The Z-Bracket: 2013 edition
Last year was the tenth season; this year is thus the tenth anniversary of the first Z-Bracket. By now the drill is pretty clear. The Bradley-Terry method for paired comparisons, known as KRACH elsewhere and as the Z-Ratings here, will guide us to a bracket that acts as a fun exercise and little more. But at least you can see how I come up with it, unlike the big bad NC$$. The Z-Ratings as of Selection Sunday (17 March 2013) give us the basis for our assessment of this year's college basketball season. (Summary of previous brackets | Jump to this year's bracket)
Selecting the field
Step 1: the automatic bids.
Same is it ever is here, with the automatic bids going to the tournament champions of the thirty conferences that play tournaments, and to the regular season winner in the Ivy League, which doesn't play one.
|Gonzaga||West Coast||1||New Mexico State||Western Athletic||91|
|Louisville||Big East||2||Harvard||Ivy League||112|
|Kansas||Big 12||4||Pacific||Big West||113|
|Ohio State||Big Ten||5||Montana||Big Sky||117|
|New Mexico||Mountain West||10||South Dakota State||Summit League||118|
|Miami (FL)||Atlantic Coast||11||Northwestern State||Southland||121|
|Saint Louis||Atlantic 10||15||Iona||Metro Atlantic Athletic||129|
|Memphis||Conference USA||17||Albany||America East||139|
|Oregon||Pacific-12||32||Florida Gulf Coast||Atlantic Sun||147|
|Creighton||Missouri Valley||35||Western Kentucky||Sun Belt||167|
|Belmont||Ohio Valley||58||James Madison||Colonial Athletic||188|
|Bucknell||Patriot League||66||North Carolina A&T||Mid-Eastern Athletic||248|
|Valparaiso||Horizon League||75||Liberty||Big South||308|
Step 2: the at-large bids.
We complete the field by inviting the 37 highest ranked teams that did not claim automatic bids... or not! Connecticut has a rating high enough to warrant inclusion, but they're ineligible for postseason play this year, thanks to a deficient Academic Progress Rate (basically, they didn't graduate enough players). Someone on the bubble will benefit from that...
|Indiana||3||Pittsburgh||22||Saint Mary's - CA||37|
|Duke||6||Notre Dame||23||Iowa State||38|
|Kansas State||12||North Carolina||27||Iowa||42|
|Marquette||14||Colorado State||29||Boise State||45|
|Oklahoma State||19||North Carolina State||33||California||48|
|Florida||20||San Diego State||36||La Salle||49|
|Butler||21|Teams The team in italics was not selected for the actual tournament field. The only team that's in the actual field but not represented here is Middle Tennessee State (52). Since the committee got the bubble pretty close to perfect this year, we can just move on.
Seeding the teams
The first round
Same rules for the First Four as each of the last two years, rules that I completely made up since the selection committee doesn't have any. The guidelines are:
- 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 20 MUST be assigned to a Friday/Sunday pod for the second and third rounds. Teams playing on Tuesday, March 19 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
Since we used the Z-Ratings to select the at-large teams, we use the very same ratings to order them for their seeding. Teams listed in the same cell will face off in the first round.
||9||33||33||North Carolina State||
||36||35||San Diego State||
||91||54||New Mexico State
||118||58||South Dakota State
||147||62||Florida Gulf Coast
North Carolina A&T
Rk = overall ranking by the Z-Ratings.
FR = Field ranking - the ranking of the team among the field of 68.
All in all, the seeding was also quite well done this year, with only four serious errors (two each way). A serious error is one wherein the seed in this bracket and the one handed out by the committee differ by three or more. By that metric, only Minnesota and Oregon are too low, and Wichita State and Villanove are too high. Also the top four teams in the Z-Ratings match the committee's No. 1 seeds, and in terms of selecting Louisville as top overall, I can understand why the people in the room discounted the strength of Gonzaga's opposition in the West Coast Conference (though I disagree with that assessment).
Establishing the bracket
Our regionals this year: East (Washington); South (Arlington); Midwest (Indianapolis); and West (Los Angeles).
As has always been the case, the bracket is built using the principles established by the selection committee. They are:
- No intraconference matchups prior to a regional final, unless nine or more teams from a conference are selected.
- The first three teams from a conference go to different regionals.
- 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 rule excludes Georgetown from the East Regional. In the second and third rounds, this affects two teams; Temple can't go to a Philadelphia pod, and Kentu- wait a second. The defending national champions were the first team squeezed out of this bracket. So, one team.
- 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; as much as I hope to try to get through a bracket without doing this, I always end up having to. This year, the committee voted itself the ability to move a team two lines from its true seed in "extraordinary circumstances."
- If all these principles fail to reconcile the bracket, we can have intraconference matchups as early as the round of thirty-two, in conferences with five or more participants.
