The Z-Bracket: 2009 edition

The Z-Bracket rides again. The seventh annual attempt to sensibly select and seed the NCAA Division I Men's Basketball Championship rolls from Naval Station Mayport in Florida, where I am on a "business trip." Normally, I'd do this before the tournament starts, but work commitments prevented that this year. We'll take the Z-Ratings, use them to select the sixty-five teams in the tournament, and then seed and place them. Our basis for this bracket is the men's basketball Z-Ratings through March 15, 2009. They are the product of the 5,234 games played between the 347 Division I schools.

Selecting the field

Step 1: the automatic bids.

As always, the Ivy regular-season champion (the same team as last year) and the tournament winners of the other leagues are admitted to the dance. For 2009:

Team Conference Rank Team Conference Rank

Duke Atlantic Coast 4 North Dakota State Summit League 100

Louisville Big East 6 Portland State Big Sky 111

Memphis Conference USA 7 American Patriot League 116

Purdue Big Ten 10 Stephen F. Austin Southland 121

Missouri Big 12 15 Akron Mid-American 127

Gonzaga West Coast 19 Binghamton America East 136

Utah Mountain West 35 Cornell Ivy League 137

Southern California Pacific-10 42 Robert Morris Northeast 153

Utah State Western Athletic 43 Radford Big South 155

Siena Metro Atlantic Athletic 60 Cal State - Northridge Big West 157

Temple Atlantic 10 66 Morgan State Mid-Eastern Athletic 163

Mississippi State Southeastern 67 East Tennessee State Atlantic Sun 164

Northern Iowa Missouri Valley 76 Chattanooga Southern 197

Cleveland State Horizon 77 Morehead State Ohio Valley 204

Western Kentucky Sun Belt 87 Alabama State Southwestern Athletic 259

Virginia Commonwealth Colonial Athletic 90

Step 2: the at-large bids.

Once all the dust settles - that is to say, all the games are final - the top 34 teams not already in get the at-large berths. The Z-Bracket is pleased to cordially invite:

Team	Rank	Team	Rank
Connecticut	1	Michigan	24
Pittsburgh	2	UCLA	25
North Carolina	3	Arizona State	26
Michigan State	5	Wisconsin	27
Oklahoma	8	Penn State	28
Villanova	9	Xavier	29
Wake Forest	11	Oklahoma State	30
Illinois	12	Texas	31
Syracuse	13	California	32
Florida State	14	Boston College	33
Ohio State	16	Maryland	34
Kansas	17	Texas A&M	36
Minnesota	18	Butler	37
Marquette	20	Louisiana State	38
Clemson	21	Brigham Young	39
West Virginia	22	Miami (FL)	40
Washington	23	Northwestern	41

Teams in italics were not selected for the actual tournament field. There are again only three discrepancies; the teams that made the real tournament but were left out of the Z-Bracket are Arizona (44), Tennessee (48), and Dayton (53).

Briefly on the differences: the three teams left out here all had very good cases, and were close to making it; there aren't any egregious cases like No. 71 Utah State back in 2006. On the other side, hte one big beef I have is with leaving out Penn State. They'd be a seven seed here, and I know they had that one good win over Michigan State (in East Lansing, no less, but that's irrelevant here). Miami and Northwestern were the last two teams in here.

Seeding the teams

It's not a hard process to seed the teams, and we start that with the following:

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

1 1 1 Connecticut 5 17 17 Kansas 9 33 33 Boston College 13 87 49 Western Kentucky

2 2 Pittsburgh 18 18 Minnesota 34 34 Maryland 90 50 Virginia Commonwealth

3 3 North Carolina 19 19 Gonzaga 35 35 Utah 100 51 North Dakota State

4 4 Duke 20 20 Marquette 36 36 Texas A&M 111 52 Portland State

2 5 5 Michigan State 6 21 21 Clemson 10 37 37 Butler 14 116 53 American

6 6 Louisville 22 22 West Virginia 38 38 Louisiana State 121 54 Stephen F. Austin

