Tim Chartier, author of Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing has turned some mathematical tricks to help better predict the outcome of this year’s World Cup in Brazil.
Along 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.
The ups and downs of March Madness are slipping into memory, but we have one final postscript to write. Who won the March Mathness challenge put forth by Tim Chartier to his students at Davidson College?
We are delighted to announce that Robin Malloch, a history major who is graduating this month, picked the best brackets out of Dr. Chartier’s class. She has joined Teach for America and will be teaching Middle School math in Charlotte, North Carolina this fall. Thankfully, before she heads off to do the good work of teaching algebra and geometry to eager (or truthfully, not so eager, we’re guessing) 7th and 8th graders, she has provided us with some insight into her bracket strategy during March Mathness:
I will describe my method as best I can. I made several brackets with different methodologies–one based on basketball gut, one on pure math, and others with a combination. My purely mathematical bracket did not fair that well. My two combination brackets which were a bit more arbitrary fared the best (89th and 92nd percentile). For those, I used the math to inform my basketball knowledge. Any time my basketball bracket contradicted the math ranking or if the rankings were nearly tied, I would look into the game further to see if either team had key players injured, how player matchups, what experience/track record the coaches had, etc.
As for my actual math rankings, I used Colley. I tried to account for strength of schedule, so I broke the season into three parts. The last couple games of the season are the conference tournament, which I gave more value to than any other games of the season. Then I broke the rest of the season in half: the first half being primarily out-of-conference games and the second half being primarily in-conference ones. For teams in a competitive conference (more than 3 teams from the conference in the tournament), I weighted the second half more heavily. For teams in weaker conferences, I weighted the first half more heavily when teams would likely face tougher competition. This method actually made my rankings closely resemble the 1-16 rankings produced by the NCAA selection committee. I enjoyed applying math brackets and looking at basketball with a new lens.
For more on the various bracketology methods Tim Chartier teaches his students, please check out our March Mathness page.
Still rushing to fill out your brackets for the NCAA tournament? This free online course from mathematician Tim Chartier, author of Math Bytes, might help.
In this course, you will learn three popular rating methods two of which are also used by the Bowl Championship Series, the organization that determines which college football teams are invited to which bowl games. The first method is simple winning percentage. The other two methods are the Colley Method and the Massey Method, each of which computes a ranking by solving a system of linear equations. We also learn how to adapt the methods to take late season momentum into account. This allows you to create your very own mathematically-produced brackets for March Madness by writing your own code or using the software provided with this course.
From this course, you will learn math driven methods that have led Dr. Chartier and his students to place in the top 97% of 4.6 million brackets submitted to ESPN!
Explore Tim Chartier’s March MATHness lectures:
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.”
Each week we post a round-up of some of our most exciting national and international PUP book coverage. Reviews, interviews, events, articles–this is the spot for coverage of all things “PUP books” that took place in the last week. Enjoy!
With George Washington’s birthday approaching, it seems fitting that we start off this week with a look at good ol’ G.W. We depend on George Washington every day — on the front of the dollar, of course. For PUP author Eswar Prasad, it is all about the dollar. The U.S. dollar’s dominance seems under threat. The near collapse of the U.S. financial system in 2008-2009, political paralysis that has blocked effective policymaking, and emerging competitors such as the Chinese renminbi have heightened speculation about the dollar’s looming displacement as the main reserve currency. Yet, as The Dollar Trap powerfully argues, the financial crisis, a dysfunctional international monetary system, and U.S. policies have paradoxically strengthened the dollar’s importance. This week, the New York Times ran a review of The Dollar Trap in the Sunday Business section. Want to preview the book? You can view the preface and Chapter One. Professor Prasad is also included in this week’s edition of BBC World Service Business Matters.
The Shanghai Daily‘s Wan Lixin reviewed Essays and Reviews, saying of the book:
[A] stimulating read for anyone who cares about the condition of the world. With characteristic clarity, insight, and humor, the author tackles a wide range of topics as diverse as philosophy, religion, science, the humanities, and pornography.
“Start spreading the news…” We reading today. We know you’d like to be a part of it — our new book on old New York. We’re channeling our inner Sinatra as we present our next book in this week’s News of the World: The New York Nobody Knows.
As a kid growing up in Manhattan, William Helmreich played a game with his father they called “Last Stop.” They would pick a subway line and ride it to its final destination, and explore the neighborhood there. Decades later, Helmreich teaches university courses about New York, and his love for exploring the city is as strong as ever. Putting his feet to the test, he decided that the only way to truly understand New York was to walk virtually every block of all five boroughs–an astonishing 6,000 miles. His epic journey lasted four years and took him to every corner of Manhattan, Brooklyn, Queens, the Bronx, and Staten Island. Helmreich spoke with hundreds of New Yorkers from every part of the globe and from every walk of life, including Mayor Michael Bloomberg and former mayors Rudolph Giuliani, David Dinkins, and Edward Koch. Their stories and his are the subject of this captivating and highly original book.
Professor Helmreich wrote an op-ed for the Daily News this week. The piece, entitled “I was on your block; here’s what I learned,” addresses what he sees as the “often underappreciated norm” of New York City’s tolerance for differences. He writes:
How is it, I wondered, that immigrants from more than 100 countries speaking more than 170 languages can coexist in relative peace and harmony, while European cities like Paris, Frankfurt and Amsterdam have far greater difficulty integrating their racial, ethnic and religious groups?
New this week, Professor Stent sits down with PBS Newshour and the Economist to discuss her views of the tense relationship between the U.S. and Russia as well as her personal interactions with Russia’s President Vladimir Putin. Check out these two videos:
Considered by many to be the father of computer science, Alan Turing is remembered today for his many contributions to the study of computers, artificial intelligence, and code breaking. On December 24, Queen Elizabeth II officially pardoned the late British mathematician and the action recalled attention to his groundbreaking work as well as his personal life. In 1952, Turing was charged with homosexuality, which was considered a criminal act in England at the time. Two years later, he took his own life. Today, mathematicians and computer scientists celebrate Turing’s broad contributions to his field.
For more on the life and work of Turing, check out these resources:
Princeton University Press recently re-released Andrew Hodges’s biography of Alan Turing: Alan Turing: The Enigma — The Centenary Edition.
It is only a slight exaggeration to say that the British mathematician Alan Turing (1912-1954) saved the Allies from the Nazis, invented the computer and artificial intelligence, and anticipated gay liberation by decades–all before his suicide at age forty-one. This classic biography of the founder of computer science, reissued on the centenary of his birth with a substantial new preface by the author, is the definitive account of an extraordinary mind and life. A gripping story of mathematics, computers, cryptography, and homosexual persecution, Andrew Hodges’s acclaimed book captures both the inner and outer drama of Turing’s life.
Turing earned his Ph.D. in mathematics from Princeton in 1938. Watch the video below to hear Andrew Appel (chair of the department of computer science at Princeton) discuss Turing’s legacy.
Andrew Appel on Alan Turing’s legacy
(Princeton School of Engineering and Applied Science)
Appel, a Princeton graduate, is the editor of another recent release by Princeton University Press, Alan Turing’s Systems of Logic: The Princeton Thesis.
Though less well known than his other work, Turing’s 1938 Princeton PhD thesis, “Systems of Logic Based on Ordinals,” which includes his notion of an oracle machine, has had a lasting influence on computer science and mathematics. This book presents a facsimile of the original typescript of the thesis along with essays by Andrew Appel and Solomon Feferman that explain its still-unfolding significance.
Preview the book by reading Chapter One.
Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures.
Wassim M. Haddad is a professor in the School of Aerospace Engineering and chair of the Flight Mechanics and Control Discipline at Georgia Institute of Technology.
Davidson College student, Jane Gribble, was our March Mathness winner this year. Below she explains how she filled in her bracket.
I love basketball – Davidson College basketball. As a Davidson College cheerleader I have an enormous amount of school pride, especially when it comes to our basketball team. However, outside of Davidson College I know little to nothing about college basketball. I knew that UNC Chapel Hill was having a tough season because this is my sister’s alma mater. Also, I knew that New Mexico, Gonzaga, Duke, and Montana were all likely teams for the NCAA tournament because we had played these non-conference teams during our season and these were the most talked about non-conference games around campus. My name is Jane Gribble. I am a junior mathematics major and this is the first year I completed a bracket.
In Dr. Tim Chartier’s MAT 210 – Mathematical Modeling course we discussed sports ranking using the Colley method and the Massey method. We were given the opportunity to apply our new knowledge of sports ranking in the NCAA Tournament Challenge. Since Davidson College was participating in the tournament my focus was on one game, the Davidson/Marquette game in Lexington, KY. When we traveled to KY I thought I had missed my opportunity to fill out a bracket, but one of my classmates was also traveling for the game with the Davidson College Pep Band and had the modeling program on his computer. We completed our brackets in the hotel lobby in Kentucky the night before our game.
My bracket used the Massey method because in previous years it has had better success than the Colley method. I decided to submit only one bracket, a bracket solely based on math (partially because I know little about college basketball). As a cheerleader and a prideful student it upset me to have Davidson losing against Marquette the following night, but I wasn’t going to let a math model crush my personal dreams of success in the tournament. The home games were weighted as .5 (it would have been 1 if it was an unweighted model) to take into account home court advantage. Similarly, away games were weighted as 1.5 and neutral games as 1. Also, the season was segmented into 6 equal sections. I believe games at the end of the season are more important than games at the beginning of the season because teams change throughout the year and the last games give the best perspective of the teams going into the tournament. There was no real reason for the numbers chosen, other than they increased each segment. The 6 equal sections were weighted: .4, .6, .8, 1, 1.5, and 2. With these weights in the Massey method my model correctly predicted the Minnesota upset, but missed the Ole Miss, LaSalle, Harvard, and Florida Gulf upsets.
After Davidson’s tragic loss I could not watch anymore basketball for a while. I even forgot that my bracket was in the competition. I only started paying attention to the brackets when a friend in the same competition congratulated me on being second going into the Elite 8; my math based bracket was in the top 10 percent of all the brackets. Once he told me my bracket had a chance of winning, I paid attention to the rest of the games to see how my bracket was doing in the competition. After Davidson’s loss against Louisville last year in the tournament I never wanted to cheer for Louisville. To my surprise, I went into the final game this year cheering for Louisville because my model had Louisville winning it all. I was not cheering for Louisville because of any connections with the team, but was cheering to receive a free ice cream cone, a prize that our local Ben and Jerry’s donates to the winner of Dr. Chartier’s class pool.
Next year I hope to compete in the NCAA tournament challenge again. This year I greatly enjoyed the experience and want to continuing submitting brackets for the tournament. Next year I will submit one bracket that uses the exact weightings of my bracket this year to see how it compares from year to year. This year I wanted to submit a math bracket that looked at teams who had injuries throughout the season. My motivation for this was Davidson’s player Clint Mann. Clint had to sit out many games towards the end of the season because of a concussion, but he had recovered in time for the NCAA tournament. I thought that our wins during the time without Clint showed our strengths as a team. Unfortunately this year I ran out of time to code this additional weighting. Hopefully next year my submissions will include a bracket using the weights from this year, a bracket that includes weights for teams with injured team members, and another bracket with varying weights.
Davidson math professor, PUP author and bracketology expert, Tim Chartier, discusses the math behind March Madness with the LA Times.
His telephone rings, he’s on the radio, he’s talking to ESPN, and for once he can explain what exactly he does for a living at North Carolina’s Davidson College.
“For the first time in my life I can talk about what I’m doing, on a higher level, and people understand,” Chartier said.
What Chartier does is use complex math to win the Final Four pool on a regular basis. How regular a basis? He’s been in the top 3% of the 4 million submissions to ESPN’s March Madness tournament challenge, which is arguably the major league of sports prognostication.
“That’s when we said, whoa, this thing really works,” Chartier said of his brush with sports handicapping superstardom.
Blame it on tiny Butler College. Chartier’s math class was among those to recognize that fifth-seeded Butler was destined for the finals in 2010. That was the second year Chartier started making bracketology — the art and science of picking winners among 68 teams in a single-elimination tournament — part of his syllabus. That’s right: take Chartier’s course and you’ll be deep into basketball come March.
Source: Los Angeles Times, “March Madness puts Davidson math professor in a bracket of his own” http://touch.latimes.com/#section/-1/article/p2p-74922641/
Skipping to the good stuff — who is going to win March Madness this year? At least according to the math?
So, who did Chartier pick? With a simplified Massey method (which gives his students a fighting chance), he agrees with Dick Vitale: Louisville wins it all, in this case beating Florida, then Indiana, which beats Gonzaga.
By the Colley method, the Final Four are Duke, Kansas, New Mexico and Miami, with New Mexico winning.
