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.
|Kentucky||Southeastern||1||Georgia State||Sun Belt||114|
|Villanova||Big East||2||Eastern Washington||Big Sky||115|
|Wisconsin||Big Ten||5||Northeastern||Colonial Athletic||118|
|Gonzaga||West Coast||6||UC - Irvine||Big West||121|
|Notre Dame||Atlantic Coast||8||North Dakota State||Summit League||133|
|Iowa State||Big 12||11||New Mexico State||Westen Athletic||134|
|Northern Iowa||Missouri Valley||13||Alabama - Birmingham||Conference USA||138|
|Southern Methodist||American Athletic||23||Belmont||Ohio Valley||141|
|Virginia Commonwealth||Atlantic 10||28||Coastal Carolina||Big South||149|
|Stephen F. Austin||Southland||42||Lafayette||Patriot League||153|
|Valparaiso||Horizon League||62||Manhattan||Metro Atlantic Athletic||164|
|Wyoming||Mountain West||63||North Florida||Atlantic Sun||165|
|Wofford||Southern||69||Texas Southern||Southwestern Athletic||170|
|Harvard||Ivy League||89||Hampton||Mid-Eastern Athletic||275|
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.
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).
|Virginia||3||Georgetown||21||San Diego State||35|
|North Carolina||14||St.John's||27||Colorado State||40|
|West Virginia||17||Texas||31||Louisiana State||44|
|Arkansas||19||North Carolina State||33||Brigham Young||46|
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:
- The last and next-to-last at-large teams will play in the first round, as will the third-to-last and fourth-to-last at-large teams. The bottom four seeds will be paired 65 v. 66 and 67. v. 68.
- The seed that teams in the "First Four" will play for is determined by the field ranking of the higher-ranked team. That ranking will also determine precedence for the placement of the winners of the first-round games into the "main" 64-team bracket.
- Teams scheduled to play Wednesday, March 18 MUST be assigned to a Friday/Sunday pod for the second and third rounds. Teams playing on Tuesday, March 17 can be sent to either a Thursday/Saturday or Friday/Sunday pod.
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.
||9||33||33||North Carolina State||
||35||35||San Diego State||
||133||58||North Dakota State
||15||134||59||New Mexico State
||42||42||Stephen F. Austin||
||138||60||Alabama - Birmingham
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.
- Teams from the same conference can meet at varying points in the tournament, depending on how often they've already played in the season so far:
- Three or more times - regional final (round of 8).
- Twice - regional semifinal (round of 16).
- Once or not at all - third round (round of 32).
- The first four teams from a conference go to different regionals, provided they are seeded on the first four lines.
- Teams seeded Nos. 1 thru 4 will not be put at a severe "home-court disadvantage" in the second round (the round of 64).
- A team cannot play in an arena where it has played more than three regular season games, excluding conference tournaments (i.e. any home court).
- A team cannot play at a site where its school is hosting. This affects none of our regional hosts; on the tournament's first weekend, North Florida, Louisville, and Ohio State can't play in their home cities, nor can Oregon play in Portland.
- If two teams from the same region are in contention for the same slot, the one with the higher rating remains in its region. (The guidelines say "true seed," formerly "S-Curve"; we instead use our ratings, as they produced our seeds.)
- If necessary, a team's seed can be adjusted up or down one spot to meet the principles; I've never been able to get through a bracket without doing this. As was true since 2013, the committee voted itself the ability to move a team two lines from its true seed in "extraordinary circumstances," which I haven't had to use and don't expect to.
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 , 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 , 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 , 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 , 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 , 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 , 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 , 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 , 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 , 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!
- Duke / North Carolina — February 18, March 7
- Notre Dame / Miami (FL) — January 17, March 12
- Michigan State / Purdue — March 4
- Utah / UCLA — January 4, January 29
|MIDWEST (Quicken Loans Arena, Cleveland)||EAST (Carrier Dome, Syracuse)|
|1||Kentucky||KFC Yum! Center|
|CONSOL Energy Center|
|9||North Carolina State||Davidson||9|
|13||Georgia State||Eastern Washington||13|
|3||Louisville||Jacksonville Vet. Mem. Arena|
|CONSOL Energy Center|
|11||Stephen F. Austin||Miami (FL)||11|
|7||Virginia Commonwealth||Value City Arena|
|Value City Arena|
|15||Alabama - Birmingham||Belmont||15|
(Lucas Oil Stadium, Indianapolis)
Midwest v. West
East v. South
|WEST (Staples Center, Los Angeles)||SOUTH (NRG Stadium, Houston)|
|1||Duke||Time Warner Cable Arena|
|Time Warner Cable Arena|
|9||San Diego State||Oklahoma State||9|
|5||Wichita State||Jacksonville Vet. Mem. Arena|
|KFC Yum! Center|
|4||North Carolina||Northern Iowa||4|
|3||Iowa State||CenturyLink Center Omaha|
|CenturyLink Center Omaha|
|14||North Dakota State||UC - Irvine||14|
|15||Coastal Carolina||New Mexico State||15|
|FIRST ROUND (UD Arena, Dayton) - Tuesday||FIRST ROUND (UD Arena, Dayton) - Wednesday|
|Brigham Young||(to East #12)||(to West #11)||LSU|
|Robert Morris||(to Midwest #16)||(to West #16)||North Florida|
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.
The Z-Ratings Center | Matt's home page