The Z-Bracket: 2011 edition

I am pleased and proud to present the 2011 Z-Bracket; for the ninth time, I'll use the Z-Ratings (also known as the Bradley-Terry system, and KRACH in the college hockey world), to draw up this year's NCAA Division I Men's Basketball Championship. The tournament may have undergone some changes in format from years past, but the Z-Bracket can change with it, while still remaining transparent in construction. The basis for everything that follows is the Z-Ratings through 13 March, produced from all 5,248 games between Division I schools. (Summary of previous brackets | Jump to this year's bracket)

(Update, Monday afternoon, 14 March: Added discussions of big seeding discrepancies between Z-Bracket and committee, and comparison under bells and whistles.)
(Update, late Monday evening, 14 March [actually Tuesday morning]: Added bracket simulations; a bit more discussion on the at-large "snubs"; discussion of Butler's seed.)

Selecting the field

Step 1: the automatic bids.

The Great West Conference is still ineligible for an automatic bid. As always, we extend these invitations to thirty conference tournament champions and the Ivy League regular season playoff winner.

TeamConferenceRankTeamConferenceRank
Ohio StateBig Ten1 Long IslandNortheast92
KansasBig 122 BucknellPatriot League98
San Diego StateMountain West3 Indiana StateMissouri Valley111
DukeAtlantic Coast7 WoffordSouthern117
ConnecticutBig East8 AkronMid-American118
KentuckySoutheastern19 St. Peter'sMetro Atlantic Athletic127
Utah StateWestern Athletic22 Morehead StateOhio Valley134
Old DominionColonial Athletic27 Northern ColoradoBig Sky143
RichmondAtlantic 1037 Boston UniversityAmerica East157
WashingtonPacific-1039 HamptonMid-Eastern Athletic161
GonzagaWest Coast43 UC Santa BarbaraBig West175
MemphisConference USA46UNC AshevilleBig South179
BelmontAtlantic Sun57 Arkansas - Little RockSun Belt197
ButlerHorizon League58 Texas - San AntonioSouthland227
PrincetonIvy League59 Alabama StateSouthwestern Athletic315
OaklandSummit League78

Step 2: the at-large bids.

The rest of the field is filled out with the 34 37 highest ranked teams not already in. For the new-but-I'm-not-so-sure-it's-improved 2011 tournament, these teams are:
TeamRankTeamRankTeamRank
Pittsburgh4 West Virginia20 Xavier34
Notre Dame5 UNLV21 Illinois35
Brigham Young6 Texas A&M23 Penn State36
Syracuse9 Villanova24 George Mason38
Texas10 Arizona25 Virginia Tech40
Louisville11 Kansas State26 UCLA41
Purdue12 Missouri28 Florida State42
Wisconsin13 Temple29 Clemson44
Cincinnati14 Marquette30 Georgia45
North Carolina15 Michigan31 Colorado47
Georgetown16 Vanderbilt32 Northwestern48
Florida17 Michigan State33 Boston College49
St. John's18
Teams in italics were not selected for the actual tournament field. The teams that made the NCAA tournament but were left out here are: Tennessee (50), UAB (52), Virginia Commonwealth (67), and Southern California (70).

I am 100 percent on board with the cognoscenti of the Self-Proclaimed Worldwide Leader, who have pilloried the Selection Committee for the way it handled the bubble. Neither USC nor VCU should have come close to sniffing a bid. They are, respectively, eighteen and twenty-one places below the Z-Bracket cut line. UAB is actually much closer, but they might have ended up on the right side of the line had they won a game or two in the Conference USA tournament. And Tennessee is the first team out here, so no big deal to me on that one.

On the other hand, nobody is going to weep for Northwestern over their exclusion, and Boston College is only marginally more worthy of sympathy. Neither the Wildcats nor the Eagles (both of whom are coached by ex-Ivy League guys) will get any pity from me. But Colorado and Virginia Tech both got hosed. For crying out loud, I am sick and tired of hearing about the canard that is the "non-conference strength of schedule." A game is a game is a game, regardless of whether or not you play an opponent every year via the league.

