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Business, Numbers, STEM

NUMBERS: The Odds of March

After a very cold winter that impacted most of the U.S. population, the best news that I thought anyone could hear this March is that spring has sprung. Yes, spring – the vernal equinox – sprung on March 20, 2014. That said, it is finally starting to warm up across the U.S although it is still cold in a number of places.

MegaMillions_LogoMore good news surfaced last week as media outlets reported that two winning tickets were sold for Tuesday’s (March 18, 2014) Mega Millions drawing. Winning tickets sold in Florida and Maryland produced two winners for the $400 million jackpot that will be split two ways. As the buying frenzy built over the weeks and the jackpot grew, members of the public were reminded that the odds or chances of winning the grand prize jackpot are 1 in 258,890,850. Oh by the way (BTW), the folks at Mega Millions also list this daunting statistic on their website [Ref 1].

How are these odds calculated? By using math and information related to the rules of play. First, you have to play to win.

Second, follow the contest rules to play the game. Here are a few brief instructions:

a)    Select five numbers from a pool of white lottery balls numbered from 1 to 75. (select five “5” individual numbers)

b)    Select one number from the Mega Ball pool of numbers 1 to 15. (select one “1” number), or

c)    Choose the “Select Pick” option and the computer will choose the six numbers above for you.

Pay for your ticket(s) prior to the cut-off time for each drawing. As shown in last week’s drawing, there were two winning tickets. You win the jackpot by matching all six winning numbers in a drawing. You can also win smaller prizes even if you don’t match all six numbers.

Similar to PowerBall, the Mega Millions Lottery is likened to two lottery drawings because you have two pools that are being drawn from to produce the set of winning numbers. Here are some more details about your odds of winning:

White Balls: You get to choose 5 white balls out of 75. The numbers do not repeat. Therefore the chances of picking Balls 1 thru 5 are:

Ball 1 = 5 of out 75 or 5/75

Ball 2 = 4 out of 74 or 4/74

Ball 3 = 3 out of 73 or 3/73

Ball 4 = 2 out of 72 or 2/72

Ball 5 = 1 out of 71 or 1/71

Mega Ball: Similar to the white balls you get to choose 1 out of 15 balls or numbers. Therefore, the odds for choosing the Mega Ball are:

Mega Ball = 1/15

To calculate the odds of having a winning ticket with six correct numbers is to multiply the odds for each number, or:

Jackpot Odds = 5 4_  x 3_ x _2 x _1_ x _1_

                       75    74    73      72     71     15

Jackpot Odds = 0.000000003862631684 = 3.862631684 E-9

Divide the above number by 1 or 1/3.862631684 E-9 to get your 1 in 258,890,850 chances of winning. Notice that the numbers do not need to appear in any particular order. This now leads to our second conversation about the odds of winning.

March Madness

Although I don’t follow college basketball or football either, I have been walking around long enough to know that the National Collegiate Athletic Association (NCAA) playoffs for basketball usually start around the Ides of March (mid-March). Sports commentators and everyone else begin talking about brackets, and not the type that you use to support shelving or mechanical parts.

Interestingly, in most of my previous work assignments – permanent, temporary or contract – it was difficult to enter or leave the work site without someone asking me if I wanted to get into their bracket pool? or if I had already filled one out?

Brackets are being discussed because we are in the middle of March Madness – the NCAA playoffs. However, this year, a new name is being associated with the games: Warren Buffet. Yes, Warren Buffet! Mr. Buffet teamed up with Quicken Loans and issued a Brackets Challenge: Correctly pick the winner of all of the men’s tournament games in the Quicken Loans Billion Dollar Bracket Challenge and win a billion dollars.

Like the Mega Millions Lottery, there are rules for the Bracket Challenge [Ref 2], however, here are the basics:

  1. Go to Yahoo.com. Registration for the competition began on March 3rd, and the participating teams were announced on March 15th   
  2. Create an account and be one of the first 15 million contestants to enter. The deadline to enter was March 20, 2014. 
  3. Sit back and wait for the tournament results.

OBTW, good luck! Special Note: the deadline has passed to enter this contest.

 PresObama_2014Brackets

President Barack Obama fills out his 2014 NCAA Division I Men’s Basketball Tournament bracket during an ESPN interview with Andy Katz in the Map Room of the White House, March 18, 2014. (Official White House Photo by Pete Souza)

As you can see, a lot of folks filled out their brackets this year including President Obama in the photo above. According to Whitehouse.gov, this is the sixth year that the president has completed a bracket for the NCAA tournament.

