Simulating the Missing March Madness: The Odds of a Dayton National Championship

This one hurts to write. I spent four years in sunny Dayton, Ohio studying mathematics at the University of Dayton. We love our basketball. In 2020, the Dayton Men’s Basketball Team was the best in University history. We had everything: an innovative, exciting coach, a large cast of reliable veterans, a probable lottery pick in Obi Toppin, and the energy from mid-major fans everywhere. We thought we had a Dayton National Championship

But, if you ask me or any of my friends, we were robbed of our guaranteed championship by a once in a lifetime pandemic. Most of us own these shirts. Some of us want to name our first sons Obi. All of us wanted to see what could happen. In this article I am going to talk about what would have happened in the 2020 NCAA Tournament.

Simulating March Madness

All my insights and claims here are the result of simulation. Using our ensemble ratings, we can accurately estimate the probability of any tournament team beating any other tournament team. Our model suggests that Kansas should beat Prairie View A&M roughly 99.5% of the times they play. So, ‘simulating’ this matchup boils down to rolling a special dice that comes up Kansas 99.5% of the time and Prairie View the other 0.5%.

Given a bracket (we used the one here), we can pick the winners of each first round game in this way. Then we can simulate the Round of 32, the Sweet 16, etc. Then, simulating the tournament thousands and thousands of times lets us see how likely any turn of events are. For instance we could answer:

• What is the probability of a University of Dayton National Championship?
• How likely is it they make the Final Four?
• What is the probability at least one of this year’s 12 seeds beats a 5 seed?
• Who is most likely to win?
• How difficult are the regions relative to one another?

And, I could go on and on (and likely will in the future). Today, though, we just focus on probabilities of teams advancing to a certain stage.

Would we Have Seen a Dayton National Championship?

Your 2020 National Champions, winning the tournament in over 20% of our simulations, is…

The Kansas Jayhawks. The best team. I don’t personally think the choice of champion is that interesting, rather I think the probability distribution of how many times each team won is the interesting part. For instance, while Kansas had essentially 4:1 odds to win the chip, Gonzaga and Duke were not far behind. Shown below is the win probability for the 6 title favorites.

I offer two comments here. First, I owe a formal apology to the Flyer Faithful. I couldn’t quite make the statistics lie enough to crown us champions. Second, the true madness is the size of the ‘Other’ portion of the above. One in three simulations had someone absurd winning. The other teams that win between 2-3% of the time are San Diego State, Arizona, Ohio State, West Virginia, Oregon, Florida State, and Creighton. That is 13 teams (almost a quarter of the field!) that have at least a snowball’s chance in our rapidly warming world.

Final Four Chances

For mid-majors, you don’t necessarily have to win the entire title to consider the season a success. Sometimes the excitement of even advancing to the final four is enough. Shown below are the final four probabilities for each team with at least a 10% chance at the final four

We notice an anomaly: Dayton has a higher chance to win the championship than San Diego state but a lower chance at making the Final Four. If you look closely at the bracket we used, the New York City Region looks pretty brutal. Not only does NYC have the best 2 seed in the tournament in Dayton, they have by far the best 3 seed in Duke. In fact 3 of the top 9 teams. What insights can we make about the determining difficulty of regions and the effect this has on championship chances.

The Impact of Region Strength and Seeding

Our methodology in this section is the same thing we used to argue the NBA’s Western Conference was significantly more difficult than the East. Using Dayton as our test subject, we’ll move them around to different slots to see how their title and final four chances change. In particular, we’ll see how the Flyers fare as the one seed and two seed in each region.

To simulate the various 2 seed locations, we simply swapped the spot of UD and the other region’s 2 seed. For the simulation of the Flyer’s as a one seed, first we swapped Dayton and San Diego State as the one seeds in the East Region. Then, to test Dayton in the other three regions, we swapped Dayton and that region’s one seed. Here is what we found.

Location	Final Four Probability	Championship Probability
NYC (East) 2 Seed	16.0%	3.4%
Indianapolis (Midwest) 2 Seed	11.3%	3.1%
Houston (South) 2 Seed	18.8%	4.1%
Los Angeles (West) 2 Seed	18.3%	4.5%
NYC (East) 1 Seed	18.5%	4.1%
Indianapolis (Midwest) 1 Seed	21.5%	4.3%
Houston (South) 1 Seed	18.2%	4.0%
Los Angeles (West) 1 Seed	25.5%	5.7%

Regional Strength Insights

I offer the following insight about ‘difficulty of region’ based on the above data. When you are the 2 seed, the region’s difficulty is overwhelmingly dictated by the quality of your 1 seed. Compare Dayton being placed in the East and Midwestern regions. Outside of the top seed, the East is superior. In fact the Eastern region’s third seed is the third best team overall in our rankings (Duke). However, because Kansas tops the Midwest and Kansas is the best team, the Final Four chances for a two seed out of the Midwest are much lower.

To further illustrate this fact, look at the probability of Dayton advancing when they are the one seed in the East v. Midwest. Dayton makes it out of the Midwest more often as the one seed than they do from the East, suggesting the rest of the Midwest is easier. Therefore, the only possible explanation for the difficulty of advancing out of the Midwest as the 2 seed is the looming presence of Kansas in the Elite 8.

In fact the varying strength of each region has such an effect on title chances that it may be better to be the 2 seed in the weakest region than the 1 seed in the strongest region. Compare Dayton’s title chances as the 2 seed out West (4.5%) to their title chances as the 1 seed in the East and South (4.1% and 4.0% resp.) and we see this to be true.

Conclusions

March Madness is truly madness. Simulating March Madness shows this. The huge field, the best-of-one format, and the inherent variability of younger, less experienced players all contribute to the excitement of the best sporting event of the year. The data from this year suggests the favorite is still expected to win only about a fifth of the time. Moreover, the variability based on where you end up in the bracket is extremely high.

And for the Flyers: The data doesn’t suggest that Dayton was the favorites by any stretch, but given the right seeding and bracketing, We had about a 1 in 20 chance of a Dayton National Championship. While that seems extremely low, remember that this tournament is the least predictable sporting event of the year. The championship was more likely than picking the right number in Roulette, hitting a natural blackjack, or flipping 5 heads in a row. As the biased Flyer fan I am, I am wearing my National Champions shirt proudly.