The Z-Bracket: 2007 edition

For the fifth consecutive year, it's my pleasure to bring cold, hard logic to the wild and crazy world of college basketball. In the HTML that follows, I'll walk you through the process of selecting and seeding the 2007 NCAA Division I Men's Basketball Championship using the Z-Ratings - the Bradley-Terry mathematical method applied to college basketball. We're not trying to predict the actions of the selection committee; rather, we're showing an alternative method for putting together the bracket. I still have full faith in the capability of this ratings system; at selection time, there was no way to know that George Mason (left out of last year's Z-Bracket) would go all the way to Indianapolis. Here are the men's basketball Z-Ratings through 11 March 2007, produced from the 5,043 games played amongst the 336 Division I teams.

Selecting the field

Step 1: the automatic bids.

The automatic bids - and they upset specials they produce - are a big part of what makes this tournament wonderful. The 31 Division I conference champions get them; the Ivy League regular-season winner and the tournament champions of the other conferences. The automatic-qualifying teams for 2007:

Ohio StateBig Ten1
North CarolinaAtlantic Coast4
KansasBig 126
GeorgetownBig East7
MemphisConference USA8
UNLVMountain West17
WinthropBig South27
CreightonMissouri Valley51
GonzagaWest Coast55
Virginia CommonwealthColonial Athletic63
New Mexico StateWestern Athletic70
George WashingtonAtlantic 1073
Texas A&M Corpus ChristiSouthland91
Long Beach StateBig West95
Wright StateHorizon League96
Holy CrossPatriot League103
Oral RobertsMid-Continent108
PennsylvaniaIvy League112
Miami (OH)Mid-American113
AlbanyAmerica East132
North TexasSun Belt150
Weber StateBig Sky153
BelmontAtlantic Sun155
NiagaraMetro Atlantic Athletic163
Eastern KentuckyOhio Valley174
Central Connecticut StateNortheast189
Jackson StateSouthwestern Athletic220
Florida A&MMid-Eastern Athletic229

Step 2: the at-large bids.

If you can read, you can select the at-large teams using the Z-Ratings. The top thirty-four teams without automatic bids get those slots, and these teams are:
Washington State11
Texas A&M13
Southern Illinois15
Southern California19
Notre Dame22
Georgia Tech25
Michigan State26
Florida State32
Boston College33
Virginia Tech36
Brigham Young39
West Virginia42
Air Force43
Teams in italics were not selected for the actual tournament field. This year, the Z-Bracket disagrees on four teams. The teams that made the actual field but were left out of the Z-Bracket: Arkansas (44), Texas Tech (53), Xavier (57), and Old Dominion (69).

On the teams that made the Z-Bracket -
I can completely understand why Clemson was left out - finishing 4-10 after a 17-0 start looks bad to anybody. Florida State benefits from its wins over Florida and Duke. West Virginia and Air Force both barely made it in here - when you're right on the cut line like that, the calls are close and could go either way.

On the teams that made the NCAAs -
The same goes for Arkansas, the first team out of my field. Texas Tech got in most likely on the strength of its big wins (one over Kansas and two over Texas A&M). Xavier was mentioned as a bubble team up until the final weekend, but only played one ranked team and their strength and schedule is No. 104. Old Dominion is in the same boat as Texas Tech - except for them, it was only big win (at Georgetown).

Seeding the teams

The Z-Ratings we already have give us a starting point for seeds. Teams will have to be bumped up or down to satisfy the bracket, but we start with:

Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team
111Ohio State 51717UNLV 93333Boston College 137349George Washington
22Wisconsin 1818Tennessee 3434Indiana 9150Texas A&M Corpus Christi
33UCLA 1919Southern California 3535Stanford 9551Long Beach State
44North Carolina 2020Nevada 3636Virginia Tech 9652Wright State
255Florida 62121Kentucky 103737Purdue 1410353Holy Cross
66Kansas 2222Notre Dame 3838Illinois 10854Oral Roberts
77Georgetown 2323Texas 3939Brigham Young 11255Pennsylvania
88Memphis 2424Marquette 4040Vanderbilt 11356Miami (OH)
399Oregon 72525Georgia Tech 114141Butler 1513257Albany
1010Pittsburgh 2626Michigan State 4242West Virginia 15058North Texas
1111Washington State 2727Winthrop 4343Air Force 15359Weber State
1212Arizona 2828Clemson 5144Creighton 15560Belmont
41313Texas A&M 82929Louisville 125545Gonzaga 1616361Niagara
1414Maryland 3030Villanova 5646Davidson 17462Eastern Kentucky
1515Southern Illinois 3131Virginia 6347Virginia Commonwealth 18963Central Connecticut State
1616Duke 3232Florida State 7048New Mexico State
OR22064Jackson State
22965Florida A&M
Rk = overall ranking by the Z-Ratings.
FR = Field ranking - the ranking of the team among the field of 65.
OR = opening round.

