By Ben Blatt and Bobby Samuels

Every year, when March Madness comes around, numerous sites offer huge jackpots to anyone who can perform the most hallowed feat in sports betting: filling out a perfect bracket. The prizes can be staggeringly large: ESPN is offering $1 million this year, and a few years ago Papa John’s promised to give away one million pepperoni pizzas. Oftentimes with large promotions, companies will instead pay a fixed fee to an insurance company who will be responsible for the actual payoff. Although most companies don’t disclose if they did insure their grand prize, the question arises: How much money would Yahoo!, for instance, have to pay to insure its $1,000,000 prize?

First, we need to find the odds of filling out a perfect bracket. This has already been studied at some length, so we’ll be as brief as possible here. If completed randomly, the odds of picking a perfect bracket are (1/2)63, or a mere 0.00000000000000001% chance. However, even someone filling out their office pool bracket after not watching a single game all season isn’t doing so completely randomly. In order to create a baseline of how probable a reasonably filled out bracket is of being perfect, we filled out a bracket utilizing Ken Pomeroy’s rankings and computed the odds of perfection using his Pythagorean win expectation. The result: 1.2 x 10-11, or a 0.0000000012% chance.

Using this number, we can simply find the probability that at least one person in a large pool would fill out the bracket perfectly and then estimate the insurance on the prize. Of course, we don’t know the markup that an insurance companies would use, so we’ll just assume that they’re breaking even: that is, the amount paid to the insurance companies is equal to the expected cost of assuming the risk of the payout. Assuming the companies choose to use insurance (we don’t know if they did or not), below is what some of the competitions would have looked like:

Original Competition: Yahoo! Sports $1,000,000 Tourney Pick’em Number of Entrants: Approximately five million Likelihood of at least one perfect bracket: 0.006085%

New Description: The verified entrant who, on a single Game Bracket, correctly predicts the outcome of all 63 games in the 2011 tournament, will receive one million dollars ($1,000,000) from the insurance company, payable in 40 equal annual installments of $25,000, without interest. Whether or not there is a winner, the insurance company will receive $60.85, payable in 40 equal annual installments of $1.52 each, without interest.

Original Competition: Hooters FOXSports.com Number of Entrants: Limited to 1.5 million Likelihood of at least one perfect bracket: 0.001826%

New Description: Enter the Hooters FOXSports.com Bracket Challenge for a chance to win $1,000,000 from the insurance company that FOXSports and/or Hooters has paid $18.26. The top scorer not to enter a perfect bracket can choose between a year’s supply of Hooters’ Wings, valued at $1,300, or the insurance costs for a $70,000,000 perfect bracket challenge, also valued at $1300.

Original Competition: The KABZ-FM 103.7 $10,000 Buzz Bracket Challenge Number of entrants: Limited to 10,000 Likelihood of at least one perfect bracket: 0.00001%

New Description: The $10,000 Buzz Bracket Challenge will award a grand prize of $10,000 to an entrant who completes a perfect bracket. The competition is only to the first 10,000 entrants, so sign up quickly if you want to win the money that we paid 0.1 cents to insure. Don’t forget to fill out the total points in the finals as your tiebreaker just in case multiple entrants (only legal residents of Arkansas aged 21 or older) fill out a perfect bracket.

Ben Blatt can be contacted at bbblatt@gmail.com.

Original Competition: Yahoo! Sports $1,000,000 Tourney Pick’emNumber of Entrants: Approximately five millionLikelihood of a perfect bracket: 0.006085% Cost of Insurance: $60.85 New Description: The verified entrant who, on a single Game Bracket, correctly predicts the outcome of all 63 games in the 2011 tournament, will receive one million dollars ($1,000,000) from the insurance company, payable in 40 equal annual installments of $25,000, without interest. Whether or not there is a winner, the insurance company will receive $60.85, payable in 40 equal annual installments of $1.52 each, without interest. Original Competition: Hooters FOXSports.com Number of Entrants: Limited to 1.5 million Likelihood of a perfect bracket: 0.001826% Cost of Insurance: $18.26 New Description: Enter the Hooters FOXSports.com Bracket Challenge for a chance to win $1,000,000 from the insurance company that FOXSports has paid $18.26. The top scorer not to enter a perfect bracket can choose between a year’s supply of Hooters’ Wings, valued at $1,300, or the insurance costs for a $70,000,000 perfect bracket challenge (when entrants are limited to 1.5 million). Original Competition: The KABZ-FM 103.7 $10,000 Buzz Bracket Challenge Likelihood of a perfect bracket: 0.0001% Cost of Insurance: .1¢ New Description: The $10,000 Buzz Bracket Challenge will award a grand prize of $10,000 to an entrant who completes a perfect bracket. The competition is only to the first 10,000 entrants, so sign up quickly if you want to win the money that we paid 0.1 cents to insure. Don’t forget to fill out the total points in the finals as your tiebreaker just in case multiple entrants fill out a perfect bracket. The contest is open to legal residents of age 21 or older from Arkansas.