Last year, I put together the probabilites of several interesting results prior to the Sweet 16 based on Nate Silver's intial attempt at forecasting March Madness for the New York Times' FiveThirtyEight blog. Mr. Silver used a combination of computer power rankings and seeds, with adjustments for geography, injury, and other factors, to generate probabilities for each team reaching a particular round in the bracket.

I didn't have time to do this before Thursday night's games, but there are still some interesting outcomes to consider.

These all assume the outcome of each region is independent. I think my math is right, but feel free to correct me if you notice anything wrong.

44.9% probability of a #1 seed winning the championship

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

11.0% probability of three #1 seeds in the Final Four

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

12.2% probability of no #1 seeds in the Final Four

A #1-free Final Four has happened three times since seeding began, including last season

16.5% probability of a Kentucky vs. Ohio State final

The most likely championship game pairing

31.5% probability of #2 seed winning the championship

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

4.3% probability of #3 seed (Baylor) winning the championship

Last year's champion (UConn) was a #3 seed.

0.8% probability of #10 seed or lower winning

Villanova (#8 seed) in 1985 is the lowest seed to win the championship

34.8% probability of all-SEC Final Four matchup (Kentucky vs. Florida)

There has never been an all-SEC Final Four game, despite ten championships between three teams

8.8% probability of both remaining Big 12 teams making the Final Four

More likely, there is an 44.7% chance neither will

2.3% probability of all-Big East final (Louisville vs. Syracuse)

Would be the first since Villanova defeated Georgetown in 1985.

0% probability of a rematch of last year's UConn/Butler championship game

A championship game rematch has not happened since 1961 and 1962 (Cincinnati defeated Ohio State both years)

8.9% probability of a rematch of the 2007 Florida/Ohio State championship game

15.8% probability of a rematch (in the semifinals) of the 2003 Syracuse/Kansas championship game (in New Orleans)

6.3% probability of a rematch of the 1996 Kentucky/Syracuse championship game

0.7% probability of a rematch of the 1987 Indiana/Syracuse championship game (in New Orleans)

1.2% probability of a rematch of the 1981 Indiana/North Carolina championship game

Several years ago, I unveiled net efficiency margin, or NEM, as a way to measure a team's game-by-game performance on a tempo-free, opponent-adjusted basis. NEM is derived from Ken Pomeroy's adjusted efficiency numbers. Charting NEM over the course of a season shows the "shape" of a team's season in a way that a single number or even a table of numbers can't.

Let's look at the teams remainig in each region to find some hidden nuggets that might not be obvious in the season power ratings. All charts show five-game running averages to smooth out the normal game-to-game noise. Remember that NEM inherents the strengths and weaknesses of Pomeroy's system.

South Regional

When Kentucky peaked, they peaked, but they've dropped off noticably over the last several games. I'd still take them to win the South, but the gap between the Cats and Indiana and Baylor isn't as large as it was several weeks ago. Perhaps, that's why...

East Regional

Ohio State just took over the #1 spot in the Pomeroy ratings, and the Buckeyes are the only team with clear NEM separation over their regionmates. Wisconsin is closest to the Buckeyes (though some of that may be the Pomeroy system's affinity for the Badgers, so an all B1G regional final wouldn't be a surprise.

Midwest Regional

Nobody outside of the Dean E. Smith Center knows the (Kendall) Marshall Plan, so assessing the Heels' chances in St. Louis is tricky. Their Triangle neighbor NC State may be playing the best right now of all four Midwest teams. The Wolfpacks' NEM trendline just converged with North Carolina's, and Kansas has been trending downward since late February. At the very best, the Heels will have a limited Marshall running the show, so the first Wolfpack berth in the Final Four since the Jimmy V era isn't as far fetched as it sounded several weeks ago.

West Regional

The West seems pretty wide open. Florida's surge is probably slightly exaggerated by their two strong tourney games, but all four seem to be peaking at the right time. Michigan State still seems like the favorite here.

All raw efficiency data is from the sublime kenpom.com. I used the ratings through last Sunday's games to make the comparisons. (For my second round reviews, I'll update the ratings through the end of the first round, and so on.)

Top overall performances

Top offensive performances

Top defensive performances (lower scores are better)

All raw efficiency data is from the sublime kenpom.com. I used the ratings through last Sunday's games to make the comparisons. (For my second round reviews, I'll update the ratings through the end of the first round, and so on.)

