## The statistics of Super Bowl squares

by Doc on Feb.02, 2013, under Geek Out

I’m taking part in a Super Bowl square for charity this year, and a number of people not familiar with these squares were taking part, so it got me thinking about what numbers and pairs are really good.

Being the geek that I am, of course I needed to figure it out. What follows is a bit dry – it is, after all, statistics. So if you want to cut to the chase, here is a quick summary of numbers that I believe from the results below are good and bad:

**Best numbers:** 0, 1, 3 and 7

**Worst numbers:** 2, 5 and 8

**Best pairs:** 0-0, 3-0, 7-0, 5-1 (yes, really), 7-1, 7-3, 7-4

Sure, there are already web pages with information on the subject, but 1) I didn’t write them, and 2) They didn’t always look at the numbers the way I wanted, and in at least one case didn’t seem to use the right scores. And I wanted to play more with Excel.

First, you may ask, “What is a Super Bowl Square?” The Square is a gambling device used in football (and really, any similar game with similar scoring and defined periods – the more “random” the scoring the better – basketball would be another good one) in which a 10×10 grid is laid out, the numbers 0-9 are written across the top and down the side, and people buy squares. The rows correspond to one particular team, and the columns the other team. If at the end of a quarter or the end of the game the last digit of each team’s score matches your square, you win the prize for that quarter. Typically the prize for the final score is worth more.

In most I’ve taken part of, it doesn’t matter a whole lot which squares you buy, as the row and column numbers are randomly assigned after the squares are purchased, although people have systems like not getting two in the same row/column, etc. This pretty much makes it a game of luck. In some cases, you choose the specific score, and so knowing what are the best numbers is important.

So, I entered in all the scores by quarter for all 46 previous Super Bowls, and went to work with the formulas and a little programming – and there are some interesting results. And it depends on how you look at them. Note: This ONLY takes into account Super Bowls…although if I can get more data that I don’t need to enter manually, I may later re-process and see how it changes. But regular season games can end in a tie, whereas playoff games can’t. That can change the probabilities against matched numbers (i.e. 7-7).

First off, what are the best numbers? Overall, the number zero happens the most, at 27.45% (101 out of 368) of the time. Kinda obvious, though – every team starts at zero, and if they don’t score in the first period, they are still zero. And a touchdown and a field goal? 10 points, which is a zero for the square. 43 out of the 101 zeros recorded happen in the first quarter. So getting 0-0 should get you a good shot at the first quarter prize at least.

The second and third are also pretty obvious – 7 (20.92%) and 3 (15.22%). After all, most scores are either touchdowns (6 points plus an almost-guaranteed point after kick) or field goals (3 points). Likewise, these are pretty common in the first quarter.

The worst numbers overall? Tied for first is 2 and 8 at a mere 2.45% each, followed closely by 5 at 2.72%. The combinations of touchdowns and field goals to result in those numbers just don’t come up much unless the scores get high.

Here is a graph of the distribution of overall scores:

But choosing numbers in a Super Bowl square isn’t always about which numbers come up most often. 0, 3 and 7 may be great in the first quarter, but what about later? Applying logic, the numbers should even out more towards the end of the game. But there are only four quarters (and perhaps a little overtime), and most scoring is done in multiples of threes and sevens, and far more rarely twos, sixes and eights. That’s why 2, 8 and 5 still don’t come up much. But there is a dramatic shift in numbers by the final score. And if the final score prize is larger (often twice that of the other three quarters), maybe you want to maximize your chances at the big prize?

Let’s compare the charts for the first quarter and the fourth quarter:

By the final score, the 7s are now the most common number (21.74%), with 0 and newcomer 1 tied for second at 13.04%. 1 was smack in the middle of the pack overall and non-existent in the first quarter, but it’s actually a good number when looking for the big prize! And 50% of all occurrences of 5 happen in the final score.

But still, does it matter much about how often a single number comes up? After all, it’s about pairs of numbers, not one. So let’s look at that instead.