Which system will do the best?
“That’s the madness for us in the math!” Chartier said.
Read the complete article here: http://touch.latimes.com/#section/-1/article/p2p-74922641/
After the Round of 32, Kyle Snipes was #1 on our leaderboard. Below he gives us an update on his bracket.
As the scores continued to roll in Friday and Saturday afternoon, I was left echoing the words of many bracketologists around the country- “Dang, thanks to ___________, my bracket is totally busted!” For me, FGCU, Oregon, and Ole Miss dealt the harshest blows. When the second round was said and done, my mathematical methods had correctly predicted 2 of the 10 first round upsets (lower seed over higher seed) while incorrectly predicting victories by Missouri and St. Mary’s over their higher seeded opponents. Once the madness of the first weekend had subsided, however, I came out looking relatively strong. As of the first weekend of the tournament, my best bracket (based on the Massey method) was sitting at the 97.2 percentile in ESPN’s nationwide pool.
While my method was unable to recognize strong teams on the lower seed lines, it did a great job of telling me which teams were strong out of the teams that everyone thought would be strong (with the exception of Gonzaga). Looking forward, I still have 7 out of 8 teams remaining in the Elite Eight, and 3 out of 4 Final Fours teams, including my National Championship participants. I’m excited to see if my bracket is able to remain near the top as the tournament plays itself, but more importantly, I’m ready for some more March Madness!
Maddie Parrish is senior Economics major with a Communications Studies concentration at Davidson College. She plays Division I field hockey.
March Madness. 65 elite NCAA Division I Basketball teams competing to win it all, the NCAA Tournament Championship. Every year fans from across the nation create brackets to predict who will ultimately be #1. I am one of those fans, and I’m excited to share my story. My name is Maddie Parrish and I am a senior Economics major with a Communication Studies concentration at Davidson College, a small, highly selective liberal arts school twenty minutes north of Charlotte, NC. We are also the alma mater to such basketball phenoms as John Belk ’43, Terrence Holland ’65, Kenneth Wilson ’84, Mike Maloy, and Stephen Curry. My hometown is Chester, VA, a suburb of Richmond and I have interests in economics, communications, sports, and many other topics. In the fall of 2012, I wrapped up my fourth and final season as a member of the Davidson Wildcats NCAA Division I Field Hockey Team. Being a student-athlete at Davidson has clearly shaped my college experience. It has made me who I am today by teaching me many lessons about dedication, respect, passion, heart, and life in general.
As a student-athlete, the pride I have in my school and its’ athletic teams is enormous. I am a huge fan of college basketball and I am close friends with many of the Davidson Basketball Team members. Our boys just won the 2013 Southern Conference Championship for a second year in a row and the entire school is supporting them in their March Madness journey to the NCAA Championship. My personal connections and interest in Davidson basketball are my main reasons for completing a March Madness bracket this year.
I am an athlete, a sports-lover, and a passionate sports enthusiast. Although a rookie to Bracketology, I know that using mathematic strategies is the best way to create a successful bracket. Being an Economics major, math comes easily to me and I find it very enjoyable. This Spring I am taking Dr. Tim Chartier’s MAT 110 – Finite Math course here at Davidson in which we spend a good chunk of class time learning about linear systems and how to solve them. The concepts of linear systems are the key behind ranking the right teams in our bracket by using matrices and weighted values. In class, we learned about the Colley Method for sports ranking, which utilizes winning percentage to determine each team’s ranking. Another method of sports ranking is the Massey Method, which utilizes actual game scores in the regular season to determine each team’s ranking. With both methods, there is an opportunity to choose your own weighted values for specific times during the season. For example, it is possible to weight games that occurred in the beginning of the season less than games mid-way through the season and at the end of the season. If games at the end of the season are weighted more than 1 game, say each game counts as 2 games; the weight is capturing a team’s final push or momentum. A team’s momentum is explained by their ability to win games at the end of the season, which is admirable because the season is so long and competition may be very tough.
