Football Squares

You bought a $100 Football Square at the local bar, along with 99 other people.

You know what the payouts are for the 1st Quarter, 3rd Quarter, Half and Final scores:

$1250 (1st), $1250 (3rd), $2500 (half), $5000 (final)

You saw the numbers randomly picked…

You drew 6 and 3. Good, right? How good? What if you had drawn 5 and 3 instead? Still good? Or is it bad? How bad? Would you trade your numbers for another pair? The answers to these and all your other Football Square questions tackled below!

To estimate the value of a Football Square, you need to know how often a pair of score combinations occur. This is done by counting the frequency of times a quarter, half or game ends with a particular score. Next, multiply the percentage of times a pair of score combinations occur at the end of each time period (1st quarter, half time, 3rd quarter and game end) by the payout for each time period. Finally, add those four products together and you will know the expected value of your particular pair of numbers.

The grid labeled ‘Value of $100 Football Square’, shows the resulting values for all number combinations, with the payout format used in the introducing example. The grids Q1, Q2, Q3 and Final show the percentage of times each pair of numbers was observed at the end of each time period.

Your numbers 6 and 3, therefore have an expected value of about $181. Pretty good considering you paid $100 for them. 5 and 3 are not as good, with an expected value of about $33 (actually pretty bad given what you paid). You can use the grids for Q1, Q2, Q3 and Final to estimate the value of any pair of numbers for any known payout.

example calculation for 6,3:

value_6,3 = (6,3_Q1% * Q1_$) +

(6,3_Q2% * Q2_$) +

(6,3_Q3% * Q3_$) +

(6,3_Final% * Final_$)

value_6,3 = (0.91/100 * $1250) +

(2.27/100 * $2500) +

(1.74/100 * $1250) +

(1.81/100 * $5000)

value_6,3 = $181.33

The score combination frequency was estimated using the scores from all regular season and playoff games in the NFL from 2009-2019. Data obtained from nflscrapR package and anaylized in R.