How are we doing after the round of 32?

John_Hussey[1]Sportscaster-John Hussey

The first weekend of the NCAA tournament was as surprising as ever, with Florida Gulf Coast’s sweet 16 appearance topping the list. FGCU put the largest dent into my bracket knocking out Georgetown, which eliminated a team from the finals for me, essentially ending what chance I had at a good score. Even though the game was a big upset, it wasn’t “entirely” a shock. Going into the tourney, I knew that FGCU had a win over Miami on their resume and Georgetown’s Princeton offense makes them susceptible to low scoring games, which makes them vulnerable. There is a reason that Georgetown lost to South Florida this year.

Out West, I had the right idea picking against Gonzaga in the second round–I just picked the wrong team in Wichita State. In the South, the basketball gods must really love Florida. This is the second straight year that Florida gets to play a 15 seed in round 2 or later. For perspective, Florida has now played a 14, 11, and 15 in their first three games, while #1 seed Kansas has played a 16, 8, and now a 4. Talk about luck of the draw for the Gators! I wish someone would have told me that would happen!

I had a near miss with Illinois over Miami (FL), which really torched my East Region. It will be interesting to see who wins that Indiana/Syracuse matchup down in Washington DC. I’ll be in attendance to see what happens.

Overall, with three Final Four teams alive (and my champion), the first weekend wasn’t a completely disaster. But it was pretty close!

 

vickie_kearn[1]Math Geek-Vickie Kearn

This was definitely a weekend of hits and misses for me. There were some big surprises from a math point of view, especially FGCU, Oregon and Ole Miss. However, I still have 7 of 8 teams scheduled to go to the Elite Eight (assuming they survive the Sweet 16). Although I was sad to see my math off track, I did love seeing some personal favorites (Temple and Lasalle) and underdogs (FGCU) go further than I expected.

After riding high the first day of play my sister, who made her picks based on the color of the team jerseys, is rethinking that strategy. Her color is blue and she did pick Duke so she may be flying high again soon.

The Sportscaster versus the Math Geek

John Hussey and Vickie Kearn both work at Princeton University Press. John is the assistant sales director and national accounts manager and Vickie is the mathematics editor. We thought it would be fun to see how they filled out their March Madness brackets. The conversation that follows took place on March 20 at our PUP offices. To get things started, we asked a single question: How did you fill out your bracket?

Vickie: You may have figured out I am the math geek. After getting my math degree at the University of Richmond, I taught math for 8 years and then ventured into publishing math books. Although I am a huge sports fan, my true love is football. I didn’t watch basketball until we began March Mathness a couple of years ago. Now I will be glued to the TV for the next few weeks. I really don’t know much about the game at all but I love watching the numbers and the great upsets, especially those we have seen so far this year.

Now to my bracket. Because of the many upsets this year, I decided to ignore the seeds.

I looked at four things when I filled in my bracket:

1. Strength of schedule (pulled from RPI). I gave this figure a weight of 1.
2. Winning percentage for the regular season earned a weight of 1.
3. The sum of the posts season wins over the past three years plus the coach’s winning record with their current team also got a weight of 1.
4. Then each team received the following bonus points.

-One point if they were the leader in their conference in the regular season.
-One point if they are a major team and if they are in a tested basketball conference like the ACC, Big East, and Big10.
-One point if they won their conference championship season
-One point for the leaders in points per game/rebounds per game/scoring offense and scoring defense

Bonus points are weighted as 2 because they reflect how the teams were playing at the end of the season.

John: What about style of play?

Vickie: I don’t know that much about basketball, I’m in March Madness for the math. I’m interested in the data and stats.

John: To get an understanding of my approach, here’s my background: I went to Syracuse University for sports broadcasting. I have friends that still work in sports. My picks are based on a personal study of the game; I watch about 20 hours of sports/week and college basketball is my favorite. My picks are similar to Vickie’s, but from a different point of view. I’m not distinguishing between conference tournament and how a team plays through the stretch of the season. I’ve been watching teams play and deciding on style of play. For example, if one team tends to make a lot of 3-pointers and they’re up against a team with a strong zone defense, the zone defense is not going to do well. Where things get tricky is making decisions about Syracuse. Since that’s my team I’m pretty biased. When you watch teams extensively, you have seen them in the good times and bad but the bad times stick in your mind. For example, Kansas’ loss at TCU or Michigan’s loss at Penn State. I also know a lot about upset histories. This year there are no #1 seeds in my final bracket because this year no one team dominated. The possibilities are wider this year…could be a five seed that wins.

Vickie: I only have one #1 seed in my final 4. We both picked #2 seed Duke as the 2013 champion.

John: Player experience is also a big factor. Some game style doesn’t translate into a tournament setting. Duke is a great team, but sometimes flakes out super early. They lost to Lehigh last year but they make lot of deep runs. It’s interesting that Miami is in Vickie’s final 4 but I have them flaming out in the 2nd round. They’re too reliant on 3pt shooting. They’re not an intelligent team and play up and down.

What does the math say the biggest upset will be in the first round?

Vickie: New Mexico State over St. Louis is a 13 over 4 and San Diego State over Michigan is a 13 over 4. California over UNLV is a 12 over 5.

John: Any upsets in your Elite 8? No major upsets but I do have 2, 3, and 4 seeds.

Vickie: No major upsets but I do have 1, 2, 3, and 4 seeds.

John: I don’t have any top seeds in my final four because they have been losing lately, but the math is backing up the top seeds.

Vickie: But here’s the real question: will we beat the president?

John: Obama takes the smart, safe approach to the bracket. Historically he has been very good, because he is conservative in his picks and doesn’t bet on upsets. Generally that’s a good way to go. This year is going to be odd since the tops aren’t doing so well. It really could be a 5, 6,or 7 that wins. Nothing crazy based on the math?

Vickie: No, but that doesn’t mean I wouldn’t like to see an upset.

John: Gonzaga has a great RPI, but they’re not ranked high. Their defense metrics must be off . They have a great winning percentage but not necessarily the RPI.

Vickie: But seriously, will we beat the president?

John: He’s playing smart and safe. I want to win, but in an interesting way. It’s a little riskier when you don’t have any #1 seeds in the final 4.

Vickie: Well it’s interesting how similar our brackets are even though we had different strategies! I just got a text from my sister who picked her teams by the color of their uniforms. Blue is her color so she also picks Duke to win this year.

In case you are wondering, the odds of having a perfect bracket are 9.2 Quadrillion to 1. Good luck and have fun.

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.

[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.