In yesterday’s article, I described our annual logistic regression model for predicting the outcome of the NCAA Division I Men’s Basketball Tournament. I applied it to this year’s tournament to get the model’s “expected” bracket and the win probability for each team in every possible matchup. You can click the link here to see all of that good stuff.
Another good way to show the results is through a simulation – we can use the modeled win probabilities to simulate the entire tournament in less than a second. For example, I just ran a simulation of the tournament and in this hypothetical scenario, the Final Four teams are Gonzaga, Villanova, Kentucky, and Kansas. The Jayhawks went on to top the Gonzaga in the championship game. Not at all difficult to imagine that playing out.
We can run this simulation any number of times and compile the results to see how likely each time is to reach each round of the tournament assuming that the modeled win probabilities are accurate. We’ll go through each region to see the results.
West Region
Gonzaga won the West in 34.0% of our simulations, ahead of Duke at 26.1% and Texas Tech at 16.9%. There’s a drop-off afterwards before we get No. 4 Arkansas at 5.2% and No. 5 Connecticut at 6.2%. In terms of who can actually win the tournament, we see the same pattern of a “Big 3” with Gonzaga at 14.3%, Duke at 7.8%, and Texas Tech at 3.5%.
South Region
Despite the previous article having Houston in the Final Four in the situation in which the model is perfectly accurate, Arizona does have a substantially higher chance of reaching the Final Four in our simulated runs. The one-seed Wildcats reach the Final Four in 33.9% of simulations versus 20.7% for Houston followed by 15.7% for No. 3 Tennessee and 15.0% for No. 2 Villanova. These are also the only four teams who won the tournament in more than 1% of simulations.
Houston is a super interesting case. Most metrics love them, but there is plenty reason for concern – a weak schedule, two key injuries, and the fact that they’ll probably run into Arizona in the Sweet Sixteen. I would personally wager that the analytics are overrating the Cougars’ chances, so I’d be weary of picking them over Arizona to make the Final Four. Their performance in the tournament is probably the thing I’m most interested in keeping an eye on.
East Region
Now we have the East, the most tightly contested region. Baylor is favored to win it at 27.1% followed by Kentucky, Purdue, and UCLA at 24.8%, 18.7%, and 16.3% respectively. That’s an incredibly tight race between the top four seeds.
It’s worth noting that the Baylor Bears are dealing with injuries right now (not explicitly accounted for in the model) which should give even more reason for you to not pick them in your Final Four. I also do not think any teams outside of the top four seeds in the region are worth picking – I would choose between Kentucky, Purdue, and UCLA.
Midwest Region
Finally, the Kansas Jayhawks won the Midwest in 37.8% of simulations. Auburn represented the region in 21.0% of the iterations followed by the five-seed Iowa Hawkeyes at 15.3%. Impressively, the 11-seed Iowa State Cyclones managed to break into the Final Four in 4.5% of the simulations.
Based on this data, it also seems that the model views the Jayhawks’ path as being the easiest. It’s not easy seeing any other team coming out of the region and winning the entire tournament.
Commentary
The two most important factors in picking a successful March Madness bracket is to have an accurate Final Four and accurately pick the champion. And part of having a strong FInal Four is to be smart with the seeds that you select. On average, 1.7 one seeds make it to the Final Four, so you don’t want to go all “chalk.” Baylor is probably not a one-seed that should be selected, leaving you to pick between Gonzaga/Kansas/Arizona.
It is also fairly common for a seven-seed or lower to make it to the Final Four. A few interesting picks to make it to the Final Four are No. 8 San Diego State (3.0%), No. 9 Memphis (2.5%), and No. 11 Iowa State (4.5%). Or maybe you’d go with slightly higher seeded sleepers like No. 5 Iowa (15.3%), No. 4 UCLA (16.3%), and No. 5 Houston (20.7%). Based on ESPN bracket data, all six of these “sleepers” are picked to advance to the Final Four at a lower rate than they actually do in simulations – perhaps they’re strong values pick in larger pools.
As for who’s going to win… well, that’s a tough question. Gonzaga (14.3%), Kansas (14.0%), and Arizona (12.8%) won the tournament most often during these 10,000 simulations, followed by a drop-off before we get teams like Houston, Duke Baylor, and Kentucky. Gonzaga is actually given a significantly higher chance of winning by sportsbooks (25% implied odds) and the public (27.8% of ESPN brackets picking them to win). Whether it’s rightful or not, the model does not view Gonzaga’s chances as highly as others. In this case, Kansas is an interesting contrarian pick as just 8.5% of brackets have them winning it all.
Unfortunately, these margins are very small. We’re just playing the numbers here – anything can happen once these teams step on the court. There’s a reason no human has selected a perfect bracket yet, and there’s a reason it’s called March Madness. Don’t put too much stock on the statistics – there’s a lot that they can’t quantify. Most pre-tournament analyses like this one did not foresee the No. 11 UCLA Bruins embarking on a miraculous Final Four run last season. We’re guaranteed to see more unexpected results this March, so don’t expect perfection. If you want to win your bracket pool, all you can do is play the numbers and hope for the best.