Paying It Forward, Using Math: Oscar Fernandez’s ‘Everyday Calculus’ Donated to Libraries in Franklin County, PA

Everyday Calculus, O. FernandezWhat a week!

It was recently announced that one of our books, Everyday Calculus by Oscar Fernandez, is to be donated by the United Way of Franklin County, in partnership with the Franklin County Library System, to public libraries all throughout Franklin County. The decision recognizes the 2013 Campaign Chair, Jim Zeger, who has demonstrated a dedication to service and a “willingness to teach others” during the course of his four-year tenure on the board of directors.

But the choice of text was far from random; Everyday Calculus was selected “because of the need for materials that support financial and mathematical literacy within our library systems,” says Mr. Zeger. He’s one to know; before coming to United Way, Zeger studied math at Juniata College and taught mathematics at the Maryland Correctional Institute. He also served for a number of years as part of the Tuscarora School District school board, and “is very supportive and understanding of the value of relating and connecting applied math to students.”

Bernice Crouse, executive director of the Franklin County Library System, accepted the books and has found them a place in each County library, including the bookmobile, in order to make them more accessible to readers. According to Crouse, this book fits perfectly with Pennsylvania Library Association’s PA Forward initiative, which “highlights Financial Literacy as a key to economic vitality in Pennsylvania.”

Mr. Fernandez is reportedly “delighted” and “honored” by the decision, and looks forward to further collaborating with United Way.

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.

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.

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.

 

Sport Science host, John Brenkus, gives his take on March Madness


Math editor, Vickie Kearn, interviews John Brenkus, host of ESPN’s Emmy Award–winning show Sport Science. You can follow John and his commentary throughout the tournament at http://twitter.com/sport_science


VK: We have 9 high school and college math classes across the US completing brackets for our March Mathness group on ESPN. They are all using different algorithms to predict their winner. However, we all know that statistics aren’t everything. What are some of the factors that are important to a team’s performance in the tournament from a sport science perspective? What are some of the key things that will make the difference between moving forward and going home?

JB: It is important to also consider where the team is playing. Through research we have found domes are louder than regular arenas because the parabolic curve of the ceiling directs sound waves toward center court. So teams with fans that travel well may have an advantage, particularly in a dome. We’ve also found that arena height affects shooting percentage. Because players rely on peripheral cues, a higher arena will usually result in a lower field goal percentage. Experience, talent and coaching are also important factors between moving forward and going home.

VK: Each year it seems a surprising team makes the NCAA tournament and actually performs really well. Last year it was VCU which lost to Butler in the semifinals. Do you have any thoughts on who might exceed expectations this year?

JB: VCU just won its conference tournament, and because of the team’s experience from last year, they have a shot at making another run. I think whichever team wins the opening round matchup between VCU and Wichita State is very capable of making a deep run. Also, Belmont is going to be a tough out for anyone. Offensively, the Bruins are great. They are in the top five in points per game and assists. They will give Georgetown all it can handle.

VK: Are there any teams that you think might under perform?

JB: Number one overall seed Kentucky has a tremendous amount of talent, but the Wildcat’s youth may present a problem in the tournament. Winning the tournament requires a blend of talent and mental toughness, and it will be interesting to see how Kentucky’s youthful talent handles the pressure.

VK: For many of the mid-major schools, the only way to make the tournament is to win a conference tournament. Davidson is in this year because they won the SoCon tournament. Duke knew they were going to the dance before the ACC tournament. Did they have anything to gain by winning the tournament?

JB: Of course, they have a banner to gain by winning the conference tournament. College kids usually want to leave their mark, and one way to do that is to win their conference tournament.

VK: Players will get hurt as the tournament progresses. Although I am sure it depends on the type of injury and its severity, how important is the decision to put in an injured player? Suppose you are in the championship game and you are in double overtime?

JB: That is really case-dependent. Injuries to the head (like a concussion) are obviously more serious and a doctor should determine playing time. Other injuries, however, require a consensus decision between player, coach and medical staff. Another factor to consider is that, when a player gets injured in a big game, their epinephrine, or adrenaline, kicks in. This may cause the player to have a fight-or-flight response and play through the pain unfazed.

