# Bracketodds for March Madness 2024

## Bracketodds: Our Story

Welcome to Bracketodds. What started (in 2007) as a simple inquiry on how seeds advance in the NCAA Men's basketball tournament has grown into a STEM (Science, Technology, Engineering, and Mathematics) Learning Laboratory in Computer Science at the University of Illinois Urbana-Champaign. Both undergraduate and graduate students have been involved in conducting research, analyzing data, and shaping this web site (first launched in 2012) into an informative tool for March Madness neophytes all the way up to skilled bracketologists. The site retains its academic focus, by providing data and information to help everyone better enjoy the tournament, and answer questions as the outcomes of the games unfold. Thank you for helping make Bracketodds a mainstay of March Madness. Let the games begin!

## How did the 2021, 2022, and 2023 Bracket Simulators do?

Not sure which 5-12 upset to pick? Which No. 13 or No. 14 seed will pull an upset in the first round? How many No. 1 seeds should be in your Final Four? We can fill in brackets for you based on our analytics model. This simulation model samples from the 9,223,372,036,854,775,808 possible brackets, in the appropriate proportions, based on historical performance of the seeds. You will notice that many of the brackets generated have a No. 1 seed winning the National Championship. That is because No. 1 seeds have won the National Championship over 63% of the tournaments for the Men since 1985 (24 of 38), and 76% of the tournaments for the Women since 1994 (22 of 29). We do not attempt to predict who will win, like other websites or sports pundits; we just sample across the 9+ quintillions possible brackets. We will fill in the 64 teams (the First Four winners are added as they become available), so you can print out your own analytically designed bracket.

Like purchasing lottery tickets, most tickets do not win, but a few do. Our model samples across the 9,223,372,036,854,775,808 possible brackets in a manner that is representative of what has occurred in the tournaments since 1985. Using the lottery analogy, this is like knowing which numbers come up most often, and picking such numbers in the right combination to enhance the likelihood of matching the winning combination (which for the tournament, is the winners of the 63 games). Therefore, to get the best results requires you to consider a basket of brackets, which from among that set, you may find one that will end up scoring well. If you have a particular team that you think will win the national championship, keep sampling until you find a bracket with that team as the winner. We do not guarantee a winning bracket; just an appropriate mix of upsets and favorites to make you look like a true bracketologist. Each screen refresh will result in a unique bracket. If you end up with a superb bracket, do let us know at bracketodds@illinois.edu. .

## Seed Match-Up Records.

The Bracketodds web site is designed as a STEM Learning Laboratory. Teachers and educators at all levels (K-12) can use the web site to demonstrate how data, statistics, and probability can be used to understand prior tournament performance and forecast future performance. Click here for a description of one such activity. Please also let us know how the website has helped in your school to make March Madness into a STEM learning event.

## Tournament Background

Under the current format of the NCAA Men's Basketball Tournament, 68 teams are selected to compete in a single elimination format1. The Selection Committee seeds each of the teams according to factors such as their performance against quality teams, particular those away from home. The tournament bracket is structured into four regions, each containing 16 teams. Narrowing the field to these 64 teams requires eight teams to participate in four play-in games, termed the First Four.

In the round of 64, each seed No. 1 plays seed No. 16, seed No. 2 plays seed No. 15, and so on, through seed No. 8 who plays seed No. 9. The winner of each game advances in the tournament, with the possible sets of seed match-ups in the round of 32 given by {1,8,9,16}, {2,7,10,15}, {3,6,11,14}, and {4,5,12,13}, corresponding to the four games in each region. The possible sets of seed match-ups in the Sweet Sixteen are given by {1,4,5,8,9,12,13,16} and {2,3,6,7,10,11,14,15}. In the remaining rounds of the tournament (the Elite Eight, the National Semifinals, and the National Championship), the possible sets of seed match-ups include the entire set of 16 seeds.

The winners of each region are designated as the Final Four, where the National Semifinals and National Championship determine the NCAA Men's Basketball Tournament champion over the final weekend of play. While any seed combination reaching the Final Four is possible for these final three games, the probability of each seed combination is not uniformly distributed.