Here’s the catch for this contest – the odds of winning are very daunting. The mathematical odds given by the contest officials of winning the grand prize, $1 billion, are 1 in 9,223,372,036,854,775,808 or, in other words, 9.2 quintillion to 1. Who knew playing Mega Millions or PowerBall had better odds. As someone said, you stand a better chance of winning Mega Millions twice than filling out a perfect bracket.

Professor Jeffrey Bergen, a math professor at DePaul University, created a video on You Tube to explain his calculations. [Ref 3] Initially, you are given 64 teams and their 63 games that will be played in the tournament. Every game has two teams, and one winner. Therefore the bracket owner has to project 63 winners.

As Professor Bergen explains it, “You have two options for the first game, two options for the second game, two options for the third game, and so on, for all 63 games. To get the total number of possible ways to fill out a bracket, you multiply together all 63 of these twos, giving us 263, or about 9.2 quintillion, possible brackets”. This also assumes that each team has a 50-50 chance of winning each game.

This is a possibility as well as an estimate of the odds against filling out a perfect bracket. If you have more knowledge of the contest, the teams, and the athletes, you definitely can improve on the above odds. The odds will vary depending on the knowledge and skills of the entrant. In addition to all of the above, the odds of being the First Prize winning is largely dependent on the outcome of each of the tournament’s games, as well as the number of eligible entries received. Filling out a perfect bracket is extremely dicey, to say the least.

Dr. Bergen also notes that the odds can improve to “one in 128 billion if you know something about college basketball.” [Ref 3] Buffett has admitted to liking the NCAA playoffs and contest like this one. Most folks who follow basketball also know that Warren Buffett is nobody’s fool. He and his advisers at Quicken Loans are strongly aware that no one has picked a perfect bracket in over 30 million entries since ESPN started their competition back in 1998.

Here’s the update: At the end of Friday, March 21, 2014, Day 2 of the playoffs, and 25 games played, there were no contenders for Quicken Loans Challenge grand prize. Results from ESPN’s Tournament Challenge after Day 1 looked similar. Only 18,741 of 11.01 million people (or 0.17 percent) got all 16 games right on the tournament’s first day, ESPN’s Kevin Ota told ABC News [Ref 4].

While there are no bracket winners for either the Quicken Loans or ESPN’s grand prize, a clear winner in this contest is math! There was and still is an awful lot of math being discussed across America in break rooms, living rooms, on public transportation, etc. The odds are being tweeted left and right and numbers are being added, subtracted, divided or multiplied at dizzying levels.

The competition itself provides a wonderful opportunity for each of us to better understand how math can be used in every day life and sports, something that most Americans love in one form or another. Most children and youth that I have worked with would definitely get more excited discussing math using real life scenarios and events like the NCAA collegiate basketball tournament than the format that is presented in most math books today. Perhaps that is one reason Mr. Buffett threw his hat into the ring. Besides, he does like college basketball, and he still gets to laugh all the way to the bank this Monday morning.

Saturday’s upset was the defeat of Syracuse University by the University of Dayton. On Sunday, yesterday, eighth-seeded Kentucky upset undefeated Wichita State 78-76. Get ready for the Sweet 16 games to come.

Oh the odds of March!

References:

  1. How to Play, Mega Millions Website, http://www.megamillions.com/how-to-play
  2. Why you won’t win a billion dollars with Warren Buffett’s bracket challenge, by Cindy Boren, March 17, 2014, http://www.washingtonpost.com/blogs/early-lead/wp/2014/03/16/why-you-wont-win-a-billion-dollars-with-warren-buffetts-bracket-challenge/
  3. The Odds Of Filling Out A Perfect NCAA Bracket Are Actually Way Better Than 1 In 9,223,372,036,854,775,808,  Andy Kiersz, Business Insider, March 17, 2014, http://www.businessinsider.com/odds-of-perfect-ncaa-tournament-bracket-2014-3#ixzz2wqtLUBN2
  4. Early Wipeout: Warren Buffett’s $1B NCAA Bracket Contest Has No Winner, Liz Fields via Good Morning America, March 21, 2014, http://abcnews.go.com/Sports/perfect-brackets-left-buffetts-billion-dollar-challenge/story?id=23003787
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About Vi Brown

Vi is principal and CEO of Prophecy Consulting Group, LLC, an Arizona firm that provides business and engineering services to private and public clients. Prior to establishing her consulting practice in 2001, Vi worked with Motorola, Maricopa County Government, Pacific Gas & Electric, CH2M Hill, and Procter & Gamble. As an adjunct faculty member, Vi teaches undergraduate calculus classes and graduate level environmental courses. She is also a professional speaker.

Discussion

One thought on “NUMBERS: The Odds of March

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