About the authors: Casey Frushour is a freelance graphic designer and web designer. Andy Frushour is an amateur stat nerd who loves Excel spreadsheets and playing sports — particularly Monkeyball. Both reside in Michigan.

We’ve all been in one of those Super Bowl Squares pools. You know, the kind – where you put a buck in the pot and are assigned a square on a 10×10 grid. Each square corresponds to a pair of numbers, one for the NFC team and one for the AFC team. The score at the end of each quarter — specifically the ones digit for each team’s score — determines which square wins 25% of the total cash pot. For instance, if the 49ers lead the Ravens 17-14 at halftime, the person with 7 on the 49ers axis and 4 on the Ravens axis wins the cash.

I’ve always wondered which squares were most likely to win. Logic tells you that a combination of 0s, 3s and 7s could be good, while 2s and 5s are not so good. So what squares are the best and which numbers should you hope to randomly draw? I looked at data for all NFL games played since the 2006-07 season to determine the answer to that question, and then I looked at results from past Super Bowls and scores from the 2012-13 49ers and Ravens games to determine your best bets for Super Bowl XLVII in New Orleans.

Run Your Football Squares Pool Online >>

The Basics (Using 2012-13 Data)

There were 256 regular season NFL games and ten postseason games so far this year for a total of 266 games…or more importantly, 1,064 quarters played and 1,064 combinations of winning scores. Even though there are 100 squares on the board, we’ll group like combinations (e.g. 3-7 and 7-3) to make our findings a little clearer.

As expected, the most frequent scores this year ended in 0 (531 times), 7 and 3 – almost two-thirds of the possible scores. The least frequent were 5 (34 times), 2, 9 and 8. And the most frequent combinations? 7-0 (120 times), 3-0, 7-3, 0-0 and 7-4. 43% of the combinations were made of these five winners. Only one combination did not happen a single time during the past NFL season – 2-9.

(A note about the graphics in this article: I used a color-coding system to show the largest numbers in dark green and the smallest numbers in dark red. The rest of the numbers fall somewhere in the green-yellow-red spectrum.)

Go to the end of the article to see a grid where squares have not been combined.

More Details (Using Data From the Past Seven Years)

The disbursement table for 2012-13 looks remarkably the same as the table that includes data from the past five years (consists of all 1,067 regular season and postseason games from 2006-07 through the 2012-13 playoffs). The latter chart, though, obviously includes seven times as many data points and may be a slightly better indicator of the true probability of each of the combinations. Here is the hit percentage (since I know some of you would rather see % rather than the raw #) for each combination.

For another version of this table, see the end of the article.

Breaking It Down Even More (Quarter-By-Quarter)

To this point, our data has simply shown the aggregate number of occurrences for each number across all quarters. What the data hasn’t shown is some numbers are better to have in one quarter over another. For instance, you might expect a 0-0 to happen much more frequently at the end of the first quarter (because of a scoreless first quarter) compared to the end of the game.

These numbers show the percentage of all quarter-winning scores over the past seven years. So, in a 7-7 quarter, 7 is actually counted twice. Although the table above does not tell us what combinations are best for each quarter, logic indicates if you have two low-percentage numbers the odds are not in your favor to win the cash.

First Quarter: If you have an 8 in the first quarter, give up. In the last seven years (over 1,800 first quarters of NFL football), there has been just three first quarter winners with an 8. In fact, when looking at the first quarter, unless you have a 0, 3 or 7, it’s not looking good. Almost 90% of first quarter scores have had scores ending in those three numbers, with 0 hitting 45.2% of the time. (And don’t celebrate if you have 2 or 5; 2 has hit seven times and 5 hit six times in the last seven years.)

Last Three Quarters: 0-3-7 continue to be the most popular numbers in the last three quarters, but not by nearly the same dominant margin — 0-3-7 account for 68.8% of numbers in the second quarter, 58.9% in the third and 47.3% at game’s end. So as the game progresses, other numbers are able to get some action. For instance, 4 more than doubles its percentage from the first to second quarter (6.1% to 12.9%), and it even overtakes 3 in the fourth quarter. And although the 2-5-8 combo are the runts of the litter in the first quarter (0.5% combined), in the fourth quarter they have accounted for 14.2% of hits in the last six years.

