[Video] New mathematical models help rank sports teams

But will these new mathematical models make sure my team is ranked higher? That is the truly important question.

For more on mathematical systems of ranking and rating, please see Who’s #1?: The Science of Rating and Ranking by Amy N. Langville & Carl D. Meyer. You might also want to peruse our March Mathness series of blog posts here where students put these mathematical models into action during March Madness. If your school is interested in participating in March Mathness next year, please contact PUP Math Editor Vickie Kearn.

March Mathness 2012 Wrap-up

March Mathness is over, so now it’s time to ask the key question: How did we do?

On March 15 many of us scrambled to complete our brackets and 64 of us placed them in the PUP March Mathness group of the ESPN Tourney Challenge. Almost everyone was in the top 50th percentile and 10 of our group did better than 90% of the 6.5 million people who entered a bracket. What we had in common was that we used a particular math algorithm or some combination to fill out our brackets. Quite a few of us also tossed in a bit of the human element because everything can and will happen in a tournament.

Math editor, Vickie Kearn,  asked Tim Chartier, Professor of Mathematics at Davidson College for his take on how we did.

“I think one of the things to note is that such methods can clearly be effective.  However, that personal modeling decision as to how to weight the season or even what part of the statistics to use is VERY important and makes a big difference.  Even so, there is that inevitable “Madness” of human endeavor that keeps us ever watching and, frankly, enjoying! What will happen?  We will never find a method to always know and as such, we keep trying and keep watching.”


And the Winner is Travis McElroy

Travis had the top rank in the PUP March Mathness Group, finishing with a total of 1470 points, in the 91.8 percentile. He is the recipient of several Princeton University Press books.

Travis is a senior math major and Spanish minor at Davidson College. Next year he will be working on his master’s in applied mathematics at the University of North Carolina at Chapel-Hill.  Following he tells us about his experience in completing his bracket.

 This bracketology experience has been fun as I normally don’t pay attention to the tournament as baseball, football, and tennis are the sports that I watch.  I used the Colley Method and tried all different weights. I split the season into 42 different parts but really only put weights on 3 different sections, pre-conference play, conference play, and conference tournaments. The conference tournaments part was mainly for major conferences. So I tried a range of .3 to 1.5 for how much each game was worth and also for some brackets I added a bonus of a win or 3 for a road win.

For my winning bracket I decided to do something crazy and pick the underdogs. I used a colley method of .3 wins for a pre-conference play win, 1 win for conference play, and 1.5 for a tournament win. Also, a road win counted as 2 wins. After the rankings were compiled, I decided that if the 2 teams were in the top 10 and the lower ranked team was within 5 rankings of the higher team, the lower ranked team would win. After the top 10, if the lower ranked team was within 10 of the higher ranked, then the lower ranked team won. The only exception I made was I said Kentucky would win the whole thing.

Next year I would create more sections of the season and make the rankings vary more. It was very difficult to get any ranking that did not have Kentucky as number one and Syracuse as number 2. I also want to compare the actual ratings to see if there was a reasonable pattern to when the “underdog” won. I am very surprised I did as well as I did as I do not follow college basketball closely (except my Davidson Wildcats) and this bracket was my fun bracket. It shows that the underdog is not to be discounted. The only big surprises for me was the same surprises as everyone had with 2 #2 teams losing in the first round.  Next year I also want to combine methods to see if that helps. My roommate (Greg Newman) used different methods than I did and we want to see if we can make a better combination for next year.


The last word(s)

Now that you have 12 months until the next tournament, you have lots of time to decide what method you will use next year. Get your copy of Who’s #1?  by Amy Langville and Carl Meyer and start reading. You can also use it to predict the outcome of any sport as well as be able to rate and rank just about anything.


How to Improve Your Bracket in 2013

Ralph Abbey was a member of the PUP March Mathness ESPN group and completed his bracket in the 91.8 percentile which is a fantastic achievement. However, we’re already looking forward to 2013, so in this post, he shares a few tips for improving your bracket next tournament.


I am a PhD graduate student in mathematics at North Carolina State University. My adviser is Dr. Carl Meyer, coauthor of Who’s #1? While sports ranking isn’t my PhD topic, I do find it very interesting, and it is actually quite a good topic of conversation, even among non-math people.

