Why Picking a Perfect Bracket is Harder Than Winning the Lottery

The Elusive Perfect Bracket: Odds and Comparisons

Every March Madness, millions of brackets are filled out, each hoping to defy the odds and predict a perfect tournament. But how likely is it that your meticulously crafted bracket will hold true? Spoiler alert: it’s much harder than you think. Think of the word Quintillion and 18 zeroes after the number type odds.

The Flawed Formula:

While it might seem intuitive to assume picking winners is a simple coin toss (win or lose), the reality is far more complex. There are 64 teams in the NCAA tournament, but each game offers more than two possible outcomes. Close games can go into overtime, and upsets are a constant threat. So, the idea of using 2^63 (which is an enormous number) to calculate the odds is off the mark.

The Odds of a Perfect NCAA Bracket

Picking a flawless NCAA March Madness bracket is an exhilarating challenge. Imagine correctly predicting the outcome of all 63 basketball games in a single-elimination tournament! But the numbers are staggering. If you were to pick randomly, the probability of achieving a perfect bracket is approximately 1 in 9.2 quintillion (that’s 1 followed by 18 zeros). 9,200,000,000,000,000,000.

Even with sports knowledge, the odds remain astronomical. Statisticians and computer scientists crunch the numbers each year, but the elusive perfect bracket remains a mystery. While some strategies can improve your bracket, it’s still a monumental task. For instance, choosing all No. 1 seed teams to win their first-round matchups is a common approach, given their historical dominance.

If you can survive the first round your odds get exponentially better!

The NCAA Bracket Challenge: A Mathematical Conundrum

If you can miraculously predict all the winners of the first round (at over 1 in 4 billion), now you’ve got a 1 in over 65,000 chance of picking the correct second round. To put that into perspective, that would be like a packed Raymond James stadium in Tampa, Fl with each person holding a number, and them picking your number as the winner.

• In the first round, there are 32 games, resulting in 2^32 (over 4 billion) potential combinations.
• In the second round, there are 16 games, leading to 2^16 (over 65,000) potential combinations.
• In the third round, with 8 games a 2^8 is narrowed to 256 combinations.
• Fourth round with only 4 games and only 16 combinations.
• This pattern continues until the championship game, where there are 2 potential outcomes.

What’s the best someones done in a NCAA bracket challenge – “The Perfect Bracket” through the Sweet 16 that’s verifiable?

Gregg Nigl, a neuropsychologist from Columbus, Ohio, gained widespread attention during the 2019 NCAA basketball tournament for his remarkable bracket performance. Nigl’s bracket, known as the “center road” bracket, achieved unprecedented success by correctly predicting the outcomes of the first 49 games of the tournament. This feat shattered the previous record for the longest streak of correct picks in a March Madness bracket, which stood at 39 games and was achieved in 2017.

Nigl’s bracket garnered significant media attention and became a sensation among basketball fans and tournament enthusiasts. His ability to accurately forecast the outcomes of nearly every game in the tournament’s early rounds captured the imagination of sports fans across the country.

However, Nigl’s remarkable run came to an end in the Sweet 16 round of the tournament. In game 50, the matchup between No. 3 seed Purdue and No. 2 seed Tennessee went into overtime, with Purdue ultimately prevailing with a 99-94 victory. This result marked the first incorrect prediction in Nigl’s bracket, ending his historic streak.

Despite the bracket’s eventual bust, Nigl’s achievement was noteworthy as the first verified bracket ever to accurately predict all the way to the Sweet 16. His accomplishment showcased the unpredictability and excitement of March Madness while demonstrating the potential for fans to achieve remarkable success with their bracket predictions.

Nigl’s astronomical odds to get that far and what that achievement was by the numbers!

For Round 1: Number of potential outcomes = 2^32 (because there are 32 games)

For Round 2: Number of potential outcomes = 2^16 (because there are 16 games)

To find the total number of potential combinations for correctly predicting the outcomes of both rounds, you multiply these two numbers together:

Total potential combinations = (2^32) * (2^16) = 2^(32+16) = 2^48

So Gregg Nigl’s bracket, which correctly predicted the outcomes of the first 49 games of the 2019 NCAA tournament, beat the astronomical odds associated with the first two rounds of the tournament, which would have been represented by 2^49 potential combinations.

To represent 2^49 as a whole number:

2^48 ≈ 562,949,953,421,312

So, the total number of potential combinations for correctly predicting the outcomes of the first two rounds of the NCAA tournament is approximately 562.9 trillion. Now this is skewed because the small percentage of teams that win as 15 and 16 seeds can typically be taken out of the equation, but if it was just a 50-50 coin flip for each team, those are the astronomical odds!

Can you beat the odds and give yourself a better chance?

Expert analysis, team statistics, and historical performance can improve bracket selections, skewing the odds slightly in favor of those with strategic insight. Nevertheless, the sheer number of possible outcomes remains astronomical, making the perfect bracket a rare and elusive achievement.

