Crashing the Dance

What are the odds?

Thu, 23 Mar 2017 04:00:00 +0000

After taking a hiatus last year, it’s once again time to play around with the FiveThirtyEight predictions and have some fun with the numbers.

42.4% probability of a #1 seed winning the championship

21 champs have been #1 seeds - most since seeding began in 1979

20.0% probability of a #2 seed winning the championship

Seven champs have been #2 seeds - second most since seeding began

10.2% probability of a #3 seed winning the championship

Five champs have been #3 seeds

17.6% probability of a #4 seed winning the championship

The only #4 seed to win a title was Arizona in 1997.

9.9% probability of a #5 or lower seed winning the championship

Only four previous champions (#6 N.C. State 1983, #6 Kansas 1988, #7 Connecticut 2014, #8 Villanova 1985) were seeded 5th or lower.

36.4% probability of a first-time champion

Gonzaga, Baylor, West Virginia, Purdue, Butler, South Carolina, and Xavier would win their first title. The other 9 teams have a combined 33 championships.

61.5% probability of a first-time Final Four team

Gonzaga, Xavier, and South Carolina have never made the Final Four. The other 13 teams have a combined 94 appearances (not including vacated appearances).

34.5% probability of the champion emerging from the West Regional

Gonzaga (18.2% percent chance) gives the West the best shot at producing the champ. The West Regional has produced the champ 7 times since seeding began in 1979. 2004 champ UConn emerged from what was officially called the Phoenix Regional during the NCAA’s brief dalliance with non-directional region naming.

13.2% probability of the champion emerging from the East Regional

Losing the #1 and #2 seeds was costly to the chances the eventual champion will pass through Madison Square Garden this week.

8.3% probability of three #1 seeds in the Final Four

Three or more #1 seeds have made it to the Final Four five times since seeding began (last in 2015)

16.7% probability of no #1 seeds in the Final Four

A #1-free Final Four has happened three times since seeding began (last in 2011)

5.5% probability of no returning Elite 8 teams from 2016

65.7% probability of no returning Final Four teams from 2016

Kansas, North Carolina, and Oregon are the only 2016 Elite 8 teams remaining this year. Only UNC made the Final Four last year.

38.0% probability of no #4 seeds in the Final Four

0.1% probability of four #4 seeds in the Final Four

All four #4 seeds are in the Sweet 16 for only the third time since seeding began.

8.9% probability of a Gonzaga vs. Kansas championship game

The most likely championship game pairing

45.9% probability of a North Carolina vs. Kentucky South Regional final

This is the most likely regional final matchup this season

1.1% probability of a rematch of the 2006 UCLA/Florida championship game

3.5% probability of a rematch of the 1997 Arizona/Kentucky championship game

1.9% probability of a rematch of the 1948 Kentucky/Baylor championship game

These are the only championship game rematches still possible

21.0% probability of a Final Four rematch of the 2012 Kentucky/Kansas championship game

5.9% probability of a Final Four rematch of the 1993 UNC/Michigan championship game

2.7% probability of a Final Four rematch of the 1969 UCLA/Purdue championship game

2.5% probability of a Final Four rematch of the 1965 UCLA/Michigan championship game

18.2% probability of a Final Four rematch of the 1957 UNC/Kansas championship game

22.0% probability of a Elite 8 rematch of the 1968 UCLA/UNC championship game

While not as exciting as a rematch in the actual championship game, these rematches would bring back memories for those who remember the original. A UNC/Kansas rematch would be their record fifth Final Four meeting.

2.5% probability of three Big 12 teams in the Final Four

0.4% probability of three Pac 12 teams in the Final Four

Each conference has three teams remaining in different regions. The SEC and Big 10 each also have three teams but two in one region. The ACC has only one team remaining.

2017 Selection Sunday Thoughts

Sun, 12 Mar 2017 22:00:00 +0000

Villanova, Kansas, and Gonzaga are solid 1 seeds according to the CTD seeding model, but after that there is a tight cluster of teams between the 4 and 9 spots on the 1-68 list. The seeding model gives each around 15 points, meaning their profile most closely matches that of a two seed based on the committee’s historical behavior. It wouldn’t surprise me to see any of those teams - particularly Duke or Arizona - take over UNC’s spot on the 1 line.
UCLA has been getting less respect from bracketologists than from the polls, largely because of their power ratings and large number of games against teams outside the RPI top 100. 17 of their 29 wins fall into that category, and 11 of those are outside the top 200. That makes their overall record a little misleading, but they should still be a protected seed (top 4 lines).
Wichita State is one of the most interesting seeding discussions because of the disparity between their record & power ratings and their paucity of quality wins. I think the seeding model has them a little low as an 11 seed, but I’d guess they won’t be any higher than a 7.
The selection model is unambiguous on its feelings about Syracuse, putting them several spots outside the field. The Orange have several good wins, though they’re all at home. They also have five losses outside the RPI top 100, including two at home and one to #219 Boston College. That’s not good.
Other than Syracuse, there seems to be consensus around the other at-large selections. Illinois State is another team that’s been debated, but neither their profile nor power ratings are strong enough to justify selection. Stranger things have happened, though.

