It’s Not Just a Bracket

How to win March Madness with Math

Filling out a bracket for March Madness is fun. “Everyone does it.” Obama fills out a bracket. Dogs fill out a bracket. Experts and non-experts alike all come together and are humbled when the great chaos of fate blows their predictions to smithereens year after year. The quest to create that perfectly predicting bracket is not a fight you try to win. Everyone loses. It’s a fight to lose the least. There has never been a perfect bracket. It’s a lottery that nobody wins. A bit poetic, isn’t it?

Poetics aside. Let’s get down to business. We’re here to win March Madness.

Now, let’s clarify what we mean by “win” here. One definition of win: fill out your bracket so that you have the highest probability of getting every pick correctly. If this were the definition we had in mind, the advice would be simple: choose no upsets. The bracket with no upsets is, strictly speaking, the single outcome that has the highest probability of occurring. If you’re filling out one bracket, and want to maximize the probability of getting a perfect bracket (or the probability of having the best bracket in your group of friends), you should fill out your bracket with no upsets.

OK, nobody does this. What’s the real definition of winning March Madness? Answer: it’s all about aesthetics. Street cred. Filling out a bracket with style. Choosing no upsets is lame and spineless. It’s better to predict a lot of upsets — but not so many that your bracket is ridiculous and has no chance of winning. This is how to win at March Madness.

The respectability of having an 8-seed in your Final Four is massive. Especially if that 8-seed is one of those “dark horse” teams people think was seeded unfairly. “Wow, look at me. I’m so cool, because I’m recklessly expecting something unlikely to happen.”

Of course, if your cavalier prediction comes true, then everyone thinks you’re a baller. You knew. You put it all on the line — and were right. It’s like all the other games guys play: the PENIS game. The “eat the hottest pepper” game. The “crawl out onto the ice that might not be frozen” game. This game gets played in fashion, politics, art — pretty much any social scene. Do you see now? Designing a good bracket is not just some pointless statistical activity. It’s all about aesthetics. If the bracket-filling scene got developed enough, there would be bracket cultures and subcultures and countercultures, trends and fads, bandwagoning and gatekeeping.

Here’s how you fill out a bracket, if you know what’s going on: Choose your upsets with style. Make about half of our 8-seeds lose to the 9-seed. But don’t stop there — or you have no guts. You need some 10–7 upsets, some 11–6 upsets. A pinch of 15–2 upset to spice up the recipe, perhaps? Or maybe a tasteful run of unexpected wins for your team of choice — but unless you’re an amateur, you don’t have them go all the way, because that’s just stupid. This continues in the later rounds — is your Final Four all 1-seeds? Super lame. Even sticking to 1- and 2-seeds is lame-o. An 8-seed in the Final Four though? “Nice.”

Can we play the meta game? When you fill out a bracket, you’re trying to be randomish. You want to choose upsets, sort of according to how likely they are. A rough heuristic is “However many upsets tend to occur, I’ll choose it so that this many upsets occur.”

Imagine a simplified scenario with a coin that lands heads 80% of the time. You flip it ten times. The “bracket” here is to predict what the outcomes of each flip will be. Now, the strictly most likely outcome is 10 heads in a row. But the most likely number of “upsets” is 2. This is also the expected number of upsets.

So the basic strategy is to fill out the bracket so that roughly two flips are tails. Or maybe three, if you want to be edgier. But putting in fewer than two is super basic.

Can we play the meta-game? Here’s a way to fill out your bracket: choose upsets randomly, proportional to the likelihood that the upset occurs. This codifies the way aesthetically-competitive people tend to fill out brackets, but fixes an important flaw: people are really bad at doing probability intuitively, and are really bad at being random. How often do 13-seeds get past the first round historically, anyway?

Luckily, there’s a way to do this without becoming an expert — copy the experts. FiveThirtyEight puts out March Madness predictions each year.

Their online tool is great — it shows you the probability of each team winning, and you can fill in your choices as you go to reassess the new chance of your 8-seed making it past the second round, third round, etc.

So here’s how to make what is mathematically guaranteed to be a stylish bracket. You’ll need a random number generator. For the technique here, you can just repeatedly ask Google to generate a random number between 1 and 100 inclusive (henceforth referred to as the RNG — Random Number Generator).

  • For each matchup, check the percent of the time the top team wins. Now “roll” the RNG to get a number.
  • If the generated number is lower or equal to the percentage, then the top team wins the matchup. If the number is higher, the other team wins. (If equal, try again.) For example, in 2021 Alabama has a 95% chance of winning its first game, so unless you roll a 96, 97, 98, 98, or 100, Alabama is winning that game.
  • As you go, fill in the team that won on your bracket, and on the 538 site. This way, you can check the percentages for direct matchups for the later rounds.
  • Continue until done.

I know what you’re thinking. “Automatically filling out a bracket is so BORING. This sucks out all of the creativity, soul, personalization out of the process of choosing our lottery ticket.”

I disagree. Give it a try. I find this to be WAY more fun than using your own predictions. For one, you can know that your predictions are correctly biased — you choose upsets at the “right” amount. More so, doing this exercise reveals just how terrible we are at being random. Once you see the types of predictions this random bracket makes, you’ll realize how pitiful your former attempts at “randomness” were. You thought you were cute, choosing a 14-seed upset? Try this: when I first filled out my bracket, I was scared because it chose no upsets at all in the first round for both the East and Midwest divisions. Yikes! That’s pretty lame. But then it went ahead and put two 8-seeds and a 9-seed through to the Elite 8—where we would expect only 1- and 2-seeds, without upsets — and no 1-seeds in the Final Four. I highly doubt any style-minded bracket-filler would ever “randomly” do both of those things in the same bracket.

Most importantly, it’s very fun giving human meaning to the predictions made by the RNG. For each matchup, you roll the RNG with anticipation — it’s like witnessing 63 little instantaneous basketball games take place one after another. Is the next one going to be an upset? Each result is a little jolt of excitement, especially when it’s an upset. As you continue, the one-of-a-kind, all-natural bracket construction takes form.

One last fun story about my RNG-based bracket this year: my bracket put Ohio State — my home team — in the national championship. The opponent? None other than Alabama: a rematch of the CFB national championship. Now that is the type of artistic, aesthetic — but not unimaginable — prediction we like to see. (FYI, RNG+538 chose OSU over Alabama.)

Try it out. At the least, the RNG will inspire you with the creative, bold, graceful, and thoroughly random-but-not-too-random combination of picks it calculates for you. At best, you can rest assured that your bracket is now way cooler than everybody else’s.

Note: the view presented here is a vastly simplified view of bracket filling, focused on the behavior of competitive sports-minded dudes. The motive for Obama’s picks is far different — notice how his picks don’t even include the seeds, to hide away the low-brow, trivial obsession about upsets.

My RNG+538 bracket.
My auto-generated, all-natural, RNG+538 bracket.




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