The counter-protest is being taken up by, among others, Jerry Beach and Joe Sheehan, who would probably love nothing more than to have Jay Bilas, Digger Phelps, Hubert Davis, and Dick Vitale paraded in front of CAA headquarters and then ceremonially beheaded. I was initially frustrated with those knocking Colorado and Virginia Tech, especially the "us vs. them" attitude they seemed to have toward the "power" leagues. But with the benefit of twenty-four hours of hindsight, I can give much more deference to their rationale. Unlike yours truly, they are not evaluating the at-large teams in a vacuum; they are giving deference to teams like UAB and VCU because of the difficulty they have in scheduling. I can't fault them too much for doing so, and it's a problem in need of a remedy. But I think it's something that should be handled by the conferences and the NCAA as a whole, and not the selection committee. That said, I think the one point on which we're all in accord is Gene Smith's horrible job with the media. I wanted to scream "ATFQ" at Smith - that's an acronym from my days of Navy training. It stands for "answer the fucking question," which Smith steadfastly refused to do with the interviewers from both CBS and ESPN.

One last thing: does anybody have a contact for Randy Bennett, head coach of St. Mary's?

Seeding the teams

The newly restructured "first round"

Before we can seed the teams, we have to determine the teams and pairings for the so-called "First Four." The only guidance given in the Principles and Procedures is that the teams to be matched up are the four lowest ranked teams in the field (e.g. field rankings 65 through 68), and the last four at-large teams. Beyond that, we have nothing to go on. This indicates that the selection committee has plenary power to seed and place the first-round participants - and therefore, so do I. That being the case, the fundamental principle of the development of the Z-Bracket is transparency, so I am going to list out my criteria for handling the four first-round games: Fortunately, the last four at-large teams all hail from different conferences, so I can use the preferred pairings. This gives us the following First Four games: Georgia v. Boston College; Colorado v. Northwestern; Arkansas - Little Rock v. Texas - San Antonio; and UNC Asheville v. Alabama State, the first sub-300 ranked team in the history of the Z-Bracket to make the field.

Creating the seed list

The Principles and Procedures seem to abandon all mention of the "S-Curve." Of course, I never used it here anyway; we'll use the rankings themselves to assign seeds, subject to the rules laid about above for the handling of the eight teams playing in Dayton. Teams slated to meet in the first round are listed in the same cell.

Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team
111Ohio State 51717Florida 93333Michigan State 135851Butler
22Kansas 1818St. John's 3434Xavier 5952Princeton
33San Diego State 1919Kentucky 3535Illinois 7853Oakland
44Pittsburgh 2020West Virginia 3636Penn State 9254Long Island
255Notre Dame 62121UNLV 103737Richmond 149855Bucknell
66Brigham Young 2222Utah State 3838George Mason 11156Indiana State
77Duke 2323Texas A&M 3939Washington 11757Wofford
88Connecticut 2424Villanova 4040Virginia Tech 11858Akron
399Syracuse 72525Arizona 114141UCLA 1512759St. Peter's
1010Texas 2626Kansas State 4242Florida State 13460Morehead State
1111Louisville 2727Old Dominion 4343Gonzaga 14361Northern Colorado
1212Purdue 2828Missouri 4444Clemson 15762Boston University
41313Wisconsin 82929Temple 1245
49
45
49
Georgia
Boston College
1616163Hampton
1414Cincinnati 3030Marquette 4646Memphis 17564UC Santa Barbara
1515North Carolina 3131Michigan 47
48
47
48
Colorado
Northwestern
179
315
65
68
UNC Asheville
Alabama State
1616Georgetown 3232Vanderbilt 5750Belmont 197
227
66
67
Arkansas - Little Rock
Texas - San Antonio
Key:
Rk = overall ranking by the Z-Ratings.
FR = Field ranking - the ranking of the team among the field of 68.