Mocking the Bracket

Sun, 12 Mar 2017 18:00:00 +0000

Click here for the latest update.

Each year for the better part of the last decade, the NCAA has invited a group of media and other folks to Indianapolis to participate in a mock selection committee meeting and report the details of the sausage factory to the masses.

The NCAA tried to pull back the curtain a bit with the early release of a top 16 seed list and “bracket”, but despite their best efforts (and pretty thorough description of the process there is still much public confusion about the process. Yes, they leave some parts of the procedure open to interpretation (How do they define “best teams” for at-large selection? Is a team’s “natural area of interest” the closest absolute site, or their most sensible geographic region?), but the process itself is well defined.

While the selection and seeding steps that Crashing the Dance tries to forecast using machine learning are highly subjective, the bracketing step is essentially an algorithm based on the 1-68 seed list and the bracketing rules and principles.

So, I’m going to once again do my part to help y’all understand, as much as I understand it anyway, how the committee does its job when taking the 1-68 list and placing each team into the bracket.

First, let’s identify which teams are prohibited from certain sites based on committee criteria.

A team will not be permitted to play in any facility in which it has played more than three games during its season, not including exhibitions and conference post-season tournaments.

Kansas played three games at Sprint Center in Kansas City, so they are allowed to play in the Midwest Region. No other team projected in the field played more than two games at any other site.

A host institution’s team shall not be permitted to play at the site where the institution is hosting. However, the team may play on the same days when the institution is hosting.

In addition to those criteria, BYU does not play on Sunday for religious reasons, so they cannot be assigned to a pod or region with Sunday games scheduled. (They’re not currently projected in the field, so this likely won’t come into play.)

Pod site prohibitions (not comprehensive)

Buffalo - None

Milwaukee - Marquette

Orlando - UCF, Stetson

Salt Lake City - Utah

Greenville, SC - None

Indianapolis - IUPUI

Tulsa - Tulsa

Sacramento - CSU Sacramento

Region site prohibitions (not comprehensive)

Kansas City - None

San Jose - None

Memphis - Memphis

New York - St. John’s

Remember, this is not my opinion of how the bracket will look at 5:30 p.m. on Selection Sunday. It is an exercise in placing teams in the bracket based on the latest 1-68 seed list generated by the CTD seeding model (as of 1 p.m. ET Sunday).

The committee will place the four No. 1 seeded teams 1 through 4 in each of the four regions, thus determining the Final Four semifinals pairings (overall 1 vs. 4; 2 vs. 3).

The main principle when placing teams into the bracket is:

Teams will remain in or as close to their areas of natural interest as possible. A team moved out of its natural area will be placed in the next closest region to the extent possible. If two teams from the same natural region are in contention for the same bracket position, the team ranked higher in the seed list shall remain in its natural region.

There is some debate over what a team’s “natural region” is for the purposes of bracketing the field. It is generally a balance between distance to each site, “fit” (Kentucky was sent to Atlanta over closer St. Louis in 2012 because it was deemed a better fit), and other factors. We’ll consider each application as it comes up.

As usual, I’ll be using the super handy CTD distance chart to find the closest site. Regardless of how the criteria is applied, the NCAA has made very clear that geography trumps just about everything when it comes to building the bracket.

Let’s go.

1. Villanova - East (Buffalo)

Big East Champ and defending national champs Villanova is the consensus #1 overall, and the CTD seeding model agrees. The geography is straightforward as well, with the nearest pod and region sites a short trip from Philadelphia.

2. Kansas - Midwest (Tulsa)

(Edit: Tulsa is closer than either Milwaukee or Indy.)

Despite their early loss in the Big 12 tournament, Kansas still grabs a 1 seed. Kansas City and Tulsa are the clear site choices.

3. Gonzaga - West (Salt Lake City)

While there is still some debate about Gonzaga’s place on the seed line, the CTD model had little debate about their place on the seed list. As the only CTD 1 seed in the West, they’ll get their preferred site placement.

