Davidson student hangs onto 97 percent March Madness ranking

Are you still mourning the loss of your perfect bracket after the multiple upsets this March Madness season? Even before the Villanova and NC State match up on Saturday, 99.3 percent of brackets were busted. As experts deem a perfect March Madness bracket impossible, having a nearly perfect bracket is something to brag about. Today, we hear from David College student Nathan Argueta, who argues that knowing a thing or two about math can help with March Madness strategy.

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March Mathness: Calculating the Best Bracket

First and foremost… I am far from a Math Major and, prior to this class, the notion that math and sports going hand in hand seemed much more theoretical than based in reality. Now, 48 games later and a 97.2% ranking percentage on ESPN’s Bracket Contest has me thinking otherwise.

In Finite Math, we have explored the realms of creating rankings for teams based on multiple factors (win percentage, quality wins, etc.). Personally, I also take into account teams’ prior experience in the NCAA Tournament. Coaches with experience in the Sweet 16, Final Four, and Championship Game (like Rick Pitino out of Louisville) also factored into my decisions when deciding close games. Rick Pitino has made the Sweet Sixteen for each of the past four years. With a roster whose minutes are primarily distributed amongst second and third year players (players who have had success in the NCAA tournament in the past couple of years) I found it difficult to picture Louisville losing to either UCI, UNI, or even the upcoming battle against upstart NC State (who have successfully busted the majority of brackets in our class’s circuit by topping off Villanova).

In theory, the quest to picking the best bracket on ESPN begins and ends with establishing rankings for each team in the contest. Sure there are four of each seeding (1’s, 2’s, etc.), yet these rankings are very discombobulating when attempting to decide which team will win between a 5th seed and a 12th seed or a 4th seed and a 13th seed. One particular matchup that I found extremely interesting was the one between 13th seeded Harvard and 4th seeded UNC. Gut reaction call—pick UNC. UNC boasts a higher ranking and has ritual success in the postseason. But hold on—Harvard had a terrific record this year (much better than UNC’s, albeit in an easier conference). The difficult thing about comparing Harvard and UNC, however, became this establishment of difficulty of schedule. I nearly chose Harvard, were it not for the fact that Harvard got beaten by about 40 points against UVA while UNC put up more of a fight and only lost by 10 points.

In order to pick the perfect bracket (which mind you, will never happen), categorizing and ranking teams based on their wins against common opponents with prior sports knowledge is imperative. My school pride got the better of me when I chose Davidson to advance out of the Round of 64 against Iowa simply because I disregarded factors like momentum, size, and location. Looking back, it is no wonder that Davidson lost by over 30 points in what many pundits were looking to be a potential upset match. While mathematically our team’s chances could have more than competed against Iowa, in reality our season was spiraling downwards out of control since the second round of the Atlantic 10 Tournament in which we hardly beat out a surprising La Salle team and got annihilated by an injury plagued VCU team that we shut-out just nine days before. Moral of the story… brackets will be brackets and while math can certainly guide you towards a higher ranking in your class pool, you can kiss perfection good-bye. This is March Madness.

Using math for March Madness bracket picks

The countdown to fill out your March Madness brackets is on! Who are you picking to win it all?

Today, we hear from Liana Valentino, a student at the College of Charleston who works with PUP authors Amy Langville and Tim Chartier. Liana discusses how math can be applied to bracket selection.

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What are the chances your team makes it to the next round?

The madness has begun! Since the top 64 teams have been released, brackets are being made all over the country. As an avid college basketball fan my entire life, this is always my favorite time of the year. This year, I have taken a new approach to filling out brackets that consist of more than my basketball knowledge, I am using math as well.

To learn more about how the math is used to make predictions, information is available on Dr. Tim Chartier’s March Mathness website, where you can create your own bracket using math as well!

My bracket choices are decided using the Colley and Massey ranking methods; Colley only uses wins and losses, while Massey integrates the scores of the games. Within these methods, there are several different weighting options that will change the ratings produced. My strategy is to generate multiple sets of rankings, then determine the probability that each particular team will make it to a specific round. Using this approach, I am able to combine the results of multiple methods instead of having to decide on one to use for the entire bracket.

Choosing what weighting options to use is a personal decision. I will list the ones I’ve used and the reasoning behind them using my basketball awareness.