Three of the four No. 1 seeds match the real bracket, but this year, there's a lot of explaining to do on these seeds...

Florida as a #2. The committee had the defending champions ranked first overall, seemingly on the basis of just that - that they were the defending champions, and had everybody back. But here, last season is just that - last season. Florida's triumph in Indianapolis last April has no bearing on the ratings that produced these seeds. The Gators may have beaten the Buckeyes in December, but they lost to three unranked teams late in the year - and these ratings don't care that those losses were all away from Gainesville.
Arizona as a #3. This is a huge discrepancy, but there's a simple explanation - the Z-Ratings care simply about record and strength of schedule, not about which specific games you win and lose. The Wildcats played a brutal slate - the toughest in the country - including ten games against AP Top 25-ranked teams. Though Arizona was 3-7 in those games, the strength of the opposition faced rewards Lute Olson's club with a high seed here.
Winthrop as a #7. The same logic that produced Arizona's seed explains Winthrop's placement. The Eagles played four AP-ranked teams in non-conference play, and lost all four - but those were their only four losses all year. On the other side of the seesaw, Winthrop wasn't even safe entering Championship Week - the Big South is so weak this year that a loss in the conference tournament final would have put the Eagles at 58, well below at-large territory.
Butler as a #11. The biggest seeding difference to date in the Z-Bracket (the Bulldogs received a No. 5 seed from the committee). Though Butler has two wins over AP-ranked teams, one of those teams (Gonzaga) is fourteen spots lower in the Z-Ratings. The Bulldogs lost three times in conference play in the No. 13 league, and got upset by Wright State in the Horizon final. Had Butler taken care of business in that game, it would have been ranked 27th - a seven seed - and we wouldn't be discussing this.

Establishing the bracket

This year, we go back to using regions (vice cities) to name the regionals. These regionals are the East (East Rutherford, NJ); South (San Antonio); Midwest (St. Louis); and West (San Jose).

As always, we use the bracketing principles established by the committee. The important points:

We also adhere to the bracketing procedure outlined in the championship handbook. The procedure is unchanged from last year.

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

Ohio State to the Midwest; Wisconsin to the East; UCLA to the West; and North Carolina to the South. We set up the Final Four so that if all four of these teams reach Atlanta (which, of course, has never happen since seeding began in 1979), the #1 and #4 overall teams meet in one semifinal, and the #2 and #3 teams play in the other. This gives us Midwest vs. South, and East vs. West - for the second straight year, different from the actual bracket.

Step 2: Place the No. 2 seeds.

Florida to the South; Kansas to the Midwest; Georgetown to the East; and Memphis to the West.

Step 3: Place the No. 3 seeds.

As the only non Pac-10 team among the #3 seeds, Pittsburgh must be placed in the West. Following that, we send Oregon to the Midwest, Washington State to the South, and Arizona to the East.

Step 4: Place the No. 4 seeds.

Texas A&M ito the South; Maryland to the East; Southern Illinois to the Midwest; and Duke to the West.

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

Balance in the bracket is determined by the sum of the field rankings of the four-team blocks in each region. Here, they range from 31 to 37. We aim for a difference of five between the lowest and highest block sums, but I'm going to call this good.

Step 6: Assign first and second round sites.

We assign the top 16 teams to pods in order of their overall ranking, respecting the restrictions on host schools. This gives us:

Lexington, KY: Ohio State, Duke
Chicago, IL: Wisconsin, Kansas
Sacramento, CA: UCLA, Washington State
Winston-Salem, NC: North Carolina, Georgetown
New Orleans, LA: Florida, Memphis
Spokane, WA: Oregon, Arizona
Buffalo, NY: Pittsburgh, Maryland
Columbus, OH: Southern Illinois, Duke

Time for the bracket's bottom four 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, we try.