4. North Carolina - South (Greenville)

The Heels tenuously hold on to the last spot on the #1 seed line. Memphis is a little farther from Chapel Hill than New York, but the South is arguably their natural region. Greenville is filling in for Greensboro as a pod site, but it’s still the closest.

The committee will then place the No. 2 seeds in each region in true seed list order.

5. Kentucky - South (Indianapolis)

Memphis is the closest regional site. With the lowest 1 seed in Memphis, there would not be any bracket balance issues adding the highest 2 seed.

6. Oregon - West (Sacramento)

Despite losing in the Pac 12 championship game, the Ducks remain the highest seed from the conference and are rewarded geographically.

7. Duke - East (Greenville)

Duke’s late run lifted them to a higher seed line than would have been expected several weeks ago. They’re also rewarded geographically, though being in the same region as Villanova might not be a reward.

8. Arizona - Midwest (Salt Lake City)

The only region left is Kansas City, but the Pac 12 tournament champs get their closest pod site.

The committee will then place the No. 3 seeds in each region in true seed list order.

Each of the first four teams selected from a conference shall be placed in different regions if they are seeded on the first four lines.

9. Florida St. - Midwest (Orlando)

With North Carolina already assigned to Memphis, the Seminoles can’t get their preferred geographic region. However, they do get to stay close to home for the first round.

10. Louisville - West (Indianapolis)

As the fourth team in the field from the ACC, the Cardinals are left with the geographic leftovers.

11. Florida - East (Orlando)

The Gators would rather be in the South, but Kentucky is already there. They also make Orlando an all-Florida pod.

12. UCLA - South (Sacramento)

The only region left for the Bruins. They get to stay in California for the first two rounds.

The committee will then place the No. 4 seeds in each region in true seed list order.

13. Baylor - South (Tulsa)

At this point, teams start to see fewer options to satisfy their geographic preferences. No Big 12 teams are in Memphis and there is still a slot in Tulsa, so the Bears are the rare 4 seed that is happy with their placement.

14. Butler - Midwest (Milwaukee)

Memphis is already booked on the 4 line, so they’re heading to Kansas City with no Big East teams there yet. Indianapolis is already full, so they’ll make the trip north for the first round.

15. West Virginia - East (Buffalo)

Wow, this is much easier than in previous years.

With three strong west coast teams filling up slots out west, there are more natural slots are available for teams closer to the Atlantic Ocean than normal. The Mountaineers benefit by getting their first choice for the pod and regional site, which is unusual for the 15th overall seed.

16. Purdue - West (Milwaukee)

Despite having to head west for the regional, the Boilermakers get to stay close to home early.

After the top four seed lines have been assigned, the committee will review the relative strengths of the regions by adding the “true seed” numbers in each region to determine if any severe numerical imbalance exists. Generally, no more than five points should separate the lowest and highest total.

No issues with balance this year. The Midwest (33) comes in slightly harder than the South (34), East (34), and West (35), but well within the guidelines.

In “true seed” order, the committee then assigns each team (and, therefore, all teams in its bracket group—e.g., seeds 1, 8, 9, 16) to second-/third-round sites.

In other words, take the 16 teams and place them into a pod site to determine where each will play its first-/second-round games. Each of these teams is the highest seeded team in pod of four teams, and the other teams in each pod automatically follow that pod site. This is important when slotting the other teams into the bracket to satisfy other rules.

1. Villanova - Buffalo

2. Kansas - Tulsa

3. Gonzaga - Salt Lake City

4. North Carolina - Greenville

5. Kentucky - Indianapolis

6. Oregon - Sacramento

7. Duke - Greenville

8. Arizona - Salt Lake City

9. Florida St. - Orlando

10. Louisville - Indianapolis

11. Florida - Orlando

12. UCLA - Sacramento

13. Baylor - Tulsa

14. Butler - Milwaukee

15. West Virginia - Buffalo

16. Purdue - Milwaukee

Mocking the Bracket

Sun, 13 Mar 2016 18:00:00 +0000

And each year, there is still much public confusion about the process, despite the NCAA’s best efforts (and pretty thorough description of the process). Yes, they leave some parts of the procedure open to interpretation (How do they define “best teams” for at-large selection? Is a team’s “natural area of interest” the closest absolute site, or their most sensible geographic region?), but the process itself is well defined.

First, let’s identify which teams are prohibited from certain sites based on committee criteria.

A team will not be permitted to play in any facility in which it has played more than three games during its season, not including exhibitions and conference post-season tournaments.

Villanova played only three games at the Wells Fargo Center, the site of the East Regional, so they are not prohibited from being placed there.

A host institution’s team shall not be permitted to play at the site where the institution is hosting. However, the team may play on the same days when the institution is hosting.

