The Z-Bracket: 2010 edition

Welcome to the eighth annual Z-Bracket, the exercise where we use the Z-Ratings, also known as the Bradley-Terry system, to produce the bracket for the NCAA Division I Men's Basketball Championship. You don't have to speculate as to how this thing came to be - it's all laid out here in front of you in green, gray, and beige (unless and until I change the style sheet). We use the ratings as of selection time, which come from all 5,263 games played between two Division I teams.

If you're interested in looking back, here are links to the previous seven Z-Brackets and the methodology I used to concoct them:
2009 (Process) | 2008 (Process) | 2007 (Process) | 2006 (Process) | 2005 (Process) | 2004 (Process) | 2003 (Process)

Selecting the field

Step 1: the automatic bids.

Team	Conference	Rank		Team	Conference	Rank
Kansas	Big 12	1		Oakland	Summit League	89
Kentucky	Southeastern	2		Wofford	Southern	90
West Virginia	Big East	4		Houston	Conference USA	116
Duke	Atlantic Coast	5		UC Santa Barbara	Big West	118
Temple	Atlantic 10	9		Montana	Big Sky	119
Ohio State	Big Ten	16		Ohio	Mid-American	127
Butler	Horizon League	18		Sam Houston State	Southland	132
Northern Iowa	Missouri Valley	24		North Texas	Sun Belt	146
St. Mary's - CA	West Coast	30		Morgan State	Mid-Eastern Athletic	162
Cornell	Ivy League	39		Vermont	America East	165
San Diego State	Mountain West	41		East Tennessee State	Atlantic Sun	183
Washington	Pacific-10	49		Robert Morris	Northeast	190
Old Dominion	Colonial Athletic	55		Winthrop	Big South	205
Siena	Metro Atlantic Athletic	58		Lehigh	Patroit League	219
Murray State	Ohio Valley	74		Arkansas - Pine Bluff	Southwestern Athletic	265
New Mexico State	Western Athletic	82

Step 2: the at-large bids.

In the immediate aftermath of the selection show, there was a lot of talk about Virginia Tech, especially how the Hokies stacked up vis-a-vis Wake Forest. Virginia Tech does have a lower strength of schedule (ranked 42) than any other ACC team that made the field. But this system doesn't separate the opposition within the league from the nonconference schedule, and the Hokies' performance in the No. 3 ranked league was enough here. I also give credit to Tech coach Seth Greenberg for pointing out that the criteria can change from year-to-year depending on who sits on the committee - perhaps the best argument for the adoption of an objective system. As for Seton Hall, they would have been the ninth team from the Big East, and as much as they claim not to look at conferences, the record haul for one league is eight.

On the other side of the coin, Minnesota has an SOS comparable to that of Virginia Tech (ranked 43), but they simply have too many losses (thirteen). Utah State is basically the opposite; their record is more than respectable, but they didn't play anybody - an SOS ranked 107. Of all the teams above them, only Siena's is worse. The worst SOS of the at-large teams that made either bracket, other than the Aggies, is UTEP at 89.

Seeding the teams

Seed	Rk	FR	Team		Seed	Rk	FR	Team		Seed	Rk	FR	Team		Seed	Rk	FR	Team
1	1	1	Kansas		5	17	17	Brigham Young		9	33	33	Oklahoma State		13	74	49	Murray State
	2	2	Kentucky			18	18	Butler			34	34	Richmond			82	50	New Mexico State
	3	3	Syracuse			19	19	Texas			35	35	Clemson			89	51	Oakland
	4	4	West Virginia			20	20	Wisconsin			36	36	Louisville			90	52	Wofford
2	5	5	Duke		6	21	21	Maryland		10	37	37	UNLV		14	116	53	Houston
	6	6	Villanova			22	22	Vanderbilt			38	38	Seton Hall			118	54	UC Santa Barbara
	7	7	Kansas State			23	23	Marquette			39	39	Cornell			119	55	Montana
	8	8	Purdue			24	24	Northern Iowa			40	40	Wake Forest			127	56	Ohio
3	9	9	Temple		7	25	25	Michigan State		11	41	41	San Diego State		15	132	57	Sam Houston State
	10	10	New Mexico			26	26	Xavier			42	42	Georgia Tech			146	58	North Texas
	11	11	Georgetown			27	27	Gonzaga			43	43	Florida			162	59	Morgan State
	12	12	Baylor			28	28	Notre Dame			44	44	California			165	60	Vermont
4	13	13	Pittsburgh		8	29	29	Florida State		12	45	45	Texas - El Paso		16	183	61	East Tennessee State
	14	14	Texas A&M			30	30	St. Mary's - CA			49	46	Washington			190	62	Robert Morris
	15	15	Tennessee			31	31	Virginia Tech			55	47	Old Dominion			205	63	Winthrop
	16	16	Ohio State			32	32	Missouri			58	48	Siena
															OR	219	64	Lehigh
																265	65	Arkansas - Pine Bluff

Key:
Rk = overall ranking by the Z-Ratings.
FR = Field ranking - the ranking of the team among the field of 65.
OR = opening round.

