Now that we have calculated the number of upsets that should occur in the Round of 64, let us use the same method to calculate the number of upsets in the Round of 32. As before, all historical considerations for this guide begin with the 1985 NCAA Men's Division I Basketball Tournament, as it was the first to include at least 64 teams.
Methodology
The statistical formula for predicting the odds of a given number of upsets of a particular type is
U^m*(1-U)^n*(m+n)! , (1)
m!*n!
where U is the odds of an upset, m is the number of upsets of that type, and n is the number of non-upsets of that type. In the Round of 32, m+n can be any integer from 1 to 4 (0 is the trivial case of a particular matchup not occurring). The factorials in the formula account for the combinatorics of the arrangements of the upsets.
#1 seed vs. #8 seed
In 54 games since 1985, #1 seeds are 44–10 against #8 seeds. This is an upset rate of 18.52%, thus U=0.1852. The most such upsets that have occurred in one year is two, in 2000. Using Equation (1), the odds are as follows:
With one matchup:
- #1 seed advances: 81.48%
- #8 seed advances: 18.52%
With two matchups:
- Both #1 seeds advance: 66.39%
- One #8 seed upsets a #1 seed: 30.18%
- Both #8 seeds advance: 3.43%
With three matchups:
- All three #1 seeds advance: 54.09%
- One #8 seed upsets a #1 seed: 36.89%
- Two #8 seeds upset #1 seeds: 8.38%
- All three #8 seeds advance: 0.64%
With four matchups:
- All four #1 seeds advance: 44.08%
- One #8 seed upsets a #1 seed: 40.07%
- Two #8 seeds upset #1 seeds: 13.66%
- Three #8 seeds upset #1 seeds: 2.07%
- All four #8 seeds advance: 0.12%
Mathematically, all #1 seeds in this matchup should be predicted to advance, although one upset pick would be reasonable if there are four #8 seeds remaining.
#1 seed vs. #9 seed
In 58 games since 1985, #1 seeds are 54–4 against #9 seeds. This is an upset rate of 6.90%, thus U=0.069. There has never been more than one upset of this type in the same year. Using Equation (1), the odds are as follows:
With one matchup:
- #1 seed advances: 93.10%
- #9 seed advances: 6.90%
With two matchups:
- Both #1 seeds advance: 86.68%
- One #9 seed upsets a #1 seed: 12.85%
- Both #9 seeds advance: 0.48%
With three matchups:
- All three #1 seeds advance: 80.70%
- One #9 seed upsets a #1 seed: 17.94%
- Two #9 seeds upset #1 seeds: 1.33%
- All three #9 seeds advance: 0.033%
With four matchups:
- All four #1 seeds advance: 75.13%
- One #9 seed upsets a #1 seed: 22.27%
- Two #9 seeds upset #1 seeds: 2.48%
- Three #9 seeds upset #1 seeds: 0.12%
- All four #9 seeds advance: 2.3*10^-3 %
Mathematically, all #1 seeds in this matchup should be predicted to advance. An upset pick of this type would not be reasonable.
#8 seed vs. #16 seed and #9 seed vs. #16 seed
These matchups have never occurred, as no #16 seed has survived the Round of 64 to get to these matchups. As such, a mathematically predicted bracket should not include these matchups. If a bracket does include these matchups, the #8 seed or #9 seed should defeat the #16 seed, as predicting two historic upsets in succession is highly unreasonable.
#2 seed vs. #7 seed
In 65 games since 1985, #2 seeds are 48–17 against #7 seeds. This is an upset rate of 26.15%, thus U=0.2615. The most such upsets that have occurred in one year is two, in 1986, 1990, and 2006. Using Equation (1), the odds are as follows:
With one matchup:
- #2 seed advances: 73.85%
- #7 seed advances: 26.15%
With two matchups:
- Both #2 seeds advance: 54.54%
- One #7 seed upsets a #2 seed: 38.62%
- Both #7 seeds advance: 6.84%
With three matchups:
- All three #2 seeds advance: 40.28%
- One #7 seed upsets a #2 seed: 42.79%
- Two #7 seeds upset #2 seeds: 15.15%
- All three #7 seeds advance: 1.79%
With four matchups:
- All four #2 seeds advance: 29.74%
- One #7 seed upsets a #2 seed: 42.13%
- Two #7 seeds upset #2 seeds: 22.38%
- Three #7 seeds upset #2 seeds: 5.28%
- All four #7 seeds advance: 0.47%
Mathematically, all #2 seeds should be predicted to advance if there are one or two matchups. With three matchups, one #2 seed should fall to a #7 seed, but no upset pick of this type would also be reasonable. With four matchups, one #2 seed should fall to a #7 seed.
#2 seed vs. #10 seed
In 41 games since 1985, #2 seeds are 24–17 against #10 seeds. This is an upset rate of 41.46%, thus U=0.4146. The most such upsets that have occurred in one year is three, in 1999. Using Equation (1), the odds are as follows:
With one matchup:
- #2 seed advances: 58.54%
- #10 seed advances: 41.46%
With two matchups:
- Both #2 seeds advance: 34.27%
- One #10 seed upsets a #2 seed: 48.54%
- Both #10 seeds advance: 17.19%
With three matchups:
- All three #2 seeds advance: 20.06%
- One #10 seed upsets a #2 seed: 42.62%
- Two #10 seeds upset #2 seeds: 30.19%
- All three #10 seeds advance: 7.13%
With four matchups:
- All four #2 seeds advance: 11.74%
- One #10 seed upsets a #2 seed: 33.27%
- Two #10 seeds upset #2 seeds: 35.34%
- Three #10 seeds upset #2 seeds: 16.69%
- All four #10 seeds advance: 2.95%
Mathematically, the #2 seed should be predicted to advance if there is one matchup. With two or three matchups, one #2 seed should fall to a #10 seed. With four matchups, two #2 seeds should fall to #10 seeds, but one upset pick of this type would also be reasonable.
#7 seed vs. #15 seed
In 2 games since 1985, #7 seeds are 2–0 against #15 seeds. The 2–0 record would suggest that the odds of a particular #15 seed upsetting the #7 seed it is paired with are less than or equal to (1/2)*ln(2), or 34.66%. Thus U≤0.3466. As there have never been more than two #15 seeds in the round of 32, our consideration should not extend beyond that point. Using Equation (1), the odds are as follows:
With one matchup:
- #7 seed advances: ≥65.34%
- #15 seed advances: ≤34.66%
With two matchups:
- Both #7 seeds advance: ≥42.69%
- One #15 seed upsets a #7 seed: ≤45.29%
- Both #15 seeds advance: ≤12.01%
Mathematically, the #7 seed should be predicted to advance if there is one matchup. With two matchups, one #7 seed should fall to a #15 seed in theory, but no upset pick of this type would also be reasonable, especially because a #15 seed has never advanced past the Round of 32.
#10 seed vs. #15 seed
In 4 games since 1985, #10 seeds are 4–0 against #15 seeds. The 4–0 record would suggest that the odds of a particular #15 seed upsetting the #10 seed it is paired with are less than or equal to (1/4)*ln(2), or 17.32%. Thus U≤0.1732. As there have never been more than two #15 seeds in the round of 32, our consideration should not extend beyond that point. Using Equation (1), the odds are as follows:
With one matchup:
- #10 seed advances: ≥82.68%
- #15 seed advances: ≤17.32%
With two matchups:
- Both #10 seeds advance: ≥68.36%
- One #15 seed upsets a #10 seed: ≤28.64%
- Both #15 seeds advance: ≤3.00%
Mathematically, all #10 seeds in this matchup should be predicted to advance, especially because a #15 seed has never advanced past the Round of 32.
