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:
|Virginia||Atlantic Coast||1||UNC Greensboro||Southern||95|
|Villanova||Big East||2||Charleston||Colonial Athletic||98|
|Kansas||Big 12||4||Marshall||Conference USA||110|
|Cincinnati||American Athletic||5||Stephen F. Austin||Southland||125|
|Michigan||Big Ten||12||Cal State - Fullerton||Big West||126|
|Gonzaga||West Coast||14||Bucknell||Patriot League||128|
|Arizona||Pacific-12||19||Wright State||Horizon League||138|
|Loyola - Chicago||Missouri Valley||55||Lipscomb||Atlantic Sun||145|
|New Mexico State||Western Athletic||63||Georgia State||Sun Belt||153|
|South Dakota State||Summit League||67||UMBC||America East||163|
|San Diego State||Mountain West||73||Iona||Metro Atlantic Athletic||176|
|Murray State||Ohio Valley||77||Radford||Big South||186|
|Davidson||Atlantic 10||84||North Carolina Central||Mid-Eastern Athletic||306|
|Montana||Big Sky||91||Texas Southern||Southwestern Athletic||315|
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:
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.
|Michigan State||6||Ohio State||22||Butler||34|
|Tennessee||10||Seton Hall||26||North Carolina State||38|
|Texas Tech||13||Texas A&M||28||Louisville||40|
|Wichita State||18||Miami (FL)||31||Alabama||43|
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.
- 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 14 MUST be assigned to a Friday/Sunday pod for the first and second rounds. Teams playing on Tuesday, March 13 can be sent to either a Thursday/Saturday or Friday/Sunday pod.
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:
||38||38||North Carolina State||
||125||56||Stephen F. Austin||
||126||57||Cal State - Fullerton||
||55||45||Loyola - Chicago||
||63||46||New Mexico State||
||12||67||47||South Dakota State||
||73||48||San Diego State||
|North Carolina Central|
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:
- Intraconference matchups are permissible at varying times, depending on how often the teams have played so far this season:
- 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 first 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, but can play at a site hosted by its conference. Creighton therefore can't play in Omaha, and Wichita State and San Diego State can't be placed in their respective cities on the opening weekend.
- 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. Since 2013, the committee has been able a team two lines from its true seed in "extraordinary circumstances"; I don't expect to have to employ this provision.
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 , San Diego )
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 , 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 , 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 , 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 , 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 , San Diego )
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 , San Diego )
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 , 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 , 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)|
|PPG Paints Arena|
|5||Wichita State||Viejas Arena|
San Diego, CA
|Taco Bell Arena|
|12||Murray State||San Diego State||12|
|3||Tennessee||American Airlines Center|
|PPG Paints Arena|
|14||Cal State - Fullerton||Marshall||14|
|11||New Mexico State||11|
|7||Creighton||Little Caesars Arena|
|Little Caesars Arena|
(Alamodome, San Antonio)
South v. Midwest
East v. West
|MIDWEST (CenturyLink Center, Omaha)||WEST (Staples Center, Los Angeles)|
|1||Kansas||Intrust Bank Center|
|9||North Carolina State||Virginia Tech||9|
San Diego, CA
|Taco Bell Arena|
|12||Buffalo||South Dakota State||12|
|3||Michigan||American Airlines Center|
|Intrust Bank Center|
|14||Bucknell||Stephen F. Austin||14|
|11||Loyola - Chicago||11|
|7||Seton Hall||Bridgestone Arena|
|FIRST FOUR (UD Arena, Dayton) - Tuesday||FIRST FOUR (UD Arena, Dayton) - Wednesday|
|Florida State||(to East #11)||(to South #16)||Radford|
|Alabama||(to West #11)||(to West #16)||North Carolina Central|
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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