Wednesday, April 4, 2012

Tournament Summary 2012 - Final Results

Here is the final chart showing how conferences did compared to expectations:

Expected Record Actual Record % of Wins Expected
SEC 8.2 - 4.8 10-3 122%
Big 12 9.6 - 6.4 10-6 104%
Big Ten 10.7 - 6.3 11-5 103%
A10 2.9 - 4.1 3-4 103%
Pac 12 1.0 - 2.0 1-2 100%
Big East 13.7 - 9.3 13-10 95%
WCC 2.1 - 2.9 2-3 95%
ACC 6.6 - 4.4 6-5 92%
MVC 1.4 - 1.6 1-2 71%
Mountain West 2.9 - 2.1 1-4 34%

Significantly better than expected: SEC
Significantly worse than expected: Mountain West

I find it interesting to look at how close to expectations conferences performed on average this year.  Compare this to last year where there were quite a few over/underacheivers and only 3 conferences finished in the 90-110% range.  7 conferences in the 90-110% range this year shows that most conferences generally performed about as we would have expected them to, given their seeding.

Don't forget, my list of the most impressive and disappointing tournament teams of the past 2 decades will be stating soon.  I will start with the most average performances and work my way out towards both ends of the spectrum.

Wednesday, March 28, 2012

Tournament Summary 2012 - Final 4

Here are the updated standings now that we are down to 4.

Expected Record Actual Record % of Wins Expected
SEC 7.0 - 4.0 8-3 114%
Big Ten 10.2 - 5.8 11-4 108%
Big 12 8.6 - 5.4 9-5 105%
A10 2.9 - 4.1 3-4 103%
Pac 12 1.0 - 2.0 1-2 100%
Big East 13.4 - 8.6 13-9 97%
WCC 2.1 - 2.9 2-3 95%
ACC 6.6 - 4.4 6-5 92%
MVC 1.4 - 1.6 1-2 71%
Mountain West 2.9 - 2.1 1-4 34%

Tuesday, March 20, 2012

Predicting A Perfect Bracket

If you are reading this blog, you are probably one of the millions of Americans who filled out a bracket predicting how the NCAA Men's Basketball Tournament would play out.  Chances are that your first miss happened sometime around Thursday afternoon.  If you were lucky, you made it to Thursday night, and a rare few of you might have even made it to Friday.  If you made it through the entire first 4 days, congratulations!  You are in the top 1% of the top 1% of the top 1% of all brackets.  You are 1 in a million!
How can it be this hard?  With millions of Americans filling out brackets (sometimes more than one bracket per person), shouldn’t there be a handful of perfect brackets every year?  Although this represents the sentiments of many, the truth is that predicting a perfect bracket is nearly impossible.  To my knowledge, there are exactly ZERO confirmed cases of perfect brackets for any of the tournament’s 27 years since expanding to 64 teams in 1985.  The expansion to 65 teams in 2001 (and to 68 teams in 2011) doesn’t seem to have had any effect since most people ignore these new play-in games and start with the round of 64 regardless.  For 27 straight years millions of people have attempted to correctly predict the outcome of 63 separate games.  Add it all together and you have close to a billion attempts to accomplish this feat, and as far as we know, a billion failures.  As hard as this seems to fathom at first, a little math can go a long way towards explaining this phenomenon.

Let’s start with something really simple.  Obviously, some games (1 vs 16) are easier to predict than others (8 vs 9), but what if everyone just flipped a coin to determine each of the winners?  50/50 seems easy enough.  Give people a billion chances at picking correctly 63 times in a row and someone will do it, right?  Wrong.

Chances of correctly picking a coin flip 2x in a row: 1 in 4
Chances of correctly picking a coin flip 5x in a row:  1 in 32
Chances of correctly picking a coin flip 10x in a row: 1 in 1,000
Chances of correctly picking a coin flip 20x in a row: 1 in a million
Chances of correctly picking a coin flip 30x in a row: 1 in a billion
Chances of correctly picking a coin flip 40x in a row: 1 in a trillion
Chances of correctly picking a coin flip 50x in a row: 1 in 1,000 trillion
Chances of correctly picking a coin flip 63x in a row: 1 in 9 quintillion (that’s 9 million trillion!!)

As you can see, while the chances of predicting a coin flip start out good, it quickly becomes almost impossible as the number of consecutive attempts increases.  Using our assumption that there have been about a billion attempts to pick the bracket over the last 27 years, there would need to be 30 games (instead of 63) for us to see a statistical expectation that someone would get them all right based on this coin flip method.

