The Z-Bracket: 2011 edition
I am pleased and proud to present the 2011 Z-Bracket; for the ninth time, I'll use the Z-Ratings (also known as the Bradley-Terry system, and KRACH in the college hockey world), to draw up this year's NCAA Division I Men's Basketball Championship. The tournament may have undergone some changes in format from years past, but the Z-Bracket can change with it, while still remaining transparent in construction. The basis for everything that follows is the Z-Ratings through 13 March, produced from all 5,248 games between Division I schools. (Summary of previous brackets | Jump to this year's bracket)
(Update, Monday afternoon, 14 March: Added discussions of big seeding discrepancies between Z-Bracket and committee, and comparison under bells and whistles.)
(Update, late Monday evening, 14 March [actually Tuesday morning]: Added bracket simulations; a bit more discussion on the at-large "snubs"; discussion of Butler's seed.)
Selecting the field
Step 1: the automatic bids.
The Great West Conference is still ineligible for an automatic bid. As always, we extend these invitations to thirty conference tournament champions and the Ivy League
regular season playoff winner.
|Ohio State||Big Ten||1|| ||Long Island||Northeast||92|
|Kansas||Big 12||2|| ||Bucknell||Patriot League||98|
|San Diego State||Mountain West||3|| ||Indiana State||Missouri Valley||111|
|Duke||Atlantic Coast||7|| ||Wofford||Southern||117|
|Connecticut||Big East||8|| ||Akron||Mid-American||118|
|Kentucky||Southeastern||19|| ||St. Peter's||Metro Atlantic Athletic||127|
|Utah State||Western Athletic||22|| ||Morehead State||Ohio Valley||134|
|Old Dominion||Colonial Athletic||27|| ||Northern Colorado||Big Sky||143|
|Richmond||Atlantic 10||37|| ||Boston University||America East||157|
|Washington||Pacific-10||39|| ||Hampton||Mid-Eastern Athletic||161|
|Gonzaga||West Coast||43|| ||UC Santa Barbara||Big West||175|
|Memphis||Conference USA||46||UNC Asheville||Big South||179|
|Belmont||Atlantic Sun||57|| ||Arkansas - Little Rock||Sun Belt||197|
|Butler||Horizon League||58|| ||Texas - San Antonio||Southland||227|
|Princeton||Ivy League||59|| ||Alabama State||Southwestern Athletic||315|
Step 2: the at-large bids.
The rest of the field is filled out with the
34 37 highest ranked teams not already in. For the new-but-I'm-not-so-sure-it's-improved 2011 tournament, these teams are:
Teams in italics were not selected for the actual tournament field. The teams that made the NCAA tournament but were left out here are: Tennessee (50), UAB (52), Virginia Commonwealth (67), and Southern California (70).
|Pittsburgh||4 ||West Virginia||20|| ||Xavier||34|
|Notre Dame||5 ||UNLV||21|| ||Illinois||35|
|Brigham Young||6 ||Texas A&M||23|| ||Penn State||36|
|Syracuse||9 ||Villanova||24|| ||George Mason||38|
|Texas||10 ||Arizona||25|| ||Virginia Tech||40|
|Louisville||11 ||Kansas State||26|| ||UCLA||41|
|Purdue||12 ||Missouri||28|| ||Florida State||42|
|Wisconsin||13 ||Temple||29|| ||Clemson||44|
|Cincinnati||14 ||Marquette||30|| ||Georgia||45|
|North Carolina||15 ||Michigan||31|| ||Colorado||47|
|Georgetown||16 ||Vanderbilt||32|| ||Northwestern||48|
|Florida||17 ||Michigan State||33|| ||Boston College||49|
I am 100 percent on board with the cognoscenti of the Self-Proclaimed Worldwide Leader, who have pilloried the Selection Committee for the way it handled the bubble. Neither USC nor VCU should have come close to sniffing a bid. They are, respectively, eighteen and twenty-one places below the Z-Bracket cut line. UAB is actually much closer, but they might have ended up on the right side of the line had they won a game or two in the Conference USA tournament. And Tennessee is the first team out here, so no big deal to me on that one.
On the other hand, nobody is going to weep for Northwestern over their exclusion, and Boston College is only marginally more worthy of sympathy. Neither the Wildcats nor the Eagles (both of whom are coached by ex-Ivy League guys) will get any pity from me. But Colorado and Virginia Tech both got hosed. For crying out loud, I am sick and tired of hearing about the canard that is the "non-conference strength of schedule." A game is a game is a game, regardless of whether or not you play an opponent every year via the league.
