March Madness Update

My interest in how a team's victory odds correlate with their seed in March Madness sparked after I read Stanford Wong's 'Sharp Sports Betting.' This knowledge is invaluable for betting propositions such as 'Can a 14-16 seed win at least one game?' or 'Will a number 1 seed clinch the tournament title?'

Round 2

Let’s kick things off by reviewing the first round results, summarized in the table below. This table illustrates how many teams from each seed managed to progress in 2023, alongside the average figures from the 37 historical seasons spanning from 1985 to 2022. Please note that the season was canceled in 2020 due to well-known reasons.

Seed	2023	Average
1	3	3.97
2	3	3.70
3	4	3.41
4	3	3.16
5	4	2.57
6	3	2.46
7	3	2.43
8	2	2.03
9	2	1.97
10	1	1.57
11	1	1.54
12	0	1.43
13	1	0.84
14	0	0.59
15	1	0.30
16	1	0.03
Total	32	32.00

A striking observation is that only three number 1 seeds advanced this year. Historically, in 148 matchups between a 1 seed and a 16 seed, the 1 seeds triumphed 147 times. This season marks just the second occurrence of a #16 seed winning a matchup.

Taking everything into account, the average remaining seed turned out to be 5.97, which is slightly higher than the historical average of 5.84. It seems the underdogs are off to a strong start, largely thanks to the unexpected victory of the 16 seed (Farleigh Dickenson over Purdue).

Round 3

The next table presents the count of teams from each seed that advanced to the third round in 2023, as well as the historical averages from 1985 to 2022.

Seed	2023	Average
1	2	3.41
2	2	2.51
3	3	2.08
4	2	1.89
5	2	1.35
6	1	1.19
7	1	0.76
8	1	0.41
9	1	0.19
10	0	0.65
11	0	0.68
12	0	0.59
13	0	0.16
14	0	0.05
15	1	0.08
16	0	0.00
Total	16	16.00

Another surprising highlight is that yet another #1 seed was eliminated (with Arkansas defeating Kansas), leaving just two remaining. Historically, around 3.41 of the #1 seeds typically reach the third round. Overall, the average seed advancing to this round is now 4.88, compared to a historical average of 4.57, indicating continued underdog success.

Round 4

The upcoming table displays how many teams from various seeds made it through to the fourth round in 2023, including historical averages from 1985 to 2022.

Seed	2023	Average
1	0	2.73
2	1	1.81
3	2	1.00
4	1	0.59
5	2	0.27
6	1	0.43
7	0	0.27
8	0	0.24
9	1	0.11
10	0	0.24
11	0	0.22
12	0	0.05
13	0	0.00
14	0	0.00
15	0	0.03
16	0	0.00
Total	8	8.00

The last two #1 seeds were also eliminated in the third round. Ordinarily, as indicated, about 2.73 #1 seeds reach the fourth round. You might ask, 'Has this happened previously?' Yes, this occurrence took place in 2006 and 2011. In general, the average seed moving on to the fourth round is 4.63, up from a historical 3.29, highlighting the impressive performance of the underdogs.

Round 5

The next table illustrates how many teams of each seed proceeded to the fifth round in 2023, along with the average from the 37 historical seasons from 1985 to 2022.

Seed	2023	Average
1	0	1.62
2	0	0.86
3	0	0.46
4	1	0.35
5	2	0.19
6	0	0.08
7	0	0.08
8	0	0.16
9	1	0.03
10	0	0.03
11	0	0.14
12	0	0.00
13	0	0.00
14	0	0.00
15	0	0.00
16	0	0.00
Total	4	4.00

Considering all factors, the average seed that advanced to the fifth round stands at 5.75, which is a notable increase compared to the historical average of 2.86. You might wonder, 'Is this the lowest average seed that has made it this far?' The answer is no; only once, in 2011, did the average seed drop lower to 6.5.

Round 6

The next table illustrates how many teams of each seed proceeded to the fifth round in 2023, along with the average from the 37 historical seasons from 1985 to 2022.

Seed	2023	Average
1	0	1.00
2	0	0.35
3	0	0.30
4	1	0.08
5	1	0.08
6	0	0.05
7	0	0.03
8	0	0.11
9	0	0.00
10	0	0.00
11	0	0.00
12	0	0.00
13	0	0.00
14	0	0.00
15	0	0.00
16	0	0.00
Total	2	2.00

The teams that moved on to the championship game this year were a 4 seed and a 5 seed, resulting in an average of 4.5. Traditionally, this stage has seen an average of only 2.35. One could ask, 'Is this the lowest-seeded higher team to reach this stage?' The response is no; in 2014, the championship featured a matchup between a 7 seed and an 8 seed.

Round 7

In 2023, the title was secured by the #4 seed, the University of Connecticut, a feat they previously accomplished only once in 1997. Historically, the average seed that ultimately wins is 1.92. In conclusion, cheers for UConn and all the resilient underdogs!

Average Wins by Seed

The following table provides my revised statistics regarding the average number of games won by teams based on their seed.

Seed	Average wins
1	3.29
2	2.32
3	1.85
4	1.55
5	1.16
6	1.07
7	0.90
8	0.74
9	0.59
10	0.61
11	0.63
12	0.51
13	0.25
14	0.16
15	0.11
16	0.01

Perfect Bracket

After revising my data spreadsheet for the 2023 season, the probability of creating a perfect bracket is estimated at 1 in 1,411,767,179. This calculation is based on a strategy that involves consistently choosing the higher-seeded team, or selecting randomly when faced with equally seeded teams.

For an employee of Warren Buffet, this results in an expected value of around 11 cents annually for a perfect bracket, calculated over an anticipated life span of 40 years. With an estimated 377,000 employees, the yearly expected cost to Mr. Buffet amounts to approximately $399.

Written by: Michael Shackleford