Warren Buffett is offering $1B to whomever produces a perfect bracket [Link]. Here is my take.
There are about 9.2 quintillion ways to fill out a perfect bracket. This is often mistakenly used to predict the odds of filling out a perfect bracket – it is not 9-quintillion-to-1 because:
(a) the tournament isn’t like the lottery where every outcome is equally likely, and
(b) monkeys are not randomly selecting game outcomes. Instead, people are purposefully selecting outcomes.
Outcomes for “good” brackets made by people who play the odds and, for example, choose 1 seeds to beat 16 seeds in the second round. These brackets have a much better chance of reaching perfection, somewhere in the range of 128 billion-to-1 or 150 million-to-1 (See here and here).
The limitation here is that these odds give an individual likelihood of getting a perfect bracket; they give no insight into how to construct a pool of brackets that collectively has a high degree of likelihood for producing a perfect bracket.
Just like in the lottery, there is a difference between you willing the lottery and someone winning the lottery (just like in the classic Birthday Problem). Let’s say we have the perfect methodology that gives us the 150 million-to-1 odds. If 150M people filled out brackets, would we expect to see a perfect bracket? Probably not. If everyone used the same methodology that maximized our individual chance of getting a perfect bracket, this wouldn’t necessarily lead to a pool of brackets that collectively guarantee that someone gets a perfect bracket. The problem is, many of the brackets will be identical or almost-identical if they use the same methodology (meaning that they are all perfect or they are all not perfect). There needs to be enough variation between the entries to probabilistically “cover” the possible brackets with a certain reliability level. We would expect to see more variation between entries in the lottery, where many people purchase lottery tickets with randomly generated numbers (and we can more easily estimate the odds that someone will win a lottery based on the number of tickets sold). Recall: randomly generated brackets aren’t the answer! In a nutshell: what is good for the goose isn’t necessarily good for the gander.
The probability of a perfect bracket depends on the tournament. Let’s look at brackets in the last 3 years on ESPN. Let’s only look at how many people correctly select all Final Four teams:
- 47 of 8.15 million brackets correctly picked all Final Four teams in 2013
- 23,304 of 6.45 million brackets correctly picked all Final Four teams in 2012
- 2 of 5.9 million brackets correctly picked all Final Four teams in 2011
Both 2011 and 2013 had “Cinderella stories” of VCU and Wichita State, respectively. A single surprise can drastically affect the number of outcomes and make it less likely for someone to have a perfect bracket. On the other hand, when a 1 seed wins the tournament, brackets have more correct picks, on average. Certain tournaments therefore provide the right atmosphere that could lead to perfect brackets than others.
While having a good methodology for filling out a bracket is key to maximizing your chances, chance plays a much larger role. However, while you cannot control the randomness of the tournament, you can control how you fill out a bracket. In terms of strategy, a person should use statistics, analytical methods, and expert opinions to fill out a bracket to maximize the chance of picking a perfect bracket.
It would be a mistake to look at the two best brackets in 2011 and use the methodology that went into creating those brackets in other tournaments. Basing your bracket methodology on a single tournament is not a good idea (a single tournament is a small sample, no statistically significant conclusions can be drawn from it). If we applied the 2011 methodology to other years, we would quickly see that in the long run, we would do very poorly in March Madness office pools.
If we are acting in our own self-interests (and we are if we want that $1 billion prize!) then we should use the best models to maximize our personal odds and then hope for the best. Luckily, my colleagues have used analytics, operations research, and math to create some pretty good methods we can use to fill out brackets. This is a terrific place to start.
For my tips on filling out a bracket based on analytical methods: read my post here.
Are you participating in the Warren Buffett contest?