Odds of Predicting a Perfect NCAA Bracket


Little Rock upsetMuch has been reported on Warren Buffett’s one billion dollar challenge to the person that can fill out their NCAA bracket correctly. A lot of numbers have been thrown around as to what are the true odds of going 63 for 63 on a bracket are.

In this post, we hope to get relatively close to the true odds and dispel some common mistakes that could throw the numbers off. It’s important to remember that the odds from year to year are never quite exactly the same as there are multiple factors that could affect the odds. The most significant factor is the parity of teams in each match. The closer in talent and ability that teams are to each other, the longer the odds are of picking a perfect bracket and vice versa. We did this experiment in 2014 and came up with odds of 1 in 46,112,373,957. This year’s odds will be much different.

So without further adieu, let’s kick this thing off.

Odds of Predicting a Perfect NCAA Bracket

This is easy! Every game is a coin flip.

Not quite. If every game were a coin flip, then the solution would be very simple. The answer would be one divided by 2 taken to the power of 63 which equals 1 in 9,223,372,036,854,780,000. In short, you have a better chance of being struck by lightning, twice, in the same night. It’s been widely reported by a bunch of web sites that these are the odds of picking a perfect bracket. Maybe journalists should stick to writing as we should stick to doing statistics. The flaw in that argument is that we know that every game isn’t exactly a coin flip, particularly in the early rounds. In fact, in some games (think 1 vs. 16 seeds), one team will have higher than a 90% chance of winning. This greatly sways the odds into our favor.

So, if every game isn’t a coin flip, then how in the world are we going to test this?

Let’s start with the basics! There are a couple of assumptions that we have to make to determine the true odds of predicting a perfect NCAA bracket. This isn’t perfect by any stretch of the imagination, but the idea is to get as close as possible.

  • We will always select the team that has the best chance of winning: Sorry, there are no underdog stories here. A statistician always picks the probable path to a perfect bracket.
  • The computer ratings that we put out on the teams accurately predict the probabilities of teams’ beating each other: Our ratings, which can be found here, are from a logistic regression formula that can be used to compare how teams would do against each other on a neutral floor. This formula has accurately predicted 72.3% of games this year, while the Vegas Line (the true standard) has predicted 74.8%. Is this 100% perfect? No. But it is unbiased and gets us very close to true probabilities.

What do the brackets look like

Assuming that the favorites win the play-in games, this is what our bracket looks like…

Seed
East
West
South
Midwest
1
Villanova
Gonzaga
North Carolina
Kansas
2
Duke
Arizona
Kentucky
Louisville
3
Baylor
Florida St
UCLA
Oregon
4
Florida
West Virginia
Butler
Purdue
5
Virginia
Notre Dame
Minnesota
Iowa St
6
SMU
Maryland
Cincinnati
Creighton
7
South Carolina
St Mary’s CA
Dayton
Michigan
8
Wisconsin
Northwestern
Arkansas
Miami FL
9
Virginia Tech
Vanderbilt
Seton Hall
Michigan St
10
Marquette
Va Commonwealth
Wichita St
Oklahoma St
11
USC
Xavier
Kansas St
Rhode Island
12
UNC Wilmington
Princeton
MTSU
Nevada
13
ETSU
Bucknell
Winthrop
Vermont
14
New Mexico St
FL Gulf Coast
Kent
Iona
15
Troy
North Dakota
N Kentucky
Jacksonville St
16
New Orleans
S Dakota St
TX Southern
NC Central

With the match ups set, what is the probability of predicting the second round?

This is actually easier then you might imagine. The table is a list of all the second round matches with a probability of the favorite winning. Note that the first round matches are now deemed the play-in games.

The lower seeds that have a higher likelihood of winning are listed in green below. Note that the higher seed isn’t always technically the “favorite” to win the game.

Region
Seed
Team
Seed
Team
Proj. Winner
Prob
East
1
Villanova
16
New Orleans
Villanova
95.3%
East
8
Wisconsin
9
Virginia Tech
Wisconsin
75.1%
East
4
Florida
13
ETSU
Florida
82.6%
East
5
Virginia
12
UNC Wilmington
Virginia
76.0%
East
3
Baylor
14
New Mexico St
Baylor
85.9%
East
6
SMU
11
USC
SMU
67.6%
East
2
Duke
15
Troy
Duke
95.4%
East
7
South Carolina
10
Marquette
Marquette
52.3%
West
1
Gonzaga
16
S Dakota St
Gonzaga
96.5%
West
8
Northwestern
9
Vanderbilt
Vanderbilt
51.1%
West
4
West Virginia
13
Bucknell
West Virginia
85.1%
West
5
Notre Dame
12
Princeton
Notre Dame
77.9%
West
3
Florida St
14
FL Gulf Coast
Florida St
86.9%
West
6
Maryland
11
Xavier
Maryland
52.3%
West
2
Arizona
15
North Dakota
Arizona
95.3%
West
7
St Mary’s CA
10
Va Commonwealth
St Mary’s CA
64.5%
South
1
North Carolina
16
TX Southern
North Carolina
96.3%
South
8
Arkansas
9
Seton Hall
Arkansas
54.6%
South
4
Butler
13
Winthrop
Butler
83.7%
South
5
Minnesota
12
MTSU
Minnesota
60.3%
South
3
UCLA
14
Kent
UCLA
94.2%
South
6
Cincinnati
11
Kansas St
Cincinnati
60.5%
South
2
Kentucky
15
N Kentucky
Kentucky
96.2%
South
7
Dayton
10
Wichita St
Wichita St
72.9%
Midwest
1
Kansas
16
NC Central
Kansas
94.9%
Midwest
8
Miami FL
9
Michigan St
Miami FL
52.9%
Midwest
4
Purdue
13
Vermont
Purdue
79.3%
Midwest
5
Iowa St
12
Nevada
Iowa St
73.6%
Midwest
3
Oregon
14
Iona
Oregon
92.7%
Midwest
6
Creighton
11
Rhode Island
Creighton
60.8%
Midwest
2
Louisville
15
Jacksonville St
Louisville
94.1%
Midwest
7
Michigan
10
Oklahoma St
Michigan
50.7%

