Football Squares - Introduction

This is a series of posts on the statistics, mathematics of Football Squares, also called Super Bowl Squares, with an emphasis on a strategy that can be used when playing this game. In these posts, we will talk about the probability or odds for different outcomes depending on this strategy. There is quite a bit to read as these posts were developed as the analysis progressed - the final post will be a short and sweet summary. You might want to jump to it now (short final summary).

Football Squares is a game that features a 10 x 10 grid of squares. Into each square, players enter their name. In principle, 100 different players could each find a vacant square. In practice, people are often able to enter multiple squares - typically between one and some modest number like five squares. After the grid is completed, Football Squares is then associated with a football game - most often the Super Bowl - where squares become winning squares depending on the score throughout the game. There are many variations and I describe one variation as to how the game is played.

Each row (arbitrarily assigned to the Home team) and each column (Visiting team) of the grid is associated with a unique number from 0-9 so that each square has a unique row and column with a corresponding number. The numbers 0-9 for the rows and columns are chosen at random after the squares have been filled in. There is a single winning square after the first three quarters of the football game (Q1, Q2, Q3) and then a final winning square at the conclusion of the game utilizing the final score (FS). The FS is used instead of Q4 in case the game goes into overtime. The numbers 0-9 represent the last digit of the score after the Q1, Q2, Q3, and FS. If the score after Q1 is Home: 7 Visitors: 0, then the winning square has the row assigned the number 7 and the column assigned the number 0. If the final score is Home:31 Visitors 24, then the winning square has the row assigned the number 1 and the column assigned the number 4. It is possible for a single square to be the winning square for more than one quarter including the final score. A low scoring game with only a single Visitor field goal in overtime would result in the square corresponding to row with number 0 and column with number 0 winning three times for Q1, Q2, Q3 and then row with 0 and column with 3 taking the final score winning square.

The game is meant to be fun and based on nothing more than pure luck. Because the numbers associated with the rows and columns are random, it is thought that there is no strategy and that any choice of picks of squares result in identical expectation values for winning. Part of the fun is joking that you'll pick a winning square by picking your square next to your buddy's. Or, it's fun to think that you have a strategy (stay away from corner squares on the grid) that makes a difference.

The game being based upon pure luck - this is mostly true ... but as I will show, there are non-random factors and your choices in picking squares can affect your winnings. This is demonstrated from running over a billion simulations that utilize 5220 actual pro football game box scores (quarter by quarter scores) from 1994-2013.

This blog is for entertainment purposes only. My interest is in this subject is academic. If the study has interest for someone to write a publication, feel free to contact.