The Math Behind Your NCAA Basketball Brackets

Is your NCAA bracket perfect? Have you picked every game so far this tournament correctly? Grabbed the upsets? Picked the favorites? If you go on to get all 63 games correct…well…that’s nearly impossible.

Warren Buffet, the longtime financier, has offered again this year a million dollars to anyone who can guess each game correctly! Tim Chartier, a mathematics professor at Davidson College interviewed in Smithsonian Magazine, says, “I don’t think there’s anything that captures the social consciousness’ attention as March Madness.”

Basic Probability

So, let’s assume you guess correctly, with no prior knowledge of sports, each game. The probability of that happening (think like a fair coin flip) would be (½)⁶³, or 1.0×10^-19. Layman’s terms? You have roughly the same probability of getting three holes in one, in golf, as a non-professional. You have a better chance of winning the Powerball twice…in a row. Likely? Nope.! Let’s dive into the numbers.

Round 1

So, let’s start with the 1985 season, where that’s the first time we have 64 teams in the tournament. There have been 144 games in round 1. Here are the breakdowns for wins and losses:

 

Seed               Wins               Losses            %

1                      143                  1                      99

2                      135                  9                      94

3                      122                  22                    85

4                      113                  31                    78

5                      93                    51                    65

6                      90                    54                    63

7                      87                    57                    60

8                      71                    73                    49

9                      73                    71                    51

10                    57                    87                    40

11                    54                    90                    38

12                    51                    93                    35

13                    31                    113                  22

14                    22                    122                  15

15                    9                      135                  6

16                    1                      143                  1

 

As you see above, the top seeds have the highest probability of winning…except the #9 seed, but that matchup with the #8 seed is roughly a toss-up anyway. 2018 saw the University of Maryland, Baltimore County defeat the #1 seed Virginia Cavaliers in the only time a 16 seed won. But for the most part, round 1 is typical. It’s in Round 2 where you see some strange things.

 

Round 2

 

Seed               Wins               Games            %

1                      123                  143                  86

2                      91                    135                  67

3                      75                    122                  61

4                      67                    113                  59

5                      49                    93                    53

6                      43                    90                    48

7                      28                    87                    32

8                      14                    71                    20

9                      7                      73                    10

10                    23                    57                    40

11                    24                    54                    44

12                    22                    51                    43

13                    6                      31                    19

14                    2                      22                    9

15                    2                      9                      22

16                    0                      1                      0

 

Now, if you are a 10, 11 or 12 seed, your chances of winning are better than the 7, 8 or 9th seed. In fact, an 11 seed is just below the winning percentage of a 6th seed. This year as of Saturday morning, three of the four 11 seeds are in round 2. Two 12 seeds and a 15 seed (St Peter’s) are all still dreaming. Pick any of them?

 

Sweet 16 to Final Four

 

The Sweet 16 is a term used to describe the remaining teams after the first weekend of the NCAA tournament. It actually goes back in time to high schools and newspapers using that term.

(From The Davenport Democrat and Leader, Davenport, IA, 1935)  

Here are the total appearances in the Sweet Sixteen by Seed:

Seed                Appearances                                       Seed               Appearances

1                      123                                                      9                      7

2                      91                                                        10                    23

3                      75                                                        11                    24

4                      67                                                        12                    22

5                      49                                                        13                    6

6                      43                                                        14                    2

7                      28                                                        15                    2

8                      14                                                        16                    0

 

Notice how the 10, 11 and 12 seeds have more appearances than an 8 or 9 seed. It will be interesting to see who makes it this year. Everyone know a high seed will be there. It’s just guessing who. In 1986, Cleveland State became the first, true, “CINDERELLA.”  As a #14 seed, they defeated #3 seed Indiana and then #6 St Joseph’s in Syracuse, NY. Picking that CINDERELLA team is the toughest challenge.

Prior to 2010, it was more likely that you would find multiple #1 seeds in the Final Four. But since 2010, there is at least one #4 or higher in the Final Four. The champion has pretty much been a #1 for the past fourteen years. Eleven times a #1 seed was crowned the champion over that period of time. However, the highest seeds to win the championship were a #8 (1985), #7 (2014), #6 (1988) and #4 (1997). Hopefully, you didn’t pick a #5 to win. They never have. So Iowa, St Mary’s, UConn, and Houston better NOT be in your Final Four.

 

Professor Chartier leads a group of students each year to create and/or evaluate the best way to pick teams. His students have realized that the worst way to create a bracket is by winning percentage only. So he challenges them to find other methods.  His students have produced brackets that often find themselves in the upper 97th percentile of ESPN brackets.  For example, the students might look at winning streaks in the season or wins at home or away. Another interesting way is to give weight to a win in the first part of the season only as 25%, not the usual 50 percent. And a loss early would be the same.

 

“That way, I’m saying that the games in the second half [of the season] are more predictive of winning in March Madness.”  (Professor Tim Chartier to author Jay Bennett)

 

Using most mathematical methods, stats gurus are often correct up to around 70%, says Professor Chartier. But honestly, in your family or office pool, the old adage “you don’t have to be faster than the bear, only the people running away from it” would work well.  So, hopefully you planned well, researched deeply, and will use some of this analysis to help you next year. Until that last game is played, enjoy!