Pod site prohibitions (not comprehensive)

Providence - Providence

Des Moines - Iowa State

Raleigh - North Carolina State

Denver - None

Brooklyn - None

St. Louis - None

Oklahoma City - None

Spokane - Idaho

Region site prohibitions (not comprehensive)

Anaheim - None

Louisville - Louisville (ineligible)

Chicago - None

Philadelphia - LaSalle

The committee will place the four No. 1 seeded teams 1 through 4 in each of the four regions, thus determining the Final Four semifinals pairings (overall 1 vs. 4; 2 vs. 3).

The main principle when placing teams into the bracket is:

Teams will remain in or as close to their areas of natural interest as possible. A team moved out of its natural area will be placed in the next closest region to the extent possible. If two teams from the same natural region are in contention for the same bracket position, the team ranked higher in the seed list shall remain in its natural region.

Let’s go.

1. Kansas - Midwest (Chicago)

Kansas is the consensus #1 overall, and the CTD seeding model agrees. Lawrence is slightly closer to Chicago than to Louisville, and the Midwest is more the Jayhawk’s natural region than is the South.

2. Virginia - East (Philadelphia)

Easy answer by natural region and distance.

3. North Carolina - South (Louisville)

The closest site for the Heels would be Philly, but Louisville is only slightly farther.

4. Villanova - West (Anaheim)

Staying on the #1 line would be worse for Villanova’s travel plans than falling to the #2 line. The only slot left is in California.

The committee will then place the No. 2 seeds in each region in true seed list order.

One significant procedural change is new this year:

The committee may relax the principle of keeping teams as close to their area of natural interest for seeding teams on the No. 2 line to avoid, for example, the overall No. 5 seed being sent to the same region as the overall No. 1 seed. The committee will not compromise the principle of keeping teams from the same conference in separate regions.

5. Michigan State - South (Louisville)

Regardless of whether Michigan State rises to the 1 seed line in real bracket land, they won’t end up in Chicago with overall #1 Kansas already there. In this case, they’re sent to the next closest site paired with overall #3 and tournament nemesis North Carolina.

6. Oregon - West (Anaheim)

The Ducks get their preferred region.

7. Oklahoma - East (Philadelphia)

Chicago is off limits because fellow Big 12 mate Kansas is already there, and Louisville is already taken by Michigan State.

8. Utah - Midwest (Chicago)

The only site left goes to Utah, and it works better from a bracket balancing standpoint matching the #1 overall with the #8 overall.

The committee will then place the No. 3 seeds in each region in true seed list order.

Each of the first four teams selected from a conference shall be placed in different regions if they are seeded on the first four lines.

9. Miami - Midwest (Chicago)

Louisville and Philly are closer, but both already taken by ACC teams.

10. West Virginia - South (Louisville)

Oklahoma is in Philly, so the Mountaineers make the trip to Louisville.

11. Xavier - East (Philadelphia)

Xavier would prefer to make the short drive to Louisville, but West Virginia just snatched it. Chicago is also taken, so the second-best Big East team heads east.

12. Kentucky - West (Anaheim)

SEC champ Kentucky gets the final spot on the 3 line.

The committee will then place the No. 4 seeds in each region in true seed list order.

13. Texas A&M - South (Louisville)

The closest (and natural region) site is available for the Aggies.

14. Purdue - Midwest (Chicago)

In the mock scenario, the Boilermakers have to be pretty happy with this turn of events, aside from being in the same region as overall #1 Kansas.

15. Indiana - West (Anaheim)

Oh, what a difference a single seed makes. Instead of staying near Bloomington, the Hoosiers get shipped out west. There were no conflicts to putting Indiana in Philadelphia, but they were moved here because putting Arizona in Anaheim would have caused a conference conflict, with Oregon already there. The committee has the ability to make these kinds of switches further down the seed list.

16. Arizona - East (Philadelphia)

Arizona also has to travel across the country, but in the opposite direction. As mentioned above, the Wildcats could not have been in Anaheim because Oregon was already there.

After the top four seed lines have been assigned, the committee will review the relative strengths of the regions by adding the “true seed” numbers in each region to determine if any severe numerical imbalance exists. Generally, no more than five points should separate the lowest and highest total.

We’re on the fringe of imbalance, but for purposes of time, we’ll let it slide. Hopefully the committee won’t use that excuse! South (31), Midwest (32), East (36), and West (37) are within six points.

Reload for the latest updates

In “true seed” order, the committee then assigns each team (and, therefore, all teams in its bracket group—e.g., seeds 1, 8, 9, 16) to second-/third-round sites.