(1)

Winning games on the road should be rewarded more than winning games at home. Because of that, I use constant rates of .6 for a winning at home, 1.6 for winning away, and 1 for winning at a neutral location; these are the numbers used by the NCAA when determining RPI. I incorporate home and away weightings when performing other weighting methods as well.

(2)

Margin of victory is another factor, but a “blow out” game is defined differently depending on the person. With that in mind, I ran methods using the margin of victory to be both 15 and 20. This means if the margin of victory if 15, then games with a point differential of 15 or higher are weighed the same. These numbers are mainly from personal experience. If a team wins by 20, I would consider that a blowout, meaning the matchup was simply unfair. If a team loses by 15, which in terms of the game is five possessions, the game wasn’t necessarily a blow out, but the winning team is clearly defined as better than the opposition.

In addition to this, I chose to weight games differently if they were close. I defined a close game as a game within one possession, therefore three points. My reasoning behind this was if a team is blowing out every opponent, it means those games are obviously against mismatched opponents, so that does not say very much about them. On the other hand, a team that constantly wins close games shows character. Also, when it comes tournament time, there aren’t going to be many blow out games, therefore teams that can handle close game situations well will excel compared to those who fold under pressure. Because of this, I weighted close games, within three points, 1.5, “blow out” games, greater than 20 points, .5, and any point differential in between as 1.

(3)

Games played at different points in the season are also weighted differently. Would you say a team is the same in the first game as the last? There are three different methods to weight time, as provided by Dr. Chartier using his March Mathness site, linearly, logarithmically, and using intervals. Linear and logarithmic weights are similar in the fact that both increase the weight of the game as the season progresses. These methods can be used if you believe that games towards the end of the season are more important than games at the beginning.

Interval weighting consists of breaking the season into equal sized intervals and choosing specific weightings for each. In one instance, I weighted the games by splitting the season in half, down weighting the first half using .5, and up weighting the second half using 1.5 and 2. These decisions were made because during the first half of the season, teams are still getting to know themselves, while during the second half of the season, there are fewer excuses the make. Also, the second half of the season is when conference games are played, which are generally considered more important than non-conference games. For the people that argue that non conference play is more important because it is usually more difficult than in conference play, I also created one bracket where I up weight the first half of the season and down weight the second half.

(4)

The last different weighting method used was incorporating if a team was on a winning streak. In this case, we would weight a game higher if one team breaks their opponents winning streak. Personally, I defined a winning streak as having won four or more games in a row.

I used several combinations of these various methods and created 36 different brackets that I have used to obtain the following information. Surprisingly, Kentucky only wins the tournament 75% of the time; Arizona wins about 20%, and the remaining 5% is split between Wisconsin and Villanova. Interestingly enough, the only round Kentucky ever loses in is the Final Four, so each time they do make it to the championship, they win. Duke is the only number 1 seed never predicted to win a championship.

Villanova makes it to the championship game 70% of the time, where the only team that prevents them from doing so is Duke, who makes it 25% of the time. The remaining teams for that side of the bracket that make it are Stephen F. Austin and Virginia, both with a 2.5% chance. Kentucky makes it to the championship game 75% of the time, while Arizona makes it 22%, and Wisconsin makes it 3%. However, if Arizona makes it the championship game, they win it 88% of the time. Furthermore, Wisconsin is predicted to play in the championship game once, which they win.

The two teams Kentucky loses to in the Final Four are Arizona, and Wisconsin. During the final four, Kentucky has Arizona as an opponent 39% of the time, where Arizona wins 50% of those matchups. Kentucky’s only other opponent in the final four is Wisconsin, where Wisconsin wins that game only 5% of the time. On the other side, Villanova makes it to the final four 97% of the time, where the one instance they did not was a loss to Virginia. Villanova’s opponent in the Final Four is made up of Duke 72%, Gonzaga 19%, Stephen F. Austin 6%, Utah at 3%. The only seeds that appear in the Final Four are 1, 2, and one 12 seed, Stephen F. Austin one time.

During the Elite 8, Duke is the only number 1 seed that does not make it 100% of the time, with Utah upsetting them in 17% of their matchups. The other Elite 8 member is Gonzaga 97% of the time. Kentucky’s opponent in this round is Notre Dame 47% and Kansas 53% of the time.

