Welcome back! My life got pretty complicated right after I started this blog a few years ago. There were a few different analytic projects I attempted and halted during the interim, and I’ve had to take some time to get my real world life back on track. But I’m doing great now and feeling rejuvenated, and I had a lot of fun putting together a tournament simulation model – finally something worthy of a blog post!

Inspired by the various 538 Predictions, as well as one of my old time favorites, Sports Club Stats, I wanted to see probabilistic forecasts for the upcoming College National Championships. This is not an immensely difficult task, but I hadn’t seen it done anywhere before in the ultimate community, so I figured I’d give it a shot. It was only after making this model that I encountered Craig Poeppelman’s very similar and fantastic work, but he is not currently looking into the college game.

Here are my results, sorted by the odds of winning the championship (based on 40,000 simulations), with all the maths details below.

Math Details:

In order to create a simulation model, I need two things. A tournament simulation, and a prediction system. For the first one, I briefly tried to find some template code for a pool-play-to-bracket tournament, but I really couldn’t find anything useful. So I whipped up a simulation and organized the code for a 20 team, 4 pool, single elimination bracket tournament. This was reasonably straightforward and should be easily adaptable for any common frisbee tournament, including the 16 team Club Championships. I will probably have to spend an annoying amount of time if I ever want to model a double elimination, 3 bid regional tournament, but that will be for another day.

Far and away, the hardest part of coding this tournament simulator was dealing with the tiebreaks. I couldn’t find any good way to streamline this process, and resolving this takes up an embarrassingly large number of lines in my code. I’m not a computer science guy, so coding is very much a means to an end for me rather than an art form. It’s ugly but it works.

As for the prediction system, I decided to adapt the USAU Rankings Algorithm into an Elo system. Elo is a great way to compare the relative strengths about different teams, and especially, to make predictions about head to head matchups. The USAU ranking is NOT an Elo system, but it is sufficiently similar that just by tweaking a few parameters in the Elo model, I am comfortable using USAU to create forecasts. This means that my estimate of team strength is entirely based off of the ranking, rather than an objective opinion. You may very well think that a team has an unreasonably high ranking in the USAU ranking, or that a certain team matches up well with another team, but that is outside the scope of this model.

Analysis:

Based on regular season results, the model predictably sees Carleton and UNC as sizable favorites in the Men’s division. In over half of my simulations, one of those two teams emerge as the champions. The more interesting results, in my opinion, show up in the odds of a given team making the bracket. Due to the volatile nature of pool play tournaments in general, combined with 3 out of 5 teams moving on to the bracket, it really only takes 1-2 upsets to dramatically shake up the results. This means that even the lowest ranked teams still have reasonable odds of scoring an upset and nabbing one of the bracket spots.

In the Women’s division, we see strong odds of a repeat championship by the juggernauts at Dartmouth. However, there are a handful of excellent teams in UNC, UCSD, and Stanford that are all within striking distance. There is greater than a 2-in-3 chance that one of those four teams wins the 2018 championship. Just like in the Men’s tournament, almost every team still has a reasonable chance to advance, with the exception of the very weak Cornell.

Future Work:

I will be able to update this model as the games get underway at Nationals this year, and I should be able to create updated predictions after each round of games. For these updates, feel free to follow me on twitter, @Discstats.

I would be curious to see how these odds would change if the entire tournament was changed to a March Madness style bracket, either single or double elimination. I will probably look into this for a future post, as well as numerous other what ifs. I may also try to incorporate this model with my earlier work on Win Probability, so I can give live updates in between each point, rather than each round.