Z-Bracket 2018 - blow out the candles...

...yes, there are now sixteen of them. Yep, that's how many editions of the Z-Bracket we're getting to with this one. I'm a little late this year, owing to working night shift over the weekend of Selection Sunday and attending to other parts of my site, but I've got to power through and make this happen. To give you an idea of how long I've kept this going on, the first one came out in 2003 - two months BEFORE I went into the United States Navy. Now, I'm almost nine years out, and still having at it. Oh yeah, I should explain what we're doing here; we'll use the men's basketball Z-Ratings (aka Bradley-Terry) as of Selection Sunday, in conjunction with the NCAA's own procedures, to select and build a 68-team bracket.

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

Selecting the field

Step 1: the automatic bids.

All 32 Division I conferences award their automatic qualification slots to the winners of their respective tournaments. This year:
VirginiaAtlantic Coast1UNC GreensboroSouthern95
VillanovaBig East2CharlestonColonial Athletic98
KansasBig 124MarshallConference USA110
CincinnatiAmerican Athletic5Stephen F. AustinSouthland125
MichiganBig Ten12Cal State - FullertonBig West126
GonzagaWest Coast14BucknellPatriot League128
KentuckySoutheastern15PennsylvaniaIvy League135
ArizonaPacific-1219Wright StateHorizon League138
Loyola - ChicagoMissouri Valley55LipscombAtlantic Sun145
New Mexico StateWestern Athletic63Georgia StateSun Belt153
South Dakota StateSummit League67UMBCAmerica East163
San Diego StateMountain West73IonaMetro Atlantic Athletic176
Murray StateOhio Valley77RadfordBig South186
BuffaloMid-American79Long IslandNortheast259
DavidsonAtlantic 1084North Carolina CentralMid-Eastern Athletic306
MontanaBig Sky91Texas SouthernSouthwestern Athletic315

Step 2: the at-large bids.

The remainder of the field is comprised of the thirty-six highest ranked teams not listed in the above table. In 2018, those squads are:
Xavier3Houston21Oklahoma State33
Michigan State6Ohio State22Butler34
Duke7Arkansas23Virginia Tech35
Purdue8Texas Christian24Baylor36
North Carolina9Florida25Marquette37
Tennessee10Seton Hall26North Carolina State38
West Virginia11Creighton27Missouri39
Texas Tech13Texas A&M28Louisville40
Auburn16Texas29Florida State41
Clemson17Oklahoma30Mississippi State42
Wichita State18Miami (FL)31Alabama43
Kansas State20Providence32Nevada44
The 2018 Z-Ratings matched 31 of the selection committee's 36 choices; the five teams in italics are those who were chosen by the ratings here but not the committee. On the actual hardwood floors, it'll be Atlantic 10 regular season champion Rhode Island (49), as well as all four of the teams the committee sent to Dayton as the "last four in" - UCLA (46), Arizona State (50), Syracuse (51), and St. Bonaventure (58). Given that the committee took two A-10 teams that I'm leaving out, I gave that league a look; it's rated the 10th best, and that's probably why Rhode Island's loss to Davidson in the championship game put the Rams on the wrong side of the cutoff line.

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

The ratings give us a ranking that we use in the place of the committee's S-Curve to seed the teams. Here's how that shakes out:

Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team
111Virginia 51717Clemson 93333Oklahoma State 138451Davidson
22Villanova 1818Wichita State 3434Butler 9152Montana
33Xavier 1919Arizona 3535Virginia Tech 9553UNC Greensboro
44Kansas 2020Kansas State 3636Baylor 9854Charleston
255Cincinnati 62121Houston 103737Marquette 1411055Marshall
66Michigan State 2222Ohio State 3838North Carolina State 12556Stephen F. Austin
77Duke 2323Arkansas 3939Missouri 12657Cal State - Fullerton
88Purdue 2424Texas Christian 4040Louisville 12858Bucknell
399North Carolina 72525Florida 1141
Florida State
Mississippi State
1010Tennessee 2626Seton Hall 43
13860Wright State
1111West Virginia 2727Creighton 5545Loyola - Chicago 14561Lipscomb
1212Michigan 2828Texas A&M 6346New Mexico State 15362Georgia State
41313Texas Tech 82929Texas 126747South Dakota State 1616363UMBC
1414Gonzaga 3030Oklahoma 7348San Diego State 17664Iona
1515Kentucky 3131Miami (FL) 7749Murray State 186
Long Island
1616Auburn 3232Providence 7950Buffalo 306
North Carolina Central
Texas Southern
Rk = overall ranking by the Z-Ratings.
FR = Field ranking - the ranking of the team among the field of 68.

