The Z-Bracket: 2008 edition

I'm back once again with another Z-Bracket. This one comes to you from Portsmouth, New Hampshire, where the Navy has me for a bit longer. Here, I'll take the Z-Ratings, and use them to select the sixty-five teams in the tournament, and then seed and place them. Our basis for this bracket is the men's basketball Z-Ratings through March 16, 2008; the 341 Division I teams played 5,153 games to get to this point.

Selecting the field

Step 1: the automatic bids.

Automatic bids are granted to all of the conference tournament champions. The Ivy League regular season champion also gets one, and that is - oh, snap! It's Cornell, bitches! Big Red in the house! (In case you didn't catch on, the author attended Cornell as an undergraduate.)

MemphisConference USA1George MasonColonial Athletic96
North CarolinaAtlantic Coast2Boise StateWestern Athletic101
UCLAPacific-103Cal State - FullertonBig West102
KansasBig 124San DiegoWest Coast105
WisconsinBig Ten7SienaMetro Atlantic Athletic106
ButlerHorizon League11BelmontAtlantic Sun127
DrakeMissouri Valley13WinthropBig South130
PittsburghBig East21Portland StateBig Sky132
Kent StateMid-American31UMBCAmerica East136
UNLVMountain West41AmericanPatriot League153
DavidsonSouthern45Austin PeayOhio Valley156
Western KentuckySun Belt56Texas - ArlingtonSouthland166
TempleAtlantic 1062Mount St. Mary'sNortheast185
GeorgiaSoutheastern77Coppin StateMid-Eastern Athletic272
Oral RobertsSummit League82Mississippi Valley StateSouthwestern Athletic298
CornellIvy League94

Step 2: the at-large bids.

On the afternoon of March 16, there were still a lot of questions concerning selection and seeding, depending on the results of the Big 12, Big Ten, and SEC championship games. The Z-Ratings avoid these problems by waiting until every game is complete, and then taking the thirty-four highest ranked teams without automatic invitations.
Tennessee5Texas A&M26
Washington State12Baylor32
Notre Dame14St. Mary's - CA33
Louisville15Arizona State34
Southern California16Miami (FL)35
Indiana17Brigham Young36
Michigan State18Oregon37
Connecticut19Kansas State38
Marquette22Illinois State40
Clemson23Mississippi State42
West Virginia25Ohio State44
Teams in italics were not selected for the actual tournament field. There are only three discrepancies this year; the teams that made the real tournament but were left out of the Z-Bracket are Kentucky (51), South Alabama (57), and St. Joseph's (63).

On the teams that made the Z-Bracket -
I heard a lot of talk about the fact that Arizona State didn't have the out-of-conference schedule the committee wanted. The Z-Ratings make no distinction between conference and non-conference play, and the Sun Devils were .500 in the nation's toughest conference. Similarly, Illinois State was the runner-up in a very good Missouri Valley. And Ohio State just barely got in; I don't find any fault with the committee leaving them out.

On the teams that made the NCAAs -
Kentucky was doomed by their early season form; in fact, if the result of their home loss to Gardner-Webb is reversed, they'd jump up to 42, and they'd be in the Z-Bracket. South Alabama has a strength of schedule of 127; not even 26-6 can overcome that. St. Joseph's did play in a good conference, but the 21-12 record very much works against the Hawks.

Seeding the teams

As always, by using the already established Z-Ratings, seeding becomes exceedingly simple. We may have to move teams one line up or down to satisfy the bracket; that said, the nominal seeds are:

Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team
111Memphis 51717Indiana 93333St. Mary's - CA 138249Oral Roberts
22North Carolina 1818Michigan State 3434Arizona State 9450Cornell
33UCLA 1919Connecticut 3535Miami (FL) 9651George Mason
44Kansas 2020Xavier 3636Brigham Young 10152Boise State
255Tennessee 62121Pittsburgh 103737Oregon 1410253Cal State - Fullerton
66Texas 2222Marquette 3838Kansas State 10554San Diego
77Wisconsin 2323Clemson 3939Arkansas 10655Siena
88Duke 2424Vanderbilt 4040Illinois State 12756Belmont
399Georgetown 72525West Virginia 114141UNLV 1513057Winthrop
1010Stanford 2626Texas A&M 4242Mississippi State 13258Portland State
1111Butler 2727Oklahoma 4343Villanova 13659UMBC
1212Washington State 2828Purdue 4444Ohio State 15360American
41313Drake 82929Gonzaga 124545Davidson 1615661Austin Peay
1414Notre Dame 3030Arizona 5646Western Kentucky 16662Texas - Arlington
1515Louisville 3131Kent State 6247Temple 18563Mount St. Mary's
1616Southern California 3232Baylor 7748Georgia
OR27264Coppin State
29865Miss. Valley 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 number one seeds agree with the actual bracket. Let's talk about some of the significant seeding differences:

Butler as a #3. A stark reversal from last year, when the Z-Bracket seeded the Bulldogs six slots lower than the committee. As for this year's squad, 26-3 says a lot. One of the three losses was to Drake (another three seed) in the Bracket Buster. The Horizon League is ranked ninth, and Butler also played enough moderately good teams outside the league.
Indiana as a #5. The program that crunches the numbers doesn't take into account that Indiana closed its season 1-3. And it doesn't even know about the recruiting scandal and change of head coach. All it sees is 25-7 against a schedule ranked 29.
Baylor as a #8. Baylor's placement is explained in the same way as Butler's. They were 10-2 against D-I opposition outside of the Big 12, and though they went 9-7 in conference, that league is ranked #3. No weight is lent to the fact that the Bears went 1-6 between January 26 and February 19.

Establishing the bracket

This year's regionals: East (Charlotte); South (Houston); Midwest (Detroit); and West (Phoenix).

Once again, we use the bracketing principles established by the selection committee. They are:

We also adhere to the bracketing procedure outlined in the championship handbook, which has been the same since 2004.

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

Here, the top four teams go exactly where the committee sent them: Memphis to the South, North Carolina to the East, UCLA to the West, and Kansas to the Midwest. The Final Four is set up so that if these are the four teams playing in San Antonio, 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 - once again, not matching the actual bracket.

Step 2: Place the No. 2 seeds.

Tennessee to the East; Texas to the South; Wisconsin to the Midwest; and Duke to the West.

Step 3: Place the No. 3 seeds.

Georgetown to the East; Stanford can't go into the West with UCLA, so they're in the South; Butler to the West; and Washington State to the Midwest.

Step 4: Place the No. 4 seeds.

Drake goes to the Midwest; Neither Notre Dame nor Louisville can be placed with Georgetown in the East, so they go to the West and South, respectively, and USC will head across the country should they get out of the first two rounds.

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, there are two regions at 32 and two at 36. We aim for a difference of five between the lowest and highest block sums, and we've achieved that here.

Step 6: Assign first and second round sites.

We assign the top 16 teams to pods in order of their overall ranking, respecting the restriction on Georgetown's placement. This gives us:

Little Rock, AR: Memphis, Texas
Raleigh, NC: North Carolina, Georgetown
Anaheim, CA: UCLA, Stanford
Omaha, NE: Kansas, Wisconsin
Birmingham, AL: Tennessee, Louisville
Washington, DC: Duke, Butler
Denver, CO: Washington State, Drake
Tampa, FL: Notre Dame, USC

We seed the 13 to 16 teams next. We try to place teams as close as possible to their campuses for the remainder of the bracket.

Step 7: Place the No. 13 seeds.

Oral Roberts to the South; my Cornell Big Red in the East; George Mason in the West; and Boise State in the Midwest.

Step 8: Place the No. 14 seeds.

Cal State - Fullerton has priority, but I'm applying the third principle above to prevent Stanford from being disadvantaged (Fullerton's campus is seven miles from the Honda Center). The Titans go to the Midwest instead, and San Diego goes to the South. Siena to the West, and Belmont to the East.

Step 9: Place the No. 15 seeds.

Winthrop to the East; Portland State to the Midwest; UMBC to the West; and American to the South. Both of the latter two teams could disadvantage Duke in Washington, but UMBC does so less - at least it's forty miles away.