Final Quarter: In some pools, the end of game score pays more than the rest of the quarters. In these pools, the most valuable combos are 3-0, 7-0, 7-4, 4-1, 7-3 and 4-0. These six account for over 34.9% of the final scores over the past seven years.

2012 Week 9 Oddities

For whatever reason, there were some strange “squares” happenings in week 9 this season. First, in the past seven year there have only been three teams that have ended on 8 in the first quarter. In Week 9 this year the Bears scored 28 in the first quarter against the hapless Titans. Second, 2-2 and 5-5 have only hit twice in the past seven years. Interestingly enough, though, both hit one time this year – and BOTH were in Week 9. The Bucs beat the Raiders 42-32 in Week 9. We thank Oakland for that last 2-point conversion to get to 32 total points. And the Super Bowl-bound Ravens beat the Browns, 25-15, that same week thanks to a Baltimore 2-point conversion and five field goals from Cleveland’s Phil Dawson.

Super Bowl History

Data from 46 years of Super Bowls tells much of the same story as the past seven NFL seasons. The top six combos from 184 Super Bowl quarters are the same as our five-year data (with 4-0 tied for 5th), and again, almost two-thirds of the scores end in 0, 3 or 7. On the flip side, 17 combinations of numbers have failed to appear in the Super Bowl. The number you certainly want to stay away from is 5 as it has partnered only with 0, 1, and 9 for winning combinations. The good news for 5? Last year in Indianapolis, 5 partnered with 7 for the first-ever 5-7 Super Bowl quarter (17-15 Patriots at the end of the third quarter).

The most common Super Bowl final score combination? 7-4 hit in five of the 46 years. Interestingly enough, the NFC had the 7 each time. 1, 2, 5 and 8 have NEVER hit in the first quarter of the Super Bowl.

Ravens vs. 49ers

While we can’t do the same type of combination matrix for individual teams as we have in the rest of the analysis, we can look at the Ravens and 49ers most frequent scores this year. The Ravens have played 19 games (76 quarters of football), while the 49ers played one less playoff game for 72 quarters.

The Ravens and the 49ers also may be more prone to particular numbers compared to what our seven-year data would suggest. This table shows the difference between the historical average and the average for each team this year.

In some years, a participating team may outpace the league average for one reason or another. For instance, in 2009-10 the Colts hit 0 about half the times they would have been expected to land on 0. In fact, the Colts had 0 only 10 times last season – and three of them were against the Jets in the AFC Championship! This year, though, it doesn’t look like anything stands out (except that the 49ers hit 0 way less often than normal – including only 5 times in the last three quarters of games).

2013 Super Bowl Squares Prediction

So what does all this analysis tell us about this year’s big game? First of all it tells me I wasted multiple hours proving to myself that 0, 3, 4 and 7 are good, and if I get 2 or 5 I’m screwed. But based on the last four years of data, Super Bowl history and this year’s competing teams, I’ll go with quarter scores of SF10-3, Tie 13-13, SF 20-16 and SF 27-23.

But really, I’d be just as happy to see an early field goal and a couple of first quarter safeties, no further scoring, and four winning 5-2 quarters. Good luck!

=============================================================

Response to Questions

In response to some great questions and observations, here are two more heat maps. The first shows all the combinations of scores from this year. The home score is on the vertical axis, the visitor score is on the horizontal access. If you add the number of times the 7-0 square hit (66 occurrences) plus the 0-7 square (54) you see a total of 120 quarters that ended with one team with 0 and the other with 7.

This final table is probably a better view of the likelihood of each combination. In one of the graphics earlier in the article, 7-0 appears to hit 13.13% of the time. In actuality, there are two 7-0s on the board (7-0 and 0-7), so a better representation is to halve 13.13% and make it 6.56%. Note that the percentage for 0-0 (and 1-1, 2-2, etc.) did not change because there is only ONE of those combinations on the board.