March Madness and, by extension, March Mathness are now over. This project was first and foremost a way to teach ratings and rankings at Davidson College and other schools. Now that it is all over, we’re checking back in with a few of the students to see if they will draw on their new math skills when they fill out their brackets next year.

Paul Britton

Overall, I was fairly happy with how my brackets performed this year. None of the brackets performed particularly well in the early stages, but both the Piecewise Massey bracket and my own observation bracket came on strong towards the end of the tournament. In the end, the Piecewise Massey bracket finished in the 94th percentile with 1350 out of 1920 possible points. This was a much better result than I was expecting, and it was largely due to Kentucky’s victory (apparently predicted in 35% of all brackets on ESPN) and getting three of the final four teams correct. This bracket stayed between the 80th and 98th percentile every round, and generally did well throughout, picking several notable first round upsets (NC State and USF) while only really missing on a few teams (the bracket liked Duke and Missouri and had Louisville losing to New Mexico in the round of 32). If a couple very close matchups had gone differently, notably Ohio State-Kansas in the Final Four, this bracket could really have been an all-star.

As far as my other mathematical bracket, based on the adjusted “4 Factors of Winning”, it sadly did not perform up to expectations, scoring only 620 points and finishing in the 23rd percentile overall. This bracket missed badly on a number of picks, among them Missouri beating Kentucky in the Final Four (whoops), UNLV in the Elite 8, and Michigan State losing in the round of 32. In all fairness, however, the bracket got fairly unlucky with Syracuse and UNC, two of its Final Four picks, each losing critical members of their rotation during the tournament at some point. The model obviously cannot take these factors into account, and with the later rounds being worth so much, a few bad breaks really cost the bracket a shot at a good final position. However, this bracket did pick a number of interesting upsets, namely Lehigh over Duke in round 1, USF over Temple, and Ohio into the Sweet 16.

I think I will definitely use math to fill in a bracket next year, although my “competition bracket” will probably be based largely on my intuition, only using math to fill in games I am unsure about. I definitely want to refine my “4 Factors” bracket to account at least a little bit for strength of schedule. I feel as though this bracket had potential, but since I did not find the data until very late in the process, I was unable to really optimize what I was trying to do with my methodology. Beyond that, I will keep watching college basketball when it starts again in November, and keep cheering for the Davidson Wildcats!

Barbara Sitton

This NCAA tournament was full of many fun, surprising, upsetting, and mind-blowing games. It was interesting to see how the mathematical ranking method (Colley Ranking method) held up this March. After all of the madness, my bracket ended up finishing in the 87th percentile–11th in our ESPN group. That was pretty amazing! With this bracket, I used math to rank teams, and I basically went in and edited some of the games based on new team information and my intuition. I knew Syracuse wouldn’t be playing with one of their best players, so although mathematically they were ranked the highest, I predicted they would lose in the Elite Eight. I knew UNC would possibly struggle, but because of personally reasons, I was gunning for them to still make it to the championship game. Their loss to Kansas was the most upsetting for me. The most surprising game was Kansas also beating Ohio St. in the Final Four. But in all, my bracket was pretty successful.

Next year, I will definitely continue to use math to rank teams and to help me determine winners of each round. This year I played it safe. But next year, I may do more research on teams so that I could go through and make changes, and hopefully predict a few upsets!

In Lawrence Weinstein and John Adam’s book, Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin, we learn how to estimate the total length of all of the pickles consumed in the US each year, how many cells there are in a human body, how much electrical energy the US uses each year and much more. In celebration of Math Awareness Month and all the fun you can have with huge data sets, we’ll be posting problems from the book and the answers the following day. Join in the fun and post your guesses below in the comments field.

Remember — this is math that can be jotted down or performed in your head, so we’re not looking for exact answers.

Question #1

If all the humans in the world were crammed together, how much area would we require? Compare this to the area of a large city, a state or small country, the US, Asia.

Extra Credit

How much area would we need if we gave every family a house and a yard (i.e., a small plot of land)?

April is Mathematics Awareness Month and the theme this year is Mathematics, Statistics, and the Data Deluge. The American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics are sponsoring many wonderful events and a website which you can find at http://www.mathaware.org/index.html. You can also contribute to the many wonderful things already posted.