In the Sweet 16, there are eight teams that make it every time: Kentucky, Wisconsin, Villanova, Duke, Arizona, Virginia, Gonzaga, and Notre Dame. Kansas is the only number 2 seed not on the list as Wichita State is predicted to beat them in 8% of their matchups. Kentucky’s opponent in the Sweet 16 is Maryland 39%, West Virginia 36%, Valparaiso 14%, and Buffalo 11%. Valparaiso is the only 13 seed predicted to make it to the Sweet 16. Villanova’s opponent is either Northern Iowa 61% or Louisville 38%. Duke appears to be facing either Utah 67%, Stephen F. Austin 19%, or Georgetown 14%.

Now, for the teams that make it into the third round. I’m not sure how many people consider a 9 seed beating an 8 seed an upset, but the number 9 seeds that are expected to progress are Purdue, Oklahoma State, and St. John’s. In regards to the 10 seed, Davidson is the most likely to continue with a 47% chance to move past Iowa, which is the highest percentage for an upset not including the 8-9 seed matchups. Following them is 11 seed Texas, who have a 42% of defeating Butler. For the 12 seeds, Buffalo is the most likely to continue with a 36% chance of beating Virginia. The 13 seed with the best chance of progressing is Valparaiso with 19% over Maryland. Lastly, the only 14 seeds that move on are Georgia State and Albany, which only happens a mere 8% of the time.

In general, Arizona seems to win the championship when using Massey and linear or interval weighting without home and away. This could be because most of their losses happen during the beginning of the season, while they win important games towards the end. Using the Colley method is when most of the upsets are predicted. For example, Stephen F. Austin making it to the championship game happens using the Colley logarithmic weighting. Davidson beating Iowa in the second round is also found many times using different Colley methods.

Overall, there are various methods that include various factors, but there are still qualitative variables that we don’t include. On the other hand, math can do a lot more than people expect. Considering Kentucky is undefeated, I presumed the math would never show them losing, but there is a lot more in the numbers than you think. Combining the various methods on 36 different brackets, I computed the probabilities of teams making it to specific rounds and decided to make a bracket using the combined data. This makes it so I don’t have to decide on solely one weighting that determines my bracket; instead, I use the results from several methods. Unfortunately, there is always one factor we cannot consider, luck! That is why we can only make estimates and never be certain. From my results, I would predict to see a Final Four of Kentucky, Arizona, Villanova, Duke; a championship game of Kentucky, Villanova; and the 2015 national champion being Kentucky.

 

 

Cinderella stories? A College of Charleston student examines March Madness upsets through math

Drew Passarello, a student at the College of Charleston, takes a closer look at how math relates to upsets and predictability in March Madness.

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The Madness is coming. In a way, it is here! With the first round of the March Madness tournament announced, the craziness of filling out the tournament brackets is upon us! Can math help us get a better handle on where we might see upsets in March Madness? In this post, I will detail how math helps us get a handle on what level of madness we expect in the tournament. Said another way, how many upsets do we expect? Will there be a lot? We call that a bad year as that leads to brackets having lower accuracy in their predictions. By the end of the article, you will see how math can earmark teams that might be on the cusp of upsets in the games that will capture national attention.

Where am I learning this math? I am taking a sports analytics class at the College of Charleston under the supervision of Dr. Tim Chartier and Dr. Amy Langville. Part of our work has been researching new results and insights in bracketology. My research uses the Massey and Colley ranking methods. Part of my research deals with the following question: What are good years and bad years in terms of March Madness? In other words, before the tournament begins, what can we infer about how predictable the tournament will be?

One way of answering this question is to see how accurate one is at predicting the winners of the tournaments coupled with how high one’s ESPN score is. However, I also wanted to account for the variability of the level of competition going into the tournament, which is why I also looked at the standard deviation of the ratings of those in March Madness. A higher standard deviation implies the more spread out the playing level is. Ultimately, a good year will have a high tournament accuracy, high ESPN score, and a high standard deviation of ratings for those competing in March Madness. Similarly, a bad year will have low tournament accuracy, low ESPN score, and a low standard deviation of the ratings. This assessment will be relative to the ranking method itself and only defines good years and bad years solely in terms of past March Madness data.

