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Probability & Statistics:

Spectacular Statistics of Shooting Hoops

Today's Snack: Try putting a pineapple ring on top of a glass in a large, deep bowl. Now "shoot" grapes through the hole. Eat your "basketballs" whether they land in the glass or the larger bowl that it sits in. Eat your "hoop," too! Wash them down with a nice glass of sassy pineapple juice.




Scratch paper | pencil | basketball | hoop!



So you think you know basketball? And you're pretty good at math?


Then you should enjoy this exercise based on information from Dr. Andrew Swift. He's a math professor at the University of Nebraska at Omaha.


An expert in probability and statistics, he took a look at how hard or easy it might be for someone to be able to perfectly predict the winners of the basketball teams who are in the NCAA tournament.


There are 64 teams in the tournament. They play down to a Final Four, and ultimately, a winner. But it's really not THAT many teams playing THAT many games. So what do you think the chances are that you could pick the winner in all of the games in the entire tournament? Maybe one in 1,000?




The answer: you have a one in 9 quintillion chance of getting it right!


That's 1 in 9,000,000,000,000,000,000!


You know how the series goes:












Swift says those are much higher odds than winning a lottery.


It's actually higher than 9 quintillion; he rounded it off. And at those high numbers, who's counting?


It kind of puts our nation's economic woes in perspective. It's kind of nice to be able to view the number "one trillion" as relatively SMALL!


Now, gambling is very, very bad and a big waste of your money. But it should be noted that there are gambling organizations which offer a lot of money - over $11 million in one case - to anyone who can correctly choose the winner of all 63 games.


How did we come up with 63 games when there are 64 teams? Easy!



+ 16

+ 8

+ 4

+ 2

+ 1



You take the first 32 games that the 64 teams play in, add the 16 games in the next round, the 8 games that match teams in the "Sweet Sixteen" round, the four games that pare down the eight teams that make the quarter-finals, the two semi-final games, and finally the championship game. 


That's 63 games that have to be chosen correctly. Quite a feat!


If you flipped a coin to pick the winner of every game, your odds would basically be 1 in 2 that you would pick the first winner correctly. You'd have about a 50% chance of getting that game right. 


But the odds of picking two games in a row correctly aren't 1 in 2. Those odds are 1 in 4 - a 25% chance of getting both games right. You have to double the odds every time you start making a string. 


So if you line up all 63 games, the odds of getting them all right is 2 to the 63rd power - shown as


That means 2 x 2 x 2 x 2 x 2 x 2 x 2 . . . 63 times. And that works out to more than 9 quintillion.


Now take your pencil and piece of paper, and start multiplying 2 times itself. Do that 63 times, and you should come up with the 9 quintillion figure.


To get you started:


1st time = 2 x 2 = 4


2nd time = 2 x 4 = 8


3rd time = 2 x 8 = 16


. . . and keep coming 'til you come to the 63rd time.


Now let's say that you had more information than just the pure luck of flipping a coin. Let's say you really studied the teams' records, their coaches' records, and any number of other pieces of data about basketball that you believe can help you pick a winner. Even though gambling is wrong, let's say you took a look at how those who set the odds on sporting events are viewing these games. 


Even if you pick all the teams that are statistically favored to win, you still only have a 1 in 19,323 chance of getting them all right. That's because so many teams so often beat the odds.

Whoa! It's a tougher task than you thought, huh?


Well, now that you've exercised your mental muscles, why don't you pick up a basketball and go shoot some hoops to exercise your physical ones as well? The odds are MUCH better than one in 9 quintillion that you'll have fun!


By Susan Darst Williams Math 2010


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