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.

Team	Conference	Rank	Team	Conference	Rank
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
Mississippi	Southeastern	44	Long Island	Northeast	186
Belmont	Ohio Valley	58	James Madison	Colonial Athletic	188
Akron	Mid-American	63	Southern	Southwestern Athletic	214
Bucknell	Patriot League	66	North Carolina A&T	Mid-Eastern Athletic	248
Valparaiso	Horizon League	75	Liberty	Big South	308
Davidson	Southern	90

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...

Team	Rank	Team	Rank	Team	Rank
Indiana	3	Pittsburgh	22	Saint Mary's - CA	37
Duke	6	Notre Dame	23	Iowa State	38
Georgetown	7	UNLV	24	Temple	39
Michigan State	8	UCLA	25	Missouri	40
Michigan	9	Illinois	26	Colorado	41
Kansas State	12	North Carolina	27	Iowa	42
Syracuse	13	Virginia Commonwealth	28	Oklahoma	43
Marquette	14	Colorado State	29	Boise State	45
Wisconsin	16	Minnesota	30	Wichita State	46
Arizona	18	Cincinnati	31	Villanova	47
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.

Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team Seed Rk FR Team

1 1 1 Gonzaga 5 17 17 Memphis 9 33 33 North Carolina State 13 66 51 Bucknell

2 2 Louisville 18 18 Arizona 34 34 Creighton 75 52 Valparaiso

3 3 Indiana 19 19 Oklahoma State 36 35 San Diego State 90 53 Davidson

4 4 Kansas 20 20 Florida 37 36 Saint Mary's 91 54 New Mexico State

2 5 5 Ohio State 6 21 21 Butler 10 38 37 Iowa State 14 112 55 Harvard

6 6 Duke 22 22 Pittsburgh 39 38 Temple 113 56 Pacific

7 7 Georgetown 23 23 Notre Dame 40 39 Missouri 117 57 Montana

8 8 Michigan State 24 24 UNLV 41 40 Colorado 118 58 South Dakota State

3 9 9 Michigan 7 25 25 UCLA 11 42 41 Iowa 15 121 59 Northwestern State

10 10 New Mexico 26 26 Illinois 43 42 Oklahoma 129 60 Iona

11 11 Miami (FL) 27 27 North Carolina 44 43 Mississippi 139 61 Albany

12 12 Kansas State 28 28 Virginia Commonwealth 45 44 Boise State 147 62 Florida Gulf Coast

4 13 13 Syracuse 8 29 29 Colorado State 12 46
49 45
48 Wichita State
La Salle 16 167 63 Western Kentucky

14 14 Marquette 30 30 Minnesota 47
48 46
47 Villanova
California 186 64 Long Island

15 15 Saint Louis 31 31 Cincinnati 58 49 Belmont 188
308 65
68 James Madison
Liberty

16 16 Wisconsin 32 32 Oregon 63 50 Akron 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:

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 [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)

1 Gonzaga EnergySolutions Arena
Salt Lake City, UT Rupp Arena
Lexington, KY Louisville 1

16 Long Island 16

8 Cincinnati Minnesota 8

9 San Diego State North Carolina State 9

5 Arizona HP Pavilion
San Jose, CA Frank Erwin Center
Austin, TX Oklahoma State 5

12 Akron 12

4 Wisconsin Saint Louis 4

13 New Mexico State Valparaiso 13

3 Kansas State Sprint Center
Kansas City, MO Frank Erwin Center
Austin, TX Miami (FL) 3

14 Montana South Dakota State 14

6 Notre Dame UNLV 6

11 Mississippi 11

7 North Carolina The Palace of Auburn Hills
Auburn Hills, MI UD Arena
Dayton, OH UCLA 7

10 Temple Iowa State 10

2 Michigan State Ohio State 2

15 Florida Gulf Coast Northwestern State 15

FINAL FOUR
(Georgia Dome, Atlanta)
West v. South
Midwest v. East

SOUTH (Cowboys Stadium, Arlington, TX) EAST (Verizon Center, Washington, DC)

1 Kansas Sprint Center
Kansas City, MO UD Arena
Dayton, OH Indiana 1

16 Western Kentucky 16

8 Oregon Colorado State 8

9 Creighton Saint Mary's 9

5 Memphis Rupp Arena
Lexington, KY HP Pavilion
San Jose, CA Florida 5

12 Iowa Belmont 12

4 Marquette Syracuse 4

13 Bucknell Davidson 13

3 New Mexico EnergySolutions Arena
Salt Lake City, UT The Palace of Auburn Hills
Auburn Hills, MI Michigan 3

14 Pacific Harvard 14

6 Butler Pittsburgh 6

11 Oklahoma Boise State 11

7 Illinois Wells Fargo Center
Philadelphia, PA Wells Fargo Center
Philadelphia, PA Virginia Commonwealth 7

10 Missouri Colorado 10

2 Georgetown Duke 2

15 Albany Iona 15

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

La Salle California

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.