It was less than 24 hours before the first games and I still hadn’t made a bracket—-to be honest, I had completely forgotten. Somehow the thought came to mind at the last minute, and I realized that I didn’t have enough time to research all the teams in depth to create my own bracket. To put off the stress (and the blame if I got things wrong) I turned to a few ranking algorithms I knew for help. The games data was found on Massey’s website: masseyratings.com

I formed a matrix in which entry i,j was the total number of points team i scored against team j over the entire season. Division 2 teams were included as well. Using this data matrix, I used both the offense defense model, and a pagerank model to rank the teams. I made 2 brackets, compiled by having the higher ranked team always beat the lower ranked team.

Additionally I formed a few other brackets: a “no-upsets” bracket that used the NCAA committee’s rankings. I also created 2 “upset” brackets. The first was a bracket in which if two teams seeded between 4 and 13 (inclusive) played, the worst ranked always won. If one or neither of the teams were in the range, then the better ranked team won. The other upset bracket was formed the same way, except by decreasing the range from 6 to 11.

In the end the winner for me was the offense defense model. It scored 1310 points on the ESPN challenge, placing above 91.8% of all ESPN brackets–absolute rank of 529,254. While it messed up on a lot of the first round upsets, the offense defense model was able to predict 3 of the 4 final four teams, 1 of the 2 championship teams, and it did predict Kentucky to win the whole tournament.

The plans for next year are uncertain, but one thing I do want to try is rank aggregation to see if it can combine the best of multiple models!

Will they use math next year? Reflections from the Davidson College students

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!


6.5 million fill in brackets. How do you rank?

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?

Q & A with Colin Stephenson and Neil Goodson

In 2008, Davidson College seniors, Colin Stephenson and Neil Goodson, used math to fill in their bracket and ended up ranking in the 100th percentile at a rank position of 834 in ESPN’s Tournament Challenge. Read about their experience below.


Q: What class were you taking when you created your brackets? How did the idea of creating brackets with math algorithms arise?

Neil: The original research project came out of an elective course I took that focused on topics in operations research, which is an area of mathematics that focuses on the application of mathematics to solving complex problems in the real world problems.  The class was a small group of graduate and undergraduate students, and we were all guided by the professor, Amy Langville.  Knowing that Colin and I had an interest in sports, Amy encouraged us to conduct our research for the class in the area of sports ranking.  Amy had already put effort in this topic as well as previous students, so we had tremendous resources available to us and were able to hit the ground running.

Colin: Our assignment was to use algorithms to solve real world problems.  Amy recommended sports ranking models to us.  It sounded perfect to combine one of our favorite sports, college basketball, and math.


Q: How did you break down tasks in your work?

Neil: The research project started in January at the onset of the Spring semester, so we had just a few months before March Madness began.  Our research process required us to study existing methods, apply them to various past seasons and the current one, discuss results with our class and see how we can improve upon existing methods.  Colin and I quickly learned to divide tasks to our strengths.  I would spend time coding certain methods, and Colin would backtest previous year’s data.  Both of use would scramble to present results to our classmates and professor each week.  The class was structured so we could all brainstorm collectively on where to head next and that helped us move forward with our project.

Colin: First we wanted to understand current ranking models.  Some were already being used in sports and others were being used for ranking things other than sports.  Neil and I also thought of factors we considered to favor teams to go further in the tournament.  We wanted to find ways to incorporate our own ideas as amatuer braketologists into our models.  We decided to focus on weighting win/loss records depending on when they were played before the tournament.  We both feel strongly that wins and losses in late February and March mean much more than those in November through January.  The “hot” teams going into the single elimination tournament usually seem to go further.


Q: Did you create one bracket or several?

Neil: We created several brackets.  We wanted to test various weighting schemes for each rating method.  For example, we had several variations of the Massey method and several others for the Markov method.  In total, I believe we tested over 30 brackets for that tournament.

Colin: We created 30 or more brackets.  We also tested them against the 4 previous years’ results in the NCAA tournament.


Q: Can you describe which methods were successful? Did you have a sense of which would be most successful?

