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 1994 NCAA Women'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 37 games since 1994, #1 seeds are 36–1 against #8 seeds. This is an upset rate of 2.70%, thus U=0.027. The only time such an upset occurred was in 2006. Using Equation (1), the odds are as follows:
With one matchup:
- #1 seed advances: 97.30%
- #8 seed advances: 2.70%
With two matchups:
- Both #1 seeds advance: 94.67%
- One #8 seed upsets a #1 seed: 5.25%
- Both #8 seeds advance: 0.073%
With three matchups:
- All three #1 seeds advance: 92.12%
- One #8 seed upsets a #1 seed: 7.67%
- Two #8 seeds upset #1 seeds: 0.21%
- All three #8 seeds advance: 2.0*10^-3 %
With four matchups:
- All four #1 seeds advance: 89.63%
- One #8 seed upsets a #1 seed: 9.95%
- Two #8 seeds upset #1 seeds: 0.41%
- Three #8 seeds upset #1 seeds: 7.7*10^-3 %
- All four #8 seeds advance: 5.3*10^-5 %
Mathematically, all #1 seeds in this matchup should be predicted to advance. An upset pick of this type would not be reasonable.
#1 seed vs. #9 seed
In 38 games since 1994, #1 seeds are 36–2 against #9 seeds. This is an upset rate of 5.26%, thus U=0.0526. There has never been more than one upset of this type in the same year. As there have never been more than three #9 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:
- #1 seed advances: 94.74%
- #9 seed advances: 5.26%
With two matchups:
- Both #1 seeds advance: 89.76%
- One #9 seed upsets a #1 seed: 9.97%
- Both #9 seeds advance: 0.28%
With three matchups:
- All three #1 seeds advance: 85.04%
- One #9 seed upsets a #1 seed: 14.16%
- Two #9 seeds upset #1 seeds: 0.79%
- All three #9 seeds advance: 0.015%
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
In 1 game since 1994, #9 seeds are 1–0 against #16 seeds. The #8 seed vs. #16 seed matchup has never occurred, as only one #16 seed has ever 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 51 games since 1994, #2 seeds are 41–10 against #7 seeds. This is an upset rate of 19.61%, thus U=0.1961. The most such upsets that have occurred in one year is two, in 2002, 2007, and 2010. Using Equation (1), the odds are as follows:
With one matchup:
- #2 seed advances: 80.39%
- #7 seed advances: 19.61%
With two matchups:
- Both #2 seeds advance: 64.63%
- One #7 seed upsets a #2 seed: 31.53%
- Both #7 seeds advance: 3.85%
With three matchups:
- All three #2 seeds advance: 51.95%
- One #7 seed upsets a #2 seed: 38.02%
- Two #7 seeds upset #2 seeds: 9.27%
- All three #7 seeds advance: 0.75%
With four matchups:
- All four #2 seeds advance: 41.76%
- One #7 seed upsets a #2 seed: 40.75%
- Two #7 seeds upset #2 seeds: 14.91%
- Three #7 seeds upset #2 seeds: 2.42%
- All four #7 seeds advance: 0.15%
Mathematically, all #2 seeds should be predicted to advance if there are one or two matchups. With three or four matchups, all #2 seeds should be predicted to advance, but one upset pick of this type would also be reasonable.
#2 seed vs. #10 seed
In 25 games since 1994, #2 seeds are 23–2 against #10 seeds. This is an upset rate of 8%, thus U=0.08. There has never been more than one upset of this type in the same year. As there have never been more than two #10 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:
- #2 seed advances: 92.00%
- #10 seed advances: 8.00%
With two matchups:
- Both #2 seeds advance: 84.64%
- One #10 seed upsets a #2 seed: 14.72%
- Both #10 seeds advance: 0.64%
Mathematically, all #2 seeds in this matchup should be predicted to advance. An upset pick of this type would not be reasonable.
#7 seed vs. #15 seed and #10 seed vs. #15 seed
These matchups have never occurred, as no #15 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 #7 seed or #10 seed should defeat the #15 seed, as predicting two historic upsets in succession is highly unreasonable.
