By Nick Jaroszewicz, Anthony Zonfrelli, and Harry Chiel
Editor’s Note: This article was featured in Sports Illustrated ahead of Super Bowl 54. You can watch Anthony Zonfrelli break down the math behind Super Bowl Squares here.
It’s no secret that Super Bowl Sunday is a day full of betting. Super Bowl prop bets are notorious indulgences during America’s most watched game, and one of the most popular games during Super Bowl parties is Squares. For those unfamiliar, Squares is a betting competition in which people try to predict the last digit of the scores for both teams at the end of each quarter. Each player puts in a certain amount of money (e.g. $10 per square) to make up a pool, and the game begins. Below is an example of an empty Squares grid from last year’s Super Bowl:
The game starts with a 10 x 10 grid, with the ten rows and ten columns labeled with the numbers 0 through 9. One team is designated as the “rows” and one team as the “columns.” The bettors take turns putting their initials in each square until all the squares are filled. After each quarter, the last digit of each team’s score is taken and the player with the corresponding square in the grid wins for the quarter. For instance, if the score was 17-14 in favor of the “rows” team after the first quarter, the player that picked the square “Row 7, Column 4” would get a certain amount of the money. Traditionally, the predictor of the first quarter gets 20% of the money, the predictor of the halftime score gets 30%, the predictor of the third quarter gets 20%, and the person that predicts the final score gets the last 30%.
So, using these weights, what is the optimal strategy, and which numbers should you stay away from?
For our game, the favored team has been placed on the columns and the underdog on the rows. Using NFL playoff data from 1980 to 2012, we compiled the frequencies of the scores at the end of each quarter. We weighted each frequency according to the quarter-by-quarter payouts (20%, 30%, 20%, 30%), divided by the number of games, and scaled the result for a $1000 pool. The numbers in each box correspond to the expected payout for each square, given a $1000 pool where the buy-in for each square is $10. The results are below:
As the graphic shows, predicting favorite-digit-7 and underdog-digit-0 has been the optimal strategy, with an average payout of $82.74. Assuming each square costs the same amount ($10 in our case), there are only 24 squares that have yielded a profit on average. In fact, there are five squares whose scores have never materialized in any quarter of any game in our sample.
So as you prepare for Super Bowl Sunday, make sure that you bring our chart with you to your party, along with your chips and salsa. After all, losing’s for squares.