Top overall performances

Top offensive performances

Top defensive performances (lower scores are better)

First, a caveat. Even a full season of games is not always enough to know whether a team's numerical assessment reflects its true talent, so when we start looking at a subset of those games, misleading numbers can be more likely.

That said, some teams may have built up their high ranking against the nether regions of Division 1, while others have played their best games against the top of the heap. Of course, winning in the NCAA Tournament means you have to beat the best.

We can use Net Efficiency Margin, or NEM, to try to identify the teams that have built up their power rating against weaker teams and those that may be underrated in the tournament because they played down to lesser competition.

These teams may be overrated by Pomeroy's ratings (minimum 5 games against 201+ teams):

Two of those teams (Wisconsin and Montana) meet up in the round of 64, and chic Final Four sleeper Wichita State also shows up in the list. Only five of the Shockers' 31 games came against teams outside the KenPom top 200, so this could just be a statistical oddity.

These teams may be underrated by Pomeroy's ratings (minimum 5 games against top 100 teams):

We have a pair of round of 64 matchups (Ohio vs. Michigan and Kansas State vs. Southern Miss) among these teams. Michigan played 22 of their 32 games against KenPom top 100 competition, giving more credibilty to their inclusion on the list. Ohio only played 6 games against the top 100.

Selection Sunday is finally here. I may make some small tweaks, but otherwise this is it. (See the BubbleGrid refresher if you have questions.)

BubbleGrid reminders:

• Hover over a value for more information
• Shaded teams are predicted to be in the field
• Teams with a * are the projected automatic qualifier (AQ) for their conference. Bold shaded teams have clinched the AQ berth
• Teams are listed in order of their selection confidence by the CTD model. In other words, the last shaded non-AQ team is the last team in, and the first non-shaded team is the first team out.

1 day to Selection Sunday. The cut line is getting a little more defined, but there will be several teams in the field that don't have at-large worthy profiles by historical standards. (See the BubbleGrid refresher if you have questions.)

To help you identify where that line is, I've added a score column to the grid. The selection score is a number from 0 to 100 describing how likely that team's profile would be an at-large selection based on at-large profiles over the past 12 years. The CTD selection model looks at all at-large teams (and conference champs that I've estimated would have been at-large selection based on their seed) during that period and calculates the score for each team. The list of CTD at-large teams is the 37 with the highest selection score among those who are not (or not forecast to be) conference champs.

This score is not a likelihood or forecast of whether each team will in fact make the field on Sunday. It is only a estimate of whether that team's profile is at-large worthy, based on what the committee has done in the past using the profile attributes they've publicly said are important.

A few other random comments:

• We've had Iona in the at-large pool for quite a while, but they've slid all the way down to the final team in the field. Precarious spot with a number of AQ spots still in play.
• Marshall has jumped into the field, but don't get too excited. If they lose to Memphis, I expect they'll drop right back out.
• The teams with selection scores less than 0.1 can move up or down quickly with only small changes in their profile, so don't get too up or down if your team is one of those. The gaps between the teams near the cut line are small (as they always are), so small changes are amplified.

BubbleGrid reminders:

• Hover over a value for more information
• Shaded teams are predicted to be in the field
• Teams with a * are the projected automatic qualifier (AQ) for their conference. Bold shaded teams have clinched the AQ berth
• Teams are listed in order of their selection confidence by the CTD model. In other words, the last shaded non-AQ team is the last team in, and the first non-shaded team is the first team out.

2 days to Selection Sunday. At this point, it's easy to overreact to one game, so remember to look at the season as a whole. (See the BubbleGrid refresher if you have questions.)

• Hover over a value for more information
• Shaded teams are predicted to be in the field
• Teams with a * are the projected automatic qualifier (AQ) for their conference. Bold shaded teams have clinched the AQ berth
• Teams are listed in order of their selection confidence by the CTD model. In other words, the last shaded non-AQ team is the last team in, and the first non-shaded team is the first team out.

Despite the NCAA's recent attempts at transparency (which I applaud), many in the public still don't understand exactly how the selection committee builds the bracket. You can become an expert by reading the full details here, but it boils down to three steps: selection, seeding, and bracketing.

Crashing the Dance attempts to predict the selection and seeding based on the committee's past behavior, but not the placing of teams into the bracket. Once the 1-68 seed list (also known as the S-Curve) is set, bracketing is essentially a straighforward algorithm.