VK: During the tournament a lower seed team could do really well and have to play a lot of games in a short period of time. What can they do to pace themselves?

JB: In the NCAA tournament, it is all about preparation. Teams that are well trained for endurance will be much better conditioned for the grind of the tournament.

VK: Schools with major basketball programs like UNC and Kentucky have little trouble recruiting. But for a mid-major school, doing well in the NCAA tournament can really help in recruiting the following year. Since this fame may be short-lived, what should a coach look for when recruiting the next season’s team?

JB: I think the most important aspect when recruiting for any team is getting a guy with a good work ethic. All of these kids are extremely athletic and filled with talent, but it’s usually the players who take the time to prepare that end up becoming great.

VK: Although we are encouraging people to use math to select their brackets, there is always that special something that is tossed in, whether it is asking your dog to help you pick or selecting schools that have the most red-headed players, or just all the schools you wish you had attended. I know you must have heard of some crazy ways to select brackets. What are some of your favorites?

JB: On Sport Science we had a chicken fill out a bracket. It didn’t do so well, guessing only 30 percent of the winners. We also brought in 100 people to our lab and had them fill out an empty bracket. Guessing based only on seed numbers, they did better than the chicken, and guessed 60 percent of the winners over the last 25 years…without even knowing the names of any of the teams!

VK: Will you fill out a bracket? Do you have a special method you use?

JB: Through testing, we have discovered that every method has flaws. When picking based on a team’s color, we found teams with blue jerseys have won 68 percent of the national titles in the last 25 years. The mascot with the highest championship winning percentage is a mammal, which has won 48 percent of the national titles over the last 25 years.  Our consensus crowd bracket has fared pretty well, guessing 60 percent of the winners over the last 25 years, and in 2007 specifically, our crowd of 100 random people picked 75 percent of all winners even though they filled out blank brackets with only the seed numbers listed.


About John Brenkus
John Brenkus has spent the last decade studying and popularizing the unique characteristics of the world’s greatest athletes. A co-founder of BASE Productions, he co-created the groundbreaking series Fight Science for the National Geographic Channel and serves as the on-air host, co-creator, and executive producer of ESPN’s Emmy Award–winning show Sport Science.

Davidson College basketball coach, Bob Mckillop, explains March Madness from an inside perspective


The Davidson Wildcats beat Western Carolina 93-91 in the Southern Conference Tournament on March 5 and received an automatic bid to the NCAA Men’s Basketball Tournament. The following interview between Vickie Kearn (VK), Princeton’s math editor and Men’s Basketball coach, Bob McKillop (Coach), reveals what lies ahead for them in March Madness and how getting a high ranking after the tournament helps in recruiting new players.


Vickie Kearn: Congratulations on winning the Southern Conference Championship. It was a fantastic finish. What is the pressure like having to win in double overtime?

Coach McKillop: The experience of what we just did is draining and  exhausting  because of dealing with three successive games, three successive preparations, and three days of anxiety. To even put yourself into the position of thinking about what is the first round  game…..it’s impossible. You want to smell the roses, you want to celebrate what you have accomplished. It’s like climbing Mount Everest and getting to your first peak and trying to get onto the next peak without getting a deep breath. We are getting a deep breath right now and we’re fortunate that our post season tournament is a week prior to selection Sunday and we have a couple of days to  reenergize. With the pressure of our tournament reenergizing is so valuable.

 

VK: How are you preparing for the next game?

Coach:  I believe it is a 12 month journey for every program in America.

As soon as their season ends the previous year, they begin planning, players and coaches, to get back to the tournament. That’s the end-game.

It’s the ultimate goal, so your 12 month journey can either continue or it comes to a crushing end as you stare at another 12 month journey.  At the end of your season, you don’t look at the next day after your final game, you look at the next year.

To expend 12 months of thought, effort, and energy and see it come to a crushing finish, there is quite a finality about it.  The objective joy is to have this journey continue. Winning the Southern Conference tournament is just a step in the process, but at least it is a step up.

It is like a stairway to heaven but if you don’t get on to that first step it’s a dramatic drop.