We also adhere to the bracketing procedure outlined in the championship handbook (also at the link just above). 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.
Gonzaga to the West; Louisville to the Midwest; Indiana to the East; Kansas to the South. We pair up the regional winners such that if these four teams are the last four standing in Atlanta, the overall 1 v. 4 and 2 v. 3 teams will meet. Thus we get West v. South (Gonzaga v. Kansas), and Midwest v. East (Louisville v. Indiana).
Step 2: Place the No. 2 seeds.
Ohio State to the Midwest; Duke to the East; Georgetown to the South; Michigan State to the West.
Step 3: Place the No. 3 seeds.
Michigan to the East (as the fourth Big Ten team, they can go in a region with Indiana); New Mexico to the South (Arlington is closer to Albuquerque than Los Angeles); Miami (FL) to the Midwest; Kansas State to the West.
Step 4: Place the No. 4 seeds.
Syracuse to the East. Marquette can't go into the Midwest with Louisville, so they go to the South. Saint Louis to the Midwest; Wisconsin to the West.
Step 5: Check for conflicts and balance in the Nos. 1 through 4 seeds.
Summing the field rankings of the four teams already placed into each regional, we get 31 (E), 33 (M), 35 (S), and 37 (W). The book says that "[g]enerally, no more than five points should separate the highest and lowest total." Right now it's six. Swapping Marquette and Wisconsin on the no. 4 line is a possibility, but it doesn't narrow the range of field rankings. I'm going to leave it as it is.
Step 6: Assign first and second round sites.
Taking the top 16 teams in order, we pair them with the available sites where they'll play their first two games. This gives us:
Salt Lake City, UT: Gonzaga, New Mexico
Lexington, KY: Louisville, Marquette
Dayton, OH: Indiana, Ohio State
Kansas City, MO: Kansas, Kansas State
Philadelphia, PA: Duke, Georgetown
Auburn Hills, MI: Michigan, Michigan State
Austin, TX: Miami (FL), Saint Louis
San Jose, CA: Syracuse, Wisconsin
Syracuse is the highest ranked of the No. 4 seeds and thus Lexington would have been the closest available pod to them, they and their fans are getting on a plane regardless of where they play. Thus I sent them to San Jose to try to minimize the overall distance traveled by the four teams on that line.
Step 7: Place the No. 5 through 16 seeds.
From here out, I place the teams based on their pod for the second and third rounds, since, based on their seeds, they're not expected to advance past that point.
Step 7a: Place the No. 5 seeds. (Available sites: Austin, Lexington, San Jose )
Memphis to the South. Arizona to the West; since buth the East and West have San Jose pods, and the Wildcats are the first Pacific-12 team into the bracket, they get the closer regional site. Oklahome State to the Midwest; Florida to the East.
Step 7b: Place the No. 6 seeds. (Available sites: Auburn Hills, Austin, Kansas City, Salt Lake City)
Butler's natural placement would be in the Auburn Hills pod in the East, but that would create problems with the other three teams; the bottom half of the South already has a Big East and an MWC team, so the Bulldogs end up in that region. Pittsburgh goes to the East, Notre Dame to the West, and UNLV to the Midwest.
Step 7c: Place the No. 7 seeds. (Available sites: Auburn Hills, Philadelphia , Dayton)
UCLA to the Midwest (can't go into the West with Arizona); Illinois is constrained into the South; North Carolina to the West; and Virginia Commonwealth to the East.
Step 7d: Place the No. 8 seeds. (Available sites: Dayton, Kansas City, Lexington, Salt Lake City)
The conference affiliations constrain the placement on this line. Cincinnati must go to the West because that's the only region without a Big East team already in its top half. Colorado State must then go to the East; as the third team from the Mountain West, the Rams must be separated from New Mexico and UNLV. Similarly, Oregon must be held apart from UCLA and goes to the South, leaving Minnesota to the Midwest.
Step 7e: Place the No. 9 seeds. (Available sites: Dayton, Kansas City, Lexington, Salt Lake City)
North Carolina State to the Midwest; Creighton to the South, pitting Dana Altman against his former team (I'm just seeing that now; it hadn't crossed my mind when I drew up the seeds). With an MWC team already in the East and Gonzaga sitting atop the West, we send San Diego State to Salt Lake City and Saint Mary's to Dayton.
Step 7f: Place the No. 10 seeds. (Available sites: Auburn Hills, Philadelphia , Dayton)
Iowa State goes first, and as Auburn Hills are about the same distance from Ames, Iowa, I'm putting the Cyclones in the Midwest. Temple must therefore go to the West, as they're hosting in Philadelphia. Missouri is only the second SEC team we've had, so they can't be put in the East with Florida, so the Tigers go to the South, and Colorado to the East.
