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Mar 5, 2012

What to expect in your next football grid pool

With the books closed on Super Bowl LI (51), and all of the parties over, I began thinking about the football grid pool. These pools are common in offices and at parties, and many people enjoy participating and eagerly await the random number assignments. In case you are not familiar with the pool, let me describe how it works. A 10x10 grid is drawn, and individuals can select or purchase (wink, wink) one or more of the squares. An example empty grid is seen in Graph 1, 10x10 Grid to Start.

Graph 1, 10x10 Grid to Start

When all 100 squares are claimed, the numbers 0 to 9 are randomly assigned to the rows and to the columns. The horizontal rows may be assigned to the AFC team, and the vertical columns assigned to the NFC team. Each cell will then represent a pair of numbers. If the square’s digits match the last digit of each team’s score at the end of a quarter or at the end of the game, then the owner of that square will be a winner.

Having participated (and lost) in many of these pools, I wondered what score combinations are better than others. I can make educated guesses knowing how points are scored in football, but I wanted to be more analytical. So, finding the scores from all of the past championship games, I created a distribution of last score digits by quarter for each NFL conference (see Graph 2, Individual Conferences).

Graph 2, Individual Conferences

### What are the more likely combinations?

As most people would expect, scores ending with 1, 2, and 5 seem the most unlikely, especially early in the game. Scores ending in 0, 7, and 3 are much better squares to hold since field goals are worth 3 points, and touchdowns with the extra point are worth 7 points.

Looking at the 10x10 grid of the scores, we see combinations that have occurred. See Graph 3, Scores by Quarter to see a breakdown for all quarters. The combination of (0, 0) at the end of the first quarter is common, occurring in 14 out of 51 games. Remember, this could be a 0-0, or 10-0, 10-10 score, any score having the last digit be 0. The score ending in (2, 2) has never been witnessed at the end of any quarter or any game.

Graph 3, Scores by Quarter