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:

TeamConferenceRankTeamConferenceRank
DukeAtlantic Coast4North Dakota StateSummit League100
LouisvilleBig East6Portland StateBig Sky111
MemphisConference USA7AmericanPatriot League116
PurdueBig Ten10Stephen F. AustinSouthland121
MissouriBig 1215AkronMid-American127
GonzagaWest Coast19BinghamtonAmerica East136
UtahMountain West35CornellIvy League137
Southern CaliforniaPacific-1042Robert MorrisNortheast153
Utah StateWestern Athletic43RadfordBig South155
SienaMetro Atlantic Athletic60Cal State - NorthridgeBig West157
TempleAtlantic 1066Morgan StateMid-Eastern Athletic163
Mississippi StateSoutheastern67East Tennessee StateAtlantic Sun164
Northern IowaMissouri Valley76ChattanoogaSouthern197
Cleveland StateHorizon77Morehead StateOhio Valley204
Western KentuckySun Belt87Alabama StateSouthwestern Athletic259
Virginia CommonwealthColonial Athletic90

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:
TeamRankTeamRank
Connecticut1Michigan24
Pittsburgh2UCLA25
North Carolina3Arizona State26
Michigan State5Wisconsin27
Oklahoma8Penn State28
Villanova9Xavier29
Wake Forest11Oklahoma State30
Illinois12Texas31
Syracuse13California32
Florida State14Boston College33
Ohio State16Maryland34
Kansas17Texas A&M36
Minnesota18Butler37
Marquette20Louisiana State38
Clemson21Brigham Young39
West Virginia22Miami (FL)40
Washington23Northwestern41
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
111Connecticut 51717Kansas 93333Boston College 138749Western Kentucky
22Pittsburgh 1818Minnesota 3434Maryland 9050Virginia Commonwealth
33North Carolina 1919Gonzaga 3535Utah 10051North Dakota State
44Duke 2020Marquette 3636Texas A&M 11152Portland State
255Michigan State 62121Clemson 103737Butler 1411653American
66Louisville 2222West Virginia 3838Louisiana State 12154Stephen F. Austin
77Memphis 2323Washington 3939Brigham Young 12755Akron
88Oklahoma 2424Michigan 4040Miami (FL) 13656Binghamton
399Villanova 72525UCLA 114141Northwestern 1513657Cornell
1010Purdue 2626Arizona State 4242Southern California 15358Robert Morris
1111Wake Forest 2727Wisconsin 4343Utah State 15559Radford
1212Illinois 2828Penn State 6044Siena 15760Cal State - Northridge
41313Syracuse 82929Xavier 126645Temple 1616361Morgan State
1414Florida State 3030Oklahoma State 6746Mississipi State 16462East Tennessee State
1515Missouri 3131Texas 7647Northern Iowa 19763Chattanooga
1616Ohio State 3232California 7748Cleveland State
OR20464Morehead State
25965Alabama 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:

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.