Two teams jump out to me as I look at the seed list, being three or more lines away from their location in the actual bracket. Kansas State is a no. 5 here vice a no. 9 in real life; they benefit here from being in the top-rated Big 12. If every Big 12 team played every team not in the conference, the league's teams are projected to win just over 88% of the time. All ten of the Big 12's members are in the top fifth of the rankings. In contrast, the eighth-ranked Mountain West has three teams in the bottom half of Division I; Nevada not only racked up three losses in conference play, it didn't even reach the MWC final.

Establishing the bracket

The regional sites for 2018: Boston (East); Atlanta (South); Omaha (Midwest); and Los Angeles (West).

Actually constructing the tournament's bracket is not nearly as rigid a process as are selection and seeding. We do it the same way the NCAA does, as they state in their principles and procedures. The principles are the same as last year:

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.

Step 1: Place the No. 1 seeds, and pair the regional winners for the national semifinals; the overall number one seed gets its choice of regional and sub-regional.

The top overall seeded Virginia Cavaliers to the South - they'll also get a Charlotte pod, since they were the actual no. 1 overall team, we know which sites they chose. Villanova to the East; Xavier to the West; and Kansas to the Midwest. The Musketeers are traveling either way, so I elected to keep Kansas closer to home. Final Four matchups are South vs. Midwest and East vs. West.

Step 2: Place the No. 2 seeds.

Cincinnati to the Midwest; Michigan State to the East; Duke has to go West because Virginia is in the South, so Purdue heads to the Atlanta regional.

Step 3: Place the No. 3 seeds.

Defending champion North Carolina to the East; Tennessee to the South; West Virginia goes West because the Mountaineers can't be slotted with Kansas; and Michigan to the Midwest.

Step 4: Place the No. 4 seeds.

Texas Tech to the South, Gonzaga to the West. We next have our second and third SEC teams, Kentucky and Auburn. As both the higher-ranked team and the conference champion, Kentucky gets its preference... but what is that? Boston is further from Lexington than Omaha, but the Wildcats, in contrast with Auburn, have a more national following. I'm going to give Kentucky the East and send the Tigers to the Midwest.

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

To quote the principles and procedures directly:
After the top four seed lines have been assigned, the committee will review the relative strengths of the regions by adding the “true seed” numbers in each region to determine if any severe numerical imbalance exists. Generally, no more than five points should separate the lowest and highest total.
The sums of those true seed numbers are 32, 32, 35, and 37... which satisfies our threshold for balance.

Step 6: Assign first and second round sites.

Now that we have the top 16 teams locked in, we send them to the sites where they'll contest the first weekend of the tournament.

Charlotte, NC: Virginia, Duke
Pittsburgh, PA: Villanova, North Carolina
Nashville, TN: Xavier, Cincinnati
Wichita, KS: Kansas, West Virginia
Detroit, MI: Michigan State, Purdue
Dallas, TX: Tennessee, Michigan
San Diego, CA: Texas Tech, Auburn
Boise, ID: Gonzaga, Kentucky

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

Subject to the principles, the pods I just assigned determine where teams will be sent - because in the eyes of the ratings, these teams shouldn't make the regionals; of course, it never pans out that way...

Step 7a: Place the No. 5 seeds. (Boise [2], San Diego [2])

Clemson to the Midwest; Wichita State to the South; Arizona to the West, which also works well because Kansas State can't be placed opposite West Virginia, so K-State heads East.

Step 7b: Place the No. 6 seeds. (Dallas [2], Pittsburgh, Wichita)

Because we're past the first four lines, I don't need to separate the first four teams into different regions anymore - that's quite helpful here. Houston to the South, Ohio State to the West so the Buckeyes avoid the Enablers Spartans and Wolverines, Arkansas to the Midwest, and TCU to the East.

Step 7c: Place the No. 7 seeds. (Charlotte, Detroit [2], Nashville)

Florida to the West... and the rest of this bracket line is constrained. Texas A&M has to be placed in the East to avoid Tennessee and Arkansas; Creighton can't play in Omaha, so they go to the South, which leaves Seton Hall in the Midwest.

Step 7d: Place the No. 8 seeds. (Charlotte, Nashville, Pittsburgh, Wichita)

The Texas Longhorns are first up on this line, either they or Oklahoma will have to potentially get an intra-conference matchup before the regional finals. The regular season of the Big 12 (Minus 2) is a full double round-robin, so neither team can be placed in the same regional as Kansas. I'll give Texas the West, and send Oklahoma to the South because Charlotte is closer than Pittsburgh. The U (of Miami, that is) goes to the East (to avoid Clemson) and Providence to the Midwest (to avoid Villanova).

Step 7e: Place the No. 9 seeds. (Charlotte, Nashville, Pittsburgh, Wichita)

Oklahoma State goes to the East; the potential Sweet Sixteen clash with Kansas State is acceptable, since those teams didn't meet in the Big 12 tournament. Butler to the South; Virginia Tech to the West; and we come to a bump! With Big 12 teams in the top quarter of all four regions, Baylor will drop to a No. 10. Bringing up Marquette, the highest ranked No. 10, doesn't help us, as the Golden Eagles can't face the Friars. NC State faced Clemson twice in the regular season, so they're good to take that Midwest No. 9 slot.