The Z-Ratings Center | Matt's home page

Seed	Rk	FR	Team	Seed	Rk	FR	Team	Seed	Rk	FR	Team	Seed	Rk	FR	Team
1	1	1	Gonzaga	5	17	17	Memphis	9	33	33	North Carolina State	13	66	51	Bucknell
	2	2	Louisville		18	18	Arizona		34	34	Creighton		75	52	Valparaiso
	3	3	Indiana		19	19	Oklahoma State		36	35	San Diego State		90	53	Davidson
	4	4	Kansas		20	20	Florida		37	36	Saint Mary's		91	54	New Mexico State
2	5	5	Ohio State	6	21	21	Butler	10	38	37	Iowa State	14	112	55	Harvard
	6	6	Duke		22	22	Pittsburgh		39	38	Temple		113	56	Pacific
	7	7	Georgetown		23	23	Notre Dame		40	39	Missouri		117	57	Montana
	8	8	Michigan State		24	24	UNLV		41	40	Colorado		118	58	South Dakota State
3	9	9	Michigan	7	25	25	UCLA	11	42	41	Iowa	15	121	59	Northwestern State
	10	10	New Mexico		26	26	Illinois		43	42	Oklahoma		129	60	Iona
	11	11	Miami (FL)		27	27	North Carolina		44	43	Mississippi		139	61	Albany
	12	12	Kansas State		28	28	Virginia Commonwealth		45	44	Boise State		147	62	Florida Gulf Coast
4	13	13	Syracuse	8	29	29	Colorado State	12	46 49	45 48	Wichita State La Salle	16	167	63	Western Kentucky
	14	14	Marquette		30	30	Minnesota		47 48	46 47	Villanova California		186	64	Long Island
	15	15	Saint Louis		31	31	Cincinnati		58	49	Belmont		188 308	65 68	James Madison Liberty
	16	16	Wisconsin		32	32	Oregon		63	50	Akron		214 248	66 67	Southern North Carolina A&T

WEST (Staples Center, Los Angeles)				MIDWEST (Lucas Oil Stadium, Indianapolis)
1	Gonzaga	EnergySolutions Arena Salt Lake City, UT		Rupp Arena Lexington, KY	Louisville	1
16					Long Island	16

8	Cincinnati				Minnesota	8
9	San Diego State				North Carolina State	9
5	Arizona	HP Pavilion San Jose, CA		Frank Erwin Center Austin, TX	Oklahoma State	5
12	Akron					12

4	Wisconsin				Saint Louis	4
13	New Mexico State				Valparaiso	13
3	Kansas State	Sprint Center Kansas City, MO		Frank Erwin Center Austin, TX	Miami (FL)	3
14	Montana				South Dakota State	14

6	Notre Dame				UNLV	6
11	Mississippi					11
7	North Carolina	The Palace of Auburn Hills Auburn Hills, MI		UD Arena Dayton, OH	UCLA	7
10	Temple				Iowa State	10

2	Michigan State				Ohio State	2
15	Florida Gulf Coast				Northwestern State	15
			FINAL FOUR (Georgia Dome, Atlanta) West v. South Midwest v. East
SOUTH (Cowboys Stadium, Arlington, TX)				EAST (Verizon Center, Washington, DC)
1	Kansas	Sprint Center Kansas City, MO		UD Arena Dayton, OH	Indiana	1
16	Western Kentucky					16

8	Oregon				Colorado State	8
9	Creighton				Saint Mary's	9
5	Memphis	Rupp Arena Lexington, KY		HP Pavilion San Jose, CA	Florida	5
12	Iowa				Belmont	12

4	Marquette				Syracuse	4
13	Bucknell				Davidson	13
3	New Mexico	EnergySolutions Arena Salt Lake City, UT		The Palace of Auburn Hills Auburn Hills, MI	Michigan	3
14	Pacific				Harvard	14

6	Butler				Pittsburgh	6
11	Oklahoma				Boise State	11
7	Illinois	Wells Fargo Center Philadelphia, PA		Wells Fargo Center Philadelphia, PA	Virginia Commonwealth	7
10	Missouri				Colorado	10

2	Georgetown				Duke	2
15	Albany				Iona	15
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		(to West #16)		(to East #16)	Liberty
Wichita State		(to Midwest #11)		(to Midwest #12)	Villanova
La Salle		(to Midwest #11)		(to Midwest #12)	California