For the past six years, I have been maintaining (on GitHub) a machine-readable record of outcomes of the NCAA men’s basketball tournaments, over the now four decades since the current 64-team format began in 1985. (I continue to refuse to acknowledge the four Tuesday-Wednesday play-in games.) This effort was originally motivated by the annual question of the probability of picking a “perfect bracket,” i.e., correctly guessing the winners of all 63 games in all six rounds of the tournament. Despite some close calls over the years, no one has ever verifiably done this, and it is unlikely that anyone ever will.

This past post describes a method of estimating this probability for any given bracket, so that, for example, a “chalk” bracket (where a higher seeded team is always selected to beat a lower seed) is a much more likely overall outcome– albeit still unlikely as a specific outcome– than a bracket picking, say, all of the #1 seeds to be beaten by #16 seeds in the first round.

We can also apply this method to historical data, aggregating and weighting each year’s games and upsets into a single number, that we can use to compare the overall prior (un)likelihood of tournament outcomes across years, as shown in the following figure.

The black line at the bottom is , the often-quoted “one in 9.2 quintillion” probability of correctly guessing all 63 games by simply flipping a coin. The blue and red lines at the top are probabilities of chalk brackets, using two different models of individual game probabilities as a function of difference in “strength” of each team. As discussed in more detail here, blue indicates a strength following a normal distribution density, and red indicates a simpler linear strength function.

From the above figure, we see that this year’s tournament was the second most likely ever in the history of the current format. This makes sense: the Final Four teams were all #1 seeds (only the second time this has happened– the other was in 2008 with champion Kansas), and there were only 11 upsets– the fewest ever, as shown in the figure below– of a higher seed losing to a lower seed. The only more likely prior probability of overall tournament outcome was in 2007, with a then-fewest 12 total upsets, and #1 seeds Ohio State and champion Florida beating #2 seeds Georgetown and UCLA, respectively, in the Final Four.

So, how (un)likely is it that someone will eventually pick a verifiable perfect bracket? The probability of a chalk bracket– the mode of the distribution– being correct is one in roughly 100 to 200 billion. Even then, there are eight different chalk brackets… and an astronomically larger number of brackets with the dozen or so upsets that we expect to see in a given year.