We Randomly Generated 10 Million March Madness Brackets — And We Still Got Beat

I should probably be happier that my alma mater, the University of Virginia, won the men’s basketball NCAA tournament. But I’m disappointed that none of the 10 million March Madness brackets I generated would have won ESPN’s Tournament Challenge, where the winning bracket racked up 185 of 192 possible points. (ESPN multiplies those scores by 10, but otherwise it uses the same standard scoring system every major site uses.) The winner of my computer-generated brackets — none of which I entered into any actual contest — scored 178 points, which would have tied for 8th place on ESPN, tied for first place on NCAA.com, finished a strong second on USAToday.com, and been the runaway winner on FoxSports.com.

As a consolation prize, I could have considerably inconvenienced Warren Buffett, who offers his 400,000-some employees $1 million a year for life if they correctly predict the Sweet Sixteen. If Buffett (and TIME) had permitted me to be an employee of Berkshire Hathaway for one day, and enter 10,000,000 brackets, I would have qualified for that prize 334 times (the number of my brackets that guessed correctly in all 16 games that feed into the Sweet Sixteen). By the time I reach age 80 — 45 years from now — Buffett, who is 88, would have owed me $15,030,000,000, or about 18% of his current estimated net worth of $84 billion.

But while perfection was never on the table in this little computational experiment, I did learn a few things about the futility of guessing March Madness results. Here’s how the chips fell for my imaginary pool:

Normally — and this was true after the first two rounds — you would expect a large population of randomly generated brackets to fall along a normal distribution, better known as a “bell curve.” As you can see, this bell would ring with horrible dissonance before tipping over.

As a data analyst, whenever you see a curve like this that doesn’t make obvious sense, you first have to ask yourself a difficult question: is the problem with the data, or with me? I feel comfortably exonerated here, having meticulously checked that all 10 million brackets were legitimate. There were no bugs that had a team advancing after losing, for example, and they adhered to common sense by weighting each random choice by the seeds of the two teams.

Digging in, we see the two humps in the data peak at 54 points (267,595 brackets) and 109 points (41,352 brackets). These precise values are probably a function of various upsets in the first few rounds, but the real reason is pretty simple: the most important factor in any bracket is whether you choose the final champion correctly. Of my 54-pointers, a few had one of the two final teams correct, but none of them guessed Virginia would win. In fact, that would be impossible, because, while guessing the champion correctly is good for 32 points in the final game, this means you also picked that team to win its previous five games, for a total of 63 points. (My lowest scoring bracket to guess the winner had 79 points, an extreme outlier.)

The second hump is the most common outcome for brackets that either won the final game or, less commonly, did very well in the final three rounds. Over 90% of the brackets with 109 points guessed Virginia to win it all, and only 11 guessed neither of the final two teams.

Which is to say, the typical scoring system, in which the points double every round, is so absurdly top-heavy that you can often win an office pool by predicting the winner even if you do horribly in many of the games leading up to the championship. (It mostly depends on how many of your fellow bracketologists also picked the right winner.) While 28 of my brackets correctly guessed 31 of 32 games in the first round, my winner guessed only 24 — still respectable, but loaded with liabilities in future rounds. It didn’t matter. The best of those 28 brackets with near-perfect first rounds ended up with 139 points, compared to my ultimate winner’s 178.

I couldn’t locate figures on the average score of the winning bracket in individual pools of a few dozen people, but I can say with extreme confidence that a healthy majority of them chose Virginia to win. This is definitely true, at least, of every bracket that placed on the leaderboard of every major site’s leaderboard. And of the 1,001,864 brackets in my experiment that predicted Virginia to win the whole thing, the average score was 114 points. Of those that didn’t, the average was 59.

This, to me, is a flaw in the way brackets are scored. I am much more impressed by an entrant who guesses extremely well through the Elite Eight but then falls apart versus someone who ekes out a victory with the winning team, papering over many predictive casualties along the way. Several alternate scoring systems are designed to address this by ramping up the rewards more gradually each round or even just treating every game as 1 point.

I don’t expect this idea to take hold, because it short-circuits the possibility that a contestant can mostly guess wrong and still win. March Madness would become less of a roulette wheel and more of a poker game, favoring the savvy over the lucky. Yes, March would be less Mad. It would also be less angry.