Throughout the month Princeton University Press will be posting articles on the ways data is collected and how it is used in everyday life. Examples include advertising, networking, the census, and how we can travel efficiently and inexpensively. The articles will discuss both the positive and negative uses of large data. We will also provide an estimation puzzle each day. You can learn about the ways large data is used and also improve your estimation skills.

Mathematics, Statistics, and the Data Deluge

The American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics announce that the theme for Mathematics Awareness Month, April 2012, is Mathematics, Statistics, and the Data Deluge.

Massive amounts of data are collected every day, often from services we use regularly, but never think about. Scientific data comes in massive amounts from sensor networks, astronomical instruments, biometric devices, etc., and needs to be sorted out and understood. Personal data from our Google searches, our Facebook or Twitter activities, our credit card purchases, our travel habits, and so on, are being mined to provide information and insight. These data sets provide great opportunities, and pose dangers as well.

ESPN’s tournament challenge set the bracket record for entries this year–read the complete article here.

Ever wonder how your bracket measures up against, not only your co-workers in the office pool, but everyone else in the country? Each year, the ESPN Fantasy section on ESPN.com logs millions of brackets to its free-to-play Tournament Challenge game, now in its 15th year. This year, ESPN logged a new record 6.45 million brackets, 8.9 percent more than 2011. Everyone can check how their brackets are doing against their friends within a specific group, but only ESPN has an inside peek at the top brackets from around the country.

This is exactly how we have been using our own tournament pool to track the various mathematical methods used by students and others to fill out their brackets. March Mathness has been a lot of fun, but it turns out we’re not the only math nuts out there. John Diver, Senior Director of Product Development at ESPN Fantasy sounds pretty mathy too. Check out some of the stats that he can pull from the pool of brackets:

After the brackets are announced on Selection Sunday, the tool goes beyond the public-facing “National Bracket” and “Who Picked Whom” pages to search different combinations of predictions. For example, we can determine what percentage of overall brackets have all the No. 1 seeds for each round up to the Final Four.

(97.7%) predicted Kentucky and Syracuse and Michigan State and North Carolina to advance to the Round of 32;
(67.9%) predicted all four No. 1 seeds to advance to the Sweet Sixteen
(28.3%) predicted all four No. 1 seeds to advance to the Elite Eight
(4.3%) predicted all four No. 1 seeds to advance to the Final Four

We just posted a Q&A with two former March Mathness winners — their bracket was ranked 834 in ESPN’s Tournament Challenge and was in the top 100th percentile (hard to beat 100%) so these math methods do work. What do you think, will you be using math to fill in your bracket next year?

Kentucky vs. Louisville. Kansas vs. Ohio State. In honor of the Final Four, we have a March Madness-inspired giveaway for you:

Who’s #1?: The Science of Rating and Ranking
by Amy N. Langville & Carl D. Meyer

A website’s ranking on Google can spell the difference between success and failure for a new business. NCAA football ratings determine which schools get to play for the big money in postseason bowl games. Product ratings influence everything from the clothes we wear to the movies we select on Netflix. Ratings and rankings are everywhere, but how exactly do they work? Who’s #1? offers an engaging and accessible account of how scientific rating and ranking methods are created and applied to a variety of uses.

Amy Langville and Carl Meyer provide the first comprehensive overview of the mathematical algorithms and methods used to rate and rank sports teams, political candidates, products, Web pages, and more. In a series of interesting asides, Langville and Meyer provide fascinating insights into the ingenious contributions of many of the field’s pioneers. They survey and compare the different methods employed today, showing why their strengths and weaknesses depend on the underlying goal, and explaining why and when a given method should be considered. Langville and Meyer also describe what can and can’t be expected from the most widely used systems.

In a delightful little article at the Wall Street Journal, reporter Rachel Bachman models the Lewis Carroll method of bracketology with some surprising and not-so-surprising results.

In addition to writing “Alice in Wonderland,” Lewis Carroll was a mathematician who was offended by blind draws in tennis tournaments. So Carroll devised a method to ensure that the most skilled players would survive to the latest rounds.

So in the spirit of adventure, The Wall Street Journal put Carroll’s radical format to the ultimate test: this year’s NCAA men’s basketball tournament. If we assigned the 64-team field randomly, then played out the tournament based on the NCAA selection committee’s overall ranking for each team, what would happen? Would the teams that got unlucky draws or suffered early upsets still make it through to the late rounds? And would there be enough surprises to keep people entertained?