7 7 Memphis 23 23 Washington 39 39 Brigham Young 127 55 Akron

8 8 Oklahoma 24 24 Michigan 40 40 Miami (FL) 136 56 Binghamton

3 9 9 Villanova 7 25 25 UCLA 11 41 41 Northwestern 15 136 57 Cornell

10 10 Purdue 26 26 Arizona State 42 42 Southern California 153 58 Robert Morris

11 11 Wake Forest 27 27 Wisconsin 43 43 Utah State 155 59 Radford

12 12 Illinois 28 28 Penn State 60 44 Siena 157 60 Cal State - Northridge

4 13 13 Syracuse 8 29 29 Xavier 12 66 45 Temple 16 163 61 Morgan State

14 14 Florida State 30 30 Oklahoma State 67 46 Mississipi State 164 62 East Tennessee State

15 15 Missouri 31 31 Texas 76 47 Northern Iowa 197 63 Chattanooga

16 16 Ohio State 32 32 California 77 48 Cleveland State

OR 204 64 Morehead State

259 65 Alabama State

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

Due to time constraints, I'm going to forgo the usual discussion on seeding discrepancies, but suffice to say there were several sizable ones this year.

Establishing the bracket

This year's regionals: East (Boston); South (Memphis); Midwest (Indianapolis); and West (Glendale).

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 Ten, who put nine in).
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. All four schools hosting regionals are in, precluding the following assignments: Boston College (East), Butler (Midwest), Memphis (South), and Arizona State (West). In the opening rounds, Minnesota can't be placed in the Metrodome, and Dayton can't play on its home floor.
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. (The Big East has five teams in the top sixteen.)
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 "S-Curve", but as noted above, we go with the simple ratings.)
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 (all the "power/BCS" conferences meet this criterion, except the SEC, who shockingly only has two teams in this Z-Bracket).

We also adhere to the bracketing procedure outlined in the championship handbook, which has been the same since 2004.

Step 1: Place the No. 1 seeds, and pair the regional winners for the national semifinals.

Connecticut to the East, Pittsburgh to the Midwest, North Carolina to the South, Duke to the West. The Final Four is set up for 1 vs. 4 and 2 vs 3 should all the top seeds make it, which happened for the first time last year. Our national semifinals will have the East vs. West, and Midwest vs. South, which differs from what will actually take place in Detroit.

Step 2: Place the No. 2 seeds.

Michigan State to the Midwest, Louisville to the South, Memphis to the East, and Oklahoma to the West.

Step 3: Place the No. 3 seeds.

Villanova goes to the East. I can't place Purdue opposite Michigan Stae in the Midwest, so I'm sending the Boilermakers to Glendale to help with balance. Wake Forest goes to the Midwest because Illinois also can't be placed with the Spartans. (My preference is to use the nine-teams exception only when absolutely necessary.)

Step 4: Place the No. 4 seeds.

Syracuse to the South due to Connecticut and Pittsburgh. That locks Florida State into the East. I'm sending Missouri to the West and Ohio State to the Midwest, primarily to keep the bracket in balance. Speaking of which...

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

Balance is measured by the sum of the field rankings of the four-team groups in each region. Ideally there highest and lowest sums should be no more than five apart. Here, it's six (31 in the East, and 37 in the West), but we'll run with it.

Step 6: Assign first and second round sites.

We've got the top sixteen set for the Sweet Sixteen; now let's set them up for the (nearly done) opening weekend. The total lack of any teams from the Mountain or Pacific time zones makes this a somewhat daunting task.

Philadelphia, PA: Connecticut, Villanova
Dayton, OH: Pittsburgh, Louisville
Greensboro, NC: North Carolina, Duke
Miami, FL: Wake Forest, Syracuse
Kansas City, MO: Memphis, Oklahoma
Minneapolis, MN: illinois, Michigan State
Boise, ID: Purdue, Missouri
Portland, OR: Florida State, Ohio State

We seed the 13 to 16 teams next. We try to place teams as close as possible to their campuses for the remainder of the bracket.

Step 7: Place the No. 13 seeds.