Looking at numbers in pairs (and assuming it doesn’t matter which score the AFC or NFC team gets), the best pair to get overall is 7-0, which comes up 10.87% of the time. This is followed closely by 3-0 (9.24%) and a tie with 0-0 and 7-3 (7.07%). I’d list the worst overall, but there are many combinations that have simply never come up at all – 16 combinations out of 55. Here is a chart so you can see:

Occurrence of score pairs: Overall |
||||||||||
---|---|---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |

0 | 7.07 | |||||||||

1 | 2.17 | 0.00 | ||||||||

2 | 1.63 | 0.00 | 0.00 | |||||||

3 | 9.24 | 0.54 | 0.00 | 3.26 | ||||||

4 | 5.98 | 1.63 | 0.54 | 3.26 | 0.54 | |||||

5 | 2.17 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 | ||||

6 | 3.26 | 0.54 | 0.00 | 3.80 | 1.09 | 0.00 | 1.09 | |||

7 | 10.87 | 3.26 | 1.63 | 7.07 | 5.98 | 0.54 | 3.26 | 3.80 | ||

8 | 1.63 | 0.54 | 0.54 | 0.00 | 0.00 | 0.00 | 1.63 | 0.00 | 0.00 | |

9 | 3.80 | 0.54 | 0.54 | 0.00 | 1.09 | 0.54 | 0.54 | 1.63 | 0.54 | 0.00 |

But of course, different numbers come up in different quarters. In the first quarter, 0-0 and 3-0 are the most common at 21.74% each, followed by 7-0 at 17.39%. In fact, these are the only combinations that come up more than 10% of the time in the first quarter, with only 8 other combinations ever having come up:

Occurrence of score pairs: First Quarter |
||||||||||
---|---|---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |

0 | 21.74 | |||||||||

1 | 0.00 | 0.00 | ||||||||

2 | 0.00 | 0.00 | 0.00 | |||||||

3 | 21.74 | 0.00 | 0.00 | 8.70 | ||||||

4 | 8.70 | 0.00 | 0.00 | 0.00 | 0.00 | |||||

5 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | ||||

6 | 0.00 | 0.00 | 0.00 | 2.17 | 2.17 | 0.00 | 0.00 | |||

7 | 17.39 | 0.00 | 0.00 | 4.35 | 4.35 | 0.00 | 0.00 | 6.52 | ||

8 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |

9 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

As you can see again, having that zero is nice in the first quarter. And I find it interesting how often 4-0 comes up as well. But the first quarter accounts for 77% of all occurrences of 0-0, and 59% of 3-0. The value of that zero fades later in the game.

Here is the chart for the final score. You can see the “sweet spot” shifts from 0 to 7…

Occurrence of score pairs: Final Score |
||||||||||
---|---|---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |

0 | 0.00 | |||||||||

1 | 2.17 | 0.00 | ||||||||

2 | 2.17 | 0.00 | 0.00 | |||||||

3 | 2.17 | 0.00 | 0.00 | 0.00 | ||||||

4 | 0.00 | 4.35 | 2.17 | 4.35 | 0.00 | |||||

5 | 4.35 | 6.52 | 0.00 | 0.00 | 0.00 | 0.00 | ||||

6 | 4.35 | 2.17 | 0.00 | 4.35 | 0.00 | 0.00 | 2.17 | |||

7 | 6.52 | 6.52 | 2.17 | 4.35 | 10.87 | 0.00 | 2.17 | 4.35 | ||

8 | 0.00 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 | 2.17 | 0.00 | 0.00 | |

9 | 4.35 | 2.17 | 2.17 | 0.00 | 2.17 | 0.00 | 2.17 | 2.17 | 2.17 | 0.00 |

But also look – in a three-way tie with 7-0 and 7-1 emerges something completely unexpected – 5-1! So that 5-1 you drew that you thought was horrible, turns out isn’t so bad in the end game.

So there it is…hope this provided some insight into the numbers you drew…but if you are seeing red spots on your numbers, don’t fret…it just means that score hasn’t happened in a Super Bowl…yet.

**Post-Super Bowl update:** So, how did the numbers fare against the analysis?

The first quarter was 7-3 – two of the three most common numbers, although not a common combination, surprisingly, at only 4.35% (only happened twice before in the 4th quarter.)

After the 2nd quarter, the numbers were 6-1. That’s actually a first – it has never come up before in the 2nd quarter and only once in any quarter.

After the 3rd, it was 8-3. This was perhaps the most surprising – it has never come up before. But perhaps not so surprising given the 2nd quarter score – once you get an improbable combination, the odds of other improbable combinations in later scores increases. Maybe the blackout at the Superdome had more far reaching circumstances. ðŸ™‚

Finally, with the final result, 4-1, we return to normality, with the combination coming up 4.35% of the time, which wasn’t great in the first quarter, but is the 3rd highest probability for the final score.

So, what can we conclude? That just because statistics say your numbers aren’t great, it doesn’t mean you can’t still win. Sports do not obey the law of averages.

And condolences to everyone who lost on that safety at the end…

*:*super bowl