The Z-Bracket: 2012 edition
Ten seasons. Has the history of the Z-Ratings and the Z-Bracket really reached a decade of college basketball? Yes, it has. Things have changed over the years - the number of teams in, the size of the venues for the Final Four - but the Bradley-Terry system and the tournament I build from it have remained steady as a rock. All the decisions about selection and seeding flow from the Z-Ratings through 11 March, a product of the 5,245 games between Division I schools played this year; the placement of the teams into the bracket will be fully explained as well. (Summary of previous brackets | Jump to this year's bracket)
Selecting the field
Step 1: the automatic bids.
Still no bid for the quite badly named Great West Conference; the automatic bids go to the other thirty conference tournament winners and this year's Ivy League regular season champion, Har - wait, is that right? Are we sure about that? Yes, for the first time since 1946, Harvard is in the Dance.
|Missouri||Big 12||3|| ||Davidson||Southern||81|
|Michigan State||Big Ten||6|| ||Belmont||Atlantic Sun||85|
|Murray State||Ohio Valley||8|| ||New Mexico State||Western Athletic||86|
|Louisville||Big East||15|| ||South Dakota State||Summit League||89|
|Creighton||Missouri Valley||17|| ||Montana||Big Sky||91|
|Florida State||Atlantic Coast||19|| ||Lehigh||Patriot League||120|
|Saint Mary's||West Coast||20|| ||Loyola - Maryland||Metro Atlantic Athletic||125|
|New Mexico||Mountain West||21|| ||Detroit||Horizon League||127|
|Vanderbilt||Southeastern||23|| ||Long Island||Northeast||139|
|Memphis||Conference USA||28|| ||Norfolk State||Mid-Eastern Athletic||143|
|Harvard||Ivy League||40|| ||Lamar||Southland||148|
|Virginia Commonwealth||Colonial Athletic||49|| ||UNC Asheville||Big South||152|
|Long Beach State||Big West||56|| ||Vermont||America East||168|
|Colorado||Pacific-12||60|| ||Western Kentucky||Sun Belt||174|
|Ohio University||Mid-American||71|| ||Mississippi Valley State||Southwestern Athletic||205|
|St. Bonaventure||Atlantic 10||80|
Step 2: the at-large bids.
There's no cross country scoring, no under consideration board. These bids go to the 37 highest ranked teams that did not claim automatic bids. They are:
Teams in italics were not selected for the actual tournament field. In 2012, these are: South Florida (51), Colorado State (52), Xavier (57), and Iona (EIGHTY-TWO).
|Kentucky||1 ||San Diego State||22|| ||Alabama||36|
|Syracuse||2 ||Gonzaga||24|| ||Northwestern||37|
|Kansas||4 ||Kansas State||25|| ||Connecticut||38|
|North Carolina||5 ||Iowa State||26|| ||Saint Louis||39|
|Ohio State||7 ||Florida||27|| ||Southern Mississippi||41|
|Baylor||9 ||UNLV||29|| ||Minnesota||42|
|Duke||10 ||Cincinnati||30|| ||West Virginia||43|
|Indiana||11 ||Purdue||31|| ||Brigham Young||44|
|Michigan||12 ||Notre Dame||32|| ||North Carolina State||45|
|Wisconsin||13 ||Temple||33|| ||Illinois||46|
|Marquette||14 ||Virginia||34|| ||California||47|
|Georgetown||16 ||Texas||35|| ||Seton Hall||48|
Once again, four discrepancies. Three of the teams taken by the Z-Bracket are from the top-overall Big Ten (will Northwestern EVER get a break?) Three of the teams taken by the committee within the first seven at-larges below the cut line. Very little to reflect on there.
But...Iona? IONA??? I'm not even going to compare tham against any of the four teams that made the Z-Bracket. Instead, I want to put them against Drexel, the CAA regular season champion. The Dragons and Gaels played roughly comparable schedules (Drexel's was slightly better). Drexel was a game and a half better overall. The Dragons went 16-2 in the No. 16 league, losing in the tournament final in a hostile arena (not that we take that into account); the Gaels, by contrast, were 16-4 in the No. 19 conference and got bounced in the semifinal on a true neutral court. Jeff Hathaway credited Iona's admission to the tournament to its superior non-conference schedule. I am sick and fucking tired of that stinky canard. A team's schedule is a single, indivisible thing. You may be able to control what games you can get, but you can't necessarily control how good those opponents will be when you play them. It's the same with the league schedule. Yes, Iona should suffer because it played in the MAAC (and was tripped up in the MAAC).
