The Z-Bracket: 2012 edition

Ten seasons. Has the history of the Z-Ratings and the Z-Bracket really reached a decade of college basketball? Yes, it has. Things have changed over the years - the number of teams in, the size of the venues for the Final Four - but the Bradley-Terry system and the tournament I build from it have remained steady as a rock. All the decisions about selection and seeding flow from the Z-Ratings through 11 March, a product of the 5,245 games between Division I schools played this year; the placement of the teams into the bracket will be fully explained as well. (Summary of previous brackets | Jump to this year's bracket)

Selecting the field

Step 1: the automatic bids.

Still no bid for the quite badly named Great West Conference; the automatic bids go to the other thirty conference tournament winners and this year's Ivy League regular season champion, Har - wait, is that right? Are we sure about that? Yes, for the first time since 1946, Harvard is in the Dance.

MissouriBig 123 DavidsonSouthern81
Michigan StateBig Ten6 BelmontAtlantic Sun85
Murray StateOhio Valley8 New Mexico StateWestern Athletic86
LouisvilleBig East15 South Dakota StateSummit League89
CreightonMissouri Valley17 MontanaBig Sky91
Florida StateAtlantic Coast19 LehighPatriot League120
Saint Mary'sWest Coast20 Loyola - MarylandMetro Atlantic Athletic125
New MexicoMountain West21 DetroitHorizon League127
VanderbiltSoutheastern23 Long IslandNortheast139
MemphisConference USA28 Norfolk StateMid-Eastern Athletic143
HarvardIvy League40 LamarSouthland148
Virginia CommonwealthColonial Athletic49 UNC AshevilleBig South152
Long Beach StateBig West56 VermontAmerica East168
ColoradoPacific-1260 Western KentuckySun Belt174
Ohio UniversityMid-American71 Mississippi Valley StateSouthwestern Athletic205
St. BonaventureAtlantic 1080

Step 2: the at-large bids.

There's no cross country scoring, no under consideration board. These bids go to the 37 highest ranked teams that did not claim automatic bids. They are:
Kentucky1 San Diego State22 Alabama36
Syracuse2 Gonzaga24 Northwestern37
Kansas4 Kansas State25 Connecticut38
North Carolina5 Iowa State26 Saint Louis39
Ohio State7 Florida27 Southern Mississippi41
Baylor9 UNLV29 Minnesota42
Duke10 Cincinnati30 West Virginia43
Indiana11 Purdue31 Brigham Young44
Michigan12 Notre Dame32 North Carolina State45
Wisconsin13 Temple33 Illinois46
Marquette14 Virginia34 California47
Georgetown16 Texas35 Seton Hall48
Wichita State18
Teams in italics were not selected for the actual tournament field. In 2012, these are: South Florida (51), Colorado State (52), Xavier (57), and Iona (EIGHTY-TWO).

Once again, four discrepancies. Three of the teams taken by the Z-Bracket are from the top-overall Big Ten (will Northwestern EVER get a break?) Three of the teams taken by the committee within the first seven at-larges below the cut line. Very little to reflect on there.
But...Iona? IONA??? I'm not even going to compare tham against any of the four teams that made the Z-Bracket. Instead, I want to put them against Drexel, the CAA regular season champion. The Dragons and Gaels played roughly comparable schedules (Drexel's was slightly better). Drexel was a game and a half better overall. The Dragons went 16-2 in the No. 16 league, losing in the tournament final in a hostile arena (not that we take that into account); the Gaels, by contrast, were 16-4 in the No. 19 conference and got bounced in the semifinal on a true neutral court. Jeff Hathaway credited Iona's admission to the tournament to its superior non-conference schedule. I am sick and fucking tired of that stinky canard. A team's schedule is a single, indivisible thing. You may be able to control what games you can get, but you can't necessarily control how good those opponents will be when you play them. It's the same with the league schedule. Yes, Iona should suffer because it played in the MAAC (and was tripped up in the MAAC).
I was convinced that the Selection Committee was driven toward this decision by the contents of an unmarked package from the Colombian jungle. Actually, it's even simpler than drugs. According to the RPI, Iona was 41 - thirty spots ahead of Drexel. College hockey fans have long said that they have it better because of the existence of the objective Pairwise Rankings that control selection to the NCAA tournament. A small subset of them, myself included, have railed against the use of the RPI as a fatally flawed statistic. This one decision incontrovertibly proves us right on the latter point.

