Football square office pools

King Yao is the author of Weighing the Odds in Hold‘em Poker, and Weighing the Odds in Sports Betting. He uses his experience in financial derivative markets and translates it into gambling. Since he left his trading position, he has been playing poker and betting on sports. He travels to Las Vegas frequently, especially during football season.

Office pools, or football squares as they are sometimes called, are popular during NFL playoffs, especially the Super Bowl. For most people, buying a square is all luck and no skill. However, it is possible to buy, sell and trade squares with positive Expected Value.

A 10” by 10” empty grid is passed around to the potential buyers of squares. Neither the columns nor the rows are numbered until all the squares are filled in. Buyers print their names in the empty squares, with each buyer paying the same price per square. Once all the squares are sold, a random process is used to select numbers for the columns and rows. The columns represent the last digit of one team’s score, and the rows represent the last digit of the other team’s score. Only the last digit, the right-most digit, of each team’s score matters. For example if the final score is 34 to 10, then for the purposes of the squares, the score is 4 to 0.

When the numbers are filled in, all square owners are given a copy of the sheet so they know which numbers they have.

The payout rules should be preset before the grid is filled out.

The rules can vary; some variations are:

• The final score of the game determines one winner and one winner only.
• The score at the end of each quarter determines four different winners with each winning the same amount. If the game goes into overtime, the final score takes place of the score at the end of the fourth quarter.
• The score at the end of each quarter determines four different winners, but the four winners pay off at different rates which are spelled out explicitly.

Good, Bad and Average Numbers

Once the columns and rows are filled in by a random process, square owners know what they are rooting for. Since football scores are predominantly field goals and touchdowns (with made extra points), the numbers that are produced by combinations of 3 and 7 are the most likely numbers to hit. In general, here are the good numbers, average numbers and bad numbers:

• Good numbers: 0, 3, 6 and 7
• Average numbers: 1 and 4
• Bad numbers: 2, 5, 8, and 9

In general, any combination that includes a bad number means the square is a dud; any combination with two good numbers is great; and any combination with one good number and one average number is okay.

Valuation of Each Square

Using a database of over 4,000 NFL regular-season and playoff games from with final scores at the end of each quarter, I was able to calculate the percentage that each square has hit. These data are not applicable for college football games, which have their own dynamic. I looked at the end of each of the first three quarters and the end of the game. If there was an overtime period, I used the final score of the game, not the score at the end of the fourth quarter, as most squares pay out this way.

The Super Bowl is played on a field selected years in advance. Unless the local team happens to qualify, the field is neutral; there is no home team. Squares are most popular for the Super Bowl, but the data are mostly from regular season games. To adjust the regular season games to fit the Super Bowl, I averaged the percentages with the same set of numbers into the same square.

For example, instead of listing the individual percentage for both 0,7 and 7,0, I averaged them and put the average in the 7,0 square. The assumption is that owners of the 0,7 and 7,0 squares have equal chances. This may not be the case for an expected blowout; more on that in a future article.

This is part of an occasional series of articles.

Excerpted with permission from the e-book version of Weighing the Odds in Sports Betting by King Yao, edited for this format.