When we actually multiply all of these probabilities together, we find that there is a 0.010% (a 1 in 9,843) chance this year of predicting the 2nd round perfectly. When we computed the probabilities back in 2014, we found that we have a 0.016% chance of going 32 for 32 if we pick all the favorites. This amounts to a probability of 1 in 6,102 of making this prediction. While this is still highly unlikely, it surely doesn’t fall too far outside the realm of possibility.

On to Round 3…

Standing by our strategy of only picking the favorites, here are the probabilities of all the favorites winning in Round 3.

Region
Seed
Team
Seed
Team
Proj. Winner
Prob
East
1
Villanova
8
Wisconsin
Villanova
56.6%
East
4
Florida
5
Virginia
Florida
58.3%
East
3
Baylor
6
SMU
Baylor
55.9%
East
2
Duke
10
Marquette
Duke
78.6%
West
1
Gonzaga
9
Vanderbilt
Gonzaga
82.2%
West
4
West Virginia
5
Notre Dame
West Virginia
60.9%
West
3
Florida St
6
Maryland
Florida St
69.9%
West
2
Arizona
7
St Mary’s CA
Arizona
66.1%
South
1
North Carolina
8
Arkansas
North Carolina
75.5%
South
4
Butler
5
Minnesota
Butler
59.2%
South
3
UCLA
6
Cincinnati
UCLA
65.0%
South
2
Kentucky
10
Wichita St
Kentucky
66.8%
Midwest
1
Kansas
8
Miami FL
Kansas
76.0%
Midwest
4
Purdue
5
Iowa St
Purdue
56.0%
Midwest
3
Oregon
6
Creighton
Oregon
67.9%
Midwest
2
Louisville
7
Michigan
Louisville
58.3%

Now things are beginning to get dicey. By itself, if you somehow managed to correctly pick the favorites correctly in the 2nd round, then you have a 0.11% chance to correctly pick the 3rd round. By continuing to multiply the numbers out, we are now have a 1 in 8,870,000 chance of calling the bracket right up to this point.

Now that your bracket is busted…

We’ve combined the final three tables into this last section. The games in these rounds are much tighter, and thus, much closer to that of a flip of the coin.

Region
Seed
Team
Seed
Team
Proj. Winner
Prob
East
1
Villanova
4
Florida
Villanova
54.9%
East
2
Duke
3
Baylor
Duke
63.8%
West
1
Gonzaga
4
West Virginia
Gonzaga
63.6%
West
2
Arizona
3
Florida St
Arizona
62.1%
South
1
North Carolina
4
Butler
North Carolina
66.7%
South
2
Kentucky
3
UCLA
Kentucky
60.1%
Midwest
1
Kansas
4
Purdue
Kansas
58.2%
Midwest
2
Louisville
3
Oregon
Oregon
53.2%

After the Sweet 16, the odds of continuing to have a perfect bracket is 1 in 513 million.

Region
Seed
Team
Seed
Team
Proj. Winner
Prob
East
1
Villanova
2
Duke
Duke
53.1%
West
1
Gonzaga
2
Arizona
Gonzaga
56.8%
South
1
North Carolina
2
Kentucky
Kentucky
61.9%
Midwest
1
Kansas
3
Oregon
Kansas
52.9%

After the Elite 8, the odds of continuing to have a perfect bracket is 1 in 5.7 billion.

Region
Seed
Team
Seed
Team
Proj. Winner
Prob
Final Four
2
Duke
1
Gonzaga
Gonzaga
53.1%
Final Four
2
Kentucky
1
Kansas
Kentucky
62.0%
Championship
1
Gonzaga
2
Kentucky
Kentucky
52.7%

The final tally after we multiply up all the probabilities of the 63 games gives us just a 1 in 29,714,235,795 chance of predicting a perfect NCAA bracket. Remember that our conclusion in 2014 was that the odds of picking a perfect NCAA Bracket were 1 in 46,112,373,957. It’s safe to say that in any given year the odds on this can change by tens of billions!

Good luck…and happy picking!

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