## March Mathness Postscript

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.

## March Mathness Winner

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.

## March Mathness is over, so now it’s time to ask the key question: How did we do?

On March 15 many of us scrambled to complete our brackets and 64 of us placed them in the PUP March Mathness group of the ESPN Tourney Challenge. Almost everyone was in the top 50th percentile and 10 of our group did better than 90% of the 6.5 million people who entered a bracket. What we had in common was that we used a particular math algorithm or some combination to fill out our brackets. Quite a few of us also tossed in a bit of the human element because everything can and will happen in a tournament.

Math editor, Vickie Kearn,  asked Tim Chartier, Professor of Mathematics at Davidson College for his take on how we did.

“I think one of the things to note is that such methods can clearly be effective.  However, that personal modeling decision as to how to weight the season or even what part of the statistics to use is VERY important and makes a big difference.  Even so, there is that inevitable “Madness” of human endeavor that keeps us ever watching and, frankly, enjoying! What will happen?  We will never find a method to always know and as such, we keep trying and keep watching.”

And the Winner is Travis McElroy

Travis had the top rank in the PUP March Mathness Group, finishing with a total of 1470 points, in the 91.8 percentile. He is the recipient of several Princeton University Press books.

Travis is a senior math major and Spanish minor at Davidson College. Next year he will be working on his master’s in applied mathematics at the University of North Carolina at Chapel-Hill.  Following he tells us about his experience in completing his bracket.

This bracketology experience has been fun as I normally don’t pay attention to the tournament as baseball, football, and tennis are the sports that I watch.  I used the Colley Method and tried all different weights. I split the season into 42 different parts but really only put weights on 3 different sections, pre-conference play, conference play, and conference tournaments. The conference tournaments part was mainly for major conferences. So I tried a range of .3 to 1.5 for how much each game was worth and also for some brackets I added a bonus of a win or 3 for a road win.

For my winning bracket I decided to do something crazy and pick the underdogs. I used a colley method of .3 wins for a pre-conference play win, 1 win for conference play, and 1.5 for a tournament win. Also, a road win counted as 2 wins. After the rankings were compiled, I decided that if the 2 teams were in the top 10 and the lower ranked team was within 5 rankings of the higher team, the lower ranked team would win. After the top 10, if the lower ranked team was within 10 of the higher ranked, then the lower ranked team won. The only exception I made was I said Kentucky would win the whole thing.

Next year I would create more sections of the season and make the rankings vary more. It was very difficult to get any ranking that did not have Kentucky as number one and Syracuse as number 2. I also want to compare the actual ratings to see if there was a reasonable pattern to when the “underdog” won. I am very surprised I did as well as I did as I do not follow college basketball closely (except my Davidson Wildcats) and this bracket was my fun bracket. It shows that the underdog is not to be discounted. The only big surprises for me was the same surprises as everyone had with 2 #2 teams losing in the first round.  Next year I also want to combine methods to see if that helps. My roommate (Greg Newman) used different methods than I did and we want to see if we can make a better combination for next year.

The last word(s)

Now that you have 12 months until the next tournament, you have lots of time to decide what method you will use next year. Get your copy of Who’s #1?  by Amy Langville and Carl Meyer and start reading. You can also use it to predict the outcome of any sport as well as be able to rate and rank just about anything.

## 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.