1. Kansas - Des Moines

2. Virginia - Raleigh

3. Villanova - Brooklyn

4. North Carolina - Raleigh

5. Michigan State - St. Louis

6. Oklahoma - Oklahoma City

7. Oregon - Spokane

8. Utah - Denver

9. Miami - St. Louis

10. West Virginia - Brooklyn

11. Xavier - Des Moines

12. Kentucky - Providence

13. Texas A&M - Oklahoma City

14. Purdue - Providence

15. Indiana - Denver

16. Arizona - Spokane

Regression to the Mean

Tue, 24 Mar 2015 13:00:00 +0000

Unlike momentum or the hot hand, regression to the mean is an actual phenomenon. (OK, maybe there is something to the hot hand)

Most measurements of human ability are partly achieved by skill and partly achieved by luck. This means that data cannot always be taken at face value. (fangraphs.com)

Regression the to mean explains why a 48-percent-shooting team likely won’t duplicate its 65 percent first half performance after halftime, despite no meaningful changes from one half to the next. Whether it’s field goal percentage or the number of heads when flipping a coin, more variablilty is possible in smaller sample sizes. Over the long run things generally settle to their expected values.

That leads us to the first weekend of the NCAA tournament. It’s tempting to see a team dominate its first two games and assume that domination will continue. However, we should not be surprised when this does not happen.

People sometimes misinterpret regression to the mean when they believe a shooter in a slump is “due” to play better. Regression to the mean isn’t a law that dictates what will happen, but is rather an simple explanation for a natural phenomenon.

(Source: xkcd)

Enough theory. What does this actually mean for the Sweet 16?

Here are the top five teams from the first weekend of the tournment ranked by their net efficiency margin (NEM).

Team	NEM per game
Duke	44.6
Arizona	37.0
Michigan St.	36.0
Xavier	32.3
Utah	29.6

Based on that alone, you might conclude that Duke and Arizona are destined to meet on a Monday night in Indianapolis. The point is not that we can say either is due to fall back to its typical level this weekend. Instead, we can use our knowledge of this natural phenomenon to watch out for teams that might be overvalued or undervalued based on the first weekend. (While I didn’t specifically say so earlier, regression to the mean works in either direction.)

Here are the five teams that outplayed their pre-tourney NEM average during the first weekend.

	pre-tourney	tourney
Team	NEM	NEM
Michigan St.	21.3	36.0
Xavier	18.7	32.3
Duke	31.8	44.6
UCLA	13.4	21.2
West Virginia	19.1	26.5

Is it possible that Duke is onto something after dismissing Rasheed Sulaimon, or that Tom Izzo has a formula for March more secret than the Coca-Cola formula? Sure, it’s possible, but the simpler and more likely explanation is a variation due to randomness (or chance or luck, if you prefer) over a small sample. Again, that doesn’t mean that any of these teams are due to return to Earth in their next game. It simply means that the more games they play, the more likely that their performance will reflect their true level. In this case, we measure that by the NEM over the entire season.

UCLA is an interesting case. Many (including the CTD selection model) did not find their profile at-large worthy, but the only opinion that counts put them in the field. Although the Bruins had the worst pre-tourney NEM (13.4) of the remaining teams, a quick look at their season trend (the dark blue line) shows they have been playing better over the last two months or so. It may still not be enough to beat Gonzaga, but their first two games aren’t as out of character as they would first appear.

Which teams are candidates for a positive regression to the mean? These teams won their first two games despite playing below their true ability, at least according to NEM.

	pre-tourney	tourney
Team	NEM	NEM
Kentucky	40.5	27.7
Wisconsin	33.8	22.5
Notre Dame	24.9	15.6
Oklahoma	24.4	19.5
North Carolina	24.7	20.0

The difficulty in recognizing the role of randomness in our everyday lives is human nature. I highly recommend Leonard Mlodinow’s The Drunkard’s Walk if you’d like to learn more.

What are the odds?

Thu, 19 Mar 2015 04:00:00 +0000

Most of these seem pointless given the predestined champion, but it’s always a fun exercise. So, using the FiveThirtyEight predictions let’s have a little fun with the numbers.

67.7% probability of a #1 seed winning the championship

20 champs have been #1 seeds - most since seeding began in 1979

26.4% probability of a #1 seed not named Kentucky winning the championship

20.3% probability of a #2 seed winning the championship

Six champs have been #2 seeds - second most since seeding began

4.8% probability of a #3 seed winning the championship

Five champs have been #3 seeds

2.1% probability of a #4 seed winning the championship

The only #4 seed to win a title was Arizona in 1997.

