College Nationals Simulation

About a year ago, I was given the opportunity by the BYU Statistics Department to do paid, independent sports analytics work after submitting a proposal. The majority of the time that I spent during the semester was on a probabilistic model for college nationals. While the simulation is still in a very basic form, it is a good starting ground for being able to create a robust simulation of Ultimate men’s college nationals.

Data

First, I began by collecting the data on men’s college nationals from USA Ultimate’s website back to 2004 (that was the furthest back I could get trustworthy data). Then, I made sure to have every game at nationals and the corresponding teams, team seeds, game scores, and game type (whether it was the first/second/third/fourth pool play game or pre-quarterfinal/quarterfinal/semifinal/championship game). One note is that the structure of college nationals changed between 2008 and 2009; previous to 2009 college nationals hosted 16 teams, as opposed to the current 20 team format since then. The argument could be made that this is a problem in the simulations since there may be a significant difference between the two nationals formats, but for the sake of sample size and because I haven’t had time to see if there is a significant difference between the two formats, I included and equally weighted all available data in the simulations.

Methods

The simulation itself is based off a few different functions that are all built off of a weighted coin flip in order to determine the outcome of a single game. While in the future I plan to implement more robust methods besides seeding, the only determining factor in who wins the simulated game is the seeding going into the tournament and historical win percentages for each seed. Historically, the one seed beats the four seed two-thirds of the time. However, not all seeds have played each other at nationals, so I created an adjusted win probability table to account for this. The adjusted win probabilities literally add one win to each matchup, while adding two games to each matchups total game count. This effectively creates a 50% win probability for seeds that have never faced each other at nationals and pushes any other probabilities towards the 50% mark. For example, if the number one seed was playing the number four seed, even though historically the four seed only has a 33% chance of beating the one seed, the adjusted win probability gives them a 36% chance of beating the one seed (the two teams have met at nationals nine times since 2004).