I was convinced that the Selection Committee was driven toward this decision by the contents of an unmarked package from the Colombian jungle. Actually, it's even simpler than drugs. According to the RPI, Iona was 41 - thirty spots ahead of Drexel. College hockey fans have long said that they have it better because of the existence of the objective Pairwise Rankings that control selection to the NCAA tournament. A small subset of them, myself included, have railed against the use of the RPI as a fatally flawed statistic. This one decision incontrovertibly proves us right on the latter point.
Seeding the teams
The first round
I'm going to handle the First Four the same way I did last year, using the following guidelines:
- Within each of the two groups of participants, the four teams will be initially paired 1 vs. 4 and 2 vs. 3.
- 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 second and third rounds. Teams playing on Tuesday, March 13 can be sent to either a Thursday/Saturday or Friday/Sunday pod.
- In the event that other principles create conflict (particularly those concerning intra-conference matchups), the First Four pairings may be altered, but only as a last resort.
Creating the seed list
Being as we have a perfectly good set of rankings already, why don't we just use that to produce our seeds?
||22||22||San Diego State||
||86||56||New Mexico State
||89||57||South Dakota State
||125||60||Loyola - Maryland
|North Carolina State|
Miss. Valley State
||56||50||Long Beach State||
Rk = overall ranking by the Z-Ratings.
FR = Field ranking - the ranking of the team among the field of 68.
I had these teams' seeds determined before the start of the selection show. As the bracket was revealed, three teams stood out for their discrepancies.
Murray State as a #2. The strength of schedule ranking may have three digits, but 30-1 is a record worth properly rewarding. The Racers had an RPI in the low 20's, which I think explains much of why the committee gave them a No. 6.
Creighton as a #5. News flash: The Missouri Valley is really good this year, better than both the Atlantic 10 and Pacific-12 overall. The Bluejays' overall SOS was comparable to Wichita State's. The Z-Ratings grade them out nearly equally, and they should have been so seeded.
Temple as a #9. The Owls' RPI was 16; their SOS by the Z-Ratings is comparable to Creighton's. By contrast, they were three games worse, including getting bounced in the quarterfinal of the Atlantic 10 tournament. The Owls got way more credit than they deserved, especially since they'll get an opponent coming off a game in Dayton.
Establishing the bracket
For 2012, the regionals are: East (Boston); South (Atlanta); Midwest (St. Louis); and West (Phoenix).
As has always been the case, the bracket is built using the principles established by the selection committee. They are:
- No intraconference matchups in the first three rounds, unless nine or more teams from a conference are selected (in 2012, the Big East and Big Ten each have nine).
- The first three teams from a conference go to different regionals.
- Teams seeded Nos. 1 thru 5 will not be put at a severe "home-court disadvantage" in the first round.
- 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. Saint Louis cannot be placed in the Midwest; for the first full weekend of play, this effects Creighton (Omaha), New Mexico (Albuquerque), Ohio State (Columbus) and Louisville (Louisville, obviously).
- Only one team from a conference can be among the top four or bottom four seeds in a region, unless a conference has five or more teams in those groupings of lines (Big Ten).
- 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. (We'll definitely need this one.)
- If all these principles fail to reconcile the bracket, we can have intraconference matchups as early as the second round, in conferences with five or more participants.
We also adhere to the bracketing procedure outlined in the championship handbook. I will once again state that 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.
From Lexington, it's 340 miles to St. Louis and 380 to Atlanta. The difference is negligible, so I place Kentucky in the South to minimize the total distance traveled by the top four teams. Syracuse to the East; Missouri to the Midwest; Kansas to the West. As we have since 2004, we set up the Final Four so that if these four teams get there, it's 1 vs. 4 and 2 vs. 3. This means the South and West winners meet in one national semifinal, and the East and Midwest winners meet in the other.
Step 2: Place the No. 2 seeds.
North Carolina to the South; Michigan State to the Midwest; Ohio State to the East; Murray State to the West.
Step 3: Place the No. 3 seeds.
Baylor must go East or South as the third Big 12 team. For balance purposes, they get sent to the East (the best No. 1 and No. 2 seeds are already in the South). Duke to the Midwest. Indiana may go into either of the remaning two regions; I'm putting them in the West, again for balance (the West already has the worst 1 and 2 seeded teams). That leaves Michigan to be placed in the South.
Step 4: Place the No. 4 seeds.