#3 seed vs. #6 seed
In 53 games since 1994, #3 seeds are 37–16 against #6 seeds. This is an upset rate of 30.19%, thus U=0.3019. The most such upsets that have occurred in one year is three, in 2003. Using Equation (1), the odds are as follows:
With one matchup:
- #3 seed advances: 69.81%
- #6 seed advances: 30.19%
With two matchups:
- Both #3 seeds advance: 48.73%
- One #6 seed upsets a #3 seed: 42.15%
- Both #6 seeds advance: 9.11%
With three matchups:
- All three #3 seeds advance: 34.02%
- One #6 seed upsets a #3 seed: 44.14%
- Two #6 seeds upset #3 seeds: 19.09%
- All three #6 seeds advance: 2.75%
With four matchups:
- All four #3 seeds advance: 23.75%
- One #6 seed upsets a #3 seed: 41.08%
- Two #6 seeds upset #3 seeds: 26.65%
- Three #6 seeds upset #3 seeds: 7.68%
- All four #6 seeds advance: 0.83%
Mathematically, the #3 seed should be predicted to advance if there is one matchup. With two matchups, both #3 seeds should be predicted to advance, but one upset pick of this type would also be reasonable. With three or four matchups, one #3 seed should fall to a #6 seed.
#3 seed vs. #11 seed
In 23 games since 1994, #3 seeds are 14–9 against #11 seeds. This is an upset rate of 39.13%, thus U=0.3913. There has never been more than one upset of this type in the same year. As there have never been more than three #11 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:
- #3 seed advances: 60.87%
- #11 seed advances: 39.13%
With two matchups:
- Both #3 seeds advance: 37.05%
- One #11 seed upsets a #3 seed: 47.64%
- Both #11 seeds advance: 15.31%
With three matchups:
- All three #3 seeds advance: 22.55%
- One #11 seed upsets a #3 seed: 43.49%
- Two #11 seeds upset #3 seeds: 27.96%
- All three #11 seeds advance: 5.99%
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 #11 seed.
#6 seed vs. #14 seed and #11 seed vs. #14 seed
These matchups have never occurred, as no #14 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 #6 seed or #11 seed should defeat the #14 seed, as predicting two historic upsets in succession is highly unreasonable.
#4 seed vs. #5 seed
In 54 games since 1994, #4 seeds are 33–21 against #5 seeds. This is an upset rate of 38.89%, thus U=0.3889. The most such upsets that have occurred in one year is three, in 2003 and 2011. Using Equation (1), the odds are as follows:
With one matchup:
- #4 seed advances: 61.11%
- #5 seed advances: 38.89%
With two matchups:
- Both #4 seeds advance: 37.34%
- One #5 seed upsets a #4 seed: 47.53%
- Both #5 seeds advance: 15.12%
With three matchups:
- All three #4 seeds advance: 22.82%
- One #5 seed upsets a #4 seed: 43.57%
- Two #5 seeds upset #4 seeds: 27.73%
- All three #5 seeds advance: 5.88%
With four matchups:
- All four #4 seeds advance: 13.95%
- One #5 seed upsets a #4 seed: 35.50%
- Two #5 seeds upset #4 seeds: 33.89%
- Three #5 seeds upset #4 seeds: 14.38%
- All four #5 seeds advance: 2.29%
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 #5 seed. With four matchups, one #4 seed should fall to a #5 seed, but two upset picks of this type would also be reasonable.
#4 seed vs. #12 seed
In 16 games since 1994, #4 seeds are 15–1 against #12 seeds. This is an upset rate of 6.25%, thus U=0.0625. There has never been more than one upset of this type in the same year. As there have never been more than two #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: 93.75%
- #12 seed advances: 6.25%
With two matchups:
- Both #4 seeds advance: 87.89%
- One #12 seed upsets a #4 seed: 11.72%
- Both #12 seeds advance: 0.39%
Mathematically, all #4 seeds in this matchup should be predicted to advance. An upset pick of this type would not be reasonable.
#5 seed vs. #13 seed
In 6 games since 1994, #5 seeds are 3–3 against #13 seeds. This is an upset rate of 50%, thus U=0.5. There has never been more than one upset of this type in the same year. As there have never been more than one #13 seed in the round of 32, our consideration should not extend beyond that point. At a 50% upset rate with a one-matchup maximum, this pairing is a true coin flip.
#12 seed vs. #13 seed
These matchups have never occurred, as all #13 seeds that have survived the Round of 64 have met #5 seeds in the Round of 32. If a bracket includes these matchups, the #12 seed should defeat the #13 seed, as novel matchups are typically won by the better-seeded team.
Overall
Since 1994, the Round of 32 has featured a mean of 3.42 upsets, a median of 3 upsets, and a mode of 4 upsets. The fewest upsets in the Round of 32 was none (1999), and the most upsets was 7 (2003).
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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