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.
TeamConferenceRankTeamConferenceRank
GonzagaWest Coast1New Mexico StateWestern Athletic91
LouisvilleBig East2HarvardIvy League112
KansasBig 124PacificBig West113
Ohio StateBig Ten5MontanaBig Sky117
New MexicoMountain West10South Dakota StateSummit League118
Miami (FL)Atlantic Coast11Northwestern StateSouthland121
Saint LouisAtlantic 1015IonaMetro Atlantic Athletic129
MemphisConference USA17AlbanyAmerica East139
OregonPacific-1232Florida Gulf CoastAtlantic Sun147
CreightonMissouri Valley35Western KentuckySun Belt167
MississippiSoutheastern44Long IslandNortheast186
BelmontOhio Valley58James MadisonColonial Athletic188
AkronMid-American63SouthernSouthwestern Athletic214
BucknellPatriot League66North Carolina A&TMid-Eastern Athletic248
ValparaisoHorizon League75LibertyBig South308
DavidsonSouthern90

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...
TeamRankTeamRankTeamRank
Indiana3Pittsburgh22Saint Mary's - CA37
Duke6Notre Dame23Iowa State38
Georgetown7UNLV24Temple39
Michigan State8UCLA25Missouri40
Michigan9Illinois26Colorado41
Kansas State12North Carolina27Iowa42
Syracuse13Virginia Commonwealth28Oklahoma43
Marquette14Colorado State29Boise State45
Wisconsin16Minnesota30Wichita State46
Arizona18Cincinnati31Villanova47
Oklahoma State19North Carolina State33California48
Florida20San Diego State36La Salle49
Butler21
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:

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.

Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team
111Gonzaga 51717Memphis 93333North Carolina State 136651Bucknell
22Louisville 1818Arizona 3434Creighton 7552Valparaiso
33Indiana 1919Oklahoma State 3635San Diego State 9053Davidson
44Kansas 2020Florida 3736Saint Mary's 9154New Mexico State
255Ohio State 62121Butler 103837Iowa State 1411255Harvard
66Duke 2222Pittsburgh 3938Temple 11356Pacific
77Georgetown 2323Notre Dame 4039Missouri 11757Montana
88Michigan State 2424UNLV 4140Colorado 11858South Dakota State
399Michigan 72525UCLA 114241Iowa 1512159Northwestern State
1010New Mexico 2626Illinois 4342Oklahoma 12960Iona
1111Miami (FL) 2727North Carolina 4443Mississippi 13961Albany
1212Kansas State 2828Virginia Commonwealth 4544Boise State 14762Florida Gulf Coast
41313Syracuse 82929Colorado State 1246
49
45
48
Wichita State
La Salle
1616763Western Kentucky
1414Marquette 3030Minnesota 47
48
46
47
Villanova
California
18664Long Island
1515Saint Louis 3131Cincinnati 5849Belmont 188
308
65
68
James Madison
Liberty
1616Wisconsin 3232Oregon 6350Akron 214
248
66
67
Southern
North Carolina A&T
Key:
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:

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 [2])

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 [2], 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 [2], 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 [2])

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 [2])

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 [2], 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)
1GonzagaEnergySolutions Arena
Salt Lake City, UT
Rupp Arena
Lexington, KY
Louisville1
16Long Island16
8CincinnatiMinnesota8
9San Diego StateNorth Carolina State9
5ArizonaHP Pavilion
San Jose, CA
Frank Erwin Center
Austin, TX
Oklahoma State5
12Akron12
4WisconsinSaint Louis4
13New Mexico StateValparaiso13
3Kansas StateSprint Center
Kansas City, MO
Frank Erwin Center
Austin, TX
Miami (FL)3
14MontanaSouth Dakota State14
6Notre DameUNLV6
11Mississippi11
7North CarolinaThe Palace of Auburn Hills
Auburn Hills, MI
UD Arena
Dayton, OH
UCLA7
10TempleIowa State10
2Michigan StateOhio State2
15Florida Gulf CoastNorthwestern State15
FINAL FOUR
(Georgia Dome, Atlanta)
West v. South
Midwest v. East
SOUTH (Cowboys Stadium, Arlington, TX)EAST (Verizon Center, Washington, DC)
1KansasSprint Center
Kansas City, MO
UD Arena
Dayton, OH
Indiana1
16Western Kentucky16
8OregonColorado State8
9CreightonSaint Mary's9
5MemphisRupp Arena
Lexington, KY
HP Pavilion
San Jose, CA
Florida5
12IowaBelmont12
4MarquetteSyracuse4
13BucknellDavidson13
3New MexicoEnergySolutions Arena
Salt Lake City, UT
The Palace of Auburn Hills
Auburn Hills, MI
Michigan3
14PacificHarvard14
6ButlerPittsburgh6
11OklahomaBoise State11
7IllinoisWells Fargo Center
Philadelphia, PA
Wells Fargo Center
Philadelphia, PA
Virginia Commonwealth7
10MissouriColorado10
2GeorgetownDuke2
15AlbanyIona15
FIRST ROUND (UD Arena, Dayton) - TuesdayFIRST ROUND (UD Arena, Dayton) - Wednesday
Southern(to West #16)(to East #16)James Madison
North Carolina A&TLiberty
Wichita State(to Midwest #11)(to Midwest #12)Villanova
La SalleCalifornia

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.

Acknowledgements

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.

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