NCAA Final 4 Bracket: All About Probability

 

Mr. Warren Buffett offered $1 bllion to anybody who completes a correct 2014 NCAA men's  basketball braket. The odds of correctly identifying each and every winner in the tournament from the first to last game is:

 

 1 In 9,223,372,036,854,775,808.

 

Sounds like the odds are really stacked against a perfect bracket.

Why are the odds so great? First the facts. There are 63  games in the tournament. Each game plays until a winner is determined. So, each  game has two possible outcomes. Incorrectly choose just one team that is upset in an overtime loss or an injury takes out a star player and your favorite team loses and your  bracket is busted. 

 

Odds, by definition,  is an expression of probability. Probability, by definition, is the chance of something happening. The probability of rain for today was 70%, and it did, indeed, rain. 

Odds are expressed as a ratio, using a symbol that we often call a colon (  :  ). A colon these days is often used to create a smiley, because it represents the eyes of a face. 

 

We use the expression of odds this way:

 

 Chances for something to happen   :   Chances against something happening

 

Since there is only one possible correct bracket we know the odds of the NCAA bracket begins with a 1 : 

Now lets place the number of possible incorrect brackets, which is 9,223,372,036,854,775,808.

 

So the odds of an creating a perfect bracket is 1 : 9,223,372,036,854,775,808, which we read as:

 

one TO 9,223,372,036,854,775,808

 

There are methods of improving your odds. One possible method is being knowledgable about the teams playing. Most expected our hometown team, Wisconsin, to defeat American, based on the fact that Wisconsin is a nationally ranked team and American is not. In addition, the rankings in the tournament had Wisconsin considered to be a top contender and American as a much lower ranked competitor. So, most would bet on the favorite in this case and would have been correct.

 

We will be using this key point, which is: Knowledge can help improve the odds; guessing is stacked against you, later in an important lesson about test taking skills.

 

Our class determined the odds of completing a perfect bracket of the remaining Sweet 16 teams. Instead of predicting 63 games they only had to predict the winner of the last 15 games. 

 

First the odds. The odds of correctly choosing the correct winner in all 15 games can be expressed mathematically using the number 2 (possible outcomes of each game) and using an exponent set to the actual number of games to be played. 2^15, or 2 . So the odds of a perfect bracket of just the final 15 games is 1 : 

Thanks to Mr. G. for his  mathematical expertise to confirm this number.

Here's my prediction to the final four, created using a table and lots of style tags: