Back in 2006 when I was 11 years old, I told my dad that the Florida Gators were going to win March Madness. I knew nothing about college basketball at the time, but I didn’t want to be left out of my dad’s bracket-making ritual. At the end of the tournament, the Florida Gators beat UCLA 73-57 to win their first-ever NCAA championship. So why did I pick Florida? Simple. Their mascot was just so cool.
By picking Florida to win, I actually had a decent chance of being correct: 1/64. This is pretty easy to see. If there were 64 teams competing and one winner, then I had a 1/64 chance of picking the correct team.
But what if I wanted to predict every game correctly? Well, let’s think of the 1/64 number another way. By choosing Florida to win, I was actually predicting the result of six different games. Florida would win in the First Round, Second Round, Sweet 16, Elite 8, Final Four, and the championship. In each game, there were two teams competing and therefore two possible winners. So through six games there were
2 x 2 x 2 x 2 x 2 x 2 = 64
possible combinations of winners. Again we see that 1/64 makes sense. Since March Madness has 63 games (excluding the First Four match-ups) with two possible winners in each game, there are
2 x 2 x 2 x … x 2 = (2)^63 = 9,223,372,036,854,775,808
possible combinations of winners. That’s over 9.2 quintillion! So if every team has a 50% chance of winning every game, your chance of a perfect bracket is 1/9,223,372,036,854,775,808.Of course, there is often more than a 50% chance that a team will win–that’s what seeds are for. If you know that a 16th seed has never beaten a 1 seed, then you might as well cross those games off of . . . Oh wait.
OK, I guess your odds are basically 1 in 9,223,372,036,854,775,808 after all. So I’m saying there’s a chance.