Z-Bracket 2015: the "baker's dozen" edition

It is indeed the thirteenth time around for the Z-Bracket. Hopefully it won't be an unlucky one. As has always been the case, this endeavor makes use of the Z-Ratings (aka the Bradley-Terry system) through March 15 to select, seed, and bracket participants in the NCAA Division I Men's Basketball Championship. It might be similar to the tournament that'll actually be played out, or it could be different entirely. Let's find out...
(Summary of previous brackets | Jump to this year's bracket)

Selecting the field

Step 1: the automatic bids.

Still 32 automatic berths into the field; the Ivy League sending the winner of a playoff between its co-champions, and the 31 others awarding them to the respective tournament champions.
KentuckySoutheastern1Georgia StateSun Belt114
VillanovaBig East2Eastern WashingtonBig Sky115
WisconsinBig Ten5NortheasternColonial Athletic118
GonzagaWest Coast6UC - IrvineBig West121
ArizonaPacific-127AlbanyAmerica East125
Notre DameAtlantic Coast8North Dakota StateSummit League133
Iowa StateBig 1211New Mexico StateWesten Athletic134
Northern IowaMissouri Valley13Alabama - BirminghamConference USA138
Southern MethodistAmerican Athletic23BelmontOhio Valley141
Virginia CommonwealthAtlantic 1028Coastal CarolinaBig South149
Stephen F. AustinSouthland42LafayettePatriot League153
ValparaisoHorizon League62ManhattanMetro Atlantic Athletic164
WyomingMountain West63North FloridaAtlantic Sun165
WoffordSouthern69Texas SouthernSouthwestern Athletic170
BuffaloMid-American77Robert MorrisNortheast174
HarvardIvy League89HamptonMid-Eastern Athletic275

Step 2: the at-large bids.

Sixty-eight minus thirty-two equals thirty-six, and so we invite that many teams without automatic bids, starting at the top of the ratings and working down.
Virginia3Georgetown21San Diego State35
Duke4Michigan State22Davidson36
North Carolina14St.John's27Colorado State40
Baylor15Ohio State29Dayton41
Oklahoma16Iowa30Miami (FL)43
West Virginia17Texas31Louisiana State44
Wichita State18Xavier32UCLA45
Arkansas19North Carolina State33Brigham Young46
Providence20Oklahoma State34Temple47
Just as last year, there were three teams picked here that not selected for the actual tournament field, denoted in italics. The committee instead chose Ole Miss (52), Cincinnati (53), and Boise State (54). There are only three teams between the three aforementioned schools and the cut-off line (actually, there are four, but the first team out by the ratings would be Syracuse, who declared itself ineligible for postseason play).

Seeding the teams

The first round

We deal with the eight teams in the First Four in the same way as previously, using the one change specified by the NCAA last year (listed first below) and the other rules I've been using the last four years:

Creating the seed list

We just use our already existing Z-Ratings seed the 68 teams from 1 to 16. When two teams share the same cell, they will play each other in the opening round in Dayton.

Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team
111Kentucky 51717West Virginia 93333North Carolina State 137751Buffalo
22Villanova 1818Wichita State 3434Oklahoma State 8952Harvard
33Virginia 1919Arkansas 3535San Diego State 11453Georgia State
44Duke 2020Providence 3636Davidson 11554Eastern Washington
255Wisconsin 62121Georgetown 103737Georgia 1411855Northeastern
66Gonzaga 2222Michigan State 3838Purdue 12156UC Irvine
77Arizona 2323Southern Methodist 3939Indiana 12557Albany
88Notre Dame 2424Butler 4040Colorado State 13358North Dakota State
399Kansas 72525Utah 114141Dayton 1513459New Mexico State
1010Maryland 2626Oregon 4242Stephen F. Austin 13860Alabama - Birmingham
1111Iowa State 2727St. John's 4343Miami (FL) 14161Belmont
1212Louisville 2828Virginia Commonwealth 44
14962Coastal Carolina
41313Northern Iowa 82929Ohio State 1246
Brigham Young
1414North Carolina 3030Iowa 6248Valparaiso 16464Manhattan
1515Baylor 3131Texas 6349Wyoming 165
North Florida
Texas Southern
1616Oklahoma 3232Xavier 6950Wofford 174
Robert Morris
Rk = overall ranking by the Z-Ratings.
FR = Field ranking - the ranking of the team among the field of 68.

The only team that is seeded significantly differently than in the actual bracket is one that many people thought shouldn't have been in the tournament at all - the Texas Longhorns. As has always been the case, the Z-Ratings make no differentiation between games within and outside of the conference. One caution about this is that for the second consecutive year, there's an undefeated team entering the Big Dance. In contrast to previous years in which I gradually lowered γ (the weight of dummy 'tied' games) and eliminated it when all teams had a loss, I held it at 1 for most of the season, before lowering it to 0.5 a few weeks ago (it was 0.05 on Selection Sunday last year). A higher value distorts the true strengths of the teams by reducing the weight of what actually happened on the court, while a lower value which would allow Kentucky's rating to spiral off into infinity. Setting γ at 1/2 represents my trade-off between these choices.