5.1% probability of a #5 or lower seed winning the championship

Only four previous champions (#6 N.C. State 1983, #6 Kansas 1988, #7 Connecticut 2014, #8 Villanova 1985) were seeded 5th or lower.

6.5% probability of no #1 seeds in the Final Four

A #1-free Final Four has happened three times since seeding began (last in 2011)

15.4% probability of an Kentucky vs. Villanova championship game

The most likely championship game pairing

44.2% probability of a rematch of last year’s Arizona/Wisconsin West Regional final

This is the most likely regional final matchup this season

23.7% probability of an Elite Eight rematch of the 2012 Kentucky/Kansas championship game

33.7% probability of a Final Four rematch of the 1997 Arizona/Kentucky championship game

38.3% probability of no ACC teams in the Final Four

0.07% probability of four ACC teams in the Final Four

The ACC has five teams with #4 seeds or better, the most of any conference

2015 Selection Sunday Thoughts

Sun, 15 Mar 2015 22:45:00 +0000

The CTD selection model currently has Temple as the first team out of the field, but it wouldn’t surprise me to see them in the field. I’m not sure what it is in their profile aside from the win over Kansas that has some with the Owls firmly in the field. They have a decent profile, but one game shouldn’t overwhelm the other 32.
Each of the next five candidates on the CTD seeding list behind Kentucky has a case at a #1 seed, and I wouldn’t be surprised to see any combination of those five fill out the final three spots. However, while Arizona is considered by some to be one of the best two or three teams right now, the committee generally rewards the entire season’s profile rather than recent acheivements. All things being equal, Arizona’s recent surge might be enough, but I can’t get over those three losses to teams below 100 on the RPI list. No team with more than one such loss received a #1 seed in the 15 years of historical CTD data.

Mocking the Bracket

Sun, 15 Mar 2015 18:00:00 +0000

Click here for the latest update.

First, let’s identify which teams are prohibited from certain sites based on committee criteria.

A team will not be permitted to play in any facility in which it has played more than three games during its season, not including exhibitions and conference post-season tournaments.

A host institution’s team shall not be permitted to play at the site where the institution is hosting. However, the team may play on the same days when the institution is hosting.

In addition to those criteria, BYU does not play on Sunday for religious reasons, so they cannot be assigned to a pod or region with Sunday games scheduled.

Pod site prohibitions (not comprehensive)

Jacksonville - Jacksonville

Louisville - Louisville

Pittsburgh - Duquesne

Portland - Oregon

Charlotte - UNC-Charlotte, BYU

Columbus - Ohio State, BYU

Omaha - Creighton, BYU

Seattle - Washington, BYU

Region site prohibitions (not comprehensive)

Cleveland - Cleveland State

Los Angeles - Pepperdine

Houston - Rice, Houston, BYU

Syracuse - BYU

Remember, this is not my opinion of how the bracket will look at 6 p.m. on Selection Sunday. It is an exercise in placing teams in the bracket based on the latest 1-68 seed list generated by the CTD seeding model (as of 1 p.m. ET Sunday).

The committee will place the four No. 1 seeded teams 1 through 4 in each of the four regions, thus determining the Final Four semifinals pairings (overall 1 vs. 4; 2 vs. 3).

The main principle when placing teams into the bracket is:

Teams will remain in or as close to their areas of natural interest as possible. A team moved out of its natural area will be placed in the next closest region to the extent possible. If two teams from the same natural region are in contention for the same bracket position, the team ranked higher in the seed list shall remain in its natural region.

So, without further ado, let’s get started. And it’s a pretty easy start.

1. Kentucky - Midwest (Cleveland)

It is no surprise that Kentucky is the overall #1 seed, and it is no surprise that the Wildcats are sent to the nearest region. Next.

2. Villanova - East (Syracuse)

The other Wildcats are also pretty easy to slot into their natural and closest region.

3. Wisconsin - South (Houston)

While better than being placed as the #2 in Kentucky’s region, the Badgers would have to travel a little more than they’d prefer. Cleveland and Syracuse are each closer to Madison, but they’re already taken. Houston it is.

4. Virginia - West (Los Angeles)

The gap between the Cavs and Duke is so razor thin that they keep flip flopping back and forth in the 4 and 5 spots. Not that they get a say in the matter, but Virginia would probably prefer traveling West for the regional than having to be the 2 seed in Kentucky’s bracket. Los Angeles is obviously farther from Charlottesville than the other three sites, but Hollywood is the only option.

Now that we’re done with the #1 seeds, there are a few other rules that start coming into play.

Each of the first four teams selected from a conference shall be placed in different regions if they are seeded on the first four lines.