Three of our No. 4 seeded teams are out of the Big East, and the other team is Wisconsin. The sixth criterion listed above constrains Wisconsin to the East. Because the Big Ten has five teams in the top sixteen, two teans from the league can be among the top four in a region. The Big East has only four teams one the Nos. 1 to 4 seed lines, so Marquette, Louisville, and Georgetown cannot be in a region with Syracuse. Marquette goes to the West, Louisville to the Midwest, and Georgetown to the South. Marquette's placement is motivated primarily by a need to keep the bracket balanced.
Step 5: Check for conflicts and balance in the Nos. 1 through 4 seeds.
The sums of the "true seeds" in each region are 31 (E), 34 (M), 34 (S), 37 (W). Normally, we look for a difference of no more than five between lowest and highest, but we're going to proceed with what we have here.
Step 6: Assign first and second round sites.
Pittsburgh, PA: Syracuse, Ohio State
Columbus, OH: Michigan State, Michigan
Greensboro, NC: North Carolina, Duke
Nashville, TN: Murray State, Indiana
Louisville, KY: Kentucky, Wisconsin
Omaha, NE: Missouri, Kansas
Albuquerque, NM: Baylor, Marquette
Portland, OR: Louisville, Georgetown
Step 7: Place the No. 5 through 16 seeds.
Keep in mind that from this point on, the teams are placed according to the site of their second/third round pod (since they're expected to be back on their campuses within seven days of Selection Sunday).
Step 7a: Place the No. 5 seeds. (Available sites: Albuquerque, Louisville, Portland )
Creighton to the Midwest; Wichita State to the South; Florida State to the East; Saint Mary's to the West.
Step 7b: Place the No. 6 seeds. (Available sites: Albuquerque, Columbus, Greensboro, Nashville)
New Mexico to the West (as host, they cannot to the Albuquerque pod in the East); San Diego State to the East; Vanderbilt to the Midwest (as the second SEC team, they cannot be placed with Kentucky); and Gonzaga to the South.
Step 7c: Place the No. 7 seeds. (Available sites: Columbus, Greensboro, Nashville, Pittsburgh)
Kansas State to the West; Iowa State to the Midwest; Florida to the East (cannot go in the South with Kentucky); Memphis to the South.
Step 7d: Place the No. 8 seeds. (Available sites: Louisville, Omaha , Pittsburgh)
Omaha is the closest pod to UNLV; they go into the Midwest because of New Mexico's presence in the West. Because the Big East and Big Ten have nine teams in the field, possible intraconference matchups involving their teams in the regional semifinals are permissible; therefore, neither Cincinnati nor Notre Dame will be bumped. Cincinnati goes to the South; Purdue to the East; Notre Dame to the West. This does give two possible Big East matchups in the round of 16, along with one from the Big Ten. This is one more from the Big East than is strictly necessary, which is a departure from the way I've handled this in prior years, and makes more use of the flexibility provided by the criteria.
Step 7e: Place the No. 9 seeds. (Available sites: Louisville, Omaha , Pittsburgh)
Temple to the East; Virginia to the West; Texas to the South; Alabama to the Midwest...
Step 7f: Place the No. 10 seeds. (Available sites: Columbus, Greensboro, Nashville, Pittsburgh)
...or perhaps not. The Crimson tide change places with Northwestern, with the Wildcats taking the Midwest No. 9 slot. Alabama goes into the South region on the No. 10 line. UConn goes to the East; Saint Louis is forced into the West because it's the host school for the Midwest, into which Harvard is placed.
Step 7g: Place the No. 11 seeds. (Available sites: Albuquerque, Columbus, Greensboro, Nashville)
Southern Mississippi to the West. Minnesota presents problems insofar as being paired against other Big Ten teams too early, but bumping them down would mean bringing up a First Four winner - potentially even more complicated. The Golden Gophers go Midwest (possible matchup against Michigan State in the round of 16 vice Michigan in the round of 32); West Virginia to the South, and Brigham Young to the East (Albuquerque and Boston are both Thursday/Saturday sites).
Step 7h: Place the No. 12 seeds. (Available sites: Albuquerque, Louisville, Portland )
It's good that Louisville is also a Thursday/Sunday site, because the very next thing I'm doing is bumping the Cougars down in favor of the North Carolina State v. Seton Hall winner. I personally prefer this, as it brackets BYU away from a team in the conference it recently left. Next is the winner of Illinois v. California (the Pac-12 finally makes an appearance!), which goes to the South. That concludes placement of the at-large teams, but we're not quite home free yet, as the tounament winners from a few leagues who got at-large teams in are still out there. But next is last year's darling, Virginia Commonwealth. They go to the Midwest (yeah, I know, mid-on-mid crime, blah, blah.) Actually, we're left with another entry on that police blotter - Long Beach State to the West to take on Saint Mary's.