Establishing the bracket

The 2015 regional sites are Syracuse (East); Houston (South); Cleveland (Midwest); and Los Angeles (West).

Though selection and seeding are done strictly by our ratings, the actual bracket construction goes according to the principles established by the selection committee. They're effectively the same as last year, accounting for the continued shifting in conference affiliations.

We also adhere to the bracketing procedure outlined in the championship handbook (also at the link just above). As always, 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.

The undefeated Kentucky Wildcats to the Midwest; another set of Wildcats, Villanova, to the East; Virginia to the South; Duke to the West. Should all four of these teams reach Lucas Oil Stadium, the overall one plays the four, and two versus three. This gives national semifinal pairings of Midwest v. West and East v. South - just the same as the committee drew it up.

Step 2: Place the No. 2 seeds.

Wisconsin to the Midwest; Gonzaga to the West; Arizona to the South; Notre Dame to the East.

Step 3: Place the No. 3 seeds.

Kansas to the South; Maryland to the East; and since Louisville must go into the Midwest as the fourth ACC team, Iowa State goes West.

Step 4: Place the No. 4 seeds.

The East and Midwest slots on this line have to be reserved for Baylor and Oklahoma, as the South and West have Big 12 teams already. We thus place Northern Iowa in the South and North Carolina in the West (allowable since the Tar Heels didn't face Duke in the ACC tournament). As for the Bears and Sooners, it's a toss-up, so I'm throwing Baylor in the East and Oklahoma in the Midwest.

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

The field rankings of the teams in each of the four regions are summed, and those sums are compared against each other. This bracket has a tight range: 32 (S), 34 (M), 35 (E and W). We move on.

Step 6: Assign second and third round sites.

We place the 16 assigned teams into second/third round "pods" in order of their ranking, subject to the constraints detailed above concerning host schools. Louisville, KY: Kentucky, Northern Iowa
Pittsburgh, PA: Villanova, Maryland
Charlotte, NC: Virginia, Duke
Columbus, OH: Wisconsin, Notre Dame
Seattle, WA: Gonzaga, Oklahoma
Portland, OR: Arizona, Baylor
Omaha, NE: Kansas, Iowa State
Jacksonville, FL: Louisville, North Carolina

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

Since only the sixteen teamy previously bracketed are supposed to be left standing at the end of the first Sunday, we place the remaining teams based on the nearest "pod" wherever possible, within the bracketing rules.

Step 7a: Place the No. 5 seeds. (Available sites: Jacksonville, Louisville, Portland, Seattle)

West Virginia to the South. Wichita is dead center of the country; I'm sending them to the warm pod in Jacksonville in the West. Arkansas goes to the East and Providence to the Midwest; neither is close to the West Coast, and those placements minimize matchups of conference opponents.

Step 7b: Place the No. 6 seeds. (Available sites: Jacksonville, Omaha [2], Pittsburgh)

Georgetown to the East (would not meet Villanova until the regional final); Michigan State to the South (keeping them away from Wisconsin, tie between Omaha pods broken by closer regional site); SMU to the South; Butler to the West.

Step 7c: Place the No. 7 seeds. (Available sites: Columbus [2], Portland, Seattle)

Utah to the West (away from Arizona); Oregon to the East (also away from Arizona, thus the Ducks are going to Columbus either way); St. John's to the South; VCU to the Midwest.

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

There are no Big Ten teams in the top half of any region, and Pittsburgh and Louisville are nearly equidistant from Columbus... I'll have the Buckeyes travel east, and place them in the East. Iowa to the Midwest; Texas to the West; Xavier to the South.

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

N. C. State to the Midwest; next up is Oklahoma State. The Cowboys didn't meet Baylor or West Virginia in the Big 12 tournament, so placement into either the East or the South is permissible. Charlotte is closer, so it's the South. San Diego State to the West and Davidson to the East (a natural fit anyway; though not required, it's not desired to give an effective home-court advantage to a lower seed, and Davidson is right outside of Charlotte).

Step 7f: Place the No. 10 seeds. (Available sites: Columbus [2], Portland, Seattle)

We haven't had an SEC team since the very first team to go in - despite that, I still bracket Georgia away from Kentucky, and thus in the East. Next, we look at Michigan State's schedule, and seeing that the Spartans played Indiana twice put Purdue only once, the Boilermakers get the South slot, while the Hoosiers get sent West. Colorado State is left with the Midwest.

Step 7g: Place the No. 11 seeds. (Available sites: Jacksonville, Omaha [2], Pittsburgh)

Not wanting to bracket Dayton against either VCU or Xavier, I send them to the South. Stephen F. Austin to the Midwest. Now, it's back to the schedules. Notre Dame and Miami (FL) played exactly twice already, as did Utah and UCLA. So the Hurricanes go to the East, and the winner between the Bruins and LSU heads West.