5. Arizona - West (Los Angeles)

Arizona would’ve been in the West region if they had moved up to the 1 line, so it probably doesn’t make that much of a difference that they’re a 2. Off to L.A. they go. “S-Curve” advocates would be happy that the best 2 would be paired with the worst 1.

6. Duke - East (Syracuse)

@nicoleauerbach Would be so much more interesting if Duke loses tonight and they're sent to Kentucky's region. Conspiracy theorist's dream!
— Crashing the Dance (@crashthedance) March 14, 2015

This is where things start to get interesting, and where “natural regions” becomes a little hazy. Durham is closer to Cleveland than to Syracuse, but “Midwest” isn’t the first thing that comes to mind when thinking about ACC teams, their most recent tournament champ aside.

So, does 100 extra miles trump regional sensibilities? We’ll assume the committee agrees that North Carolina is not in the Midwest and send Duke to Syracuse. Conspiracy theorists will have to wait, unless they think that Virginia was sent west so Duke could stay closer to home.

7. Iowa St. - Midwest (Cleveland)

Straightforward here. The Big 12 champs are sent to their closest and most natural region.

8. Kansas - South (Houston)

While the South isn’t the Jayhawks’ most natural region fit, Houston is the closest site so it’s not a bad compromise.

The committee will then place the No. 3 seeds in each region in true seed list order.

9. Gonzaga - South (Houston)

The fall to the 3 line actually would benefit the Bulldogs geographically, as they stay closer to home than they likely would have if they were a 2 behind Arizona.

(Update: Gonzaga was moved to the South to accommodate the Big 12 conflicts on the 3 seed line. Not so much a geographic benefit after all.)

10. Notre Dame - Midwest (Cleveland)

The ACC tournament champs are a better fit in the Midwest than their conference comrades, and with Cleveland being closest and open on the 3 line, there they would normally go. However…

11. Oklahoma - West (Los Angeles)

12. Baylor - East (Syracuse)

Houston, we have a problem. (Sorry.) The next two teams on the mock seed list are both in the Big 12, and one of the primary bracketing rules is:

Each of the first four teams selected from a conference shall be placed in different regions if they are seeded on the first four lines.

There are only two regional spots left on the 3 seed line, and one of them (South) already has a Big 12 team. That means that neither Oklahoma or Baylor could go to the South region.

Rather than reaching up and shifting teams around on the 2 line, which would unfairly punish teams higher up the list, we’ll have to shuffle teams on the 3 line to make things work. Gonzaga would move to Houston (its next closest site) and Notre Dame would stay in Cleveland.

Oklahoma is marginally closer to L.A. than to Syracuse, to the Sooners go west while Baylor heads east.

Whew.

The committee will then place the No. 4 seeds in each region in true seed list order.

13. Maryland - East (Syracuse)

14. North Carolina - South (Houston)

15. Arkansas - West (Los Angeles)

16. SMU - Midwest (Cleveland)

North Carolina must go to Houston with the other three regions full of ACC teams. Maryland’s best options are within 50 miles of each other, and I debated whether the Midwest (with Maryland now in the Big 10 and all) or the East (with Maryland being on the east coast and all) is a better fit, but the unofficial bracketing committee decided to put the Terps in Syracuse.

Kentucky is already in Cleveland, so Arkansas has to go west. (It’s possible the committee could consider Maryland and Arkansas together and optimize the total distances by putting Maryland in Cleveland and Arkansas in Syracuse, but that doeesn’t seem to be how they do it.) The final four seed then goes to Cleveland, which will make the “S-Curve” activists happy.

Reload for the latest updates

After the top four seed lines have been assigned, the committee will review the relative strengths of the regions by adding the “true seed” numbers in each region to determine if any severe numerical imbalance exists. Generally, no more than five points should separate the lowest and highest total.

No problem on the balance here. East (33), Midwest (34), South (34), and West (35) are all within two points. “S-Curve” purists, rejoice!

In “true seed” order, the committee then assigns each team (and, therefore, all teams in its bracket group—e.g., seeds 1, 8, 9, 16) to second-/third-round sites.

In other words, take the 16 teams and place them into a pod site to determine where each will play its second-/third-round games. Each of these teams is the highest seeded team in pod of four teams, and the other teams in each pod automatically follow that pod site. This is important when slotting the other teams into the bracket to satisfy other rules.