 

VK: Davidson had to win the Southern Conference tournament to make it into the NCAA tournament. What about teams that have an automatic bid and will be a part of the NCAA tournament whether or not they win their division. Do coaches tend to keep their best players on the bench so they won’t risk being hurt before the NCAA tournament?

Coach: You could look at it from the standpoint of are you content with yesterday’s glory or do you want your journey to continue.  And for some people they are just happy to have reached this level. They are just happy to get into the tournament and if you are just happy to get into the tournament you are going to be facing a very quick exit.  You must think you can accomplish more and you must understand this is just the first step of the journey. This is the only way you can mentally prepare yourself to continue in the tournament.

Basketball is a game of rhythm. Any time you interrupt rhythm, you invite chaos. Continuity is so important. I will give you a typical season-type experience. You have a key player who is hurt. He is able to play in a game but he is not 100%.The temptation is to put him on the court because you need what he is when he is healthy, but in reality it might be better not to play him because he is hurt.  He is not 100% so he is not going to be in the rhythm that is necessary for the team to have rhythm.  We experienced that with Stephen Curry back in 2009. Stephen hurt his ankle very badly on a Saturday and we had an important game the following Saturday.  He wanted to play but he wasn’t 100%. We played him but he did not play with his usual rhythm and of course we lost the game. I think rhythm is a big factor for individuals as well as collectively for the team.

 

VK: Now that the brackets have been revealed, are there any teams you hope to play?

Coach:  No. If I start  thinking about who I would like to play I am going to have  anxiety about preparing and what I want  to do right now is prepare my team to be the best they can become. One of the joys of teaching is to teach your team to get better-not to prepare a team exclusively for one opponent.

 

VK: Do your coaching strategies change from round to round? I imagine playing in the first rounds is quite different than when you made it to the Elite 8 for example.

Coach: I don’t have a lot of experience at that.  But I believe the rhythm of the season becomes the rhythm of the post season and that’s the lesson I learned from the Elite 8 year.

 

VK:  As you move forward does the confidence of your players increase or do they get more nervous?

Coach: Absolutely. The confidence is accentuated by the perception that surrounds the whole tournament by the people associated with your program as well as the exposure in the media. A team that has the fortune of winning receives even more exposure from the media and there is a change in the perception of alums and fans and all of  a sudden, their inspiration, their  energy, their embrace now feeds the team’s own appetite so it becomes a bit more inspired. People who were just there for the ride are now thinking this ride may be taking us somewhere.

 

VK: In addition to promoting sports and math, we are kicking off the publication of Who’s #1? by Amy Langville and Carl Meyer. The book is all about rating and ranking of all kinds of things but this month we are mostly concerned with basketball. When your team made it to the Elite 8 and ended the season ranked #9 in the ESPN/USA Today poll, did it make a difference in your recruiting?

Coach: Absolutely. We had a presence on the national stage instead of the regional stage. It was an identification and that identification also became associated with Stephen Curry who was like a Pavarotti for us-a once in a lifetime performer.  The combination of what we did in the Elite 8 year plus the presence of a national star in Stephen Curry tremendously impacted our recruiting.  And what’ is interesting  is that the current junior class that we have  which is a potent part of our team were recruited  after the 2008 season.

 

VK: Has your success in 2008 continued to help in recruiting?

Coach: Fame is fleeting. Big programs like Duke and Kentucky can do it every year but it is more difficult for a mid-major program.

 

VK: How did the student body react to your success in 2008?  I remember that the board of trustees provided funding for tickets, transportation, and lodging for any students who wanted to attend the Sweet 16 and Elite 8 games.  Did the students take advantage of this offer? Did your success make a difference in attendance at basketball games the following season?

Coach: Over 65% of the student body went to see us play in the Sweet 16 and Elite 8 rounds. It really pumped up home attendance the following season.

Fans were lined up outside before the game and others were scalping tickets.  Our current attendance is about 80 -85% of what it was after the Elite 8 year.

 

VK:  Every year a team receives a lot of attention for surprising everyone with their play. Huge upsets also occur in the tournament. Who do you think the surprise of the season will be?

Coach: I can answer that in a general way. There usually is a team that performs really well even when they are not expected to. In 2006 it was George Mason, in 2008, Davidson, Butler the past 2 years and Virginia Commonwealth University last year. The pressure on mid-major programs to reach the level of these teams is extraordinary. That is also true for higher level conferences. The feeling is, if they can do it, why can’t you?