It turns out that Carroll’s method yields 119 games in 11 rounds vs 67 games in 7 rounds in the real tourney, and results in a Sweet Six instead of the Sweet Sixteen. But even in this alternate reality, the Kentucky Wildcats are predicted to win it all.

For the background on the model, read this earlier article: http://online.wsj.com/article/SB10001424052702304636404577297821444746352.html

Check out the updates on our own March Mathness ESPN Group here: http://press.princeton.edu/blog/march-mathness/

Out of 6.5 million entries, the participants in the March Mathness group of the ESPN Tournament Challenge are doing very well. One third of our group is in the top 20%. Following are summaries from some of those in our group. They describe how they designed their brackets and how they are embracing the excitement of the tournament. The methods mentioned are described in the recently published Who’s #1? By Amy Langville and Carl Meyer.

Additional student reports here: http://press.princeton.edu/blog/2012/03/22/how-are-we-doing-checking-in-with-our-march-mathness-teams/

Bryan Kelley

Bryan Kelley is a sophomore Math major at Davidson College. He is from Rockland, Massachusetts. In the following, he describes how he selected his bracket using the PageRank method from Who’s #1? by Amy Langville and Carl Meyer. You can find more on PageRank in Google’s PageRank and Beyond, also by Langville and Meyer.

The experience of filling out a March Madness bracket is completely new to me this year. I have always resisted it in the past because as a die hard competitor and a passionate sports fan, I cannot enjoy the tournament if I have picked a team that I think will win over a team that I want to win. It is a conundrum I’m sure many other Americans also find themselves in this time of year.

This year, however, I put my internal conflict aside, and in the name of math filled out my first March Madness bracket. To create the bracket, Tim Chartier and I referenced Amy Langville and Carl Meyer’s new book, Who’s #1?. Using that book, I coded an algorithm in MatLab that solves for the stationary eigenvector of a stochastic matrix and used that vector to rank the teams. For the matrix entries, Tim and I decided to use the point differential in teams’ wins/losses.

Considering many of the experts had Kentucky winning this year (which is not surprising considering the season the Wildcats have had) Tim and I did not expect to see the algorithm give us Michigan State as this year’s champion. However, that is what it gave us, and to avoid my internal conflict, that is how I filled out the bracket. In fact, I filled out every spot in the bracket precisely how the algorithm dictated me to fill out the bracket.

Click through to read more.

Out of 6.5 million entries, the participants in the March Mathness group of the ESPN Tournament Challenge are doing very well. One third of our group is in the top 20%. Following are summaries from some of those in our group. They describe how they designed their brackets and how they are embracing the excitement of the tournament. The methods mentioned are described in the recently published Who’s #1? By Amy Langville and Carl Meyer.

More reports from our student teams: http://press.princeton.edu/blog/2012/03/23/more-from-our-leaderboard-students-describe-their-march-mathness-brackets/

Calley Anderson

Calley Anderson is a sophomore English Major with a Film and Media Studies Concentration at Davidson College. She is from Memphis, Tennessee. She is in the 86.1 percentile after the round of 32.

To me, it’s actually pretty shocking that I’m doing so well. I’ve done brackets several times before, but I guess the application of linear algebra gave me an extra kick. That, and the fact that this time around, it was for a class, my decisions were based on the mathematical rankings more so than my personal and emotional thoughts of teams. I used the Colley method (given to our class by Dr. Chartier) and separated the season into 4 parts. If my memory serves me correctly, I weighted Part I as 1/4, Part II as 1/2, Part III as 1, and Part IV as 2. From there, after I put all the teams in the brackets by their mathematical ranking, I used a small amount of personal intuition and changed a few (most notably having Memphis beat St. Louis because it’s my hometown team).

I never thought that my bracket would actually get this far, especially after all of the upsets that occurred in the Round of 32. After taking 2 major hits due to these upsets, I thought that my bracket had reached the end. Being a sports fan in general, I wanted my bracket to have real potential this time around. Most of my previous brackets had Memphis returning to the Championship or going rather far regardless of their season. Everyone else seemed to just fall into a random place, with exceptions for teams that I liked that year. This year, I didn’t let my school or home team influence my decision as much.