Step 7: Place the No. 13 seeds.

George Washington to the South; Texas A&M Corpus Christi to the South; Long Beach State to the West; and Wright State to the East.

Step 8: Place the No. 14 seeds.

Holy Cross to the West; Oral Roberts to the South; Pennsylvania to the East; and Miami of Ohio to the Midwest.

Step 9: Place the No. 15 seeds.

Albany in the East; North Texas in the South; Weber State in the West; and Belmont in the Midwest.

Step 10: Place the No. 16 seeds.

The only Friday/Sunday pod with a No. 1 Seed is Chicago, so Wisconsin gets the winner of Jackson State and Florida A&M. Niagara goes to the Midwest; Eastern Kentucky to the South; and Central Connecticut State to the West.

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

The field ranking sums range from 224 to 228, so no problems here, as we turn the corner...

Step 12: Place the No. 5 seeds.

UNLV in the West; Tennessee in the Midwest (out of Florida's region); Southern California to the East; and Nevada to the South.

Step 13: Place the No. 6 seeds.

Kentucky to the West; Notre Dame to the Midwest; Texas to the East, because Marquette must go to the South to avoid Georgetown.

Step 14: Place the No. 7 seeds.

Georgia Tech to the South; Michigan State to the West (avoids Ohio State and Wisconsin); Winthrop to the East; and Clemson to the Midwest.

Step 15: Place the No. 8 seeds.

Louisville to the Midwest, and the Lexington pod; Villanova to the East. The next two teams, Virginia and Florida State, are from the ACC; one potential third-round intraconference matchup is necessary, but I wish to avoid two if possible. We thus come to our first seed bump of the bracket - Virginia goes up to a seven. Clemson would ordinarily come down, being the lowest true #7, but bringing the Tigers down does us no good; thus Winthrop is dropped a line instead, and the Eagles go to the South (still in the Winston-Salem pod). Florida State goes to the West, with the potential to meet Duke in a regional semifinal.

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

The FR sums are 96, 96, 97, 103 - the East is a bit bottom heavy. I'm going to leave it be, since there's not an easy fix. Sixteen left.

Step 17: Place the No. 9 seeds.

The intraconference matchup restrictions make this an easy line - Boston College has to go to the Midwest, thus Stanford has to go to the South, thus Indiana has to go to the West, and Virginia Tech gets bumped down to a #10. Who comes up? It'll actually be Vanderbilt, the lowest true ten seed. Neither Purdue nor Illinois can be placed in the East with Wisconsin, and Brigham Young cannot fill the Chicago pod due to the school's policy of not playing on Sunday. The Commodores take the number nine slot in the East.

Step 18: Place the No. 10 seeds.

Virginia Tech to the West; Purdue to the Midwest; Illinois to the South, so that BYU (in the East) can play in the Thursday/Saturday Winston-Salem pod.

Step 19: Place the No. 11 seeds.

Butler to the Midwest. West Virginia gets bumped down to a #12 because of Big East teams already in the bottom halves. Air Force goes to the South; Creighton to the East; and Gonzaga, who comes up from the #12s, to the West.

Step 20: Place the No. 12 seeds.

West Virginia to the South; Davidson to the East; Virginia Commonwealth to the Midwest; and New Mexico State to the West.

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

The lowest field ranking sum is 158, and the highest is 169 - this section's balance is unsatisfactory. After several minutes of head-scratching, I come up with a fairly simple change: swap Winthrop and Villanova on the #8 line, and West Virginia and Davidson on the #12. This improves the balance in both the 5-8 section (96 to 100) and the 9-12 section (158 to 165), and we're now good.

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

We've followed all the rules, ensured no major imbalance, and minimized to one possible third-round intraconference matchup. I give you the 2007 Z-Bracket.

Parting thoughts

Once again, I'll be out to sea when the nets are cut down in Atlanta. And like last year, the last several days have been one horror story after another, and I'm ready to just sit back and enjoy the tournament in what little time I have to do so.

For the entire crew of USS Memphis, the Cornell University Big Red Bones, and Northport HS alumni everywhere, this is Matt Carberry reminding you to help control the pet population - have your pet spayed or neutered. Goodbye, everybody.