Thankfully, for those of us who want to someday see a perfect bracket, the coin flip method is too restrictive.  It assumes that every game is truly a tossup, something we know not to be true.  In reality, 1 seeds have never lost to a 16 seed, 2 seeds (other than this year) almost always win against 15 seeds, and even 3, 4, and 5 seeds win significantly more than 50% of their 1st round games.  We need to adjust our initial analysis to account for these increased odds.

Let’s pretend that our hypothetical average Joe has a:
- 90% chance of correctly predicting any round of 64 game involving seeds 1-4
- 70% chance of correctly predicting any round of 64 game involving seeds 5-6
- 50% chance of correctly predicting all other games

Does this new adjusted scenario give us much hope of a perfect bracket?  Only a little bit.  Under this scenario, the odds of correctly picking the 32 games in the round of 64 are 1 in 1,600.  Making a perfect bracket up to the Sweet 16?  1 in 100 milion.  In fact, a perfect bracket’s odds would still be less than 1 in 3 trillion.  With 1 billion attempts over the last 27 years, that is a 1 in 3,400 chance of anyone submitting a perfect bracket.  This suggests we could likely go hundreds of years without ever seeing one.

Although I think the last hypothetical was actually too generous, let’s look at one last scenario with even more favorable odds.  Let’s say that every one of the billion attempts we have seen in the past 27 years was made by an expert.  Let’s say they studied every single matchup and made extremely informed decisions.  Let’s even make some rounding errors in their favor.  What if we pretended that everyone had a 90% chance for ALL games in the round of 64, an 80% chance for all games in the round of 32, a 70% chance for Sweet 16 games, and then a 60% chance for all games after that?  In this ideal situation, would we see some perfect brackets?  Check this out:

Chances of correctly picking 32 games (round of 64) with a 90% chance each time: 1 in 29
Chances of correctly picking 16 games (round of 32) with an 80% chance each time: 1 in 36
Chances of correctly picking 8 games (Sweet 16) with a 70% chance each time: 1 in 17
Chances of correctly picking 7 games (Elite 8 through final) with a 60% chance each time: 1 in 36
Combined chances of doing all 4 of the above: 1 in 641,000

Amazingly, if the odds were as easy as our final scenario suggests, we would still only see a handful of perfect brackets each year.  Obviously, the real odds are hard to calculate.  Who’s to say how likely a person is to guess the correct outcome?  What we do know is that the “real” odds fit in somewhere between the extremes that I outlined here.  Although they are much better than the 1 in 9 quintillion coin flip example, they are much worse than the 1 in 641,000 scenario with our “panel of experts”.  The odds are probably even worse than my middle scenario involving an “average Joe”, and those weren’t great at 1 in 3.4 trillion.

Hopefully you feel a little better now about your level of success (or lack thereof) attempting to produce a perfect bracket in years past.  Any given game may feel like a nearly sure thing, but when you stretch things out into a 63 game tournament, things get very difficult very quickly.  If you are one of the extremely rare few who have a perfect bracket going as of today (Tuesday, March 20th, 2012) and are crossing your fingers that you can get another 15 games right, congratulations on your accomplishment to this point, but don’t get your hopes up.  Assuming that the rest of the games from here on out are close to 50/50 toss-ups, your odds of adding another 15 games to your streak: 1 in 32,000.  Good luck!

Monday, March 19, 2012

Tournament Summary 2012 - Sweet 16

I have updated my chart through this weekend's games.  Take a look.

Expected Record Actual Record % of Wins Expected
Big Ten 7.7 - 3.3 9-2 117%
A10 2.7 - 3.3 3-3 111%
SEC 5.0 - 2.0 5-2 100%
Pac 12 1.0 - 2.0 1-2 100%
Big 12 6.0 - 4.0 6-4 100%
ACC 5.1 - 2.9 5-3 98%
Big East 10.3 - 5.7 10-6 97%
WCC 2.1 - 2.9 2-3 95%
MVC 1.4 - 1.6 1-2 71%
Mountain West 2.9 - 2.1 1-4 34%

I am amazed at how close to expectations things have played out so far.  The Big Ten is the only conference with any level of significant overachievement while the Mountain West is the only truly disappointing conference.  In fact, now the the Mountain West has been completely eliminated for the year and have no chance to improve from here on out, I am officially going to nominate them for the "most dissapointing" conference award for not only 2012, but for recent years.  I will write more on this topic in other post, but you can reference last year's conference performances here and see that the Mountain West was disappointing last year as well.

