## Wednesday, January 30, 2013

### Super Bowl Squares - Every Score Pays Out

2/3/2013 Update: A more mobile friendly version of the chart: Squares Payouts.

My most recent two posts covered the concept of in-game Super Bowl squares probabilities, based on score, time, field position, and down.  I still hope to complete that project in time for the Super Bowl this Sunday, but there are only a few days left, and I saved the hard part (the 4th quarter score) for last.

As I indicated in my in-game squares post, there are plenty of sites out there which will give you the expected payout for each square, and many will give you the payouts for each quarter as well.  However, I haven't seen any site that calculates the probabilities for a somewhat less popular version of the squares pool: The "Every Score Pays" pool.

### Every Score Pays (Even Extra Points)

Under the "Every Score Pays" option, instead of waiting for the end of each quarter, the pool pays out every time the score changes, even extra points and two point conversions.  I am not sure if there is a standard payout per score, but for the numbers below I am assuming that 5% of the pool is paid out with each score change.  Whoever holds the square matching the final score receives any remaining balance in the pool.  If there are more than 20 score changes, the pool stops paying out.

In order to calculate expected payouts, you need play by play data (for the standard squares pool, you have all the data you need in the standard box scores).  I used the play by play data provided by Advanced NFL Stats for the 2002-2011 seasons, calculated payouts for each game, and then averaged the results.

The table below shows the expected value (per dollar bet) for each square.  I also added the more common Q1, Q2, Q3, and Final Score expected values for comparison.

Under "Every Score Pays", the 3, 6, and 9 squares are more valuable compared to the standard squares pool, which makes sense given that touchdowns are worth six points, and the pool pays out before the (virtually certain) extra point is kicked.

Click on the chart below to zoom.  Also, here is a pdf version: Super Bowl Squares Payouts