Seeding the teams

The first round

I'm going to handle the First Four the same way I did last year, using the following guidelines:

Creating the seed list

Being as we have a perfectly good set of rankings already, why don't we just use that to produce our seeds?

Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team
111Kentucky 51717Creighton 93333Temple 136051Colorado
22Syracuse 1818Wichita State 3434Virginia 7152Ohio
33Missouri 1919Florida State 3535Texas 8053St. Bonaventure
44Kansas 2020Saint Mary's 3636Alabama 8154Davidson
255North Carolina 62121New Mexico 103737Northwestern 148555Belmont
66Michigan State 2222San Diego State 3838Connecticut 8656New Mexico State
77Ohio State 2323Vanderbilt 3939Saint Louis 8957South Dakota State
88Murray State 2424Gonzaga 4040Harvard 9158Montana
399Baylor 72525Kansas State 114141Southern Mississippi 1512059Lehigh
1010Duke 2626Iowa State 4242Minnesota 12560Loyola - Maryland
1111Indiana 2727Florida 4343West Virginia 12761Detroit
1212Michigan 2828Memphis 4444Brigham Young 13962Long Island
41313Wisconsin 82929UNLV 1245
North Carolina State
Seton Hall
1614363Norfolk State
1414Marquette 3030Cincinnati 46
1515Louisville 3131Purdue 4949Virginia Commonwealth 152
UNC Asheville
Miss. Valley State
1616Georgetown 3232Notre Dame 5650Long Beach State 168
Western Kentucky
Rk = overall ranking by the Z-Ratings.
FR = Field ranking - the ranking of the team among the field of 68.

I had these teams' seeds determined before the start of the selection show. As the bracket was revealed, three teams stood out for their discrepancies.
Murray State as a #2. The strength of schedule ranking may have three digits, but 30-1 is a record worth properly rewarding. The Racers had an RPI in the low 20's, which I think explains much of why the committee gave them a No. 6.
Creighton as a #5. News flash: The Missouri Valley is really good this year, better than both the Atlantic 10 and Pacific-12 overall. The Bluejays' overall SOS was comparable to Wichita State's. The Z-Ratings grade them out nearly equally, and they should have been so seeded.
Temple as a #9. The Owls' RPI was 16; their SOS by the Z-Ratings is comparable to Creighton's. By contrast, they were three games worse, including getting bounced in the quarterfinal of the Atlantic 10 tournament. The Owls got way more credit than they deserved, especially since they'll get an opponent coming off a game in Dayton.

Establishing the bracket

For 2012, the regionals are: East (Boston); South (Atlanta); Midwest (St. Louis); and West (Phoenix).

As has always been the case, the bracket is built using the 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.

From Lexington, it's 340 miles to St. Louis and 380 to Atlanta. The difference is negligible, so I place Kentucky in the South to minimize the total distance traveled by the top four teams. Syracuse to the East; Missouri to the Midwest; Kansas to the West. As we have since 2004, we set up the Final Four so that if these four teams get there, it's 1 vs. 4 and 2 vs. 3. This means the South and West winners meet in one national semifinal, and the East and Midwest winners meet in the other.

Step 2: Place the No. 2 seeds.

North Carolina to the South; Michigan State to the Midwest; Ohio State to the East; Murray State to the West.

Step 3: Place the No. 3 seeds.

Baylor must go East or South as the third Big 12 team. For balance purposes, they get sent to the East (the best No. 1 and No. 2 seeds are already in the South). Duke to the Midwest. Indiana may go into either of the remaning two regions; I'm putting them in the West, again for balance (the West already has the worst 1 and 2 seeded teams). That leaves Michigan to be placed in the South.

Step 4: Place the No. 4 seeds.

Three of our No. 4 seeded teams are out of the Big East, and the other team is Wisconsin. The sixth criterion listed above constrains Wisconsin to the East. Because the Big Ten has five teams in the top sixteen, two teans from the league can be among the top four in a region. The Big East has only four teams one the Nos. 1 to 4 seed lines, so Marquette, Louisville, and Georgetown cannot be in a region with Syracuse. Marquette goes to the West, Louisville to the Midwest, and Georgetown to the South. Marquette's placement is motivated primarily by a need to keep the bracket balanced.

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

The sums of the "true seeds" in each region are 31 (E), 34 (M), 34 (S), 37 (W). Normally, we look for a difference of no more than five between lowest and highest, but we're going to proceed with what we have here.