Don't forget that following the season I will begin to release a list of the most impressive and dissapointing teams over the last 2 decades.  It will be done using the same method as my conference analysis, but should be more helpful because there will be a much larger sample size of games.

Saturday, March 17, 2012

Tournament Summary 2012 - Down to 32 Teams

Just like last year, I am going to once again provide a look at how the conferences are doing relative to expectations based on seeding.  For a more detailed breakdown of how I do my analysis, click here for last year's post.  By running the numbers on all the conferences, we can see which conferences have truly over performed and which ones have been disappointing.  It is still early, and the sample size is small, but things are beginning to take shape.

Expected Record Actual Record % of Wins Expected
Pac 12 0.8 - 1.2 1-1 125%
A10 1.7 - 2.3 2-2 118%
WCC 1.8 - 2.2 2-2 111%
SEC 2.8 - 1.2 3-1 107%
Big Ten 4.7 - 1.3 5-1 106%
Big 12 4.0 - 2.0 4-2 100%
Big East 6.6 - 3.4 6-4 91%
ACC 3.5 - 1.5 3-2 86%
MVC 1.2 - 0.8 1-1 83%
Mountain West 2.4 - 1.6 1-3 42%
MAAC 0.6 - 1.4 0-2 0%
CUSA 1.0 - 1.0 0-2 0%

A few notes on the table above:
  • % of Expected Wins is calculated as (actual wins) / (expected wins)
  • First Four games were included. In those cases, games were between evenly matched seeds, so I simply gave each team a 50% chance of winning. This is why the Big East has played 10 games with only 9 teams. (South Florida has won twice already)
  • Only multibid leagues were considered. One bid leagues are way too small a sample size.  For example, Norfolk State won as a 15 seed, giving the MEAC a 1000% in the far right column.
  • The MAAC and CUSA are both really small sample sizes too.  I included them in this chart but will be leaving them off of all updates the rest of the way.

Wednesday, March 14, 2012

Letter to the Selection Committee 2012

Dear 2012 Selection Committee,

I greatly appreciate all the hard work you just went through in order to select the field of 68 for the 2012 NCAA Men's Basketball Tournament. I know that you spent hours studying numerous resumes, probably to the point where they all began to run together. I believe your intentions were honorable and your work ethic commendable, but I would like to make some observations on the results of your labor.

1) Your top 4 seeds were very good.   In fact, I haven't come across a single bracketologist that disagreed with any of those selections by more than 1 seed.  Personally, I think you put a little too much emphasis on Florida's State's ACC Tournament Title, but overall I rate your job in this area as an "A".

2) Let me jump to the other end of the spectrum for a moment.  Long Beach State was an interesting case this year, with a record of 21-1 against teams outside the top 100 but only 2-7 against the top 100.  I'm pleased to see that you looked into those "quality losses" and saw that they were almost all close games, including losing by 4 at San Diego State, 8 at Kansas, 6 at North Carolina, and 2 at Creighton.  It would have been easy to take a team who lost almost every time they faced a quality opponent and dump them in the 13 or 14 seed range, but I am glad that you saw that this is truly a quality team and deserving of a 12 seed.  For looking beyond just wins and losses, I give you an "A+"

3) Before you start thinking I have nothing but compliments, let me address your choice of NC State as an 11 seed and 6 spots ahead of BYU on the S-Curve.  Sending BYU to a play-in game and then to a match up with a #3 seed while NC State gets a bye into the 2nd round where they will face a 6 seed is just plain silly.  Look at the following comparison:

NC State had 2 more chances than BYU to pick up top 50 wins but still tied BYU with just 1
BYU's best win (Gonzaga) was better than NC State's best win (Texas)
BYU was 4-0 against teams 51-100... NC State was 5-2
Each team had 2 bad losses.  BYU's were to RPI #118 & #143.  NC State's were to  RPI #151 & #197

NC State might have played a better non-conference schedule, but they didn't do much with it.  Clearly, BYU had the better resume, and for forcing them into a much less desirable position, I give you a "C-"

4) Some decisions are difficult, while others are easy.  Norfolk State should have been an easy decision.  The fact that you placed them anywhere but the play-in game as a #16 seed makes no sense.  How in the world did you find 6 teams in this year's field that they should be ahead of?  Let's compare them specifically to Long Island, a #16 seed that you ranked behind Norfolk State on your S-Curve.