Administrators, alums, fans expect that their team can make it to the Final 4. They know it can and does happen. The pressure has increased tremendously.

 

VK: We have 9 high school and college math classes across the US completing brackets for the March Mathness site on ESPN. They are all using different algorithms to predict their winner. However, we all know that statistics aren’t everything. What are some of the factors that are important to a team’s performance?

Coach: The important elements are collective talent, experience, and confidence and the mental toughness to perform with consistency. There are ebbs and flows in a team’s success but these are the vital factors.

 

 

 

This is Bob McKillops’ 23rd season with the Davidson Wildcats. To read more about him see http://www.davidsonwildcats.com/coaches.aspx?rc=323&path=mbball

 

 

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

March Mathness Wrap-up

On March 24 we posted some bold predictions on who would win the NCAA basketball championship game. We now have a winner and send our congratulations to Kelly Davis.

Vickie Kearn: My bold pick was Duke based on a little math, past performance, and the luck factor. The one thing missing from my equation was the upset factor and I will be sure to add that next year.

The winner of the ESPN bracket challenge is Joe Pearlman who filled out his bracket in 10 minutes and based his picks on a hunch. Out of 5.9 million entries, he is only one of two people who picked the final four and he will be taking home the $10,000 prize. Does this mean we should throw out all of our math models and go solely on hunches or throw darts at a bracket next year? Absolutely not! As you will see, Tim Chartier and his students did very well with their brackets.

Tim Chartier: Any prediction method is, at some level, working on the odds of longterm success. This can be seen by our methods producing brackets that were in the 90th percentile 3 of the past 4 years. However, this year was, indeed, quite different. Still, Kelly Davis, a senior math major at Davidson College, produced a bracket that beat many celebrity sports analysts’ brackets. We were only using the results of games, the time it occurred in the season, and whether the game was home, away or on neutral ground.

Caption: Kelly Davis with her prizes of Ben and Jerry’s and Princeton University Press books.

Vickie Kearn: What method did you use when preparing your bracket?

Kelly Davis: Like most students in my Math Modeling class, I used a linear weighted Colley Ranking method that we learned about in class, which uses a system of linear equations. Different derivations of the Colley Ranking Method are often used in sports rankings, including for the Bowl Championship Series. Each student then modified this method, to emphasize or add in different factors that each student felt was important. Not knowing much about college basketball, I had to pull from my somewhat limited knowledge of sports to help me decide what factors from the regular season were important to help predict the tournament outcomes. The three major factors that I implemented into my coding were the point difference between the winner and loser, when in the season the game was played and whether the game was home, away or on neutral ground.

Let me give a few more details on this. Factoring in point difference helps to indicate the strength of the win. Winning by a lot is a stronger win than only winning by a little. It also helps to factor in games that are very close in point systems and ultimately come down to a bunch of fouls being called. Considering when in the season the game is played allowed me to give heavy emphasis on the end of the season. If a team is playing poorly at the end (such as due to the injury of a major player) then they will probably not do well. All teams are playing intensely at the end of the season in their conference tournaments, which I consider as a good predictor for tournament play. Finally, I fold in a weight for location. Teams that typically do poorly at away games, will have a hard time in March Madness where no one plays a home game.

Dr. Chartier included the brackets generated by the linear and the uniform Colley methods into our ESPN group so that we could see how our brackets compared to the simplistic/conservative, non-modified versions. Despite ranking lower than the majority of the class last year, the linear Colley method ironically ended up being the next highest bracket after mine, placing in the 64.4 percentile. Last year it placed in the 82 percentile. Perhaps sometimes the safest approach is the best approach!

Vickie: Did you submit more than one bracket? If so, which performed the best?