Step 7g: Place the No. 11 seeds. (Available sites: Auburn Hills, Austin, Kansas City, Salt Lake City)
The bottom halves of all four regions already contain Big Ten teams, so we bump Iown down to a No. 12. In its place, we bring up the winner of Wichita State/La Salle. But we place Oklahoma next, and do so in the South. SEC champion Ole Miss to the West; Boise State to the East; and either the Shockers or the Explorers (A-plus-plus nickname matchup, by the way) to the Midwest.
Step 7h: Place the No. 12 seeds. (Available sites: Austin, Lexington, San Jose )
Iowa needs to go to the South. Next up is the Villanova/California winner. We've already got Big East teams in all four top halves. I'm going to keep it on this side and place it in the Midwest; that would mean a possible Big East matchup in the regional semifinal, vice a pairing of conference opponents in the third round. Those are the last at-large teams in, so the big thing now is to watch the home-court disadvantage to the top four seeds in each region. But before that, let's get Belmont in the East (closer regional, in the event they got out of San Jose) and Akron in the West.
Step 7i: Place the No. 13 seeds. (Available sites: Austin, Lexington, San Jose )
Bucknell to the South; Valparaiso to the Midwest; Davidson to the East; New Mexico State to the West.
Step 7j: Place the No. 14 seeds. (Available sites: Auburn Hills, Austin, Kansas City, Salt Lake City)
Harvard to the East; Pacific to the South; Montana to the West; South Dakota State to the Midwest.
Step 7k: Place the No. 15 seeds. (Available sites: Auburn Hills, Philadelphia , Dayton)
Northwestern State to the Midwest; Iona to the East; Albany to the South; Florida Gulf Coast to the Midwest.
Step 7l: Place the No. 16 seeds. (Available sites: Dayton, Kansas City, Lexington, Salt Lake City)
I'm invoking the home-court disadvantage rule to preclude Western Kentucky from playing in Lexington; they instead go to the South and to Kansas City. Long Island to the East; the James Madison v. Liberty winner to the Midwest; and the Southern v. North Carolina A&T winner to the West.
Step 8: Re-check the entire bracket for conflicts.
The first round does work as shown here, but it would require all four 16 seeds to play on Tuesday and the last four at-large teams to all play on Wednesday. This is alleviated by swapping the East and Midwest on the no. 16 line (Long Island goes into the Midwest, and James Madison/Liberty goes into the East). This also removes the anomaly of having three of the first round games feed into the same regional.
|WEST (Staples Center, Los Angeles)||MIDWEST (Lucas Oil Stadium, Indianapolis)|
Salt Lake City, UT
|9||San Diego State||North Carolina State||9|
San Jose, CA
|Frank Erwin Center|
|13||New Mexico State||Valparaiso||13|
|3||Kansas State||Sprint Center|
Kansas City, MO
|Frank Erwin Center|
|14||Montana||South Dakota State||14|
|7||North Carolina||The Palace of Auburn Hills|
Auburn Hills, MI
|2||Michigan State||Ohio State||2|
|15||Florida Gulf Coast||Northwestern State||15|
(Georgia Dome, Atlanta)
West v. South
Midwest v. East
|SOUTH (Cowboys Stadium, Arlington, TX)||EAST (Verizon Center, Washington, DC)|
Kansas City, MO
San Jose, CA
|3||New Mexico||EnergySolutions Arena|
Salt Lake City, UT
|The Palace of Auburn Hills|
Auburn Hills, MI
|7||Illinois||Wells Fargo Center|
|Wells Fargo Center|
|FIRST ROUND (UD Arena, Dayton) - Tuesday||FIRST ROUND (UD Arena, Dayton) - Wednesday|
|Southern||(to West #16)||(to East #16)||James Madison|
|North Carolina A&T||Liberty|
|Wichita State||(to Midwest #11)||(to Midwest #12)||Villanova|
Bells and whistles
As in prior years, I've run through both this bracket and the actuall NCAA Tournament one million times each, based on probabilities of victory that result from the Z-Ratings. The results: 2013 Z-Bracket | 2013 NCAA tournament. In keeping with the theme of this year's college basketball season (that is, tumult), no team wins moe than 20 percent of the trials in either bracket.
The usual ones...QB64, for providing me a much better and faster platform on which to run this endeavor. Ken Pomeroy, for the raw game data that I use to build the Z-Ratings. John Whelan and Ken Butler, who started this with the KRACH nearly two decades ago.
Last word for 2013 - while I do notice that what I've done agrees much more with the committee than in previous years, I most certainly do not take it as a sign that that the powers that govern NCAA basketball are moving in the direction of objective analysis. Until I see a couple more years, I chalk it up to a fluke.
The Z-Ratings Center | Matt's home page