As the college basketball fans awaits best four days of the year, I am sure that there are some people out there that are struggling to finalize their office pool bracket. As they stress about which No. 12 seed team to select in an first round upset or which dark horse team to advance to the Final Four, it is natural to have one of two related thoughts:

"What if this winds up being exactly how the tournament actually plays out?"

Alternatively:

"What are the odds to correctly pick the results of the entire tournament?"

This is a question that a lot of people have tried to answer over the years, myself included. As we will see, this is actually a much more complex question than it might appear on the surface. It is also a question that a lot of smart people don't get right.

But I think that I have found the answer.

But for clarity, although there are 68 teams in tournament, all mainstream bracket contests ignore the results of the First Four.

The remaining 64 teams play in 63 total games, with one team being eliminated in each game until one team remains. For the purpose of this analysis going forward, I am assuming that the goal is to pick the winner of those 63 games only.

There is one extremely simple way to think about this problem. If you assume a person is simply randomly guessing on the winner of each game, the odds are very easy to calculate. It is the same as the odds of correctly guessing the result of 63 consecutive coin flips, which is one half multiplied by itself 63 times (i.e. 1/2^63 or one half to the sixty-third power). In other words:

1 in 9,223,372,036,854,780,000

Those are pretty long odds.

A lot of people will reference the number above, and it isn't correct. As it turns out, it is not even close.

That is because games are clearly not just coin flips where both teams have an equal probability of victory. The obvious example of this is the set of first-round games between No. 1 seeds and No. 16 seeds.

If one were to enter a contest where one only needs to pick the winner of these four games, the obvious strategy is to take all the No. 1 seeds. In the first 33 years of the tournament after it expanded to 64 teams in 1985, this would have been the winning strategy.

However, in 2018, that strategy would have failed as No. 16 UMBC upset No. 1 Virginia in historical fashion. Four years later, it happened again as No. 16 Fairleigh Dickenson upset No. 1 Purdue.

This particular example gives valuable insight into how to think about the problem of the odds of a perfect bracket. What would the odds be to "win" the No. 1 vs No. 16 Seed Challenge?

In most years, the odds would be close to 100% as long as one knew that No. 1 seeds (almost) always win in the first round.

But, what about in 2018 or in 2024?

Let's say that there was one brave UMBC graduate that decided to take a flier on his alma mater. What would his odds have been? My math suggests that this type of upset should occur about one percent of the time (about once every 25 years). So, I think that it is reasonable to say that this UMBC fan had about a one percent chance to win this contest with that bracket.

This simple thought experiment tells us several things:

1) The odds to pick a "perfect bracket" are equivalent to the odds of that bracket occurring.

2) Therefore, the odds of a perfect bracket are not the same from year to year and can vary widely depending on the number of upsets and general "chaos" in the bracket.

3) If you can estimate the probability of victory for any potential matchup, that should allow you to make the appropriate calculations.

Over the years, I have read several articles that claim to be able to make the perfect bracket odds calculation. Several years ago there were University professors that came up with values of 1 in 2 trillion or "as low as" 1 in 120 billion.

Renowned sports statistician Nate Silver estimated the odds to be around 1 in 7 billion back in 2014. This year he has upped his estimate to about 1 in 1 in 10 quintillion

A recent article article published by the NCAA get a value of 1 in 120 billion.

The NCAA article gets close to an understanding of the most important variable needed to correctly make the calculation. They point out that the key is to understand the average odds to correctly pick the winner of each game.

As discussed above, while some NCAA Tournament games are 50-50 toss ups, in some games the favorited team's odds approach 100%. If we knew the "correct" average odds for all 63 games, calculating the odds to generate a perfect bracket would simply involve raising that number to the 63rd power.

In the NCAA article, they mentioned one calculation using 75% as that value. In the estimate leading to the value of 1 in 120 billion, they use a value of 66.7%. This is roughly the rate at which bracket challenge contestants correctly guess each game.

Both values are getting closer to the truth, but both are still wrong.

My hypothesis is that the value that is needed is the geometric (and not athematic) average odds for the winning team in all 63 contents.

If we accept this as true (and I am very confident that it is) there are a few different calculations that we can make.

The best way to generate this average would be to have the Vegas spread for every possible tournament game. Those spreads can be converted into probabilities through standard correlations and then the geometric average is trivial to calculate.