Kelly: Each student in our class was allowed to submit up to three brackets and I ended up submitting two. My bracket that ended up being the most successful was my initial one that I had to complete for a homework assignment. In this bracket, except for the very first portion of the season, I divided the season up into 10 segments and weighted each segment by an increasing 10% and then weighted the last two segments with a bit higher percentile because most teams are playing conference championship games during this time. In this bracket, I also subtracted a 3 point home court advantage from the score of the home team. For my second one, I placed in the 64.4 percentile, which placed it at the same percentile as the linear Colley method. For this one, I mostly shifted more weight to the end of the season in terms of how important it was to be winning at the end of the season instead of the beginning. I also penalized teams who tended to lose more at away games.

Vickie: Were there any surprises this year that you did not count on and that affected your bracket in a big way?

Kelly: With only 4.7% of over 5.9 million brackets submitted to the Tournament Challenge accurately predicting Connecticut to win, let alone only two people in the entire country correctly picking the final four, I think it is safe to say there were many surprises that most people did not count on! In terms of my bracket, early on in the tournament, my model actually did very well at predicting the outcomes of the first two rounds, with me finishing the second round in the 91.0 percentile, which placed me above many experts on this subject such as Mike Greenberg, Dick Vitale, and Matthew Berry, who ended up in the 21.3, 21.3, and 11.9 percentiles, respectively. Then again, Matt Hasselbeck’s (quarterback for the Seattle Seahawks) 5-year-old son finished in the 93.4 percentile.

As the tournament progressed and more of the upsets started occurring/becoming more apparent, my bracket, along with many others such as President Obama’s bracket, started to be less successful at predicting these surprises. Many of the unpredicted surprises in my bracket were pretty unexpected for most people, such as Kentucky’s win over Ohio, the team that over a quarter of the brackets, including mine, had predicted would win and Butler’s surprising series of wins, as evident by the fact that only 11,326 of the 5.2 million had accurately predicted Butler being in the finals.

Vickie: Each round of the competition provides a certain number of points for a correct pick. For example, you get 10 points for each winner you pick in the second round of play, 80 points for selecting the Elite 8 and 320 points for selecting the champion. The most points you can get is 1920. What was your ESPN score? You didn’t win the $10,000 but what was your prize?

Kelly: As Dr. Chartier mentioned earlier, for the first time in the past four years, my class’s mathematical models were not as successful at predicting all of this year’s surprises and my ESPN score ended up being 560 points, placing me in the 68.1 percentile, which was the same percentile as Colin Cowherd, an American sports radio personality.

Despite not doing as well as other students in previous years, I was a bit more successful within my modeling class and end up winning our inner-class pool. As part of winning our class pool, I received $100 worth of books from Princeton University Press, a t-shirt from the Davidson College Athletics Department and several free cones to Ben & Jerry’s. The picture above shows me sitting in our local Ben & Jerry’s with some books on ranking published by Princeton University Press while I enjoy one of my victory cones.

I think the largest prize of all, however, was the opportunity to show my friends and fellow college students an exciting and cool application of math to a topic most people would never associate with math. Some of my friends hated seeing their carefully thought out brackets lose to a bracket generated by a “math nerd” who knows very little about college basketball, which made my ice cream victory taste even sweeter!

Vickie: What would you do differently next year?

Kelly: After having had a lot of success with running my coding on some of the past few seasons in terms of fairly consistently predicting a large portion of the elite eight’s each year, in some ways I would be tempted to change very little. As with most mathematical models, my model has many limitations and flaws, and consequentially will have instances such as this year where it is less successful at accurately predicting real world outcomes, but then again so were many experts. I think one of the coolest things about using math modeling to predict tournament outcomes is that you can use the same coding to predict outcomes each year without having to spend the entire regular season keeping track of scores and top teams.

A couple of things I would be interested in exploring would be to look at a team’s patterns of wins and losses as an indicator of how to weight wins at different points in the season. After seeing how successful Butler was for the second year in a row, I also think it would be interesting to consider the success rates of teams in previous March Madness tournaments.

Vickie: In the earlier post, Lucy McMurry was doing well. How did her bracket do in the end?

Tim Chartier: Lucy was, indeed, doing very well. However, many of her picks did not lead to points as the tournament progressed and so she ended up in the 50.9 percentile. So, she was better than over half the brackets but it was indeed a difficult year! We look forward to next year and maybe this year will give us new ideas and even new statistics to fold into our methods. Nevertheless, there will also be upsets and a certain amount of madness in March as the tournament unfolds.