I focused on ratings from uniformly weighted Massey and Colley ranking methods as the weighting might add some bias. However, my simple assessment can be applied for other variations of weighting Massey and Colley. I found the mean accuracy, mean ESPN score, and mean standard deviation of ratings of the teams in March Madness for years 2001 – 2014, and I then looked at the years which rested below or above these corresponding means. Years overlapping were those deemed to be good or bad, and the remaining years were labeled neutral. The good years for Massey were 2001, 2004, 2008, and 2009, and the bad years were 2006, 2010 – 2014. Neutral years were 2002, 2003, and 2007. Also, for Colley, the good years were 2005, 2007 – 2009; bad years were 2001, 2006, and 2010 – 2014; neutral years were 2002 – 2004. A very interesting trend I noticed from both Massey and Colley was that the standard deviation of the ratings of those in March Madness from 2010 to 2014 were significantly lower than the years before. This leads me to believe that basketball has recently become more competitive in terms of March Madness, which would also partially explain why 2010 – 2014 were bad years for both methods. However, this does not necessarily imply 2015 will be a bad year.

In order to get a feel for how accurate the ranking methods will be for this year, I created a regression line based on years 2001 – 2014 that had tournament accuracy as the dependent variable and standard deviation of the ratings of those in March Madness as the independent variable. Massey is predicted to have 65.81% accuracy for predicting winners this year whereas Colley is predicted to have 64.19%accuracy. The standard deviation of the ratings for those expected to be in the tournament was 8.0451 for Massey and 0.1528 for Colley, and these mostly resemble the standard deviation of the ratings of the March Madness teams in 2002 and 2007.

After this assessment, I wanted to figure out what defines an upset relative to the ratings. To answer this, I looked at season data and focused on uniform Massey. Specifically for this year, I used the first half of the season ratings to predict the first week of the second half of the season and then updated the ratings. After this, I would use these to predict the next week and update the ratings again and so on until now. For games incorrectly predicted, the median in the difference of ratings was 2.2727, and the mean was 3.0284. I defined an upset for this year to be those games in which the absolute difference in the ratings is greater than or equal to three. This definition of an upset is relative to this particular year. I then kept track of the upsets for those teams expected to be in the tournament. I looked at the number of upsets each team had and the number of times each team gets upset, along with the score differential and rating differences for these games. From comparing these trends, I determined the following teams to be upset teams to look for in the tournament: Indiana, NC State, Notre Dame, and Georgetown. These teams had a higher ratio of upsets over getting upset when compared to the other teams. Also, these teams had games in which the score differences and rating differences were larger than those from the other teams in March Madness.

I am still working on ways to weight these upset games from the second half of the season, and one of the approaches relies on the score differential of the game. Essentially, teams who upset teams by a lot of points should benefit more in the ratings. Similarly, teams who get upset by a lot of points should be penalized more in the ratings. For a fun and easy bracket, I am going to weight upset games heavily on the week before conference tournament play and a week into conference tournament play. These two weeks gave the best correlation coefficient in terms of accuracy from these weeks and the accuracy from March Madness for both uniform Massey and Colley. Let the madness begin!

 

May the odds be in your favor — March Mathness begins

Let the games begin! After the excitement of Selection Sunday, brackets are ready for “the picking.” Have you started making your picks?

Check out the full schedule of teams selected yesterday, and join the fun by submitting a bracket to the official Princeton University Press March Madness tournament pool.

Before you do, we recommend that you brush up on your bracketology by checking out PUP author Tim Chartier’s strategy:

 

 

For more on the math behind the madness, head over to Dr. Chartier’s March Mathness video page. Learn three popular sport ranking methods and how to create March Madness brackets with them. Let math make the picks!

Be sure to follow along with our March Mathness coverage on our blog, and comment below with your favorite strategy for making March Madness picks.

The math behind March Madness

It’s almost that time again. The beginning of the March Madness basketball tournament is a few days away, and here at PUP, we cannot wait!

We’re marking our calendars (find the schedule here) and going over our bracketology, with a little help from PUP author Tim Chartier.

To kick off the countdown, we bring you an article from the Post and Courier, who checked in with Dr. Chartier about how numbers can be the best strategy in bracketology.

College basketball fans seeking to cash in on March Madness need to turn on their calculators and turn off their allegiances.

That was the message Dr. Tim Chartier, a math professor at Davidson and published author, brought to cadets at The Citadel on Monday night.