Step 6: Assign first and second round sites.

Pittsburgh, PA: Syracuse, Ohio State
Columbus, OH: Michigan State, Michigan
Greensboro, NC: North Carolina, Duke
Nashville, TN: Murray State, Indiana
Louisville, KY: Kentucky, Wisconsin
Omaha, NE: Missouri, Kansas
Albuquerque, NM: Baylor, Marquette
Portland, OR: Louisville, Georgetown

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 they're expected to be back on their campuses within seven days of Selection Sunday).

Step 7a: Place the No. 5 seeds. (Available sites: Albuquerque, Louisville, Portland [2])

Creighton to the Midwest; Wichita State to the South; Florida State to the East; Saint Mary's to the West.

Step 7b: Place the No. 6 seeds. (Available sites: Albuquerque, Columbus, Greensboro, Nashville)

New Mexico to the West (as host, they cannot to the Albuquerque pod in the East); San Diego State to the East; Vanderbilt to the Midwest (as the second SEC team, they cannot be placed with Kentucky); and Gonzaga to the South.

Step 7c: Place the No. 7 seeds. (Available sites: Columbus, Greensboro, Nashville, Pittsburgh)

Kansas State to the West; Iowa State to the Midwest; Florida to the East (cannot go in the South with Kentucky); Memphis to the South.

Step 7d: Place the No. 8 seeds. (Available sites: Louisville, Omaha [2], Pittsburgh)

Omaha is the closest pod to UNLV; they go into the Midwest because of New Mexico's presence in the West. Because the Big East and Big Ten have nine teams in the field, possible intraconference matchups involving their teams in the regional semifinals are permissible; therefore, neither Cincinnati nor Notre Dame will be bumped. Cincinnati goes to the South; Purdue to the East; Notre Dame to the West. This does give two possible Big East matchups in the round of 16, along with one from the Big Ten. This is one more from the Big East than is strictly necessary, which is a departure from the way I've handled this in prior years, and makes more use of the flexibility provided by the criteria.

Step 7e: Place the No. 9 seeds. (Available sites: Louisville, Omaha [2], Pittsburgh)

Temple to the East; Virginia to the West; Texas to the South; Alabama to the Midwest...

Step 7f: Place the No. 10 seeds. (Available sites: Columbus, Greensboro, Nashville, Pittsburgh)

...or perhaps not. The Crimson tide change places with Northwestern, with the Wildcats taking the Midwest No. 9 slot. Alabama goes into the South region on the No. 10 line. UConn goes to the East; Saint Louis is forced into the West because it's the host school for the Midwest, into which Harvard is placed.

Step 7g: Place the No. 11 seeds. (Available sites: Albuquerque, Columbus, Greensboro, Nashville)

Southern Mississippi to the West. Minnesota presents problems insofar as being paired against other Big Ten teams too early, but bumping them down would mean bringing up a First Four winner - potentially even more complicated. The Golden Gophers go Midwest (possible matchup against Michigan State in the round of 16 vice Michigan in the round of 32); West Virginia to the South, and Brigham Young to the East (Albuquerque and Boston are both Thursday/Saturday sites).

Step 7h: Place the No. 12 seeds. (Available sites: Albuquerque, Louisville, Portland [2])

It's good that Louisville is also a Thursday/Sunday site, because the very next thing I'm doing is bumping the Cougars down in favor of the North Carolina State v. Seton Hall winner. I personally prefer this, as it brackets BYU away from a team in the conference it recently left. Next is the winner of Illinois v. California (the Pac-12 finally makes an appearance!), which goes to the South. That concludes placement of the at-large teams, but we're not quite home free yet, as the tounament winners from a few leagues who got at-large teams in are still out there. But next is last year's darling, Virginia Commonwealth. They go to the Midwest (yeah, I know, mid-on-mid crime, blah, blah.) Actually, we're left with another entry on that police blotter - Long Beach State to the West to take on Saint Mary's.

Step 7i: Place the No. 13 seeds. (Available sites: Albuquerque, Louisville, Portland [2])

Colorado to the West; Ohio to the East; St. Bonaventure to the Midwest (which puts us free and clear of conflicts); and Davidson to the South.

Step 7j: Place the No. 14 seeds. (Available sites: Albuquerque, Columbus, Greensboro, Nashville)

Belmont to the South (not the Nashville pod in the West due to the "home-court disadvantage" criterion); New Mexico State to the West (not the Albuquerque pod in the East for the same reason); South Dakota State to the Midwest; Montana to the East.