For my March Madness bracket this year, I am choosing to use the Colley Method because I am curious to use my newly learned knowledge from class in a life application and see how well it really works. I split the season into four even intervals, one for games at the beginning of the
season, one for games leading up to mid-way through the season, one for games in the second half of the season, and one for games at the very end of the season. I am creating my weights for each season interval based on the hypothesis that as a basketball team plays more games, it gains momentum and wins more frequently. I also am using the Davidson Men’s Basketball schedule results from this year to create my weights. In the first two intervals of the season, the team lost a good number of games. However, they have not yet lost a game in the third and fourth intervals of this year’s season. Using this intuition, I am weighting the first interval at 0.5/1 game, the second interval at 0.75/1 game, the third interval at 1.25/1 game, and the fourth interval at 2/1 games. This means that games played in the beginning of the season are only worth half of a game and games at the end of the season are worth two games. Therefore, if a team is winning more at the end of the season due to momentum then those wins will be worth more in my ranking method.
I understand that using the Colley Method may not factor in specific scores of games and because of this will not capture strength of opponents throughout the season. Yet, I am confident that using the Colley Method and the particular weights I have chosen will produce solid results. After the 65 teams (1 play-in) were announced on Selection Sunday, I filled in my bracket according my method rankings. Of course, I ranked Davidson higher due to the success of their season thus far and due to my personal bias.
As a student-athlete, I have always been interested in how we can harness the talents of individual teams throughout the nation and celebrate sports through common mediums such as love for the game, competition, and passion for your school. The NCAA Division I Men’s Basketball Tournament provides a venue for all of these values. It also allows for fans to express their passion for the game, pride for their school, and their intuitive math sense in a fun way. Using my intuition as an athlete and my knowledge of math, I have created a bracket that I hope will perform well during the March Madness basketball tournament. I am curious to see how it turns out and wish the best of luck to all of the teams who have the honor and privilege of participating in the tournament! Here at Davidson, we have a saying that runs throughout campus each day that follows “It’s a Great Day to be a Wildcat!” Hopefully, my bracket will sing this tune throughout the tournament! Go ‘Cats!
Kyle Snipes is a senior Math major at Davidson College. He is from Indian Trail, NC. He is a volunteer Younglife leader and a lifelong basketball fan. He will be spending this March Madness season cheering on the Davidson Wildcats!
I have competed in bracket pools for a long as I can remember. In the past I have picked games based on what I know about basketball with a fairly high success rate. Since my senior year of high school, I have won at least one of the couple of pools that I have competed in. This will be my first year applying mathematics to my March Madness selections.
I will use ranking methods adapted from the Colley and Massey ranking methods. Since all NCAA tournament games are played at neutral sites, I will count road and neutral site games as a full game, while weighting home games as partial games to account for any homecourt advantage a team might have during the regular season.
I will weigh different portions of the season differently. Generally teams will play the toughest part of their nonconference schedule in preseason tournaments and standalone nonconference games early in the season. On the other hand, a team’s performance early of the season is less likely to be representative of their performance at the end of the season. Therefore, I will give games during the first quarter of the season a weight of 0.7. The second quarter of the season is still a bit early to be representative of a team’s performance come tournament time. Since there are generally fewer nonconference games during this part of the season, I will give these games a weight of 0.6. Teams begin playing the important part of their nonconference during the third quarter of the season. It is also the point in the season where teams poised to make a deep run in the tournament will begin hitting their stride. I will give the games during this quarter of the season a weight of 0.85. Teams that succeed during the last quarter of the regular season are the teams that will be hot coming into the tournament. I will give these games a weight of 1. I have noticed that teams that rely solely on winning their conference tournaments to get to the Big Dance will be burnt out by the time they play the next weekend. Furthermore, teams that have already secured a spot in the Big Dance may have more of an incentive to rest players and avoid injury than to perform to the best of their potential during their conference tournament, making these games even more illegitimate. Therefore, I will only use data from regular season games in my rankings.
One last idea I would like to implement into my ranking is to reward teams who go on long winning streaks as well as teams who are able to beat teams on long winning streaks. I imagine that this will help pick out teams who are able to win successive games, as they must do in the tournament, as well as the giant killers who are able to beat teams that are in the middle of a strong run. If I have the time, I will do this by incrementing a game’s weight by 0.05 for each game in the winning streak for whichever team comes into the game with a longer winning streak. I will cap this at a weight of 1.5 games to avoid over-rewarding strong teams playing in weak conferences in which long winning streaks are common. I plan on submitting three bracket– two using different ranking methods and one where I will synthesize the math with my intuition. I’m excited to see how my picks stand up against the rest of the country!
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!
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.