It’s that time of year again, when the the super bowl “football squares” sheet begins to be passed around the office. While I don’t think participating is a good financial decision, it is interesting to know optimal strategy.

In case you are not familiar with the typical office football pool, here is a brief introduction from southofboston.com:

Betting “squares” are probably the most common form of Super Bowl pool. It requires no knowledge of the game, just some luck.

To set up the pool, the organizer draws up a 10-by-10 grid. The grid’s length is designated for one team and the width for the other. For a price, bettors choose or are assigned “squares” within the grid.

After the squares are filled, a number between zero and 9 is assigned to each row and column, giving each square holder a number for each team. If the number in the bettor’s square match the last digit in the score at the end of each quarter, that bettor wins.

For example, a bettor could draw the 7-3 square, 7 for the Patriots and 3 for the Eagles. If, at the end of the first quarter, the Patriots were ahead 17-3 the 7-3 square would be a winner. Smaller prizes are usually awarded to the winners of each quarter and a grand prize goes to the person whose square reflects the game’s final score.

With 100 squares available, prize totals are 100 times the cost of each square. So charging $50 a square will yield a $5,000 pot.

At any rate, which squares give you the best chance of winning?

Doug Drinen, performed an analysis on Sabernomics.com in a post titled “Squares for squares“. He looked at all regular season NFL games from 1994 (when the two point conversion rule was implemented) through 2005. According to his analysis, these are the best squares to have:

- 7-0/0-7 Ending score 3.80% of the time.
- 7-4/4-7 Ending score 3.71% of the time.
- 0-3/3-0 Ending score 3.21% of the time.
- 4-1/1-4 Ending score 2.23% of the time.
- 0-4/4-0 Ending score 2.04% of the time.

A little explanation is required. In the games analyzed, one team had a score ending in 7, while the other team had a score ending in 0, 7.60% of the time. Because there are two 7-0 squares on the board, the 7.60% is divided in half, hence the 3.80% probability of winning.

By the way, the worst possible square is 2-2, this was the ending score only .04% of the games analyzed.

Please checkout Doug’s full article, to see the probabilities of all squares.

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