I decided to try my hand at following the committee's published bracketing procedure using the latest (through Wednesday's games) Crashing the Dance 1-68 seed list. Keep in mind this is in no way meant to predict how Sunday's bracket will turn out. This is merely an exercise to demonstrate how the committee could bracket a theoretical S-Curve using the actual sites and bracketing principles. That said, we may gain some insight into decisions the committee will have to make Sunday and how some scenarios could play out.

Before we start assigning region and pod sites, let's identify which teams are prohibited from certain sites based on the committee's 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 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)

Albuquerque - New Mexico

Louisville - Louisville

Pittsburgh - Duquesne

Portland - Oregon

Columbus - Ohio State, BYU

Omaha - Creighton, BYU

Greensboro - BYU

Nashville - BYU

Region site prohibitions (not comprehensive)

Boston - Boston College

Phoenix - Arizona State

Atlanta - Georgia Tech, BYU

St. Louis - Saint Louis, BYU

The committee will then place the four “number 1 seed” teams seeded 1 through 4 in each of the four regions, then determine the Final Four semifinals pairings, making best effort to pair the top No. 1 seed’s region against the fourth No. 1 seed’s region and the second No. 1 seed’s region against the third No. 1 seed’s region.

The main principle to follow on the first line is teams will remain in or as close to their areas of natural interest as possible.

1. Kentucky - South (Atlanta)

Atlanta and St. Louis are roughly the same distance from Lexington, depending on exactly how you measure, and St. Louis could actually be much closer for travelers from the western part of the bluegrass state. With Missouri moving to the SEC, you could argue that St. Louis is also a "natural" region forKentucky. However, Atlanta seems the more natural region for Kentucky, especially given the recent frequency of the Georgia Dome as host of the SEC Tournament.

2. Syracuse - East (Boston)

Boston is closer to Syracuse than any regional site, so the Orange get their first choice.

3. North Carolina - Midwest (St. Louis)

Of the two remaining regions, St. Louis is the closer site to Chapel Hill. It is possible that the committee could put Kentucky in St. Louis in order to put North Carolina in Atlanta, saying that it would minimally affect Kentucky's travel and substantially help North Carolina's, though precedent for this is unclear. We'll keep it simple.

4. Kansas - West (Phoenix)

No teams on the top several seed lines claim the West as their natural region, so the fourth No. 1 seed will almost certainly be shipped to Phoenix.

In this scenario, the Final Four pairings will be South vs. West and East vs. Midwest. (I'm not clear why the "making best effort" part is in there. I can see no other bracket principles that conflict pairing 1 vs. 4 and 2 vs. 3.)

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

This is when several of the bracketing principles can come into play, including:

Each of the first three teams selected from a conference shall be placed in different regions.

Conference teams shall not meet prior to the regional final unless a ninth team is selected from a conference. If the committee is unable to reconcile the bracket after exhausting all reasonable options, it has the flexibility to waive this principle to permit two teams from the same conference to meet each other after the second round.

5. Ohio State - Midwest (St. Louis)

St. Louis is slightly closer than Atlanta to Columbus, and there are no conflicts yet for a Big Ten team, so there they go.

6. Michigan State - South (Atlanta)

Michigan State would also prefer St. Louis, but the Buckeyes have already claimed the Jones Dome. All four Big 10 teams claim St. Louis as their closest and most "natural" region, so there is plenty to play for this weekend even if the conference yields no 1 seeds.

7. Duke - West (Phoenix)

8. Missouri - East (Boston)

On the first pass, Duke was assigned to the East with Boston as the second-closest region to Durham. That would then leave the West as the only option for Missouri on the No. 2 line, but with Kansas already in Phoenix the Tigers cannot be placed there. We could keep Duke in Boston and move Missouri down to the No. 3 line, but moving a team up or down a line does not happen often for teams in the top 4 lines, so we'll just swap Duke and Missouri. We may need to revisit this later when we assess competitive balance.

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

Additional bracketing principles can come into play on the third line, including:

No more than one team from a conference may be seeded in the same grouping of four in line Nos. 1-4 and 13-16 in a region, unless a conference has four or more teams seeded in line Nos. 1-4. In lines No. 5-12, two teams from the same conference may be placed in the same group of four

9. Marquette - Midwest (St. Louis)

Despite playing the Big East, Marquette claims St. Louis as its closest region. No conference conflicts prevent this.