Neil: The most successful results were the methods that placed more weight on games occurring later in the season.  Most sports fans would agree that this is a no brainer.  What is interesting though is that we found that you can place too much weight on the end of the season as well.  If you were to emphasize the conference championships in a model for instance, you probably would not do very well.  So there is a trade-off between teams that have played well consistently throughout the season and ones that have positive momentum going into the post-season play.

Colin: The Colley and Ken Massey models that we weighted logarithmically worked the best for us, exponential weighting also worked well.  We thought those models would work well because they were already used in sport ranking.  We also thought that log and exponential weight would be best because the games closer to the end of the season get gradually more important than the last.  They also did the best while testing previous years.


Q: What data went into making your predictions? scores? dates? anything else?

Neil: Our rating methods took into account each head-to-head match-up in Division I basketball, the point spread for each of those games, and when they were played.  Strength of schedule also played an important factor for some of the methods. The major differences arose between the mathematical techniques used to rank the teams given this vast web of conference and non-conference match-ups throughout the season.


Q: What kind of excitement did you experience during the tournament? Were you ever on a leaderboard? What did it feel like to be in such a high percentile?

Colin: The tournament excitement was awesome.  After all our preparation and work we were able to sit back and watch basketball for a couple weeks.  When Neil went on NPR the morning before the first games he told them a couple upsets our models were showing.  I think all the ones he told ended up happening.  It was also great to go on national live tv on the CBS Early Show.  We were live on the Davidson campus the night they were playing Kansas.  When we let them know we had Kansas winning it all, then we got boo’d out of the building.  The best models were in the 100th percentile on espn.com.  They were doing better than any bracket I had ever put together myself.  They were also beating all of my friends, so I had bragging rights with them.  Kansas ended up winning in the last seconds of the championship.  Neil and I went crazy when it ended the way it did, one last second missed shot and we would have been well out of the 100th percentile.

Neil: I have always enjoyed March Madness every Spring, but working on this project brought the excitement to a whole new level.  After spending so much time in the lab crunching the data, I couldn’t help but constantly check how each model was performing when each tournament game ended.  Since we submitted all of our brackets to the ESPN Challenge, we could instantly get a sense of how each stood compared to the 4+ plus other brackets out there.  For most of the tournament, our best models were consistently in the 95th percentile and we ultimately finished in the 99.9th percentile with our best models.  For me, it felt great to see the long hours of writing code, crunching data, and presenting research results payoff with winning brackets, but honestly even if we hadn’t been as successful, I would have enjoyed the project just as much.  In that case there would have been so much else to try.  I might never have wanted to graduate!


Q: Were you surprised about anything in the tournament? Were you surprised by how well or poorly certain methods performed? Were you surprised by the media attention you got?

Neil: Every year there are always upsets in the tournament, so of course some of those came as a surprise to me.  I was also surprised at how well we did in picking the upsets.  My feeling on upsets is that there are two kinds.  Some upsets happen truly because some teams are less recognized in their ability throughout the season.  Maybe it is because they are in smaller divisions or had a few notable losses and the pundits wrote them off.  Other upsets happen because the best team had a bad day, but if they were to play the same team again, would probably win.  I think the algorithms do a good job handling the first type of upset.  I am not sure anyone can do well consistently picking the second.

I was definitely surprised by the media attention.  When I heard that there may be some media interest in our story, I was thinking we may get a write up in the local paper.  I was shocked when I had a voicemail from a producer at NPR and then the CBS Early Show.


Q: So far, no one has ever submitted a perfect bracket to the ESPN Challenge. Do you think this is possible, at least for a math algorithm?

Colin: I bet someone will eventually get a perfect bracket one day.  It would take a lot of luck for them.  I would like to think we could use math to get a perfect bracket, but it would also take a lot of luck.  A lot comes down to the fact the NCAA selection committee puts together the bracket on Selection Sunday.  The rest is about the unpredictabilty of the human element.  The unpredictability is what draws so many people to watch the tournament.

Neil: It is just as possible for an algorithm as it is for any human being.  Without a doubt, it will take a tremendous amount of luck for either.  That is what makes March Madness so much fun.


Q: Have you tried making brackets in subsequent years? How did the methods do? Did you make any changes?