“The biggest mistake people make in bracketology is they go with their heart no matter what the data says,” said Chartier, who has made studying the mathematics of the NCAA basketball tournament part of his students’ course work at Davidson. “They just can’t let a certain team win or they just have to see their team do well.

“It’s hard not to do that, because that is part of the fun.”

Chartier has made it easier for the average fan to use math in filling out their own brackets at the March Mathness website marchmathness.davidson.edu. The site will get a lot of traffic after the NCAA tournament field is announced on March 15.

 

Read the full article on the Post and Courier website.

Dr. Tim Chartier is a numbers guy, and not only during basketball season. He likes to show students how math can apply outside of the classroom. How can reposting on Twitter kill a movie’s opening weekend? How can you use mathematics to find your celebrity look-alike? What is Homer Simpson’s method for disproving Fermat’s Last Theorem? Dr. Chartier explores these and other questions in his book Math Bytes.

(Photo courtesy of Davidson College)

(Photo courtesy of Davidson College)

 

As Dr. Chartier and others gear up for basketball lovers’ favorite time of year, PUP reminds you to mark your calendars for these key dates.

Check back here soon for more hoop scoop!

• Selection Sunday, March 15, ESPN

• First and Second Rounds, March 20, 22 or March 21, 23

• Greensboro Regional, March 27, 29, Greensboro Coliseum (Greensboro, North Carolina)

• Oklahoma City Regional, March 27, 29, Chesapeake Energy Arena (Oklahoma City, Oklahoma)

• Albany Regional, March 28, 30, Times Union Center (Albany, New York)

• Spokane Regional, March 28, 30, Spokane Veterans Memorial Arena (Spokane, Washington)

• National Semifinals, April 5, Amalie Arena (Tampa Bay, Florida)

• Championship Game, April 7, Amalie Arena (Tampa Bay, Florida)

Calculus predicts more snow for Boston

Are we there yet? And by “there,” we mean spring and all the lovely weather that comes with it. This winter has been a tough one, and as the New York Times says, “this winter has gotten old.”

snow big[Photo Credit: John Talbot]

Our friends in Boston are feeling the winter blues after seven feet of precipitation over three weeks. But how much is still to come? You may not be the betting kind, but for those with shoveling duty, the probability of more winter weather may give you chills.

For this, we turn to mathematician Oscar Fernandez, professor at Wellesley College. Professor Fernandez uses calculus to predict the probability of Boston getting more snow, and the results may surprise you. In an article for the Huffington Post, he writes:

There are still 12 days left in February, and since we’ve already logged the snowiest month since record-keeping began in 1872 (45.5 inches of snow… so far), every Bostonian is thinking the same thing: how much more snow will we get?

We can answer that question with math, but we need to rephrase it just a bit. Here’s the version we’ll work with: what’s the probability that Boston will get at least s more inches of snow this month?

Check out the full article — including the prediction — over at the Huffington Post.

Math has some pretty cool applications, doesn’t it? Try this one: what is the most effective number of hours of sleep? Or — for those who need to work on the good night’s rest routine — how does hot coffee cool? These and other answers can be found through calculus, and Professor Fernandez shows us how in his book, Everyday Calculus: Discovering the Hidden Math All around Us.

This book was named one of American Association for the Advancement of Science’s “Books for General Audiences and Young Adults” in 2014. See Chapter One for yourself.

For more from Professor Fernandez, head over to his website, Surrounded by Math.

 

Photo Credit: https://www.flickr.com/photos/laserstars/.

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

Tim ChartierTim 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.

Happy calculating!

March Mathness Postscript

march-mathness1-150x150[1]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.

Need help filling out your brackets? Watch these free videos from Tim Chartier

Chartier_MathStill 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:

Top Tips for 2014 March Madness Brackets from Tim Chartier

Chartier_MathWith 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.”

March Mathness Winner

Davidson College student, Jane Gribble, was our March Mathness winner this year. Below she explains how she filled in her bracket.

 


 

Gribble

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.

 

LA Times Article with Tim Chartier

Davidson math professor, PUP author and bracketology expert, Tim Chartier, discusses the math behind March Madness with the LA Times.

chartierMathematician Tim Chartier has the best job on Earth once a year: when the NCAA men’s basketball tournament begins, so does March Mathness.

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/