Long Island had a much better RPI (80 vs 128)
Long Island had a better record vs the top 100 (3-2 vs 2-3)
Long Island had a better record vs teams 101-200 (5-4 vs 2-2)
Long Island had fewer losses outside the top 200 (2 vs 3)
Long Island won a better conference (24th best vs 30th best)

What exactly did Norfolk State do to warrant being ahead of Long Island?  Sure, they beat Long Island head to head, but it was a home game for Norfolk State.  One game should not override every other comparison point.  Most fans don't care that much about the 15 and 16 seeds, but your job is to seed everyone fairly, not just the "big boys".  For this "oversight", I give you a "D+"

5) Last but not least, let me ask you about Iona.  This has been your most scutinized decision in the last 3 days, and rightfully so.  I believe Iona was a bad choice.  They had 0 wins against atlarge worthy tournament teams.  In the loss column, they had 2 losses to teams outside the top 200 and 2 more to teams ranked #115 & #149.  4 bad losses (2 of which were terrible) shouldn't be overcome by a bunch of mediocre wins.  I give you credit for thinking outside the box, but Iona simply beat the teams that atlarge worthy teams should beat.  Due to the bad losses, I don't think they should have been selected, and for this I give you a "C".

For anyone who read my letter to the committee last year, you will notice that this year's letter is much shorter.  Overall, I feel that this was a very good year with few places for significant criticism.  Setting up a bracket is a tough job... much tougher than it first seems.  For doing a quality job I commend you.

For all bracketologists, as well as college basketball fans everywhere,


Official S-Curve released by Selection Committee for 2012

This was the first year that the Selection Committee released their official "S-Curve".  This is the ranking of teams 1-68 prior to attempting to place each of them into the bracket.  Due to rules about matchups that can't happen, the committee is sometimes forced to move teams around slightly.  For example, they might swap a 4 seed and a 5 seed in order to avoid matching up 2 conference opponents in the first round.

Here is the official S-Curve from the Committee:
01) Kentucky
02) Syracuse
03) North Carolina
04) Michigan State
05) Kansas
06) Duke
07) Ohio State
08) Missouri
09) Baylor
10) Marquette
11) Florida State
12) Georgetown
13) Michigan
14) Wisconsin
15) Indiana
16) Louisville
17) Temple
18) Vanderbilt
19) Wichita State
20) New Mexico
21) UNLV
22) Cincinnati
23) Murray State
24) San Diego State
25) Notre Dame
26) Saint Mary's
27) Gonzaga
28) Florida
29) Creighton
30) Iowa State
31) Memphis
32) Kansas State
33) Alabama
34) Connecticut
35) Southern Miss
36) Saint Louis
37) Purdue
38) West Virginia
39) Virginia
40) Xavier
41) Colorado State
42) NC State
43) Texas
44) Colorado
45) California
46) Harvard
47) South Florida
48) BYU
49) VCU
50) Iona
51) Long Beach State
52) Ohio
53) Davidson
54) New Mexico State
55) Montana
56) South Dakota State
57) Belmont
58) Saint Bonaventure
59) Loyola-MD
60) Lehigh
61) Detroit
62) Norfolk State
63) Long Island
64) UNC Asheville
65) Lamar
66) Vermont
67) Mississippi Valley State
68) Western Kentucky

I will have commentary about the S-Curve included in my letter to the selection committee which should be posted sometime tonight.

Monday, March 12, 2012

March_24_7 vs the Bracketology World - 2012 Edition

Here are the results of some of the Bracketologists that you might know:

This was a very good year for March_24_7. As you can see, I beat Joe Lunardi of ESPN (yet again) as well as almost every other nationally known bracketologist. Out of over 100 brackets posted at the Bracket Project, March_24_7 came in 8th.

The following table shows a breakdown of all the big misses (3 seed lines or more). As you can see, BYU was a big surprise to fall to a 14 seed. Creighton was a bit of a surprise to fall to an 8 seed, and on the other end of the spectrum, a few bracketologists were projecting Southern Miss much closer to the bubble than they actually were.