Math, however, is far from my favorite. We never really seem to get along. This bracket would be the first case in which I have applauded any type of math as being useful. That’s one of the great things about Dr. Chartier; he takes regular, terrible math and makes its useful and interesting. For this brief moment, I get to be proud that something involving math did me some good. More importantly, this is math that I actually cared about and strived for success with. Math, sometimes, can be awful. But other times, with the right application, it can be fun!

All in all, this has been one of the most memorable experiences in terms of March Madness that I’ve ever had. The intensity that I felt with each game, rather than just a select few, was new but exciting for me. I even went to the lengths to install the Bracket Bound iPhone app so that I wouldn’t miss any game or change in my bracket standings! I feel rather optimistic that I can hold onto my top spot in our class. If I can make it through a round of the most unpredictable upsets, then I can make it to the finish. Even if I don’t, I can still be proud of my short reign of success. I’ve got math on my side and, sometimes, it’s pretty hard to beat that.

Click through to read three more student responses.

Continued »

Greg Newman is currently at the top of the March Mathness ESPN Tournament Challenge leaderboard with two separate brackets and is ranked 131,052 out of 6.5 million brackets. That means that only 2% are doing better than he is. Greg is a senior Political Science major at Davidson College who spends a lot of time working on Computer Science/Mathematics. Last summer he interned at ESPN and he continues to work for them while in school. We asked him to describe how he picked his brackets this year.

Greg Newman on his “picks” for March Mathness

I think I would fall into a category of liking both math and sports but, since I have been obsessed with sports since I was three and work at ESPN, I think I’m more of a sports fan. I have two brackets that are doing very well. I joined your group with the second one and think I will explain them separately.

My “Picks as an analyst” Bracket:

As the name suggests I made picks as an analyst with little math. I did use “simple math” (by simple I mean something that I could explain to someone who never took Calculus but has basic knowledge of probability theory).
 
…
 

My “Harvard” Bracket:

This was very mathy. I had looked into many different methods including Colley, Massey, LRMC, Pythagorean ratings, Power rankings, S-Curve rankings, ELO and a bunch of other “saber metric” like ratings and rankings. The reason I called it “Harvard” was that it is based off of the Harvard College Sports Analysis Collective blog. Specifically, I looked at their “Survival bracket.” I really liked how they used numbers/analytics to try to make “intangibles” tangible. An example would be tournament experience, which experts agree is important. You can look at past tournament minutes play and say it correlates (and I would say correlates pretty well) with experience. It also had a ranking for consistency, which is hard to measure but incredibly important.
 

Continue reading this article after the jump to download PDFs of Greg’s brackets and for his tips on bracketology and things he wishes he did better this time around.
 
 

Princeton University Press is the publisher of The Collected Papers of Albert Einstein. We are happy to announce that the Hebrew University and Einstein Papers Project have launched a new website that will make records of all archived Einstein documents available to the general public.

If you visit the site, you can enter a carousel gallery to explore objects from Einstein’s personal life, his professional science life, his work as a public figure in the Zionist movement, and other aspects of Einstein’s life. It is also possible to do a deep archival search on keywords and names.

Here is the press release announcing the new digital archive, posted at http://www.einstein.caltech.edu/NewBlueSite.html

On March 19, the Hebrew University of Jerusalem will launch Albert Einstein’s digital archive in commemoration of his 133rd birthday. One of the founders of the Hebrew University, Einstein’s birthday is celebrated in Israel as National Science Day, which, this year, will feature a press conference to launch the newly expanded Einstein Archives Online website.

The website’s launch will simultaneously be marked at Princeton University Press, Caltech, the Hebrew University’s Friends organizations and Israeli embassies around the world.

The site, http://www.alberteinstein.info will contain the complete catalog of more than 80,000 records of all the documents currently held jointly in the Einstein Archives at the Hebrew University and at the Einstein Papers Project at Caltech.

They include: more than 40,000 documents contained in the personal papers of Albert Einstein (1879-1955) and over 30,000 additional Einstein and Einstein-related documents discovered, since the 1980s, by the editors of The Collected Papers of Albert Einstein, and the staff of the Einstein Archive at the Hebrew University.

Advanced search technology will enable the display of all related documents by subject, and, in the case of letters, by author and recipient. The first line or title of each document will be displayed, alongside information on date, provenance and publication history. “In this way the content of the archives can be explored via a new user friendly interface customized for this goal. This interface provides easy navigation through the life and scientific career of Albert Einstein” explained Dalia Mendelsson, Project Manager.

Continue reading after the jump.

Continued »