Let's talk just a bit about some of these seedings, shall we?
San Diego State as a #1. Given that the committee placed the Aztecs in the West and with the lowest No. 1 seed, they might have been the No. 5 overall team in the committee's eyes. But a 29-2 season, including 14-2 in the No. 7 conference, with the only two losses to BYU with Brandon Davies? Even without the benefit of these ratings, I'd have SDSU in the top four in the nation.
Florida as a #5. I agree with Pat Forde that the actual bracket has Florida too high. The SEC was, relatively speaking, down this year, and for that, the Gators suffer here.
Utah State as a #6. The Aggies get the "Charlie Sheen justification": DUH! WINNING! Um, twenty-eight and three? Utah State might be (from my perspective) the most mis-evaluated team I've seen over the last nine years.
Butler as a #13. I don't think the committee seeded the Bulldogs so high based on their run to last year's national final; I bet it was more because of their hot streak down the stretch. But the Z-Ratings don't recognize those games as any more important than Butler's five Horizon League losses, including one to Youngstown State.
I think the committee did a good job with the Big East teams, recognizing the superior quality of that league. And down below the bracket, I'll have something to say about differences in evaluation between two mid-major conferences near and dear to my heart.

Establishing the bracket

The regionals for 2011: East (Newark); Southeast (New Orleans); Southwest (San Antonio); and West (Anaheim).

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. I will once again state that the three "additional considerations" listed after the procedure (relating to rematches of games from the regular season and last year's championship, and moving teams out of their natural region an inordinate number of times) and are not used in the construction of the Z-Bracket.

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

Ohio State to the East; Kansas to the Southwest; San Diego State in the West; Pittsburgh to the Southeast. This yields a Final Four of East vs. Southeast and Southwest vs. West.

Step 2: Place the No. 2 seeds.

Notre Dame is placed in the East. BYU cannot be placed opposite SDSU in the West, and since they must be bracketed to play Thursday and Saturday due to religious requirements, they must go to the Southeast. Duke ends up in the Southwest and Connecticut is sent West.

Step 3: Place the No. 3 seeds.

Syracuse to the Southeast (must avoid Notre Dame and Connecticut); Texas to the East. As the second big 12 team, the Longhorns must be bracketed away from Kansas, and they cannot go in the West because Purdue can't be placed in the East (due to Ohio State); Louisville must go to the Southwest to avoid the other Big East teams in the bottom halves; and as mentioned, Purdue ends up in the West.

Step 4: Place the No. 4 seeds.

Wisconsin is limited to the Southeast and West; they go to New Orleans. Cincinnati to the East; North Carolina to the West (must avoid Duke); and Georgetown to the Southwest.

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

We sum the field rankings of the top four teams in each region, and there should be a difference of no more than five between the highest and lowest. Right now, we have the East at 30 and the West at 38, so we need to do some shuffling. I'm going to apply Occam's razor and conduct a single move - swap Connecticut and Notre Dame on the No. 2 seed line. The Fighting Irish do lose out somewhat on this (in terms of distance), but they'd be getting on a place to the regional either way - and they have a potentially more favorable Elite Eight matchup. This shifts the regional sums to 32, 33, 35, and 36, so we are in good shape.

Step 6: Assign first and second round sites.

Cleveland, OH: Ohio State, Syracuse
Tulsa, OK: Kansas, Texas
Tucson, AZ: San Diego State, Georgetown
Washington, DC: Pittsburgh, Connecticut
Chicago, IL: Notre Dame, Louisville
Denver, CO: Brigham Young, Wisconsin
Charlotte, NC: Duke, Purdue
Tampa, FL: Cincinnati, North Carolina

Step 7: Place the No. 5 through 16 seeds.

Keep in mind that from this point on, the teams are placed according to the site of their second/third round pod (since, by their seeding, they're expected to be gone by the end of the first weekend).

Step 7a: Place the No. 5 seeds. (Available sites: Denver, Tampa [2], Tucson)

Florida to the East; St. John's to the West. Kentucky is going to the Southwest in order to place West Virginia in the Southeast. This allows for a potential Big East matchup to take place in the regional semifinal (against Pittsburgh) vice the second round (versus Georgetown).