No team's seed differs by more than three from what the committee handed out. As should be obvious by now, only the totality of any team's season is taken into account in determining these numbers. Northern Iowa racked up enough wins to counterbalance any weakness in their slate (like DePaul, or the MVC in general). Texas still started 17-0 and played through the second best conference in the country. I don't care how long it's been since Cal won the Pac-10 regular-season title, and neither do the ratings. And the computer has never heard of Robbie Hummel, and certainly doesn't know he's out for the season.

Establishing the bracket

Once again, we use the bracketing 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 (this applies to the Big East, which supplied us with nine teams).
• 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. At the regional level, this precludes us from sending Syracuse to the East and Houston to the South. The only restriction for the first two rounds is that Marquette cannot play in Milwaukee.
• 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 (i.e. the Big East).
• 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.)
• The winner of the opening-round game is sent to a Friday/Sunday pod for its first/second round games.
• 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. It's different from prior years in a couple of important ways. Instead of placing the bottom teams immediately after the top sixteen, we go down the seeds in numerical order from 1 to 16. In addition, after the top four seeds are assigned, the rest of the teams on a line have the same numerical value. Finally, checks for balance in the 5-8, 9-12, and 13-16 sections have been eliminated from the procedure.

I should also explicitly state a policy that I've observed previously and will maintain. There are 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. These are not part of the official procedure, 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.

Step 2: Place the No. 2 seeds.

Step 3: Place the No. 3 seeds.

Step 4: Place the No. 4 seeds.

Step 5: Check for conflicts and balance in the Nos. 1 through 4 seeds.

Step 6: Assign first and second round sites.

As with last year, this part is made a bit tricky by the lack of very many teams from out weest in this part of the bracket.

Providence, RI: Villanova, Temple
Buffalo, NY: Syracuse, West Virginia
New Orleans, LA: Baylor, Pittsburgh
Jacksonville, FL: Duke, Georgetown
Oklahoma City, OK: Kansas, Kansas State
Milwaukee, WI: Kentucky, Purdue
San Jose, CA: New Mexico, Tennessee
Spokane, WA: Texas A&M, Ohio State

(Revision, Tues 16 March: Kentucky and Georgetown have swapped pods. After reading a post on ESPN's hoops blog about various chicanery by the committee, I realized that Kentucky should have been assigned to Milwaukee. I went back through all sixteen pods, and the Wildcats and Hoyas ended up being the only two altered. But that did raise the potential for some follow-on effects. I'm not going to shoehorn the pod change in and call it good. The procedure must be followed, and that means back to the number 5 line.)

Step 7: Place the No. 5 through 16 seeds.

Step 7a: Place the No. 5 seeds. (Available sites: New Orleans, San Jose, Spokane [2])

Step 7b: Place the No. 6 seeds. (Available sites: Providence, New Orleans, Jacksonville, San Jose)

Step 7c: Place the No. 7 seeds. (Available sites: Providence, Jacksonville, Oklahoma City, Milwaukee)

Step 7d: Place the No. 8 seeds. (Available sites: Buffalo [2], Milwaukee, Oklahoma City)

Step 7e: Place the No. 9 seeds. (Available sites: Buffalo [2], Milwaukee, Oklahoma City)

Step 7f: Place the No. 10 seeds. (Available sites: Providence, Jacksonville, Oklahoma City, Milwaukee)

Step 7g: Place the No. 11 seeds. (Available sites: Providence, New Orleans, Jacksonville, San Jose)

Step 7h: Place the No. 12 seeds. (Available sites: New Orleans, San Jose, Spokane [2])

Step 7i: Place the No. 13 seeds. (Available sites: New Orleans, San Jose, Spokane [2])

Step 7j: Place the No. 14 seeds. (Available sites: Providence, New Orleans, Jacksonville, San Jose)

Step 7k: Place the No. 15 seeds. (Available sites: Providence, Jacksonville, Oklahoma City, Milwaukee)

Step 7l: Place the No. 16 seeds. (Available sites: Buffalo [2], Milwaukee, Oklahoma City)

Step 8: Re-check the entire bracket for conflicts.

Testing both brackets

Acknowledgements

Last but not least: yeah, I think Cornell got screwed on its seed, but it doesn't matter. If any year is going to be "the" year for the Big Red, it's this one.