The NCAA Men’s Basketball Tournament (hereafter “the tourney”) is an American institution. Conservative estimates place the number of Americans that fill out a NCAA Men’s Basketball Tournament bracket (hereafter “a bracket”) at 40 million. And most of these happen in bracket pools.
So it’s time to address America’s most pressing annual question: What’s the best way to fill out your bracket so you can win your bracket pool?
Now, obviously, you’d like to fill out your bracket such that you’ve got the greatest chance of your bracket being the best one in your pool.
But notice that your goal here is a relative one, not an absolute one. Amongst the tens of millions of brackets completed across the country, you could win your pool with one of the worst brackets — just so long as everyone else’s bracket that you’re competing against is just a little bit worse than yours. Conversely, your amazing bracket could be trumped by your neighbor’s bracket that’s just a little bit better. Your strategy, then, needs to be a function of those you are competing against.
This is troublesome for two reasons. First, your opponents are asking the same question as you, so their strategy is a function of what you do. As your opponents respond to your strategy, you respond to their responses, which elicits additional responses from your opponents … on and on. This gets mathematically very cumbersome, very quickly. (At this point I will say: If you find problems of this nature intriguing, search out and take a course in game theory.)
The larger issue, though, is that you do not know your opponent’s strategy — in other words, you cannot see their bracket (nor they yours) until they all have been submitted and the tourney has begun.
But we can make a broad assumption about how your competitors will behave, and that assumption is the following: They will tend to select outcomes that they think are more likely to occur. More directly: People pick favorites.
Maximizing Your Probability of Success
We need another concept before arriving at your strategy. Imagine the simplest of uncertain outcomes: flipping a coin. Let’s temporarily ignore those people at the party who say it could land on its edge — we’ll get back to them in a bit — and say that there are two possible, and equally likely, outcomes to flipping a coin.
Now draw a line in your head. The length of that line represents the totality of possible outcomes; we’re going to split up that line into different segments that represent the likelihood of each outcome. In our example, there are only two outcomes and they are both equally likely. So, we’ve got our line split into two equal segments, each representing the 50% chance that the coin lands on either side.
Let’s now consider those other people at the party, those who point out the third possible outcome — the coin landing on the edge. Crucially, note that all three outcomes are not equally likely. So, when we split up our line into segments we are not going to have three equally sized pieces.
We will end up with two larger pieces representing the two sides of the coin and one very small piece representing the YouTube-worthy edge landing. The Internet tells me that the probability of a nickel landing on its edge is approximately 0.02%, so we would have two large segments at 49.99% and one small segment at 0.02%.
Now, when we consider splitting up our line to represent the conceivable outcomes of the NCAA tournament, there are a lot more possibilities. There are 67 different games, each of which could go one of two ways. So we end up with a staggering number of segments in our line — somewhere in the range of 150,000,000,000,000,000,000. That’s greater than the estimated number of grains of sand on Earth.
And while there are a remarkable number of outcomes, not all of corresponding line segments are going to be the same size. There are more-likely and less-likely outcomes for the tourney. A tourney outcome with, say, defending-champion Villanova winning the title is likely going to constitute a larger segment of our line than one where, say, Northern Kentucky wins the tournament.
Your strategy, then, should be to the capture the widest part of that line you can, so that you have the largest chance of capturing the eventual outcome of the tourney. Under the assumption that most people select favorites to win, selecting favorites yourself leaves you very little margin for error with regards to winning your pool. If your bracket is similar to one or more of your pool-mates’ brackets, then even a tiny bit of inaccuracy could leads to someone else being just a little bit better.
Functionally speaking, this means that the larger your bracket pool is, the more unlikely a bracket you should choose.
All of this is within reason, of course — picking the underdog in every matchup might not lead to much bracket pool success. However, a few well-placed upsets — and maybe a bit of a reach as a champion — might position you for bracket pool success and a year’s worth of gloating over your peers.