And between North Carolina and Duke, the two schools rank #3/#4 in all-time wins, have 48/42 NCAA tournament appearances, 20/16 Final Fours, and 11/11 championship game appearances (all figures are respective). So it's fairly surprising that we've never met in the NCAA tournament (we met once in the NIT, in 1971).
The committee never puts us in the same region, so the Final Four would be the earliest meeting. And even for the best teams, it's more likely than not that they won't make the Final Four. So this proposition is definitely a long shot, but not impossible; it almost happened in 1991 in the title game. So when is it expected to happen?
I started by gathering the seedings for both us and Dook over the past 20 seasons (we also missed the tournament 3 times...):
We've had more variance, but the most likely seed for both teams is a 2. We also have been on the same side of the bracket only 5 times in this period, or 25% of the time (in other words, 25% of the time we could have met in the Final Four, and the rest of the time would have been in the title game).
Next, I drew a fairly deep sample of the odds a generic 1 through 8 seed makes the Final Four using the past 5 seasons of my model:
Note: I threw out Kentucky's region from 2015. Talk about an outlier: 78.5% to make the Final Four!
So now for the math on an outcome I certainly hope to never see; I actually agree with Coach K, who stated in '91 "that he never wanted the two schools to play in the last game of the season because it would be too devastating for the loser." (Chansky, Blue Blood: Duke-Carolina)
For simplicity I assumed the following:
- We both make the tournament every year (just gonna gloss over the 3 times in the past 20 years UNC didn't make it)
- Our seeds will be, at worst, the minimum we achieved in the dataset (6 for D00k, 8 for UNC)
- The committee won't put us in the same region
- One team making the Final Four doesn't influence the other (each tournament run is independent)
I then ran 10,000 simulations, matching the variance in our seedings against the odds a typical 1 through 8 seed will make the Final Four, and if on opposite sides of the bracket (75% of the time), the championship game.
1.01% of the time we met in the Final Four, and 1.65% in the championship, for a total of a 2.66% chance in a given year of playing eachother in the NCAA tournament, or about 1 in 37.5.
The math is straightforward to determine how many seasons are expected to pass until we would play eachother: (1 - 0.0266) ^ 26 = 49.61%, so 26 seasons from now is when it's a 50/50 proposition that we would have played eachother by then.
I also went ahead and ran 10,000 distinct sims to see the distribution of how long it might take, as well as the extremes:
There's about a 27% chance it doesn't happen in my lifetime, but if it does happen, it will probably take place sooner rather than later:
In fact, as illustrated above by the mode and in the below table, the single most likely scenario is that it happens in the proverbial next season:
This is a result of our likely high seeds in any given year, since when both teams are good, it's more likely to happen.
With that in mind, this season is on the higher end, as we're both 1 seeds. Using the odds from this year's Bracket Math, the odds of it happening this tournament are fairly high at 4.05%, or 1 in 25.
One thing was certain in every single simulation run though: To Hate Like This Is To Be Happy Forever.
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