This was the first year that the Selection Committee released their full 1-68 "S-Curve" rankings. This is the order that they ranked each of the 68 teams prior to placing them in the bracket. Due to the multitude of rules for bracketing (avoiding early matchups between schools from same conference, avoiding re-matches from the non-conference season, etc.) the Selection Committee is always forced to make some "adjustments" to this initial S-Curve. The biggest adjustment this year seems to be BYU who was originally slotted as a 12 seed but fell all the way to a 14 in order to fit all the pieces together. Without having been a part of the Committee, it is hard to comment on this move, but it does seem at first glance to be a rather large shift, and Marquette can't be happy with the potential of facing a #14 seed BYU while other #3 seeds will be getting a much easier first round matchup. At the very least, we can conclude that most bracketologists were right to have BYU seeded as an 11 or 12 as forseeing adjustments to the initial S-Curve is almost impossible from an outsiders perspective.

Stay tuned for more analysis of the specifics of this year's brackets. I will once again be writting a "letter to the committee" where I will outline the good and bad I saw in this year's bracket. It should be posted in the next couple days.

Once the games begin, I will be keeping track of conference performances relative to expectations. This will allow us to get a look at which conferences might have been over/underrated based on their total number of qualifying teams as well as the seeding of those teams.

Finally, I am excited to announce a new feature that will begin once the 2012 Tournament comes to a close. Starting in April, I will be building a list of the best and worst NCAA teams based on performance relative to expectations. It will be a way to see just which teams over the last 2 decades have overperformed their seeds and which teams have been most likely to be upset early. My plan is to add 1-2 teams a week to the list so that it is complete sometime around the start of the 2012-2013 season.

Sunday, March 11, 2012

A quick initial reaction to the 2012 Selections

At first look, I'm very pleased with how I did.  I'm completely baffled by the selection of Iona (maybe the worst resume to ever receive an atlarge bid?), and I don't understand how the winner of Iona/BYU will end up as a 14 seed, however, overall I do think the committee did a pretty good job.  Here's a quick summary of my performance.

March 24 7's Results (2012):
67 of 68 teams correctly selected (99%)
62 of 68 teams seeded within 1 seed (91%)
39 of 68 teams seeded exactly correct (57%)

It has been a long stretch of studying resume's leading up to Selection Sunday and I will leave my analysis for tomorrow and the coming week.  Check back regularly for comparisons vs. other notable bracketologists (yes, I beat Joe Lunardi of ESPN... again), a "letter to the Selection Committee", and other general observations as we wait for Thursday and the kick-off to the best sporting event of the year!

Final Projections 2012

Here are my final projections for the 2012 NCAA Tournament.

Multi-Bid Leagues:
Big East:. . .10 (Min: 9, Max: 10)
Big 10:. . . . 6 (Min: 6, Max: 6)
Big 12:. . . . 6 (Min: 6, Max: 6)
ACC: . . . . . 5 (Min: 4, Max: 6)
SEC: . . . . . 4 (Min: 4, Max: 5)
Mountain West: 4 (Min: 4, Max: 4)
A-10:. . . . . 4 (Min: 3, Max: 4)
WCC: . . . . . 3 (Min: 3, Max: 3)
Pac 12:. . . . 2 (Min: 2, Max: 3)
CUSA:. . . . . 2 (Min: 2, Max: 2)
MVC: . . . . . 2 (Min: 2, Max: 2)
Colonial:. . . 1 (Min: 1, Max: 2)

The Seeds
Ranked in order within each seed line, teams in bold have earned auto-bids, teams with * will be in play-in games

1 - Kentucky, Syracuse, North Carolina, Kansas

2Michigan StateMissouri, Ohio State, Duke

3 - Baylor, Marquette, Michigan, Georgetown

4 - Wisconsin, Indiana, Florida State, Louisville

5 - Wichita State, Vanderbilt, Florida, Temple

6 - UNLV, New Mexico, Notre Dame, Murray State

7 - Cincinnati, San Diego State, CreightonMemphis

8 - St. Mary's, Gonzaga, Iowa State, Kansas State

9 - Purdue, Connecticut, St. Louis, Alabama

10 - Virginia, West Virginia, Southern Mississippi, California

11 - Harvard, BYU, Colorado State, Texas

12 - Virginia Commonwealth, Xavier*, South Florida*, North Carolina State*, Seton Hall*, Long Beach State

13 - Colorado, Belmont, New Mexico State, South Dakota State

14Davidson, St. Bonaventure, Ohio, Montana

15 - Lehigh, Loyola-MD, Detroit, Long Island

16 - Lamar, UNC Asheville, Vermont*, Norfolk State*, Mississippi Valley State*, Western Kentucky*

Last 6 In:
Colorado State
South Florida
North Carolina State
Seton Hall

First 6 Out:
Mississippi State