Step 7i: Place the No. 13 seeds. (Available sites: Albuquerque, Louisville, Portland )
Colorado to the West; Ohio to the East; St. Bonaventure to the Midwest (which puts us free and clear of conflicts); and Davidson to the South.
Step 7j: Place the No. 14 seeds. (Available sites: Albuquerque, Columbus, Greensboro, Nashville)
Belmont to the South (not the Nashville pod in the West due to the "home-court disadvantage" criterion); New Mexico State to the West (not the Albuquerque pod in the East for the same reason); South Dakota State to the Midwest; Montana to the East.
Step 7k: Place the No. 15 seeds. (Available sites: Columbus, Greensboro, Nashville, Pittsburgh)
Lehigh to the East; Loyola - Maryland to the South; Detroit to the Midwest; and Long Island to the West.
Step 7l: Place the No. 16 seeds. (Available sites: Louisville, Omaha , Pittsburgh)
The two previously bracketed First Four games constrain the options for the other two. The last four at-large teams would all play on Thursday if they get out of Dayton, so the bottom four teams in the field all play on Wednesday - and thus the two winners of those games both go to Omaha. Before we deal with them, we have Norfolk State and Pat Knight's shiftless seniors - um, I mean Lamar. The Spartans go to the East; the Cardinals to the South; and for whatever it's worth, the UNC Asheville/Mississippi Valley State winner has priority, so they get fed to the lion with the slightly less sharp teeth - that is, Kansas in the West. The Vermont v. Western Kentucky winner goes to the Midwest.
Step 8: Re-check the entire bracket for conflicts.
Here's the 2012 Z-Bracket:
|SOUTH (Georgia Dome, Atlanta)||EAST (TD Garden, Boston)|
|1||Kentucky||KFC Yum! Center|
|Consol Energy Center|
|5||Wichita State||Rose Garden|
|KFC Yum! Center|
|6||Gonzaga||San Diego State||6|
|Consol Energy Center|
|2||North Carolina||Ohio State||2|
|15||Loyola - Maryland||Lehigh||15|
(Mercedes-Benz Superdome, New Orleans)
South v. West
East v. Midwest
|WEST (US Airways Center, Phoenix)||MIDWEST (Edward Jones Dome, St. Louis)|
|1||Kansas||CenturyLink Center Omaha|
|CenturyLink Center Omaha|
|5||Saint Mary's||The Pit|
|12||Long Beach State||Va. Commonwealth||12|
|14||New Mexico State||South Dakota State||14|
|7||Kansas State||Bridgestone Arena|
|2||Murray State||Michigan State||2|
|FIRST ROUND (UD Arena, Dayton) - Tuesday||FIRST ROUND (UD Arena, Dayton) - Wednesday|
|North Carolina State||(to East #11)||(to West #16)||UNC Asheville|
|Seton Hall||Mississippi Valley State|
|Illinois||(to South #12)||(to Midwest #16)||Vermont|
Bells and whistles
A couple of months ago, I changed the generation of the Z-Ratings from the old MS-DOS based QBasic 4.5 to the much more powerful QB64 in order to finish my Hofstra senior design project. Nevertheless, I've kept the bracket simulations at one million plays each. Here they are: 2012 Z-Bracket | 2012 NCAA tournament. The combined probability of Kentucky or Syracuse winning it all is a smidge over 53 percent in each bracket. But funny things happen when ten men throw a ball around on a hardwood rectangle; last year, Connecticut had a 1.43 percent chance at the outset, and the Huskies' number came in.
Since I started this endeavor nearly a decade ago, Ken Pomeroy has supplied the raw data that make happen the college basketball ratings - and thus, this bracket. I tip my cap to him for keeping that data file outside the paywall he set up at the beginning of this year. John Whelan and Ken Butler showed me the better way back when I was an undergrad at Cornell. This year, I also mention Dr. Richard Puerzer, my faculty advisor and Chair of Engineering at Hofstra, for allowing me to build on the Bradley-Terry system as my senior project. I haven't applied that system to basketball...yet.
Final word: whether you prefer something like this or an "eye test," can we all agree that the Rating Percentage Index should be consigned to one of the lower circles of hell?
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