Z-Bracket 2019 - affix the stamp...

This year's Z-Bracket is late and it's going to be sparse. There won't be quite as much commentary, but I did get it done. It's an exercise in using the Z-Ratings (aka Bradley-Terry) as of Selection Sunday for NCAA Division I men's basketball, along with the NCAA's own procedures, to construct a tournament.

(Summary of previous brackets | Jump to this year's bracket)

Selecting the field

Step 1: the automatic bids.

This year's thirty-two conference tournament winners are:
TeamConferenceRankTeamConferenceRank
DukeAtlantic Coast2VermontAmerica East86
Michigan StateBig Ten8YaleIvy League89
AuburnSoutheastern14Saint LouisAtlantic 1094
CincinnatiAmerican Athletic16Georgia StateSun Belt95
WoffordSouthern18NortheasternColonial Athletic97
VillanovaBig East23Northern KentuckyHorizon League123
BuffaloMid-American25MontanaBig Sky129
Iowa StateBig 1226ColgatePatriot League139
Utah StateMountain West50BradleyMissouri Valley149
New Mexico StateWestern Athletic56Abilene ChristianSouthland157
Murray StateOhio Valley60Gardner-WebbBig South177
OregonPacific-1267North Dakota StateSummit League200
UC IrvineBig West69Prairie View A&MSouthwestern Athletic223
Saint Mary'sWest Coast71Fairleigh DickinsonNortheast228
Old DominionConference USA82IonaMetro Atlantic Athletic231
LibertyAtlantic Sun84North Carolina CentralMid-Eastern Athletic320

Step 2: the at-large bids.

The next thirty-six best remaining teams are:
TeamRankTeamRankTeamRank
Virginia1Wisconsin17Nevada33
North Carolina3Kansas State19Seton Hall34
Tennessee4Virginia Tech20Ohio State35
Kentucky5Maryland21Florida36
Michigan6Mississippi State22UNC Greensboro37
Houston7Marquette24Texas Christian38
Gonzaga9Louisville27Washington39
Florida State10Iowa28Mississippi40
Louisiana State11Minnesota29Baylor41
Texas Tech12Oklahoma30Syracuse42
Kansas13North Carolina State31Temple43
Purdue15Central Florida32Nebraska44
This year, the Z-Ratings and the committee disagreed on four selections. Those in the Z-Bracket are denoted in italics in the table above; in their stead, it's St. John's (46), Virginia Commonwealth (52), Arizona State (59), and Belmont (66) actually playing.

Seeding the teams

The first round

We use the following rules to set up the four games in Dayton that precede the first round. They're the same rules that I've used since 2011, subject to what the NCAA's procedure for building the bracket prescribes.

Creating the seed list

We go straight off the rankings to produce our seedings, and that gives us:

SeedRkFRTeamSeedRkFRTeamSeedRkFRTeamSeedRkFRTeam
111Virginia 51717Wisconsin 93333Nevada 138251Old Dominion
22Duke 1818Wofford 3434Seton Hall 8452Liberty
33North Carolina 1919Kansas State 3535Ohio State 8653Vermont
44Tennessee 2020Virginia Tech 3636Florida 8954Yale
255Kentucky 62121Maryland 103737UNC Greensboro 149455Saint Louis
66Michigan 2222Mississippi State 3838Texas Christian 9556Georgia State
77Houston 2323Villanova 3939Washington 9757Northeastern
88Michigan State 2424Marquette 4040Mississippi 12358Northern Kentucky
399Gonzaga 72525Buffalo 1141
42
41
42
Baylor
Syracuse
1512959Montana
1010Florida State 2626Iowa State 43
44
43
44
Temple
Nebraska
13960Colgate
1111Louisiana State 2727Louisville 5045Utah State 14961Bradley
1212Texas Tech 2828Iowa 5646New Mexico State 15762Abilene Christian
41313Kansas 82929Minnesota 126047Murray State 1617763Gardner-Webb
1414Auburn 3030Oklahoma 6748Oregon 20064North Dakota State
1515Purdue 3131North Carolina State 6949UC Irvine 223
228
65
66
Prairie View A&M
Fairleigh Dickinson
1616Cincinnati 3232Central Florida 7150Saint Mary's 231
320
67
68
Iona
North Carolina Central
Key:
Rk = overall ranking by the Z-Ratings.
FR = Field ranking - the ranking of the team among the field of 68.

Establishing the bracket

The regional sites for 2018: Washington (East); Louisville (South); Kansas City (Midwest); and Anaheim (West).

The actual bracket building is done the same way as the committee says it does it; their principles and procedures are publicly available, and have been relatively constant for as long as I've been doing this. The basics:

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.Just makes for a quicker construction process. There is one tweak to the procedure, and it's right in the first step.

I'm not going to give my usual detail of building the bracket this time around. I will note the two instances that teams had to be swapped out of their seed lines stated above: Iowa and North Carolina State (nos. 7 and 8), and Ohio State and UNC Greensboro (nos. 9 and 10). Here's the final product.

EAST (Capital One Arena, Washington, D.C.)SOUTH (KFC Yum! Center, Louisville)
1VirginiaColonial Life Arena
Columbia, SC
Colonial Life Arena
Columbia, SC
Duke1
1616
8IowaCentral Florida8
9Seton HallFlorida9
5WoffordSAP Center
San Jose, CA
SAP Center
San Jose, CA
Kansas State5
12Saint Mary'sUC Irvine12
4KansasPurdue4
13YaleOld Dominion13
3Louisiana StateBOK Center
Tulsa, OK
Vivint Smart Home Arena
Salt Lake City, UT
Texas Tech3
14NortheasternNorthern Kentucky14
6MarylandVillanova6
1111
7BuffaloWells Fargo Arena
Des Moines, IA
VyStar Veterans Memorial Arena
Jacksonville, FL
North Carolina State7
10Texas ChristianOhio State10
2MichiganKentucky2
15ColgateAbilene Christian15
FINAL FOUR
(U.S. Bank Stadium, Minneapolis)
East v. West
South v. Midwest
WEST (Honda Center, Anaheim)MIDWEST (Sprint Center, Kansas City)
1TennesseeNationwide Arena
Columbus, OH
Nationwide Arena
Columbus, OH
North Carolina1
16North Dakota StateGardner-Webb16
8MinnesotaOklahoma8
9NevadaUNC Greensboro9
5Virginia TechXL Center
Hartford, CT
XL Center
Hartford, CT
Wisconsin5
12Murray StateOregon12
4CincinnatiAuburn4
13VermontLiberty13
3Florida StateVyStar Veterans Memorial Arena
Jacksonville, FL
Vivint Smart Home Arena
Salt Lake City, UT
Gonzaga3
14Georgia StateSaint Louis14
6Mississippi StateMarquette6
11Utah StateNew Mexico State11
7Iowa StateWells Fargo Arena
Des Moines, IA
BOK Center
Tulsa, OK
Louisville7
10WashingtonMississippi10
2Michigan StateHouston2
15MontanaBradley15
FIRST FOUR (UD Arena, Dayton) - TuesdayFIRST FOUR (UD Arena, Dayton) - Wednesday
Baylor(to East #11)(to South #16)Prairie View A&M
SyracuseFairleigh Dickinson
Temple(to South #11)(to East #16)Iona
NebraskaNorth Carolina Central

Bracket simulation

This will follow soon. Right now I just wanted to get the bracket up.

Acknowledgements

Ken Pomeroy for the master file of game data; John T. Whelan for the inspiration back at the beginning; and QB64 for the engine.

This may not be as extensive a Z-Bracket as usual, but I do intend to keep it going to 20... or at least to 18.

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