Step 7b: Place the No. 6 seeds. (Available sites: Charlotte, Chicago, Cleveland, Tulsa)

UNLV to the East; Utah State to the Southwest; Texas A&M to the Southeast, and Villanova to the West, which again puts the possible all-Big East game in the third fourth round.

Step 7c: Place the No. 7 seeds. (Available sites: Charlotte, Chicago, Denver, Washington)

Arizona to the Southeast; Kansas State to the West; Old Dominion to the East; Missouri to the Southwest.

Step 7d: Place the No. 8 seeds. (Available sites: Cleveland, Tucson, Tulsa, Washington)

Temple to the Southeast; Marquette to the East (and we're done with the Big East); Michigan to the Southwest and Vanderbilt to the West (must be separated from Kentucky).

Step 7e: Place the No. 9 seeds. (Available sites: Cleveland, Tucson, Tulsa, Washington)

The very next team placed is Vanderbilt's opponent; Michigan State is forced into the West due to the Big Ten teams in the other three top halves. Xavier to the East. Illinois and Penn State are the first two bumps of the 2011 Z-Bracket; to get them into the bottom half, they both have to go down to the No. 10 line. In their place we bring up Richmond and George Mason. We can't place the Spiders against Temple, so they are put in the Southwest. And so, as much as it pains me to do this (due to my Hofstra ties), I have to put George Mason in the Southeast and into a Washington pod - effectively at home, much as they were in 2006.

Step 7f: Place the No. 10 seeds. (Available sites: Charlotte, Chicago, Denver, Washington)

We take up Illinois and Penn State first, since they were bumped down. The Illini go to the Southwest (the West, with a Chicago pod, is unavailable due to Purdue's presence) and the Nittany Lions go East. That leaves us with Washington in the West (can't be placed with Arizona) and Virginia Tech in the Southeast (as the third ACC team, they can't be in the same region as UNC, even though they're on the other side of the bracket).

Step 7g: Place the No. 11 seeds. (Available sites: Charlotte, Chicago, Cleveland, Tulsa)

UCLA to the Southeast; Florida State to the West; Gonzaga to the Southeast; Clemson to the East. Tulsa may be closer to Westwood than Chicago, but it's a plane ride either way, and if UCLA had been placed in the East, it would have forced either Florida State or Clemson to be bumped down in favor of a First Four winner.

Step 7h: Place the No. 12 seeds. (Available sites: Denver, Tampa [2], Tucson)

The winner of the Georgia - Boston College game goes into the Southeast. Memphis to the East. We now come to the case of the winner of Colorado vs. Northwestern. Since the Big Ten and the Big 12 both have more than five teams in the field, I'm going to place the winner of this game in the West, where Northwestern could meet Michigan State in a regional semifinal. Belmont ends up in the Southwest.

Step 7i: Place the No. 13 seeds. (Available sites: Denver, Tampa [2], Tucson)

Butler to the East; Princeton to the West; Oakland to the Southeast; Long Island to the Southwest.

Step 7j: Place the No. 14 seeds. (Available sites: Charlotte, Chicago, Cleveland, Tulsa)

Bucknell to the Southeast; Indiana State to the Southwest; Wofford to the East; Akron to the West. Wofford is not in the Charlotte pod because putting them there would put Purdue at a "potential home court disadvantage."

Step 7k: Place the No. 15 seeds. (Available sites: Charlotte, Chicago, Denver, Washington)

St. Peter's to the East; Morehead State to the Southwest; Northern Colorado to the West; Boston University to the Southeast. Once again, the rule regarding home-court disadvantage is invoked to prevent Northern Colorado from playing in Denver.

Step 7l: Place the No. 16 seeds. (Available sites: Cleveland, Tucson, Tulsa, Washington)

Hampton to the Southeast; UC Santa Barbara to the West; the UNC Asheville/Alabama State winner to the East; and the Arkansas - Little Rock/Texas - San Antonio to the Southwest.