Western Kentucky to the South; Virginia Commonwealth to the East; North Dakota State to the Midwest, and Portland State to the West. (Oregon is hosting the sub-regional at the Rose Garden, but Missouri is a No. 4 seed, so the home-court disadvantage rule applies.)

Step 8: Place the No. 14 seeds.

American to the East; Stephen F. Austin to the Midwest; Akron to the South; Binghamton to the West.

Step 9: Place the No. 15 seeds.

Repeat Ivy champion Cornell in the South; Robert Morris to the West; Radford to the East; and Cal State Northridge to the Midwest.

Step 10: Place the No. 16 seeds.

Morgan State to the West; East Tennessee State to the South; Chattanooga to the East; and the opening round winner to the Midwest, due to the Dayton pod being Friday/Sunday.

Step 11: Check for conflicts and balance in the Nos. 13 through 16 seeds.

Highest: 223. Lowest: 229. Again, we'll take it and move on.

Step 12: Place the No. 5 seeds.

Kansas to the Midwest; Minnesota to the South; Gonzaga to the East, because Marquette can't go with Connecticut. The Golden Eagles head West.

Step 13: Place the No. 6 seeds.

We have to place Michigan in the East, because the Big Ten is already in all the other bottom halves. That sends Clemson to the South, West Virginia to the Midwest, and Washington to the West.

Step 14: Place the No. 7 seeds.

UCLA to the East; Arizona State to the Midwest. I'll take by option for a third-round Big Ten matchup here by placing Wisconsin in the South. But that leaves us with Penn State, who can't go West, so we bump them down, and Xavier comes up and takes that spot.

Step 15: Place the No. 8 seeds.

Since the Nittany Lions were knocked down, they get placed first, and they'll go West. Oklahoma State to the South; Texas to the East, and California to the Midwest.

Step 16: Check for conflicts and balance in the Nos. 5 through 8 seeds.

Only a difference of four here, from 96 to 100. Into the home stretch...

Step 17: Place the No. 9 seeds.

Boston College to the Midwest. Fellow ACC team Maryland binds us at this point, so we bump them down to a No. 10. Utah goes to the West, but we also have to take down Texas A&M down. The highest natural ten seed is Butler, and they go to the East. And out of nowhere, it's...an SEC team! The LSU Tigers head to the South.

Step 18: Place the No. 10 seeds.

Maryland is the higher of the two teams bumped down; they go to the East. That locks Miami into the West. I'll put Texas A&M in the Midwest. Brigham Young is the next team up, but both Minneapolis and Dayton are Friday-Sunday pods, and the Cougars will not play on the day of the rest. (Recall that the committee took significant flak by forgetting that in 2003.) We solve this by bumping them to a No. 11. I'd bring Northwestern up, but we're Big Ten-precluded, so up comes Pac-10 champ USC; the Trojans take the remaining spot in the South.

Step 19: Place the No. 11 seeds.

BYU in the East, playing on Thursday-Saturday in Philadelphia, and potentially in Boston. Northwestern will go down to a No. 12. Utah State to the West; Siena to the South; and Temple, who comes up, to the Midwest.

Step 20: Place the No. 12 seeds.

Northwestern to the East; Mississippi State to the Midwest; Northern Iowa to the South; and Cleveland State to the West.

Step 21: Check for conflicts and balance in the Nos. 9 through 12 seeds.

East sums to 151, South sums to 171. No good. One easy swap: Miami and Maryland on the No. 10 line. In fact, those two teams are at the same site in the first two rounds. That drops the difference to fourteen. Swap Louisiana State and Utah (both in Greensboro), and we're down to eleven. That also allows me to reverse Northern Iowa and Mississippi State, dropping the South's sum to 167. With the teams locked in for other reasons, particularly in the East, I don't see the ability to improve the situation any further.

Step 22: Re-check the entire bracket for conflicts.

Lots of seed bumps this year, but everything was followed and we minimized to the one possible third-round Big Ten matchup. And so we have the 2009 Z-Bracket.