10. Indiana - East (Boston)

St. Louis and Atlanta are closer to Bloomington, but both have already been claimed by Big Team teams, so the Hoosiers are shipped up to Boston.

11. Georgetown - South (Atlanta)

Syracuse is already in Boston, so Georgetown goes to the next closest site.

12. Michigan - West (Phoenix)

With four Big Ten teams in the field so far, Michigan could be placed in the same region as one of its conference brethren. However, all four are on the No. 2 or 3 lines and could meet before the regional final, which is prohibited. We'll put Michigan in the West region for that reason, but with the last No. 1 and No. 3 seed in Phoenix, competitive balance could be a problem down the road. We may have to come back to this.

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

13. Baylor - Midwest (St. Louis)

Interestingly, no Big 12 teams are yet in St. Louis, so Baylor get its wish. For now. St. Louis has the best team on three of the four lines, so somebody will probably have to move when we assess competitive balance.

14. Wisconsin - South (Atlanta)

The fifth Big Ten in the field means we'll have to be careful again with conference placement as with Michigan. St. Louis is already taken on the No. 4 line, and Atlanta is the next closest region. Michigan State is the 2 seed there, but they wouldn't meet Wisconsin until the regional final.

15. Wichita State - West (Phoenix)

Finally, a fresh conference means no worries about conflicts. The Shockers end up in Phoenix with St. Louis and Atlanta already taken.

16. UNLV - East (Boston)

The only slot left for UNLV is Boston, which unfortunately is the farthest from Vegas of the four regions. All hope is not yet lost for the Rebels, because…

After the top four seed lines have been assigned, determine 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.

Uh oh. Here's how the numbers add up:

Midwest: 30

South: 32

East: 36

West: 38

For now, the Midwest and South regions are more difficult (based on each team's "true seed" number) than the East and West. That means we'll have to do a little tweaking to balance that.

What options do we have? This is where the published guidance from the committee gets vague. We do know that teams ranked higher on the 1-68 seed list generally should get geographical preference:

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.

(By the way, this principle is why I think Kentucky will stay in the South.)

First, let's swap Wisconsin and Baylor to balance the South and Midwest

Having two Big Ten teams on each of the No. 2 and No. 3 lines makes many of the possible swaps impossible. We want to keep Ohio State in St. Louis as its preferred geography, but beyond that we may have to make some changes. We're going to swap the 2 and 3 seeds between the South and West.

Now we have:

Midwest: 31

South: 33

East: 36

West: 36

Five points difference between the lowest and highest. Good enough for now.

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, we need to assign pod sites for each of the 16 teams we've placed in regions. Most in the first several lines get their preferred site.

1. Kentucky - Louisville

2. Syracuse - Pittsburgh

3. North Carolina - Greensboro

4. Kansas - Omaha

5. Ohio State - Pittsburgh

Ohio State is prohbited from the Columbus pod.

6. Michigan State - Columbus

7. Duke - Greensboro

8. Missouri - Omaha

9. Marquette - Columbus

10. Indiana - Louisville

11. Georgetown - Nashville

Georgetown is the first team that wouldn't get its preferred pod site (Pittsburgh). In fact, their first four pod sites are already filled.

12. Michigan - Nashville

13. Baylor - Albuquerque

This is actually the closest site to Baylor, so as long as they are on the third seed line or one of the better four seeds, that's where they should end up.

14. Wisconsin - Albuquerque

15. Wichita State - Portland

16. UNLV - Portland

In Episode II, we'll tackle the remainder of the seed lines. There are fewer restrictions in the 5-12 lines, and generally fewer conference conflicts in the 13-16 lines, so they may not be quite as exciting.

5 days to Selection Sunday. Several of the better mid-major teams failed to win their conference tournaments, leaving therir fate in the hands of the committee. Drexel, Iona, MTSU, and Oral Roberts must wait, and each has a marginal at-large profile at best by historical standards. We'll see how much the "eye test" comes into play. (See the BubbleGrid refresher if you have questions.)

• Hover over a value for more information
• Shaded teams are predicted to be in the field
• Teams with a * are the projected automatic qualifier (AQ) for their conference. Bold shaded teams have clinched the AQ berth
• Teams are listed in order of their selection confidence by the CTD model. In other words, the last shaded non-AQ team is the last team in, and the first non-shaded team is the first team out.

Cincy fan. Has anyone +3 vs top 50 ever missed? Stands out huge on bubble grid.

And the answer is… yes and no.