Neil:  I have continued to use the models in subsequent tournaments and they have continued to do well.  Well enough to win a pool here and there.  I have been using the same methods we used in 2008.  I would love to continue to tinker with them, but there is never enough time.

Colin: We have used our best performers every year since then.  The following year my dad, uncles, aunts, brothers, coworkers all wanted a copy of the magical bracket.  Of course I gave them out, and of course it failed miserably.  The next year I kept it to myself, and I won my office pool.  Last year I gave it out to everyone who asked, and it bombed again.  So this year, it will be kept a secret again.

This Week’s Book Giveaway

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.

The science of rating and ranking touches virtually every facet of our lives, and now you don’t need to be an expert to understand how it really works. Who’s #1? is the definitive introduction to the subject. It features easy-to-understand examples and interesting trivia and historical facts, and much of the required mathematics is included.

“Langville and Meyer provide a rigorous yet lighthearted tour through the landscape of ratings methodologies. This is an enjoyable read that looks at ratings through the lens of sports, but also touches on how ratings affect our everyday lives through movies, Web search, online shopping, and other applications.”—Chris Volinsky, member of the winning Netflix Prize team

We invite you to read Chapter 1 here: http://press.princeton.edu/chapters/s9661.pdf

Don’t miss our March Mathness blog: http://blog.press.princeton.edu/march-mathness/

The random draw for this book with be Friday 3/30 at 3 pm EST. Be sure to “Like” us on Facebook if you haven’t already to be entered to win!

Anyone up for a Sweet 6?

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://blog.press.princeton.edu/march-mathness/

Using Ranking Schemes to Fill in Brackets

James Keener, Professor of Mathematics and the University of Utah, explains his ranking method.


More from our leaderboard, students describe their March Mathness brackets

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://blog.press.princeton.edu/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.

This turned out to be a good thing because in my heart  I thought Missouri was going to win the tournament this year, but instead, as we saw on the first weekend, they were taken down by the formidable 15 seed Norfolk St. In addition, as a college student, I don’t have time to follow every Division 1 Men’s basketball team in the country so there were also many picks that I had no idea about. Thus, it was nice to have an algorithm to tell me what to do. By the end of the first night of the tournament, I was in the 98.6 percentile, only missing the VCU upset, and by the end of the first round, I fell a little to the 90.1 percentile. The first time I logged on and saw that I was in the top 98.6% of all brackets was a nice jolt. I probably checked my ranking ten more times that night to make sure there was not a mistake.

What has been most exciting to me this during this experience was finally finding a way to combine my academic passions and my love for sports. I think using math to predict a typically unpredictable tournament is about as cool as it gets because it is exciting to math people and non-math people alike. Even at Davidson alone, it has created a lot of conversation between my math friends and my non-math friends because everyone wants to be able to predict who is going to win. The one downfall of this experience is that I have had the pleasure of watching my Davidson Wildcats all season long and was so excited to see them make it back to the tournament this year that it killed me to pick Louisville over them…and then have it come true.

The first night of March Madness 2012 was pretty standard, and thus my bracket did pretty well. And then came the second day. With two 15 over 2 seed upsets this tournament, my bracket was brought back down to life a little bit. However, I suspect most of the rest of the country also did not see that happening so I expect to move on from those losses and perform well in the Sweet 16. As long as Michigan St. keeps winning, I’ll be happy.

I should also mention that in addition to competing in the PUP group, I have several other brackets  in a different group that is part of ongoing research. In that group, I developed several variations of the PageRank algorithm, and many of those are also doing well. Tim and I are anxious to see how those results turn out in addition to the standard PageRank algorithm.


David Heilbron

David Heilbron is a junior Math major at Davidson College .  In selecting his bracket he has used the probability of given seeds to advance and then picked a random number to decide if they do. He is doing very well. Here he describes how he filled in his bracket.

So here are the nuts and bolts of my bracket. Basically I went through each bracket from 1985-2011 and saw how many of each seed number made it to each specific round (Sweet Sixteen, Elite Eight, etc). So say over that time period, eight #5 seeds have made it to the Elite Eight. I took this number and then divided it by the total possible #5 seeds that could have been in the Elite Eight over all those years. There were 4 each year,  times 27 years, or 108. I did this for each seed and each round to get all these probabilities of a certain seed making it to each round.