#3 seed vs. #6 seed
In 61 games since 1985, #3 seeds are 34–27 against #6 seeds. This is an upset rate of 44.26%, thus U=0.4426. The most such upsets that have occurred in one year is three, in 1997 and 2000. Using Equation (1), the odds are as follows:
With one matchup:
- #3 seed advances: 55.74%
- #6 seed advances: 44.26%
With two matchups:
- Both #3 seeds advance: 31.07%
- One #6 seed upsets a #3 seed: 49.34%
- Both #6 seeds advance: 19.59%
With three matchups:
- All three #3 seeds advance: 17.32%
- One #6 seed upsets a #3 seed: 41.25%
- Two #6 seeds upset #3 seeds: 32.76%
- All three #6 seeds advance: 8.67%
With four matchups:
- All four #3 seeds advance: 9.65%
- One #6 seed upsets a #3 seed: 30.66%
- Two #6 seeds upset #3 seeds: 36.52%
- Three #6 seeds upset #3 seeds: 19.33%
- All four #6 seeds advance: 3.84%
Mathematically, the #3 seed should be predicted to advance if there is one matchup. With two or three matchups, one #3 seed should fall to a #6 seed. With four matchups, two #3 seeds should fall to #6 seeds, but one upset pick of this type would also be reasonable.
#3 seed vs. #11 seed
In 35 games since 1985, #3 seeds are 23–12 against #11 seeds. This is an upset rate of 34.29%, thus U=0.3429. The most such upsets that have occurred in one year is two, in 1985 and 2011. Using Equation (1), the odds are as follows:
With one matchup:
- #3 seed advances: 65.71%
- #11 seed advances: 34.29%
With two matchups:
- Both #3 seeds advance: 43.18%
- One #11 seed upsets a #3 seed: 45.06%
- Both #11 seeds advance: 11.76%
With three matchups:
- All three #3 seeds advance: 28.37%
- One #11 seed upsets a #3 seed: 44.42%
- Two #11 seeds upset #3 seeds: 23.18%
- All three #11 seeds advance: 4.03%
With four matchups:
- All four #3 seeds advance: 18.64%
- One #11 seed upsets a #3 seed: 38.92%
- Two #11 seeds upset #3 seeds: 30.46%
- Three #11 seeds upset #3 seeds: 10.60%
- All four #11 seeds advance: 1.38%
Mathematically, the #3 seed should be predicted to advance if there is one matchup. With two matchups, one #3 seed should fall to a #11 seed, but no upset pick of this type would also be reasonable. With three matchups, one #3 seed should fall to a #11 seed. With four matchups, one #3 seed should fall to a #11 seed, but two upset picks of this type would also be reasonable.
#6 seed vs. #14 seed
In 13 games since 1985, #6 seeds are 11–2 against #14 seeds. This is an upset rate of 15.38%, thus U=0.1538. There has never been more than one upset of this type in the same year. As there have never been more than two #14 seeds in the round of 32, our consideration should not extend beyond that point. Using Equation (1), the odds are as follows:
With one matchup:
- #6 seed advances: 84.62%
- #14 seed advances: 15.38%
With two matchups:
- Both #6 seeds advance: 71.61%
- One #14 seed upsets a #6 seed: 26.03%
- Both #14 seeds advance: 2.37%
Mathematically, all #6 seeds in this matchup should be predicted to advance. An upset pick of this type would not be reasonable.
#11 seed vs. #14 seed
In 3 games since 1985, #11 seeds are 3–0 against #14 seeds. The 3–0 record would suggest that the odds of a particular #14 seed upsetting the #11 seed it is paired with are less than or equal to (1/3)*ln(2), or 23.10%. Thus U≤0.231. As there have never been more than two #14 seeds in the round of 32, our consideration should not extend beyond that point. Using Equation (1), the odds are as follows:
With one matchup:
- #11 seed advances: ≥76.90%
- #14 seed advances: ≤23.10%
With two matchups:
- Both #11 seeds advance: ≥59.14%
- One #14 seed upsets a #11 seed: ≤35.53%
- Both #14 seeds advance: ≤5.34%
Mathematically, all #11 seeds in this matchup should be predicted to advance. An upset pick of this type would not be reasonable.