## Probabilistic Analysis

Using data from the past 38 tournaments (1985 through 2023), prior seed match-ups and winners can be used to identify a distribution that models the probability of certain seed combinations playing in each round of the tournament. This is accomplished by determining the frequency that each seed reaches a given round, then fitting this data to a truncated geometric distribution2, a nonnegative discrete random variable formed by the number of independent and identically distributed Bernoulli random variables, with success probability p (defined as the probability that the higher seed wins a particular game) that occurs until reaching the first success. Given that the NCAA tournament is single elimination, then a team cannot reach a round unless it has won in all the previous rounds.

#### Peer-Reviewed Research Papers

1 Jacobson, S. H., King, D. M., 2009, “Seeding in the NCAA Men’s Basketball Tournament: When is a Higher Seed Better?” Journal of Gambling Business and Economics, 3(2), 63-87. Click here for pdf.

2 Jacobson, S. H., Nikolaev, A. G., King, D.M.,  Lee, A. J., 2011, “Seed distributions for the NCAA Men’s Basketball Tournament”, OMEGA, 39(6), 719-724. Click here for pdf.

3 Khatibi, A., King, D. M., Jacobson, S. H., 2015, “Modeling the Winning Seed Distributions of the NCAA Division I Men’s Basketball Tournament”, OMEGA, 50(1), 141-148. Click here for pdf.

4 Dutta, S., Jacobson, S. H., Sauppe, J.J., 2017, “Identifying NCAA Tournament Upsets using Balance Optimization Subset Selection”, Journal of Quantitative Analysis in Sports, 13(2), 79–93. Click here for pdf.

5 Dutta, S., Jacobson, S.H., 2018, “Modeling the NCAA Basketball Tournament Selection Process Using a Decision Tree”, Journal of Sports Analytics, 4, 65-71. Click here for pdf.

6 Ludden, I.G., Khatibi, A., King, D.M., Jacobson, S.H., 2020, “Models for Generating NCAA Men's Basketball Tournament Bracket Pools”, Journal of Quantitative Analysis in Sports.Click here for pdf.

#### Acknowledgements

The authors of this web site would like to thank Adrian Lee (CITERI), Alexander Nikolaev (University of Buffalo), Arash Khatibi, Ian Ludden (Rose Hulman) for their comments and feedback on this web site.

Web Developers in 2011-2012: Ammar Rizwan, Emon Dai (Students, Department of Computer Science, University of Illinois at Urbana-Champaign)

Web Developer in 2015: Andrew Yang (Student, Department of Computer Science, University of Illinois at Urbana-Champaign)

Contributors in 2016-2017: Arash Khatibi, Kevin Li, Daniel Zurawski (Students, Department of Computer Science, University of Illinois at Urbana-Champaign)

Contributors in 2017-2018: Ian Ludden, Nestor Bermudez Sarmiento, Meghan Shanks (Students, Department of Computer Science, University of Illinois at Urbana-Champaign)

Contributors in 2018-2019: Ian Ludden, Abhinav Singh (Students, Department of Computer Science, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign)

Contributors in 2019-2020: Ian Ludden, An-Jie Tu (Students, Department of Computer Science, University of Illinois at Urbana-Champaign)

Contributors in 2020-2021: Ian Ludden, Kaahan Motwani, Andrea Roy (Students, Department of Computer Science, University of Illinois at Urbana-Champaign)

Contributors in 2021-2023: Ian Ludden (Student, Department of Computer Science, University of Illinois at Urbana-Champaign)

This is a student-driven project supervised by Professor Sheldon H. Jacobson (Department of Computer Science, University of Illinois at Urbana-Champaign) and Professor Douglas M. King (Department of Industrial and Systems Engineering, University of Illinois at Urbana-Champaign).

#### Outreach

For comments and feedback, send an email to bracketodds@illinois.edu. .

Media requests? Send an email to bracketodds@illinois.edu  or call 612-460-0480.

#### How You Can Help

If you would like to support the ongoing student development activities for this project, tax-deductible contributions can be made to the Department of Computer Science at the University of Illinois. Tax-deductible contributions can be made to the Department of Computer Science at the University of Illinois. Under "Computer Science Annual Fund", enter the gift amount. On the next page, in the "Additional Instructions" box, please type "Bracketodds Project". Thank you for your support

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