The counter-protest is being taken up by, among others, Jerry Beach and Joe Sheehan, who would probably love nothing more than to have Jay Bilas, Digger Phelps, Hubert Davis, and Dick Vitale paraded in front of CAA headquarters and then ceremonially beheaded. I was initially frustrated with those knocking Colorado and Virginia Tech, especially the "us vs. them" attitude they seemed to have toward the "power" leagues. But with the benefit of twenty-four hours of hindsight, I can give much more deference to their rationale. Unlike yours truly, they are not evaluating the at-large teams in a vacuum; they are giving deference to teams like UAB and VCU because of the difficulty they have in scheduling. I can't fault them too much for doing so, and it's a problem in need of a remedy. But I think it's something that should be handled by the conferences and the NCAA as a whole, and not the selection committee. That said, I think the one point on which we're all in accord is Gene Smith's horrible job with the media. I wanted to scream "ATFQ" at Smith - that's an acronym from my days of Navy training. It stands for "answer the fucking question," which Smith steadfastly refused to do with the interviewers from both CBS and ESPN.
One last thing: does anybody have a contact for Randy Bennett, head coach of St. Mary's?
Seeding the teams
The newly restructured "first round"
Before we can seed the teams, we have to determine the teams and pairings for the so-called "First Four." The only guidance given in the Principles and Procedures is that the teams to be matched up are the four lowest ranked teams in the field (e.g. field rankings 65 through 68), and the last four at-large teams. Beyond that, we have nothing to go on. This indicates that the selection committee has plenary power to seed and place the first-round participants - and therefore, so do I. That being the case, the fundamental principle of the development of the Z-Bracket is transparency, so I am going to list out my criteria for handling the four first-round games:
Fortunately, the last four at-large teams all hail from different conferences, so I can use the preferred pairings. This gives us the following First Four games: Georgia v. Boston College; Colorado v. Northwestern; Arkansas - Little Rock v. Texas - San Antonio; and UNC Asheville v. Alabama State, the first sub-300 ranked team in the history of the Z-Bracket to make the field.
- 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 16 MUST be assigned to a Friday/Sunday pod for the second and third rounds. Teams playing on Tuesday, March 15 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
The Principles and Procedures seem to abandon all mention of the "S-Curve." Of course, I never used it here anyway; we'll use the rankings themselves to assign seeds, subject to the rules laid about above for the handling of the eight teams playing in Dayton. Teams slated to meet in the first round are listed in the same cell.
|3||3||San Diego State||
||175||64||UC Santa Barbara
|Arkansas - Little Rock|
Texas - San Antonio
Rk = overall ranking by the Z-Ratings.
FR = Field ranking - the ranking of the team among the field of 68.
Let's talk just a bit about some of these seedings, shall we?
San Diego State as a #1. Given that the committee placed the Aztecs in the West and with the lowest No. 1 seed, they might have been the No. 5 overall team in the committee's eyes. But a 29-2 season, including 14-2 in the No. 7 conference, with the only two losses to BYU with Brandon Davies? Even without the benefit of these ratings, I'd have SDSU in the top four in the nation.
Florida as a #5. I agree with Pat Forde that the actual bracket has Florida too high. The SEC was, relatively speaking, down this year, and for that, the Gators suffer here.
Utah State as a #6. The Aggies get the "Charlie Sheen justification": DUH! WINNING! Um, twenty-eight and three? Utah State might be (from my perspective) the most mis-evaluated team I've seen over the last nine years.
Butler as a #13. I don't think the committee seeded the Bulldogs so high based on their run to last year's national final; I bet it was more because of their hot streak down the stretch. But the Z-Ratings don't recognize those games as any more important than Butler's five Horizon League losses, including one to Youngstown State.
I think the committee did a good job with the Big East teams, recognizing the superior quality of that league. And down below the bracket, I'll have something to say about differences in evaluation between two mid-major conferences near and dear to my heart.
Establishing the bracket
The regionals for 2011: East (Newark); Southeast (New Orleans); Southwest (San Antonio); and West (Anaheim).
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 sent a tournament-record eleven).
- 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. No assignments are precluded in the regionals; for the second and third rounds, Arizona can't be put in Tucson and Georgetown cannot be in Washington, DC.
- 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.)
- 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. 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.
Ohio State to the East; Kansas to the Southwest; San Diego State in the West; Pittsburgh to the Southeast. This yields a Final Four of East vs. Southeast and Southwest vs. West.
Step 2: Place the No. 2 seeds.