1. Kentucky - Louisville

2. Villanova - Pittsburgh

3. Wisconsin - Columbus

4. Virginia - Charlotte

5. Arizona - Portland

6. Duke - Charlotte

7. Iowa St. - Omaha

8. Kansas - Omaha

9. Gonzaga - Seattle

10. Notre Dame - Columbus

11. Oklahoma - Louisville

12. Baylor - Jacksonville

13. Maryland - Pittsburgh

14. North Carolina - Jacksonville

15. Arkansas - Portland

16. SMU - Seattle

Wisconsin is almost the same distance from Omaha, Louisville, and Columbus. We’ll take the NCAA at their word about regional “fit” and send them to Columbus. Same with Virginia and Charlotte vs. Pittsburgh. Same with Arizona and Omaha vs. Portland. The rest are relatively straightforward.

What does Gonzaga deserve?

Sun, 22 Feb 2015 01:00:00 +0000

The funny thing about #1 seeds is that there are only 4 of them. If there are more than 4 teams that “deserve” one, guess what happens?

Right now, the CTD seeding model says that Gonzaga’s resume does in fact “deserve” a #1 seed. However, so do the resumes of 5 other teams.

If Kentucky, Wisconsin, Villanova win out, and Duke and Virginia win out until the ACC final, you could easily say each of them also deserves a #1 seed.

Gonzaga may end up with a #1 seed (and if they do, they’ll follow the Seattle to Los Angeles path, but if they win out and don’t get a #1 seed, it doesn’t mean that they didn’t deserve it.

It’s just like at-large selections. There might be more or fewer than 36 teams that “deserve” spots, but the committee has to pick exactly 36.

What are the odds?

Wed, 26 Mar 2014 03:27:13 +0000

Much like FiveThirtyEight after leaving the New York Times, our blog went dark until March. Fortunately, another March has brought another year of FiveThirtyEight NCAA tournament probabilities and with it our annual attempt to use those to calculate the probabilities of interesting results starting with the Sweet 16.

43.4% probability of a #1 seed winning the championship

20 champs have been #1 seeds - most since seeding began in 1979

9.7% probability of #2 seed winning the championship

Six champs have been #2 seeds - second most since seeding began

2.8% probability of #3 seed winning the championship

Five champs have been #3 seeds

29.4% probability of #4 seed winning the championship

The only #4 seed to win a title was Arizona in 1997. Louisville (16.8%) and Michigan State (8.0%) have non-trivial chances this season.

14.6% probability of #5 or lower seed winning the championship

Only three previous champions (#6 N.C. State 1983, #6 Kansas 1988, #8 Villanova 1985) were seeded 5th or lower.

9.3% probability of three #1 seeds in the Final Four

Three or more #1 seeds have made it four times since seeding began

13.9% probability of no #1 seeds in the Final Four

A #1-free Final Four has happened three times since seeding began (last in 2011)

9.9% probability of an Arizona vs. Florida final

The most likely championship game pairing

3.4% probability of a team from the play-in game first round in the Final Four

Tennessee has a chance to do what VCU also did in 2011 as an 11 seed.

3.3% probability of all-B1G championship game matchup

One Big Ten team has won the national championship in the last 24 seasons (2000 Michigan State)

1.4% probability of all three remaining B1G teams in the Final Four

The 1985 Final Four saw three teams from the Big East. No other conference can get three teams in the Final Four this season.

42.2% probability of no B1G teams in the Final Four

For completeness, the conference could also place two teams (13.8%) or one team (42.7%). Michigan State (32.2%) is the most likely to make it.

20.3% probability of two remaining SEC teams in the Final Four

The Pac 12 (15.0%), Big 10 (13.8%), AAC (9.1%), and Big 12 (2.3%) could also see two teams reach North Texas.

20.2% probability of a first-time national champion

Dayton, Virginia, Iowa State, Baylor, San Diego State, and Tennessee have yet to cut down the last nets of the season. The other 10 schools have a combined 33 championships.

64.5% probability of a team from the state of Kentucky in the Final Four

Kentucky (15) and Louisville (10) have a combined 25 Final Four appearances.

35.6% probability of an Elite Eight rematch of last year's Louisville/Michigan championship game

19.2% probability of a Final Four rematch of the 2000 Michigan State/Florida championship game

14.2% probability of an Elite Eight rematch of the 1967 UCLA/Dayton championship game

8.8% probability of a Final Four rematch of the 1997 Arizona/Kentucky championship game

2.4% probability of a rematch of the 1980 Louisville/UCLA* championship game

UCLA and Louisville met three times in the Final Four (1972, 1975, 1980). Only one Final Four matchup has occurred more times (North Carolina and Kansas have met in four Final Fours).

2.3% probability of a Final Four rematch of the 1948 Baylor/Kentucky championship game

0.7% probability of a rematch of the 1965 UCLA/Michigan championship game

100% probability of a Sweet 16 rematch of the 2006 Florida/UCLA championship game