If you are reading this blog, you are probably one of the millions of Americans who filled out a bracket predicting how the NCAA Men's Basketball Tournament would play out. Chances are that your first miss happened sometime around Thursday afternoon. If you were lucky, you made it to Thursday night, and a rare few of you might have even made it to Friday. If you made it through the entire first 4 days, congratulations! You are in the top 1% of the top 1% of the top 1% of all brackets. You are 1 in a million!
How can it be this hard? With millions of Americans filling out brackets (sometimes more than one bracket per person), shouldn’t there be a handful of perfect brackets every year? Although this represents the sentiments of many, the truth is that predicting a perfect bracket is nearly impossible. To my knowledge, there are exactly ZERO confirmed cases of perfect brackets for any of the tournament’s 27 years since expanding to 64 teams in 1985. The expansion to 65 teams in 2001 (and to 68 teams in 2011) doesn’t seem to have had any effect since most people ignore these new play-in games and start with the round of 64 regardless. For 27 straight years millions of people have attempted to correctly predict the outcome of 63 separate games. Add it all together and you have close to a billion attempts to accomplish this feat, and as far as we know, a billion failures. As hard as this seems to fathom at first, a little math can go a long way towards explaining this phenomenon.
Let’s start with something really simple. Obviously, some games (1 vs 16) are easier to predict than others (8 vs 9), but what if everyone just flipped a coin to determine each of the winners? 50/50 seems easy enough. Give people a billion chances at picking correctly 63 times in a row and someone will do it, right? Wrong.
Chances of correctly picking a coin flip 2x in a row: 1 in 4
Chances of correctly picking a coin flip 5x in a row: 1 in 32
Chances of correctly picking a coin flip 10x in a row: 1 in 1,000
Chances of correctly picking a coin flip 20x in a row: 1 in a million
Chances of correctly picking a coin flip 30x in a row: 1 in a billion
Chances of correctly picking a coin flip 40x in a row: 1 in a trillion
Chances of correctly picking a coin flip 50x in a row: 1 in 1,000 trillion
Chances of correctly picking a coin flip 63x in a row: 1 in 9 quintillion (that’s 9 million trillion!!)
As you can see, while the chances of predicting a coin flip start out good, it quickly becomes almost impossible as the number of consecutive attempts increases. Using our assumption that there have been about a billion attempts to pick the bracket over the last 27 years, there would need to be 30 games (instead of 63) for us to see a statistical expectation that someone would get them all right based on this coin flip method.
Thankfully, for those of us who want to someday see a perfect bracket, the coin flip method is too restrictive. It assumes that every game is truly a tossup, something we know not to be true. In reality, 1 seeds have never lost to a 16 seed, 2 seeds (other than this year) almost always win against 15 seeds, and even 3, 4, and 5 seeds win significantly more than 50% of their 1st round games. We need to adjust our initial analysis to account for these increased odds.
Let’s pretend that our hypothetical average Joe has a:
- 90% chance of correctly predicting any round of 64 game involving seeds 1-4
- 70% chance of correctly predicting any round of 64 game involving seeds 5-6
- 50% chance of correctly predicting all other games
Does this new adjusted scenario give us much hope of a perfect bracket? Only a little bit. Under this scenario, the odds of correctly picking the 32 games in the round of 64 are 1 in 1,600. Making a perfect bracket up to the Sweet 16? 1 in 100 milion. In fact, a perfect bracket’s odds would still be less than 1 in 3 trillion. With 1 billion attempts over the last 27 years, that is a 1 in 3,400 chance of anyone submitting a perfect bracket. This suggests we could likely go hundreds of years without ever seeing one.
Although I think the last hypothetical was actually too generous, let’s look at one last scenario with even more favorable odds. Let’s say that every one of the billion attempts we have seen in the past 27 years was made by an expert. Let’s say they studied every single matchup and made extremely informed decisions. Let’s even make some rounding errors in their favor. What if we pretended that everyone had a 90% chance for ALL games in the round of 64, an 80% chance for all games in the round of 32, a 70% chance for Sweet 16 games, and then a 60% chance for all games after that? In this ideal situation, would we see some perfect brackets? Check this out:
Chances of correctly picking 32 games (round of 64) with a 90% chance each time: 1 in 29
Chances of correctly picking 16 games (round of 32) with an 80% chance each time: 1 in 36
Chances of correctly picking 8 games (Sweet 16) with a 70% chance each time: 1 in 17
Chances of correctly picking 7 games (Elite 8 through final) with a 60% chance each time: 1 in 36
Combined chances of doing all 4 of the above: 1 in 641,000
Amazingly, if the odds were as easy as our final scenario suggests, we would still only see a handful of perfect brackets each year. Obviously, the real odds are hard to calculate. Who’s to say how likely a person is to guess the correct outcome? What we do know is that the “real” odds fit in somewhere between the extremes that I outlined here. Although they are much better than the 1 in 9 quintillion coin flip example, they are much worse than the 1 in 641,000 scenario with our “panel of experts”. The odds are probably even worse than my middle scenario involving an “average Joe”, and those weren’t great at 1 in 3.4 trillion.
Hopefully you feel a little better now about your level of success (or lack thereof) attempting to produce a perfect bracket in years past. Any given game may feel like a nearly sure thing, but when you stretch things out into a 63 game tournament, things get very difficult very quickly. If you are one of the extremely rare few who have a perfect bracket going as of today (Tuesday, March 20th, 2012) and are crossing your fingers that you can get another 15 games right, congratulations on your accomplishment to this point, but don’t get your hopes up. Assuming that the rest of the games from here on out are close to 50/50 toss-ups, your odds of adding another 15 games to your streak: 1 in 32,000. Good luck!
