Tim Chartier, author of

Math Bytes:has turned some mathematical tricks to help better predict the outcome of this year’s World Cup in Brazil.Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in ComputingAlong with the help of fellow Davidson professor Michael Mossinghoff and Whittier professor Mark Kozek, Chartier developed FIFA Foe Fun, a program that enables us ordinary, algorithmically untalented folk to generate a slew of possible match outcomes. The tool weighs factors like penalty shoot-outs and the number of years of matches considered, all with the click of a couple buttons. Chartier used a similar strategy in his March Mathness project, which allowed students and basketball fans alike to create mathematically-produced brackets – many of which were overwhelmingly successful in their predictions.

Although the system usually places the most highly considered teams, like Brazil, Germany, and Argentina at the top, the gadget is still worth a look. Tinker around a bit, and let us know in the comments section how your results pan out over the course of the competition.

In the meantime, check out the video below to hear Chartier briefly spell out the logic of the formula.

Happy calculating!

## Place Your Bets: Tim Chartier Develops FIFA Foe Fun to Predict World Cup Outcomes

## Top Tips for 2014 March Madness Brackets from Tim Chartier

With a $1 billion dollar payday on the line, we predict there will be more people filling out March Madness brackets this year than ever before, so it isn’t surprising that everyone is looking to mathematician Tim Chartier for tips and tricks on how to pick the winners. Tim has been using math to fill out March Madness brackets with his students for years and his new book Math Bytes will have an entire section devoted to best tips and tricks. In the meantime, we invite you to check out these tips from an interview at iCrunchData News.

ICrunchData: What are a few variables that are used that are out of the ordinary?

Chartier: “In terms of past years, it helps if you look at scores in buckets. For instance, you decide close games are within 3 points and count those as ties. Medium wins are 4 to 10 points and could as 6 points and anything bigger is an 11 point win. That’s worked really well in some cases and reduces some of the noise of scores.”

“Here is another that comes out of our most current research. This year’s tournament will enable us to test it in brackets. We tried it on conference tournaments and it had good success. We use statistics (specifically Dean Oliver’s 4 Factors) and look at that as a point, in this case in 4D space. Then we find another team that has a point in the fourth dimension closest to that team’s point. This means they play similarly. Suddenly, we can begin to look at who similar teams win and lose against.”

## The Madness begins!

Don’t forget to join our ESPN bracket challenge group before Thursday, March 21st!

To learn more about March Mathness this year and to glean tips from years’ past, please visit the March Mathness site.

Use the widget below to explore Tim Chartier’s lectures on March Mathness and to find more advice on how to fill out your brackets this year.

## 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!

## Using Ranking Schemes to Fill in Brackets

## 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

**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.

## Math Improves March Madness Predictions: Tim Chartier Interviewed on Inside Science

Inside Science Television spoke with Tim Chartier about how math can be used to predict the winners of March Mathness. They also provide additional resources for those who wish to learn more or teach this in their classrooms.

Tim notes in the interview that: “To do well in bracketology, you need to know how teams will do earlier. It’s often those teams that are very difficult to predict and those games that often our methods are picking up.”

He also reveals that, using data available at the time of the interview, his methods currently predict Kentucky will be the winner. Does that match up with your bracket?

You can view the complete article and the video here: http://www.insidescience.org/television/1-2563

## Tim Chartier’s rating method explained

In this Huffington Post article, Tim Chartier explains the method he uses for filling in his bracket.

http://www.huffingtonpost.com/tim-chartier/march-madness-math_b_1341829.html

You still have until noon today to compete with us at PUP! Don’t forget to join our ESPN group.

From Tim’s article:

*It’s March. This past Sunday, the first round match-ups in the Division I NCAA Men’s basketball tournament were announced and with that, the madness began! Sports channels offer (seemingly, if not literally) nonstop analysis on the match-ups. Over the next few days, millions of people will decide how to fill out a bracket. They use a variety of techniques ranging from one’s preference of mascots to personal algorithms based on one’s knowledge of the season. Even with over 5 million brackets submitted to ESPN alone last year, there has never been a perfect bracket submitted to ESPN, CBS or Yahoo Sports. Surprising? Keep in mind, there are 9,233,372,036,854,775,808 (which is said 9 quintillion) ways to fill out a 64-team bracket. *

Want some help? Turn to algebra.

## Still need bracket advice? Tim Chartier offers some insight in a MAA Distinguished Lecture

The Math Association of America writes up Tim’s Chartier’s distinguished lecture on bracketology.

http://maa.org/news/2012DL-Chartier.html

From their description it sounds like Tim provides absolutely essential background to fill out those brackets:

*Improbable as it sounds, Tim Chartier can leverage math to foretell such outcomes, to “predict how 18- to 22-year-old young men will perform in high-pressure situations.” The basis of Chartier’s mathemagic is the Colley Method, named for its developer, Wesley Colley. *

*…*

*Math and mathematicians, in other words, work in mysterious ways.*

*Chartier dispelled the mystery a little, though, by describing how to derive from team statistics—number of wins, total games played—values that, slotted into a massive 350 by 350 matrix, represent a system of equations that can be solved to yield team ratings. To make a bracket based on these ratings, you just assume that the higher rated team always wins.*

*You can, of course, “usurp the math and make your own decisions,” Chartier said, but consider the Colley Method’s none-too-shabby track record: When Chartier entered a Colley-generated bracket in the 2009 ESPN Challenge, it beat 62 percent of the more than 4 million entrants. In 2010 Colley outperformed everyone from LeBron James and Davidson alum Stephen Curry to Dick Vitale and Barack Obama.*

## Another helpful link for building your bracket!

Sheldon Howard Jacobson, Professor of Computer Science at the University of Illinois at Urbana-Champaign has this helpful website to share: http://bracketodds.cs.illinois.edu/BI.html

Remember you only have until **Thursday, March 15** to submit to our ESPN site and be sure to check out *Who’s #1 *for any last-minute tips.