Step 7f: Place the No. 10 seeds. (Charlotte, Detroit [2], Nashville)

Having been bumped down, Baylor goes first, and they'll go to the Midwest. I want to send Marquette to Detroit, but I have to do so through the East with Creighton already in the South; thus Missouri goes to the South and Louisville to the West, which works because the Cardinals only faced Duke once in the regular season and not in the ACC Tournament.

Step 7g: Place the No. 11 seeds. (Dallas [2], Pittsburgh, Wichita)

Florida State only faced North Carolina once, as did Mississippi State and Texas A&M; thus the East is a good region for that winner to go. Alabama faced Florida twice and Tennessee once; I'm putting the winner of their matchup with Nevada in the West. Loyola - Chicago to the Midwest and New Mexico State to the South.

Step 7h: Place the No. 12 seeds. (Boise [2], San Diego [2])

South Dakota State to the West; San Diego State thus has to go to the East; Murray State to the South, and Buffalo to the Midwest.

Step 7i: Place the No. 13 seeds. (Boise [2], San Diego [2])

Davidson to the South... and with Montana next up, the rule against disadvantaging teams on the top four lines comes into play. Missoula is sufficiently close to Boise that I'm sending the Grizzlies to San Diego in the Midwest region. UNC Greensboro to the East, and the College of Charleston to the West.

Step 7j: Place the No. 14 seeds. (Dallas [2], Pittsburgh, Wichita)

Marshall to the East. Now... where exactly is Stephen F. Austin? Can I send them to Dallas? No, I can't. They head West. Cal State - Fullerton to the South, and Bucknell to the Midwest.

Step 7k: Place the No. 15 seeds. (Charlotte, Detroit [2], Nashville)

Penn to the East; Wright State to the Midwest; Lipscomb to the West; Georgia State to the South (recall that Georgia State isn't hosting the South Regional; additionally, they didn't play in Philips Arena this season).

Step 7l: Place the No. 16 seeds. (Charlotte, Nashville, Pittsburgh, Wichita)

UMBC to the East; Iona to the West; the Radford-LIU winner to the South; and the North Carolina Central - Texas Southern winner to the Midwest... or perhaps not. That leaves three First Four winners heading to Thursday first round games; the easiest fix is to swap Iona with NCC/TX Southern, which balances the First Four.

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

SOUTH (Philips Arena, Atlanta)EAST (TD Garden, Boston)
1VirginiaSpectrum Center
Charlotte, NC
PPG Paints Arena
Pittsburgh, PA
8OklahomaMiami (FL)8
9ButlerOklahoma State9
5Wichita StateViejas Arena
San Diego, CA
Taco Bell Arena
Boise, ID
Kansas State5
12Murray StateSan Diego State12
4Texas TechKentucky4
13DavidsonUNC Greensboro13
3TennesseeAmerican Airlines Center
Dallas, TX
PPG Paints Arena
Pittsburgh, PA
North Carolina3
14Cal State - FullertonMarshall14
11New Mexico State11
7CreightonLittle Caesars Arena
Detroit, MI
Little Caesars Arena
Detroit, MI
Texas A&M7
2PurdueMichigan State2
15Georgia StatePennsylvania15
(Alamodome, San Antonio)
South v. Midwest
East v. West
MIDWEST (CenturyLink Center, Omaha)WEST (Staples Center, Los Angeles)
1KansasIntrust Bank Center
Wichita, KS
Bridgestone Arena
Nashville, TN
9North Carolina StateVirginia Tech9
5ClemsonViejas Arena
San Diego, CA
Taco Bell Arena
Boise, ID
12BuffaloSouth Dakota State12
3MichiganAmerican Airlines Center
Dallas, TX
Intrust Bank Center
Wichita, KS
West Virginia3
14BucknellStephen F. Austin14
6ArkansasOhio State6
11Loyola - Chicago11
7Seton HallBridgestone Arena
Nashville, TN
Spectrum Center
Charlotte, NC
15Wright StateLipscomb15
FIRST FOUR (UD Arena, Dayton) - TuesdayFIRST FOUR (UD Arena, Dayton) - Wednesday
Florida State(to East #11)(to South #16)Radford
Mississippi StateLIU
Alabama(to West #11)(to West #16)North Carolina Central
NevadaTexas Southern

Bracket simulation

Here are the simulation results based on one million playings of:


Late as this edition of the Z-Bracket may be, it's always a pleasure to compose it. I couldn't keep this tradition going without Ken Pomeroy's games file, nor without the seed planted in my head by JTW way back in the day. And of course, QB64.

Another fun year doing this... I can only hope that it continues until Z-Bracket 58 or so.

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