Notre Dame is placed in the East. BYU cannot be placed opposite SDSU in the West, and since they must be bracketed to play Thursday and Saturday due to religious requirements, they must go to the Southeast. Duke ends up in the Southwest and Connecticut is sent West.
Step 3: Place the No. 3 seeds.
Syracuse to the Southeast (must avoid Notre Dame and Connecticut); Texas to the East. As the second big 12 team, the Longhorns must be bracketed away from Kansas, and they cannot go in the West because Purdue can't be placed in the East (due to Ohio State); Louisville must go to the Southwest to avoid the other Big East teams in the bottom halves; and as mentioned, Purdue ends up in the West.
Step 4: Place the No. 4 seeds.
Wisconsin is limited to the Southeast and West; they go to New Orleans. Cincinnati to the East; North Carolina to the West (must avoid Duke); and Georgetown to the Southwest.
Step 5: Check for conflicts and balance in the Nos. 1 through 4 seeds.
We sum the field rankings of the top four teams in each region, and there should be a difference of no more than five between the highest and lowest. Right now, we have the East at 30 and the West at 38, so we need to do some shuffling. I'm going to apply Occam's razor and conduct a single move - swap Connecticut and Notre Dame on the No. 2 seed line. The Fighting Irish do lose out somewhat on this (in terms of distance), but they'd be getting on a place to the regional either way - and they have a potentially more favorable Elite Eight matchup. This shifts the regional sums to 32, 33, 35, and 36, so we are in good shape.
Step 6: Assign first and second round sites.
Cleveland, OH: Ohio State, Syracuse
Tulsa, OK: Kansas, Texas
Tucson, AZ: San Diego State, Georgetown
Washington, DC: Pittsburgh, Connecticut
Chicago, IL: Notre Dame, Louisville
Denver, CO: Brigham Young, Wisconsin
Charlotte, NC: Duke, Purdue
Tampa, FL: Cincinnati, North Carolina
Step 7: Place the No. 5 through 16 seeds.
Keep in mind that from this point on, the teams are placed according to the site of their second/third round pod (since, by their seeding, they're expected to be gone by the end of the first weekend).
Step 7a: Place the No. 5 seeds. (Available sites: Denver, Tampa , Tucson)
Florida to the East; St. John's to the West. Kentucky is going to the Southwest in order to place West Virginia in the Southeast. This allows for a potential Big East matchup to take place in the regional semifinal (against Pittsburgh) vice the second round (versus Georgetown).
Step 7b: Place the No. 6 seeds. (Available sites: Charlotte, Chicago, Cleveland, Tulsa)
UNLV to the East; Utah State to the Southwest; Texas A&M to the Southeast, and Villanova to the West, which again puts the possible all-Big East game in the
third fourth round.
Step 7c: Place the No. 7 seeds. (Available sites: Charlotte, Chicago, Denver, Washington)
Arizona to the Southeast; Kansas State to the West; Old Dominion to the East; Missouri to the Southwest.
Step 7d: Place the No. 8 seeds. (Available sites: Cleveland, Tucson, Tulsa, Washington)
Temple to the Southeast; Marquette to the East (and we're done with the Big East); Michigan to the Southwest and Vanderbilt to the West (must be separated from Kentucky).
Step 7e: Place the No. 9 seeds. (Available sites: Cleveland, Tucson, Tulsa, Washington)
The very next team placed is Vanderbilt's opponent; Michigan State is forced into the West due to the Big Ten teams in the other three top halves. Xavier to the East. Illinois and Penn State are the first two bumps of the 2011 Z-Bracket; to get them into the bottom half, they both have to go down to the No. 10 line. In their place we bring up Richmond and George Mason. We can't place the Spiders against Temple, so they are put in the Southwest. And so, as much as it pains me to do this (due to my Hofstra ties), I have to put George Mason in the Southeast and into a Washington pod - effectively at home, much as they were in 2006.
Step 7f: Place the No. 10 seeds. (Available sites: Charlotte, Chicago, Denver, Washington)
We take up Illinois and Penn State first, since they were bumped down. The Illini go to the Southwest (the West, with a Chicago pod, is unavailable due to Purdue's presence) and the Nittany Lions go East. That leaves us with Washington in the West (can't be placed with Arizona) and Virginia Tech in the Southeast (as the third ACC team, they can't be in the same region as UNC, even though they're on the other side of the bracket).
Step 7g: Place the No. 11 seeds. (Available sites: Charlotte, Chicago, Cleveland, Tulsa)
UCLA to the Southeast; Florida State to the West; Gonzaga to the Southeast; Clemson to the East. Tulsa may be closer to Westwood than Chicago, but it's a plane ride either way, and if UCLA had been placed in the East, it would have forced either Florida State or Clemson to be bumped down in favor of a First Four winner.