For example picking #1 and #2 seeds can improve your odds somewhat, but March Madness is “madness” for a reason as we’ve seen many top seeds go down early. Here are some examples:

• Perhaps the most famous upset in NCAA tournament history, the #16 seed UMBC Retrievers defeated the #1 seed Virginia Cavaliers in the first round of the 2018 tournament. It marked the first time in history that a #16 seed defeated a #1 seed.
• 2012 NCAA tournament, the #15 seed Lehigh Mountain Hawks stunned the #2 seed Duke Blue Devils in the first round
• In the 2010 NCAA Tournament, #1 seed Ohio State Buckeyes were defeated by the #10 seed Dayton Flyers (64-61) in the second round.
• In the 2001 tournament, the #15 seed Hampton Pirates upset the #2 seed Iowa State Cyclones in the first round, shocking college basketball fans.
• In the 2012 NCAA tournament, the #15 seed Norfolk State Spartans defeated the #2 seed Missouri Tigers in the first round, pulling off one of the biggest upsets of the tournament.
• In the 1997 NCAA Tourney the Eagles dominated the Gamecocks No. 15 Coppin State 78 over No. 2 South Carolina 65 (1997) This was the first-ever 15-over-2 upset.

Do you have a memorable top seed getting taken down by a lower seed early on? Let us know in the comments!

Using some artificial intelligence to show how much better your odds are to win either the mega millions or the powerball vs picking a perfect NCAA Bracket

Because my math skills have diminished over the years, I turned to our trusty AI to do the heavy lifting. If you don’t want to read the boring math/formula babble below. In a nutshell, you have just under a 30 Quadrillion better chance of picking the powerball or mega millions than a perfect bracket. Yes you read that right, 30,000,000,000,000,000 times higher.

When comparing the odds of winning the Powerball or Mega Millions jackpot to the odds of a perfect NCAA bracket, the difference is indeed massive. However, when expressing this as a percentage, it becomes extremely small due to the large discrepancy in the numbers involved.

Let’s recalculate the percentages without using scientific notation to provide a clearer understanding:

For Powerball:

• Odds of Powerball: 1 in 292,200,000
• Odds of Perfect NCAA Bracket: 2^63

Ratio = (Odds of Powerball) / (Odds of Perfect NCAA Bracket) Ratio ≈ (1 / 292,200,000) / (2^63)

To express this ratio as a percentage, we’ll first find the reciprocal of the ratio and then multiply by 100 to convert it to a percentage:

Percentage = (1 / Ratio) * 100

Let’s calculate this:

Ratio ≈ (1 / 292,200,000) / (2^63) Ratio ≈ 3.4255 * 10^-15

Now, let’s find the percentage:

Percentage ≈ (1 / 3.4255 * 10^-15) * 100 Percentage ≈ 2.919 * 10^16%

Similarly, for Mega Millions:

• Odds of Mega Millions: 1 in 302,600,000
• Odds of Perfect NCAA Bracket: 2^63

Ratio ≈ (1 / 302,600,000) / (2^63)

Let’s find the percentage:

Percentage ≈ (1 / Ratio) * 100

Percentage ≈ (1 / 3.350 * 10^-15) * 100 Percentage ≈ 2.985 * 10^16%

So, in terms of whole numbers:

For Powerball: Approximately 2.919 * 10^16% For Mega Millions: Approximately 2.985 * 10^16%

This means that your chances of winning either the Powerball or Mega Millions jackpot are approximately 29,190,000,000,000,000 times (Powerball) and 29,850,000,000,000,000 times (Mega Millions) greater than your chances of picking a perfect NCAA bracket.

This highlights the staggering difference in probability between the two events.

Let’s look at some daily life odds to put all this into perspective

From accidents, to lightning, to giving birth, here are some odds in your lifetime that are WAY more likely to happen than either the lottery or the perfect bracket. (Except the space debris)

• Lifetime odds of dying from heart disease: are 1 in 6 .
• Dying in a Car Accident: 1 in 107 (in the United States)
• Dying from a fall in the United States: 1 in 127
• Giving Birth to Identical Twins: 1 in 250
• Having a Hole-in-One (amateur golfer): 1 in 12,500
• Being Struck by Lightning: 1 in 15,300 (lifetime)
• Being bitten by a venomous snake in the United States: 1 in 37,500
• Winning the Olympics (individual athlete): 1 in 662,000
• Giving Birth to Identical Quadruplets: 1 in 15 million
• The chances of a specific individual being hit are even more remote—about one in a trillion.

Nailing a perfect bracket might be a dream, and understanding the magnitude of these odds can add a layer of fun to March Madness. You can still enjoy the thrill of the tournament and the challenge of bracket pools, even if your picks don’t go all the way. Remember, sometimes the best part is the journey, not the destination.

So, as you fill out your bracket this year, remember: while perfection may be improbable, the excitement of the tournament is always guaranteed.