March Madness Probabilities

Every year during the NCAA Basketball National Championship, or March Madness, fans make bracket predictions and often make bets on them. Warren Buffet, the billionaire investor of Berkshire Hathaway, once offered one billion dollars for anyone who could predict a perfect bracket.

But what exactly are the odds of predicting a perfect bracket? Buffet actually made one of the safest bets he could. First, let’s assume that each team has a 50% chance of winning any given game. The probability is calculated by simply taking the number of outcomes from a game, one team could win or the other team could win, so 2, and taking that to the power of the number of games, which for the 64-team tournament, is 63 games, so 263. What is that, you ask? The odds of completing a perfect bracket are about 1 in 9.2 quintillion (9,223,372,036,854,775,808). To put that into perspective; the odds of winning the Powerball lottery are 1 in 175,223,510, the odds of being struck by lightning in a year are 1 in 1,042,000, and the odds of becoming President of the United States are about 1 in 10,000,000.

Supposedly, there are ways to increase the likelihood by making a few assumptions based on history. For instance, a sixteen-seed has yet to beat a number one-seed team, and in general higher seed teams are indeed more likely to win, so making the assumption that every team has 50-50 shot at winning doesn’t really help. With all that, one can supposedly increase their odds to about 1 in 128 billion. That being said, this year, someone had a perfect bracket until the 40th game, the longest record for ever. The odds of correctly predicting that many games being 1 in 239, or about 1 in 549,755,813,888

Did you make a bracket? How far did you make it?

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