A Square’s Guide to Super Bowl Squares

Football and betting go hand in hand, and the big game is no exception to this. Among the more casual forms of football betting is Super Bowl Squares. Even if you’ve never played it, odds are (HA) that you’ve seen someone around the office passing around one of these sheets. Here’s an introduction for the uninitiated.

Each year playing this (and fretting over receiving a 5/8 or 2/2 square), I wondered – what are the odds for each square? We know 3s and 7s are good to have, but how good?

Luckily, through the powers of computers and the world wide web, we can easily run the numbers for this.

I looked up the results for every game from 2000 all the way through 2016. This included grabbing the score at the end of each individual quarter, since the payout occurs quarterly. I threw out any overtime games since that threw off the results, and was left with a sample size of 3,962 games. That’s more than enough to be fairly confident with my results.

From there, I split the results by quarter, and counted how often a square got “hit” each quarter. Dividing how often a square hit by the total number of games, and we get the percentage of time each square hits.

Here are the best squares for Quarter 1. 96% of the time, it will be among the squares listed below.

q1-best

A couple of quick notes. Here, I combined 0-7 and 7-0. So while almost a quarter of the time, an 0 and 7 block will hit, the odds for the individual squares are half of that. That makes 0,0 the champion and best square to have for the first quarter. Another note – you’ll notice that there are only 19 squares accounted for above. Early in the game, there are only so many offensive possessions that will have occurred. So the total number of outcomes is much smaller. As the game progresses, the variety of squares getting hit will grow.

Now that we have laid that groundwork – here are the best squares for Q2, Q3, and Q4, highest odds first.rkjfaht

All of these results make sense, intuitively. 0, 3, and 7 represent the cream of the crop. “Okay”, you might be saying to yourself. “But what are the best squares overall? And how much MONEY can I expect to get?” I can answer the first question for you. The second is a little bit more complicated, because every pool pays out slightly differently. Just for example’s sake, let’s assume that there’s a $5 buy in, and every quarter pays out $125. Then your expected payout would be the odds you win Q1 * $125 + Odds for Q2 * $125 + Odds for Q3 * $125 + Odds for Q4* $125. That will give you your square’s expected value. Doing this for each square, I came up with the below chart. These are all of the squares, sorted by best expected value to worst expected value.

689ro6k

0,0 and 0,7 holders, rejoice! 2,2 and 5,5…always remember that a non-zero chance is infinitely better than 0. That’s just math.

So what can you do with all of this knowledge? You could gloat. You could groan. Or you can be a real winner, and inundate your friends with so much information their eyes gloss over and you are left with a smug sense of intellectual superiority, regardless of the square you happened to be dealt.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s