, at least that's what I try to do.

Step 7: Place the No. 13 seeds.

Xavier to Washington, Wisconsin - Milwaukee to Minneapolis, Iona to Atlanta, and Northwestern State to Oakland.

Step 8: Place the No. 14 seeds.

South Alabama to Minneapolis, Murray State to Oakland, Pacific to Washington, and Montana to Atlanta.

Step 9: Place the No. 15 seeds.

Winthrop to Atlanta; Penn to Washington; Davidson to Minneapolis; and Oral Roberts to Oakland.

Step 10: Place the No. 16 seeds.

Albany to Atlanta; Monmouth to Minneapolis; Belmont to Oakland; and the winner of the Southern v. Hampton opening-round game to Washington, to face Connecticut.

Step 11: Check for conflicts and balance in the Nos. 13 through 16 seeds.

No conflicts, and the FR sums range between 224 and 229, so our balance works here.

Just over halfway there.

Step 12: Place the No. 5 seeds.

Tennessee goes to the Atlanta regional, since they can't be placed in Washington with Florida. We've got the same problem with LSU, so we place them in the Minneapolis region. Kansas goes to Washington, and West Virginia to Oakland - for the time being.

Step 13: Place the No. 6 seeds.

As mentioned above, Georgetown cannot be placed in the Washington region; they instead head to Oakland. There isn't room for both Michigan State and Indiana on the No. 6 line, so we bump the Spartans to the other side of the bracket, in this case, up to a five. This drops West Virginia down to a six; the Mountaineers go into the Washington regional. Indiana goes into the Atlanta regional, and North Carolina State to Minneapolis.

Step 14: Place the No. 7 seeds.

Arkansas to Dallas; Washington (the school) to Washington (D.C.); Oklahoma to Oakland. The next team on the board is Wisconsin, but the bottom half is full of Big Ten teams. We therefore drop the Badgers to a No. 8. Ideally, we'd bring up Michigan, but that would simply swap one Big Ten team for another. Thus, the beneficiary is Patriot League champion Bucknell, who slide into the Minneapolis region.

Step 15: Place the No. 8 seeds.

Since they came down a line, Wisconsin has priority on the eight line; they go to Minneapolis, which helps balance this section. Michigan goes to Washington; Marquette to Minneapolis (a potential third-round matchup with Syracuse is created here); and Texas A&M to Oakland.

Step 16: Check for conflicts and balance in the Nos. 5 through 8 seeds.

We got all the bracketing rules right; but with FR sums ranging from 94 to 102, we're out of balance. There's a simple way to fix this - swap the No. 5 and No. 8 teams in the Washington and Oakland regionals (Michigan and Kansas to Oakland, Texas A&M and Michigan State to Washington). This gives us two regions of 96 and two of 100. Let's finish this thing off.

Step 17: Place the No. 9 seeds.

Cincinnati goes to the Oakland region; Nevada to Minneapolis; Kentucky to Washington; Wichita State, the first of the four Missouri Valley teams, to Atlanta.

Step 18: Place the No. 10 seeds.

Florida State to Washington; UAB to Atlanta; Northern Iowa to Minneapolis; and Maryland to Oakland.

Step 19: Place the No. 11 seeds.

Seton Hall goes to Minneapolis; Louisville will be bumped to a No. 12, to allow for a potential Big East matchup in the third round instead of the second round. We place Missouri State next, and they to to Oakland. Arizona goes to Atlanta, and Southern Illinois comes up from the No. 12 line and goes to Washington.

Step 20: Place the No. 12 seeds.

Louisville to Washington; UNC Wilmington to Oakland; Kent State to Atlanta, and San Diego State to Minneapolis.

Step 21: Check for conflicts and balance in the Nos. 9 through 12 seeds.

No conflicts with the principles, and with FR sums of 159/162/162/165, the 9 through 12 seeds are balanced.

Step 22: Re-check the entire bracket for conflicts.

We've followed all the rules and minimized third-round intraconference matchups to those necessary. The 2006 Z-Bracket is ready.

Parting thoughts

The last two days have been grueling - and not simply due to making this bracket. I have no parting thoughts this year, other than the thought of being underwater when the national champions cut down the nets in Indianapolis doesn't sit so well with me. But that's life.

ET2 Carberry - out.