Step 7h: Place the No. 12 seeds. (Available sites: Jacksonville, Louisville, Portland, Seattle)

Next up is the winner of the first round game between BYU and Temple. The Midwest is out for either team (Seattle is a Friday/Sunday pod and thus no good for the Cougars, and SMU is already in the region). I give a sliht nod to BYU's higher rating and place the winner in the Portland pod in the East. Those are the last two at-large teams, and only one multi-bid conference's automatic qualiier has yet to be placed. Might we make it without bumping a team? Anyway... Valparaiso to the South, Wyoming to the Midwest, and Ben Ingram's Wofford Terriers to the Jacksonville pod in the West.

Step 7i: Place the No. 13 seeds. (Available Jacksonville, Louisville, Portland, Seattle)

Buffalo to the South; Harvard to the West (coincidence, I assure you!); Georgia State to the Midwest; Eastern Washington to the East.

Step 7j: Place the No. 14 seeds. (Available sites: Jacksonville, Omaha [2], Pittsburgh)

Northeastern to the East; UC Irvine to the South (Omaha is closer than Jacksonville, and the Anteaters get the South so they don't give a (highly unlikely) Sweet 16 opponent a home court disadvantage); Albany to the Midwest; North Dakota State to the West.

Step 7k: Place the No. 15 seeds. (Available sites: Columbus [2], Portland, Seattle)

The champion of the shell-of-its-former-self WAC, New Mexico State, gets the South; UAB, the champion (and soon to be former member of?) Conference USA to the Midwest; Belmont to the East; and the Chanticleers of Coastal Carolina to the West.

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

Lafayette to the East, yielding another matchup identical to the actual bracket. Manhattan to the South; the winner of North Florida and Texas Southern to the West. We opened with Kentucky, and we close by matching them against one of the two lowest rated teams in the field in their first game, Robert Morris or Hampton.

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

No bumps this year! Let's look at the potential interconference matchups before the Elite Eight. None of them are in the third round, and as for the Sweet 16 possibilities: No problems on that front, and the same-conference teams in the top 16 (except UNC, as the fifth team from the ACC) are regionally separated. Looks like we're good to go!

MIDWEST (Quicken Loans Arena, Cleveland)EAST (Carrier Dome, Syracuse)
1KentuckyKFC Yum! Center
Louisville, KY
CONSOL Energy Center
Pittsburgh, PA
8IowaOhio State8
9North Carolina StateDavidson9
Seattle, WA
Moda Center
Portland, OR
13Georgia StateEastern Washington13
3LouisvilleJacksonville Vet. Mem. Arena
Jacksonville, FL
CONSOL Energy Center
Pittsbugh, PA
6Southern MethodistGeorgetown6
11Stephen F. AustinMiami (FL)11
7Virginia CommonwealthValue City Arena
Columbus, OH
Value City Arena
Columbus, OH
10Colorado StateGeorgia10
2WisconsinNotre Dame2
15Alabama - BirminghamBelmont15
(Lucas Oil Stadium, Indianapolis)
Midwest v. West
East v. South
WEST (Staples Center, Los Angeles)SOUTH (NRG Stadium, Houston)
1DukeTime Warner Cable Arena
Charlotte, NC
Time Warner Cable Arena
Charlotte, NC
9San Diego StateOklahoma State9
5Wichita StateJacksonville Vet. Mem. Arena
Jacksonville, FL
KFC Yum! Center
Louisville, KY
West Virginia5
4North CarolinaNorthern Iowa4
3Iowa StateCenturyLink Center Omaha
Omaha, NE
CenturyLink Center Omaha
Omaha, NE
14North Dakota StateUC - Irvine14
6ButlerMichigan State6
Seattle, WA
Moda Center
Portland, OR
St. John's7
15Coastal CarolinaNew Mexico State15
FIRST ROUND (UD Arena, Dayton) - TuesdayFIRST ROUND (UD Arena, Dayton) - Wednesday
Brigham Young(to East #12)(to West #11)LSU
Robert Morris(to Midwest #16)(to West #16)North Florida
HamptonTexas Southern

Bells and whistles

This year, I've got the time to set up the simulation program, and with the γ much higher, I've run the simulator a million times on this bracket and the real one. Given Kentucky's sky-high rating, it's not surprising that the Wildcats have a better than four in five chance of completing their perfect season in either bracket setup.


QB64 has been integral to keeping this going; it's now been the fourth year since I switched from QBasic 4.5 to QB64. This wouldn't be impossible without Ken Pomeroy's master data file of games played, but it would be much more difficult and I likely wouldn't undertake it. And it certainly wouldn't have happened without my initial exposure to Bradley-Terry ratings, by way of Cornell hockey (whose season is surprisingly over well before Selection Sunday), and particularly Ken Butler and John Whelan.

I'm glad I've got this done sooner than it was last year. With it being done, it's time to enjoy the games, and to see if Kentucky will wilt under the pressure or flourish.

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