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 Continue reading March Madness Probabilities

On Tails

Tail events, in probability speak, are extreme events with the potential for a very large impact but which have a very low likelihood of occurring. Many people (I think accurately) view the most recent financial crisis as the occurrence of a tail event: it was highly unlikely that the system would experience such a drastic collapse, but it happened. We might consider the change of nuclear war or alien invasion as a tail risk. In N. Nassim Taleb’s The Black Swan, Taleb discusses the dangers of such risks with an analogy: even if you have encountered thousands of swans in your lifetime, and have never Continue reading On Tails