From there, it is a simulation that runs each head-to-head match-up moving through the games. To find the winner of a certain game, we take each seed number’s probability and scale it to make a standard probability that the teams can be judged from. Finally, we get a random number which, if less than or equal to the probability, one team goes on, and if not then the other team goes on.

Long story short, we find each seeds chance of getting to a certain round and then use those in the head to head match-ups to print out the winners of each game and then just put them into a bracket.

In terms of which is more exciting, I really do love the basketball. I grew up watching a lot of ACC basketball so watching the games is so much fun. I actually have been finding the math more interesting though. It is cool to see how everyone thinks up different weightings and strategies.

The Murray State loss may come back to haunt my bracket as the tournament continues and Syracuse really has not looked that good, but I have a good feeling going forward. One game that concerns me though is Louisville vs. Michigan State. I’d love to see Louisville win and keep my bracket going but I do have to be a homer for Davidson and keep licking my wounds after the first round loss.


How are we doing? Checking in with our March Mathness teams

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://blog.press.princeton.edu/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.


Jonah Galeota-Sprung

Jonah Galeota-Sprung is a junior Math Major at Davidson College. He is from South Orange, New Jersey, and he enjoys birdwatching and pickle making. He is in the 79.0 percentile after the round of 32.

Which method did you chose and why?

I ended up using the Colley ranking method with a cotangent weighting function. The choice of Colley was pretty arbitrary, but I chose the cotangent weighting function because I figured I needed a pretty bizarre bracket if I was to have any chance of doing well, given the unpredictable nature of the tournament. We’ll see how far that idea gets me.

Who do you predict will be in the final 4?

Mr. Colley and the cotangent function predict Kentucky, Florida State, Michigan State, and UNC in the Final Four, but they don’t speak for me personally–I’m seeing a Davidson/’Zags final clearly written in my tea leaves.

Things looked good for about half a day. I was on top of the pool, beating the president and my math professors and about 99 percent of the country, too. Dreams of cash prizes and maybe the Fields Medal for cotangentially managing to predict the VCU and Colorado upsets filled my head. I could practically taste the gold on my tongue (the first thing I do when I receive medals is lick them, just to be sure).

Before long though, it all fell apart. I’ve been told things have a tendency to do that. Pesky NC State kept winning, and peskier Missouri had been knocked out in the first round. The un-predictions piled up, and over the course of a weekend half of my Elite Eight was out of the tournament and my national champion had lost to a six seed.  I was able to take some consolation in the fact that Duke was among the casualties, but that did little to assuage the pain I felt when I looked at my bracket shot through with red holes.

There’s always next year.


Barbara Sitton

Barbara Sitton is a junior at Davidson College. She plays on the Davidson Division I women’s basketball team and is a huge basketball fan. She is in the 86.1 percentile after the round of 32.

I’ve only had a little experience with brackets. Before, I chose teams from instinct, it was just for fun. But this time, I used the Colley ranking system to rank teams and predict the outcomes of the games. For the men’s tournament, I predicted Kentucky, Michigan State, UNC, and Ohio State to be in the final four. For the women’s tournament, I predicted Baylor, Stanford, Maryland, and UConn to be in the final four.

I am truly impressed with the way my bracket has held up, although there has been a lot of madness in the NCAA tournament already! I actually have 2 brackets in the group, which I will distinguish as bracket #1 and bracket #2. Bracket #1 has been the most successful so far, and it is in the 86.1 percentile. Some of the biggest upsets have been all of the 12-15 seeded teams who have beaten the 2-5 seeded teams: VCU beating Wichita State, Lehigh beating Duke, USR beating Temple, and Ohio beating Michigan. I’m pretty excited to see what will happen during the Sweet 16!



Paul Britton

Paul Britton is a senior Math Major and Philosophy Minor at Davidson College. He is a campus tour guide and a member of the Sigma Phi Epsilon fraternity. He is from Castle Rock, Colorado and is ranked in the 86.1 percentile after the round of 32.

My family always sponsored a bracket pool and I started participating when I was 8 or 9 years old. I have done at least one bracket, and often multiple brackets, every year since then.