Step 10: Place the No. 16 seeds.

Austin Peay to the East; Texas-Arlington to the Midwest; Mount St. Mary's to the West; and the opening round winner to the South (a Friday/Sunday pod).

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

The field ranking sums range from 224 to 228 - within specification.

Step 12: Place the No. 5 seeds.

Indiana to the South; Michigan State to the East; Connecticut to the Midwest; Xavier to the West.

Step 13: Place the No. 6 seeds.

Pittsburgh to the West; Marquette to the Midwest; Clemson to the East; and Vanderbilt to the South. Yes, Clemson is the third team from the ACC and in the same region as UNC, but they're on opposite sides of the regional, and I thought it better to place them there than have a Big East or SEC intraconference matchup before the regional final. The beauty of not being the committee is that I can overlook the rules if I see a good reason to do so.

Step 14: Place the No. 7 seeds.

West Virginia to the South; Texas A&M to the East; Oklahoma to the Midwest; Purdue to the West.

Step 15: Place the No. 8 seeds.

Gonzaga to the West; Arizona to the Midwest; Kent State to the East; and Baylor to the South.

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

The FR sum is 98 for all four good as it gets.

Step 17: Place the No. 9 seeds.

St. Mary's to the East; Arizona State to the South; Miami to the West; BYU to the Midwest. These were dictated not only by potential conference matchups, but by BYU's policy of not playing on Sunday.

Step 18: Place the No. 10 seeds.

Kansas State can't be placed anywhere but the West, so that locks Oregon into the East, and thus Arkansas into the Midwest. Illinois State ends up in the South.

Step 19: Place the No. 11 seeds.

UNLV to the South; Mississippi State has to go in the West; and since Villanova can't be placed in any region's bottom half, I'm bumping them down to a No. 12. Ohio State goes to the East, and Davidson, which takes Villanova's place, goes to the Midwest.

Step 20: Place the No. 12 seeds.

Villanova has to go to the East. Western Kentucky to the South; Temple to the Midwest; and the last and most unlikely team in is the last one placed - SEC champion Georgia to the West.

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

The lowest field ranking sum is 157, and the highest is 167 - no good. The change to be made is a simple one: swap Temple and Western Kentucky. This improves the balance slightly (157 to 166); while not ideal, it's good enough.

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

All the rules have been followed, all the t's crossed, all the i's dotted, and only one seed bump was made. Here's the 2008 Z-Bracket.

Parting thoughts, two days later

Having now had a bit of time to mull over both this bracket and the one that'll actually be played, I want to touch on two cool things I can do with the Z-Ratings.

"If only we had that one back..."

Because the Z-Ratings are based only on the wins and losses on the court, we don't have to wonder whether a team would get in if had won or lost a particular game. I showed you this above with Kentucky - I flipped the Gardner-Webb result in the games file, ran a new set of ratings,and Kentucky came up at 42, which would have been good enough to put them in. There were two other examples last year, Butler and Winthrop. It's just another great advantage of a purely objective selection system.

The bracket is nice, but can we actually do anything with it?

As a matter of fact, we can! As the Z-Ratings home page shows, we can use two teams' ratings to obtain probabilities of victory for each in a hypothetical matchup. We can use these to randomly pick winners - and advance those winners in the bracket until we have a national champion. A single such playing - or ten, or even a thousand - is far too small a sample size. So I wrote a program to simulate playing the Z-Bracket, and ran ten million playings. The results of this are here; shown are both championships and trips to the Final Four.


Here are some long overdue props to people who helped make this happen, and inspired it to happen.

First, and probably most important, Ken Pomeroy, whose master games file provides the source data for my men's basketball Z-Ratings. Also, providing the data for the NBA, MLB, NHL, and NFL ratings, as well as quick access to teams' schedules when I'm making arguments for or against a selection or seeding on this page. Of course, I would never have started doing this if it wasn't for the KRACH and John Whelan, and Ken Butler before him.

I'll close out this year's document by stating the obvious; words that haven't been heard at March Madness in two decades...LET'S GO RED!!