The spread data is available at the end of the tournament for the games that actually took place. So it is possible to calculate the odds of a perfect bracket after the tournament is concluded.

If one wants to estimate the odds before the tournament starts, one must first assign a winner in all 63 games. Then one must use a predictive tool such as Kenpom efficiency margin data to generate the odds that the choosen winners will be victorious.

One way to accomplish this is to make the assumption that the favorite team will win all 63 games. This bracket is actually the single most likely way for the tournament to play out and it represents an important boundary condition for this mathematical exercise. It defines the lower bound for the odds of a perfect bracket.

In 2026, I ran the numbers for the most likely perfect bracket based on the current Kenpom efficiency margin values for all 68 teams and for all 63 projected contents. The geometric average of the odds for the winning teams works out to 72.4%.

This means that the lower bound on the odds to predict a perfect bracket in 2026 is approximately 1 in 700 million.

But this value is actually historically low. Figure 1 below presents the geometric average for the most likely bracket in each Tournament from 2002 through 2025.

Figure 1: Geometric average of the odds that the winning team has in all 63 NCAA tournament games assuming that the favored team wins all 63 games. The odds were generated based on Kenpom efficiency margin data from 2002 to 2026.

The values generally fall between 65% and 70%, so the estimate from the NCAA article does have some merit.

The lowest value on record was 65.2% in 2006. This corresponds to perfect bracket odds of 1 in 500 billion. A low average win percentage corresponds to longer odds to predict a perfect bracket.

Practically, this means that there was more parity in the 2006 tournament than in every other tournament back to 2002. On average, the 63 games were closer to tossups than at any other time. Before the tournament started, this parity could reasonably be expected to result in more upset, more chaos, and therefore longer odds to create a perfect bracket.

As it turned out, there were a total of 21 upsets in the 2006 Tournament, which is the second highest tally in the last 23 tournaments.

On the other end of spectrum are the years when the average victory probability is 70% or above. The tournaments in 2015, 2019, 2025, and 2026 all fall into this category. Parity was/is lower, fewer upsets were likely, and the odds to pick a perfect bracket were also better.

Note that the 2015 and 2025 tournament saw just 12 and 11 upsets respectively, which are the lowest two values in history. The odds of the most likely bracket in these years varied from about 1 in 1 billion to 1 in 6 billion.

Once the tournament starts, however, upsets invariably happen. As a result, the average victory odds for the winning teams start to decrease. Along with it, the odds of a perfect bracket start to go down.

But how much can one expect these values to change? Literally anything can and will happed during March Madness. One way to get a sense of what is most likely to happen is to run multiple simulations of each tournament bracket and then to measure the geometric average of the victory probability for all 63 winning teams in each simulation.

Once again, I used Kenpom efficiency margins to define the victory probability for any potential matchup in every NCAA Tournament back to 2002. Using this data I ran 5,000 Monte Carlo simulations of each tournament and calculated the geometric average of victory probabilities of the winning teams in each simulation.

I then took the average of all 5,000 geometric averages to get a global average winning percentage for the set of 5,000 statistically reasonable tournament results.

Figure 2 shows the result of this set of calculations and compares the results to the values from the most likely bracket of each tournament shown in Figure 1.

Figure 2: Geometric average of the odds that the winning team has in all 63 NCAA tournament games assuming that the favored team wins all 63 games compared to the geometric average of the winning teams' odds from 5,000 tournament simulations.

As expected, the average victory probabilities of the simulated tournaments is consistently about 10 percentage points lower than in the cases where the favorites always win. The average victory probabilities range from 55% to 63%.

These values correspond to odds of picking the perfect bracket between 1 in 5 trillion in 2026 and 1 in 10 quadrillion (i.e. 1 in 10,000,000,000,000,000) in 2006.

Figure 2 also demonstrates that the two data set are very strongly correlated. Figure 3 below shows this correlation more directly.

Figure 3: Correlation between the average victory probabilities of the most likely bracket where all the favorites win and the average victory probabilities in the simulated tournaments.

Practically, the odds to predict the perfect bracket in the more realist simulation scenarios drop by a factor of about 15,000 from the ideal case where the favorites all win.

Fortunately, the tournament actually take place in the real world. Once the full tournament is concluded, we can use the actual Vegas lines to calculate the real set of victory probabilities for the 63 actual games.

Figure 4 below shows the results of these calculations for each tournament back to 2002. For comparison, the simulation results for each tournament are also shown in the figure.

Figure 4: Geometric averages of the victory probabilities of the actual winning teams for each NCAA Tournament back to 2002. For comparison, the same data derived from 5,000 simulations of each tournament is also shown.

Unsurprisingly, the range of actual average victory probabilities varies over a wider range than the simulation results. The actual tournament values range from 53% to 66%. This corresponds to odds of picking a perfect bracket ranging between 1 in 200 billion in 2025 to 1 in 350 quadrillion in 2022.

This range provides part of the answer to the core question asked at the beginning of this article. The real odds to correctly pick the winner of all 63 NCAA Tournament games in recent history has varied from 1 in 200 billion in to 1 in 350 quadrillion. That is a range of six orders of magnitude or in other words, a factor of one million.

The other thing to note about Figure 4 is that unlike Figure 3, the results from the simulation are essentially uncorrelated from each other. What this means is that even though some tournaments start with more or less parity and the expectation for more or less chaos, there is still a lot of randomness once the ball is tipped.

In some cases the actual tournament is more "well behaved" with fewer upsets than the simulation would suggest. This occurs in Figure 4 where the green bar is higher than the striped blue bar. I count 14 such occurrences in the past 23 tournaments.

But in the other nine tournaments, the actual results showed more upsets and chaos (and thus a lower average victory probability) than precited by the average of the simulations.

As an illustration, consider the 2007, 2011, and 2016 NCAA Tournaments. In all three cases, the simulation average gave virtually identical results of a predicted average victory percentage of around 58%. But the three tournament played out very differently.

In 2007, there were only a total of 12 upset and the lowest seed to advance to the regional final/elite eight round was a No. 3 seed. The actual average victory percentage of the Tournament ended up at a value of 62.8% which corresponds to a 1 in 5 trillion chance to pick a perfect bracket.

In 2011, chaos reigned once play started. There were a total of 20 upsets, including several big ones. Five total teams seeded No. 8 or lower made the Sweet 16 and the Final Four was comprised of a No. 3 seed, a No. 4 seed, a No. 8 seed, and a No. 11 seed. The actual average victory percentage was 53.4% which corresponds to a 1 in 150 quadrillion chance to pick a perfect bracket.

In 2016, the tournament proceeded along a very average path. There were also a total of 20 upsets, but with the exception of a certain No. 2 losing in the first round, most of the higher seeds advanced. The Final Four consisted of a No. 1 seed, two No. 2 seeds, and a No. 10 seed. The actual average victory percentage was 57.9% which corresponds to a 1 in 800 trillion chance to pick a perfect bracket.

The 2025 Tournament saw the fewest upsets in history. But fundament elements of the bracket where similar to those in 2015 where No. 7 Michigan State advanced to the Final Four. The well-behaved nature of the tournament last year was as much a function of randomness as it was of the lack of parity.

It also should be noted that the 2025 Tournament followed on the heals of four straight tournaments where there was more chaos than expected.

But perhaps the most interesting aspect of Figure 4 is that although the two data set have different ranges, the average value of the victory probabilities in the two data sets is very similar. In fact, it differs by less than 0.1% (58.4% versus 58.3%).

This is no accident. At the end of the day, the average value from the actual tournaments should match average value from a large number of simulations. Both numbers are converging towards the answer to the question posed at the beginning of this exercise.

In the past 23 NCAA Tournaments, the global average victory probability is just over 58%. The odds that this value corresponds to are the average odds to select the winner in all 63 tournament games in an average tournament. This value is the true average chance to correctly pick a perfect bracket.

That value is about 1 in 500 trillion.

As we learned above, year-to-year variability in both initial parity and simple randomness can impact the final odds in any given year by a factor of 1,000 in either direction.

And that, my friends, is the real, precise, and correct answer to the question "what are the odds to pick a perfect NCAA tournament bracket?"

Quod erat demonstrandum.

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What are the odds of picking a perfect NCAA Tournament bracket?

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What are the odds of picking a perfect NCAA Tournament bracket?