Step 7k: Place the No. 15 seeds. (Available sites: Columbus, Greensboro, Nashville, Pittsburgh)

Lehigh to the East; Loyola - Maryland to the South; Detroit to the Midwest; and Long Island to the West.

Step 7l: Place the No. 16 seeds. (Available sites: Louisville, Omaha [2], Pittsburgh)

The two previously bracketed First Four games constrain the options for the other two. The last four at-large teams would all play on Thursday if they get out of Dayton, so the bottom four teams in the field all play on Wednesday - and thus the two winners of those games both go to Omaha. Before we deal with them, we have Norfolk State and Pat Knight's shiftless seniors - um, I mean Lamar. The Spartans go to the East; the Cardinals to the South; and for whatever it's worth, the UNC Asheville/Mississippi Valley State winner has priority, so they get fed to the lion with the slightly less sharp teeth - that is, Kansas in the West. The Vermont v. Western Kentucky winner goes to the Midwest.

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

Here's the 2012 Z-Bracket:

SOUTH (Georgia Dome, Atlanta)EAST (TD Garden, Boston)
1KentuckyKFC Yum! Center
Louisville, KY
Consol Energy Center
Pittsburgh, PA
16LamarNorfolk State16
5Wichita StateRose Garden
Portland, OR
KFC Yum! Center
Louisville, KY
Florida State5
12Brigham Young12
3MichiganNationwide Arena
Columbus, OH
The Pit
Albuquerque, NM
6GonzagaSan Diego State6
11West Virginia11
7MemphisGreensboro Coliseum
Greensboro, NC
Consol Energy Center
Pittsburgh, PA
2North CarolinaOhio State2
15Loyola - MarylandLehigh15
(Mercedes-Benz Superdome, New Orleans)
South v. West
East v. Midwest
WEST (US Airways Center, Phoenix)MIDWEST (Edward Jones Dome, St. Louis)
1KansasCenturyLink Center Omaha
Omaha, NE
CenturyLink Center Omaha
Omaha, NE
8Notre DameUNLV8
5Saint Mary'sThe Pit
Albuquerque, NM
Rose Garden
Portland, OR
12Long Beach StateVa. Commonwealth12
13ColoradoSt. Bonaventure13
3IndianaBridgestone Arena
Nashville, TN
Greensboro Coliseum
Greensboro, NC
14New Mexico StateSouth Dakota State14
6New MexicoVanderbilt6
11Southern MississippiMinnesota11
7Kansas StateBridgestone Arena
Nashville, TN
Nationwide Arena
Columbus, OH
Iowa State7
10Saint LouisHarvard10
2Murray StateMichigan State2
15Long IslandDetroit15
FIRST ROUND (UD Arena, Dayton) - TuesdayFIRST ROUND (UD Arena, Dayton) - Wednesday
North Carolina State(to East #11)(to West #16)UNC Asheville
Seton HallMississippi Valley State
Illinois(to South #12)(to Midwest #16)Vermont
CaliforniaWestern Kentucky

Bells and whistles

A couple of months ago, I changed the generation of the Z-Ratings from the old MS-DOS based QBasic 4.5 to the much more powerful QB64 in order to finish my Hofstra senior design project. Nevertheless, I've kept the bracket simulations at one million plays each. Here they are: 2012 Z-Bracket | 2012 NCAA tournament. The combined probability of Kentucky or Syracuse winning it all is a smidge over 53 percent in each bracket. But funny things happen when ten men throw a ball around on a hardwood rectangle; last year, Connecticut had a 1.43 percent chance at the outset, and the Huskies' number came in.


Since I started this endeavor nearly a decade ago, Ken Pomeroy has supplied the raw data that make happen the college basketball ratings - and thus, this bracket. I tip my cap to him for keeping that data file outside the paywall he set up at the beginning of this year. John Whelan and Ken Butler showed me the better way back when I was an undergrad at Cornell. This year, I also mention Dr. Richard Puerzer, my faculty advisor and Chair of Engineering at Hofstra, for allowing me to build on the Bradley-Terry system as my senior project. I haven't applied that system to basketball...yet.

Final word: whether you prefer something like this or an "eye test," can we all agree that the Rating Percentage Index should be consigned to one of the lower circles of hell?

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