#4 seed vs. #5 seed
In 60 games since 1985, #4 seeds are 32–28 against #5 seeds. This is an upset rate of 46.67%, thus U=0.4667. The most such upsets that have occurred in one year is three, in 2007. Using Equation (1), the odds are as follows:
With one matchup:
- #4 seed advances: 53.33%
- #5 seed advances: 46.67%
With two matchups:
- Both #4 seeds advance: 28.44%
- One #5 seed upsets a #4 seed: 49.78%
- Both #5 seeds advance: 21.78%
With three matchups:
- All three #4 seeds advance: 15.17%
- One #5 seed upsets a #4 seed: 39.82%
- Two #5 seeds upset #4 seeds: 34.85%
- All three #5 seeds advance: 10.17%
With four matchups:
- All four #4 seeds advance: 8.09%
- One #5 seed upsets a #4 seed: 28.31%
- Two #5 seeds upset #4 seeds: 37.17%
- Three #5 seeds upset #4 seeds: 21.68%
- All four #5 seeds advance: 4.74%
Mathematically, the #4 seed should be predicted to advance if there is one matchup, but an upset pick would be reasonable. With two matchups, one #4 seed should fall to a #5 seed. With three matchups, one #4 seed should fall to a #5 seed, but two upset picks of this type would also be reasonable. With four matchups, two #4 seeds should fall to #5 seeds.
#4 seed vs. #12 seed
In 28 games since 1985, #4 seeds are 17–11 against #12 seeds. This is an upset rate of 39.29%, thus U=0.3929. There has never been more than one upset of this type in the same year. As there have never been more than three #12 seeds in the round of 32, our consideration should not extend beyond that point. Using Equation (1), the odds are as follows:
With one matchup:
- #4 seed advances: 60.71%
- #12 seed advances: 39.29%
With two matchups:
- Both #4 seeds advance: 36.86%
- One #12 seed upsets a #4 seed: 47.71%
- Both #12 seeds advance: 15.44%
With three matchups:
- All three #4 seeds advance: 22.38%
- One #12 seed upsets a #4 seed: 43.44%
- Two #12 seeds upset #4 seeds: 28.12%
- All three #12 seeds advance: 6.07%
Mathematically, the #4 seed should be predicted to advance if there is one matchup. With two or three matchups, one #4 seed should fall to a #12 seed.
#5 seed vs. #13 seed
In 14 games since 1985, #5 seeds are 11–3 against #13 seeds. This is an upset rate of 21.43%, thus U=0.2143. There has never been more than one upset of this type in the same year. As there have never been more than two #13 seeds in the round of 32, our consideration should not extend beyond that point. Using Equation (1), the odds are as follows:
With one matchup:
- #5 seed advances: 78.57%
- #13 seed advances: 21.43%
With two matchups:
- Both #5 seeds advance: 61.73%
- One #13 seed upsets a #5 seed: 33.68%
- Both #13 seeds advance: 4.59%
Mathematically, all #5 seeds in this matchup should be predicted to advance. An upset pick of this type would not be reasonable.
#12 seed vs. #13 seed
In 10 games since 1985, #12 seeds are 8–2 against #13 seeds. This is an upset rate of 20%, thus U=0.2. There has never been more than one upset of this type in the same year. As there have never been more than two #13 seeds in the round of 32, our consideration should not extend beyond that point. Using Equation (1), the odds are as follows:
With one matchup:
- #12 seed advances: 80.00%
- #13 seed advances: 20.00%
With two matchups:
- Both #12 seeds advance: 64.00%
- One #13 seed upsets a #12 seed: 32.00%
- Both #13 seeds advance: 4.00%
Mathematically, all #12 seeds in this matchup should be predicted to advance. An upset pick of this type would not be reasonable.
Overall
Since 1985, the Round of 32 has featured a mean of 4.75 upsets, a median of 5 upsets, and a mode of 5 upsets. The fewest upsets in the Round of 32 was none (1991), and the most upsets was 9 (2000).
If you follow these calculations, you should have a reasonably good chance of doing well with the Sweet 16. Next week, we will consider the probabilities of the remaining teams as they make their way to the Final Four.
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