In my 12 years of historical selection and seeding data, there are 129 teams with records +3 over .500 or better against RPI top 50 teams. Of those teams, none of the eligible teams missed the field.

Notice how I said that.

In 2005, Ohio University was 5-1 against top 50 teams (though all were ranked 26-50) and were ranked 48th as of Selection Sunday. The Bobcats eliminated any at-large doubt by winning the MAC Tournament, but since they were seeded 13th - two seed lines behind the last at-large - they likely would not have been selected at-large.

After beating Arizona State on January 2, 2010, Southern Cal sported a 10-4 record and sat 30th in RPI. On January 3, 2010 the university announced self-imposed sanctions against the men's basketball program, including a ban on postseason that season.

The Trojans lost 10 of their last 16 games, including the final five, and finished the season ranked 112th and would not have made the field had they been eligible. Oddly enough, three wins after the sanctions announcement were over top 50 teams, propelling USC to a 6-3 record against the top 50.

So, while technically no eligible teams +3 or more over .500 against the top 50 missed the field, two of them probably would not have been selected at-large. Still, I'd take those odds.

The best month of the year is now here. 10 days to Selection Sunday. (See this to learn what it's all about.)

• Hover over a value for more information
• Shaded teams are predicted to be in the field
• Teams with a * are the projected automatic qualifier (AQ) for their conference. Bold shaded teams have clinched the AQ berth
• Teams are listed in order of their selection confidence by the CTD model. In other words, the last shaded non-AQ team is the last team in, and the first non-shaded team is the first team out.

I'll break out NEM in full force during the NCAA Tournament as I have the last few seasons, but here are few nuggets to whet your appetite. All numbers are through Tuesday's games.

South Florida

With three key players missing parts of the first month, South Florida was not at full strength until mid-December. Since then, the Bulls have gone 11-5 against a relatively weak Big East schedule. NEM shows us that even considering the quality of their opponents, USF has been playing solid defense since getting back to full strength.

Reminder: Larger numbers are better for offensive NEM and smaller numbers are better for defensive NEM. NEM values are points per 100 possessions and are adjusted for quality of opponent and game location.

To put the -13.0 in context, that would be rank their defense in the top 15 nationally. The committee may consider the impact of missing players on the their early season struggles, which may be enough to keep them on the good side of the cut line.

Duke and Indiana

These two schools are linked by the two winningest coaches in D-1 men's history, but they couldn't be more different in one aspect this season.

While Duke's defense has improved since bottoming out in late January, the Blue Devils are still playing about 5 points per 100 possessions better away from Cameron. This isn't surprising, given how they just completed a perfect ACC road season while dropping two home conference games with one more remaining.

Indiana, on the other hand, is taking advantage of the rejuvenated crowds at Assembly Hall this season. Again, given the powerhouse teams the Hoosiers have beaten at home, this is no surprise.

I'll use this more over the last 13 days before Selection Sunday, but tonight I'll just post the BubbleGrid without comment. (See this to learn what it's all about.)

• Hover over a value for more information
• Shaded teams are predicted to be in the field
• Teams with a * are the projected automatic qualifier (AQ) for their conference. Bold shaded teams have clinched the AQ berth
• Teams are listed in order of their selection confidence by the CTD model. In other words, the last shaded non-AQ team is the last team in, and the first non-shaded team is the first team out.

I'm here to set the record straight: this year's bubble is not historically bad. In fact, the teams around the at-large cut line in any given year are not bad teams at all. Let me explain with a little bit of high school math.

Most power rankings (e.g., Sagarin) and statistics (including Pomeroy's adjusted efficiencies) show that teams roughly follow a normal distribution. You may know this as a bell curve, though perhaps a slightly asymmetric one.

While this has several implications, two are relevant here. First, there are fewer teams at each end of the distribution. You generally hear few disagreements about which are the very best teams or the very worst teams. More importantly, as you move toward the middle of the distribution, teams are more bunched together and therefore less distinguishable.

These teams are still good teams, mind you; they are the best 50(ish) teams out of about 350 that play in the best of three NCAA divisions. They are just harder to compare to each other because a normal distribution means the difference between the 41st and 51st best teams is much smaller than the difference between the 1st and 11th best. Expanding the at-large field by three teams has slightly worsened the effect, but it is still nothing more than an inherent statistical property.

So, no, the bubble isn't full of "historically" bad teams this year or any other year for that matter.

It's just normal.