I submitted 2 mathematically based brackets into the PUP pool this year. The first bracket used the Massey rating method with a piecewise game weighting where I divided the season into thirds and weighted the last third of games at .75, the first third at .5, and the middle third at .25. The first third corresponds to the non-conference schedule, which is an indicator of a team’s talent compared to the rest of the country, and is also indicative of games they will face in the tournament itself. The most recent third is the second half of the conference game slate, which is a strong indicator of a team’s recent performance, and thus was weighted more than the other two segments

The second method was an (imperfect) attempt to weight the teams based on their performance according to Dean Oliver’s “4 Factors of Winning,” which you can read about here: http://www.basketball-reference.com/about/factors.html. Essentially, I gathered statistics on Field Goal percentage and Turnover percentage on offense and defense, and additionally on Rebound rate and Free Throw percentage, then weighted these factors according to Oliver’s specifications. I would have liked to adjust for strength of schedule, but couldn’t figure out an effective way to do so, so I left the initial rankings as they were.


Who’s #1 on the March Mathness Leaderboard?

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).

The major advantage to this method is the ability to look at match-ups. I would compare the traditional basketball statistics (points, rebounds, strength of schedule) and would do this for each match-up. I also used my own head when picking (this was both an advantage and a disadvantage). Having seen many of these teams play I had an idea of teams that would do well or would not. However, I had not seen all these teams play and did not have full data information.

This was the bracket that took the most time for me to complete since I was using math and my own opinion while making it. For an example of how watching a team can deceive you, I would talk about Missouri. I had seen them play a few times and they always looked very good. In this bracket I had them getting into the elite eight. As most will know, they lost in the first round to Norfolk State (in a huge upset). I had not watched any Norfolk State basketball and did not know how balanced their offense was (in the game against Missouri they had four players score in the double figures).

Download Greg’s “Picks as an analyst” bracket as a PDF.


My “Harvard” Bracket:


At this point I feel like I should note that I do not attend Harvard nor does it have anything to do with Harvard doing well in the tournament (it had them losing in the first round, which they did).

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.

The idea of survival is also very important and is crucial to the success of this bracket. Even with the crazy upsets (that this bracket did not get) all of the elite eight teams are still playing. This means that my PPR (Points Possibly Remaining) is very high at 1280 and means that this bracket could possibly end up doing even better (since many people have lower PPRs) at the end of the tournament.

 Download Greg’s “Harvard” bracket as a PDF.


Tips in selecting a bracket:


Pay less attention to seeds/history.

A committee chooses seeds and we can’t always figure out why a team is given the seed. The art of “bracketology” is something entirely different and hard to understand. At some point a number 1 seed will lose to a 16 seed (even though it hasn’t happened yet). Coming into the tournament 2 seeds were 104-4 against 15 seeds (96%), this year they are 106-6 (95%) but does that mean number 15 seeds have a better shot next year? Also, even if you magically figure out what seeds will advance there are four of each seeds!


Don’t try to be perfect.

A perfect bracket is hard! Of everyone in the ESPN bracket, everybody had at least two wrong after the first round. The current leader had six incorrect picks. Don’t worry about being perfect, chances are nobody else will be either.

Rankings are good but Ratings are better.  Some people just looked at rankings. Many of the teams were rated very closely, so a team ranked five spots ahead of another may not be a sure win.


What I wish I did:


Game Theory

I really focused on getting the most right, not highest percentile. I wish I had tried to pick the upsets (almost) nobody else picked. This would make me seem very smart, help me in brackets with different formats and possibly given me an advantage. If 95% of the country has team A beating team B but my model was team A only has a 60% chance, it would probably make sense to pick team B (note: I probably would not pick team B to advance further as to minimize the penalty and because neither team seems as good as everyone else thinks).


Tried another style of tournament

I like that each round is worth the same number of points (so each game as you get further in the rounds is worth more points). I wonder how well different models would work in different bracket scoring systems.


Saved/Organized all of my data better

I got a lot of data and all of it around the same time. I’m not sure that I will even be able to find all of it after the tournament is over.


Made more brackets

I made ten brackets in total. I would have made so many more with each method individually and different combinations of all of them but scoring them myself was not something I had time for.