The operational test

Using the Z-Ratings at the time of selection, we can project a winner in any matchup, and thus play out the entire tournament. If you do this enough times - say, ten million - it's a good indicator of each team's chances of advancement through the bracket. Last year, I showed just championships and Final Four appearances; this time around, I expanded it to show progress to each stage of the Big Dance. Here is the analysis. Based on this ratings set, I have also done the same thing, but based on the actual tournament bracket. Interestingly, the committee's top overall seed (Louisville, no. 6 in the Z-Ratings) has a better chance of winning my bracket than the real one.

Acknowledgements

Let me repeat the thanks that I posted last year.

First, and probably most important, Ken Pomeroy, whose master games file provides the source data for my men's basketball Z-Ratings. Also ESPN.com, providing the data for the NBA, MLB, NHL, and NFL ratings, as well as quick access to teams' schedules when I'm making arguments for or against a selection or seeding on this page. Of course, I would never have started doing this if it wasn't for the KRACH and John Whelan, and Ken Butler before him.

Team	Conference	Rank	Team	Conference	Rank
Duke	Atlantic Coast	4	North Dakota State	Summit League	100
Louisville	Big East	6	Portland State	Big Sky	111
Memphis	Conference USA	7	American	Patriot League	116
Purdue	Big Ten	10	Stephen F. Austin	Southland	121
Missouri	Big 12	15	Akron	Mid-American	127
Gonzaga	West Coast	19	Binghamton	America East	136
Utah	Mountain West	35	Cornell	Ivy League	137
Southern California	Pacific-10	42	Robert Morris	Northeast	153
Utah State	Western Athletic	43	Radford	Big South	155
Siena	Metro Atlantic Athletic	60	Cal State - Northridge	Big West	157
Temple	Atlantic 10	66	Morgan State	Mid-Eastern Athletic	163
Mississippi State	Southeastern	67	East Tennessee State	Atlantic Sun	164
Northern Iowa	Missouri Valley	76	Chattanooga	Southern	197
Cleveland State	Horizon	77	Morehead State	Ohio Valley	204
Western Kentucky	Sun Belt	87	Alabama State	Southwestern Athletic	259
Virginia Commonwealth	Colonial Athletic	90

Seed	Rk	FR	Team	Seed	Rk	FR	Team	Seed	Rk	FR	Team	Seed	Rk	FR	Team
1	1	1	Connecticut	5	17	17	Kansas	9	33	33	Boston College	13	87	49	Western Kentucky
	2	2	Pittsburgh		18	18	Minnesota		34	34	Maryland		90	50	Virginia Commonwealth
	3	3	North Carolina		19	19	Gonzaga		35	35	Utah		100	51	North Dakota State
	4	4	Duke		20	20	Marquette		36	36	Texas A&M		111	52	Portland State
2	5	5	Michigan State	6	21	21	Clemson	10	37	37	Butler	14	116	53	American
	6	6	Louisville		22	22	West Virginia		38	38	Louisiana State		121	54	Stephen F. Austin
	7	7	Memphis		23	23	Washington		39	39	Brigham Young		127	55	Akron
	8	8	Oklahoma		24	24	Michigan		40	40	Miami (FL)		136	56	Binghamton
3	9	9	Villanova	7	25	25	UCLA	11	41	41	Northwestern	15	136	57	Cornell
	10	10	Purdue		26	26	Arizona State		42	42	Southern California		153	58	Robert Morris
	11	11	Wake Forest		27	27	Wisconsin		43	43	Utah State		155	59	Radford
	12	12	Illinois		28	28	Penn State		60	44	Siena		157	60	Cal State - Northridge
4	13	13	Syracuse	8	29	29	Xavier	12	66	45	Temple	16	163	61	Morgan State
	14	14	Florida State		30	30	Oklahoma State		67	46	Mississipi State		164	62	East Tennessee State
	15	15	Missouri		31	31	Texas		76	47	Northern Iowa		197	63	Chattanooga
	16	16	Ohio State		32	32	California		77	48	Cleveland State
												OR	204	64	Morehead State
												OR	259	65	Alabama State