Step 8: Re-check the entire bracket for conflicts.

We have minimized the number of possible Big East matchups in the regional semifinals at three, and as stated above, there is the one possible pairing of Big Ten teams in the Sweet Sixteen. I present the 2011 Z-Bracket below:

EAST (Prudential Center, Newark)SOUTHWEST (Alamodome, San Antonio)
1Ohio StateQuicken Loans Arena
Cleveland, OH
BOK Center
Tulsa, OK
Kansas1
1616
8MarquetteMichigan8
9XavierRichmond9
5FloridaSt. Pete Times Forum
Tampa, FL
McKale Center
Tucson, AZ
Kentucky5
12MemphisBelmont12
4CincinnatiGeorgetown4
13ButlerLong Island13
3TexasBOK Center
Tulsa, OK
United Center
Chicago, IL
Louisville3
14WoffordIndiana State14
6UNLVUtah State6
11ClemsonUCLA11
7Old DominionVerizon Center
Washington, DC
Time Warner Cable Arena
Charlotte, NC
Missouri7
10Penn StateIllinois10
2ConnecticutDuke2
15St. Peter'sMorehead State15
FINAL FOUR
(Reliant Stadium, Houston)
East v. Southeast
Southwest v. West
SOUTHEAST (New Orleans Arena, New Orleans)WEST (Honda Center, Anaheim)
1PittsburghVerizon Center
Washington, DC
McKale Center
Tucson, AZ
San Diego State1
16HamptonUC Santa Barbara16
8TempleVanderbilt8
9George MasonMichigan State9
5West VirginiaPepsi Center
Denver, CO
St. Pete Times Forum
Tampa, FL
St. John's5
1212
4WisconsinNorth Carolina4
13OaklandPrinceton13
3SyracuseQuicken Loans Arena
Cleveland, OH
Time Warner Cable Arena
Charlotte, NC
Purdue3
14BucknellAkron14
6Texas A&MVillanova6
11GonzagaFlorida State11
7ArizonaPepsi Center
Denver, CO
United Center
Chicago, IL
Kansas State7
10Virginia TechWashington10
2Brigham YoungNotre Dame2
15Boston UniversityNorthern Colorado15
FIRST ROUND (UD Arena, Dayton) - TuesdayFIRST ROUND (UD Arena, Dayton) - Wednesday
Georgia(to Southeast #12)(to East #16)UNC Asheville
Boston CollegeAlabama State
Colorado(to West #12)(to Southwest #16)Arkansas - Little Rock
NorthwesternTexas - San Antonio

Bells and whistles

Before we get to the bracket simulator results, let's do a side-by-side on two teams:
Team ATeam B
Ranking3938
Record25-426-6
SOS10190
BSWP.8422.8194
Natural Z-Bracket seed1010
NCAA seed128
Pretty similar except for that last row, right? On the left is 2010 Cornell; on the right is 2011 George Mason. (I say "natural Z-Bracket seed" because George Mason was bumped up to a #9.) As much as I try to eliminate my own biases from the selection and seeding of teams, I'm going to use them here as a springboard to highlight a possible disparity in treatment, even between mid-major conferences.

In the interests of time, I've truncated the simulation of each bracket to one million repetitions each. Even though my program can iterate through the bracket about 7,000 times per second, that still means it takes a really long time to get through ten million plays. Anyway, here are the results: 2011 Z-Bracket | 2011 NCAA tournament. The two simulations are closely aligned at the top; each says there's roughly a one in two chance that either Ohio State or Kansas will hoist the gold trophy in Houston.

Acknowledgements

As always, thanks are due to Ken Pomeroy, who supplies the data generate the men's basketball Z-Ratings. This would be a lot harder without his raw data files. Of course, I must again pay homage to our roots in Cornell hockey - the KRACH, John Whelan, and Ken Butler.

Unlike last year I've got no dog in the fight this time around - so just enjoy the tournament.

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