Step 7h: Place the No. 12 seeds. (Available sites: Denver, Tampa , Tucson)
The winner of the Georgia - Boston College game goes into the Southeast. Memphis to the East. We now come to the case of the winner of Colorado vs. Northwestern. Since the Big Ten and the Big 12 both have more than five teams in the field, I'm going to place the winner of this game in the West, where Northwestern could meet Michigan State in a regional semifinal. Belmont ends up in the Southwest.
Step 7i: Place the No. 13 seeds. (Available sites: Denver, Tampa , Tucson)
Butler to the East; Princeton to the West; Oakland to the Southeast; Long Island to the Southwest.
Step 7j: Place the No. 14 seeds. (Available sites: Charlotte, Chicago, Cleveland, Tulsa)
Bucknell to the Southeast; Indiana State to the Southwest; Wofford to the East; Akron to the West. Wofford is not in the Charlotte pod because putting them there would put Purdue at a "potential home court disadvantage."
Step 7k: Place the No. 15 seeds. (Available sites: Charlotte, Chicago, Denver, Washington)
St. Peter's to the East; Morehead State to the Southwest; Northern Colorado to the West; Boston University to the Southeast. Once again, the rule regarding home-court disadvantage is invoked to prevent Northern Colorado from playing in Denver.
Step 7l: Place the No. 16 seeds. (Available sites: Cleveland, Tucson, Tulsa, Washington)
Hampton to the Southeast; UC Santa Barbara to the West; the UNC Asheville/Alabama State winner to the East; and the Arkansas - Little Rock/Texas - San Antonio to the Southwest.
Step 8: Re-check the entire bracket for conflicts.
We have minimized the number of possible Big East matchups in the regional semifinals at three, and as stated above, there is the one possible pairing of Big Ten teams in the Sweet Sixteen. I present the 2011 Z-Bracket below:
|EAST (Prudential Center, Newark)||SOUTHWEST (Alamodome, San Antonio)|
|1||Ohio State||Quicken Loans Arena|
|5||Florida||St. Pete Times Forum|
|7||Old Dominion||Verizon Center|
|Time Warner Cable Arena|
|15||St. Peter's||Morehead State||15|
(Reliant Stadium, Houston)
East v. Southeast
Southwest v. West
|SOUTHEAST (New Orleans Arena, New Orleans)||WEST (Honda Center, Anaheim)|
|San Diego State||1|
|16||Hampton||UC Santa Barbara||16|
|9||George Mason||Michigan State||9|
|5||West Virginia||Pepsi Center|
|St. Pete Times Forum|
|3||Syracuse||Quicken Loans Arena|
|Time Warner Cable Arena|
|2||Brigham Young||Notre Dame||2|
|15||Boston University||Northern Colorado||15|
|FIRST ROUND (UD Arena, Dayton) - Tuesday||FIRST ROUND (UD Arena, Dayton) - Wednesday|
|Georgia||(to Southeast #12)||(to East #16)||UNC Asheville|
|Boston College||Alabama State|
|Colorado||(to West #12)||(to Southwest #16)||Arkansas - Little Rock|
|Northwestern||Texas - San Antonio|
Bells and whistles
Before we get to the bracket simulator results, let's do a side-by-side on two teams:
Pretty similar except for that last row, right? On the left is 2010 Cornell; on the right is 2011 George Mason. (I say "natural Z-Bracket seed" because George Mason was bumped up to a #9.) As much as I try to eliminate my own biases from the selection and seeding of teams, I'm going to use them here as a springboard to highlight a possible disparity in treatment, even between mid-major conferences.
|Team A||Team B|
|Natural Z-Bracket seed||10||10|
In the interests of time, I've truncated the simulation of each bracket to one million repetitions each. Even though my program can iterate through the bracket about 7,000 times per second, that still means it takes a really long time to get through ten million plays. Anyway, here are the results: 2011 Z-Bracket | 2011 NCAA tournament. The two simulations are closely aligned at the top; each says there's roughly a one in two chance that either Ohio State or Kansas will hoist the gold trophy in Houston.
As always, thanks are due to Ken Pomeroy, who supplies the data generate the men's basketball Z-Ratings. This would be a lot harder without his raw data files. Of course, I must again pay homage to our roots in Cornell hockey - the KRACH, John Whelan, and Ken Butler.
Unlike last year I've got no dog in the fight this time around - so just enjoy the tournament.
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