## 2013 Super Bowl Squares Odds

*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.

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### 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!

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### 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.

Hi Casey,

Interesting analysis! I’m actually trying to create a super bowl squares spreadsheet that assigns the score numbers so that everyone has roughly an equal chance of winning. So I need the odds like you have shown, but for more games if possible (and for each quarter, if possible). Where did you get your raw data?

Thanks,

Dean

Fun analysis and good use of heat maps. This will be my first year playing so I like having a bit of an edge.

Dean, why would you want to make it such a level playing field? wheres the fun in that? It should be up to the decisions players make instead of randomly being assigned a number. You might as well randomly assign a winner in that sense.

Instead of randomly assigning #s, I’ve always wanted to try to assign a dollar figure to each square. So the 0-0 square might sell for $10, but the 2-2 square could sell for $0.10. So the trick is finding the square with the most value.

Or, have an auction for each square. That would be fun to try, too.

Casey- Love it! Nice work. Hopefully it will help me win some money!

Looked into this myself. Worth pointing out that (0,0) is the best square to have: If you land the “Ravens 7, 49ers 0” square, you can still lose if some version of “Ravens 0, 49ers 7” comes up. The odds in those first two tables don’t make that clear.

As Bryan above mentioned, the probabilities in the “More Details (Using Data From the Past Seven Years)” table are very misleading. The probabilities along the diagonal are actually correct, while the probabilities below the diagonal are twice what they should be for that particular combination.

For example, the ‘7-0’ score is listed as 13.13% which is true if you account for BOTH combinations, ‘7-0’ and ‘0-7’. However, when you get a square in a football pool, you only get ONE of these combinations, effectively halving the probability you listed. This makes 0-0 a better square to have, which is not reflected in your table (7-0 is a darker green). It should look something like:

0-0: 7.88%

7-0: 6.57%

0-7: 6.57%

Bryan and Mark: very good and accurate points. I did mention in the article that 0-7 and 7-0 would be combined, but it certainly does skew the heat map (I should do a new map that takes this into account). The idea, of course, is to make this article somewhat digestible for those who want to read it — even though I could make it way more complex! BTW, in the 7-0/0-7 example, over the past seven years the home team had 7 6.83% of the time, and the visitor had 7 6.30% of the time.

So, looking at this, I would say that 2 – 9 is very due and probably roll this super bowl.

Hey everyone! I am doing a block pool I need 9 people to fill it still I will txt anyone a picture of the squares I have left you can pick your two blocks so it is (2) blocks for 50.00 pay outs are as follows

1st 400

half 600

3rd 400

Final 1000

TOTAL AFC TD TOTAL NFC TD 100 example how that works lets say you have the blocks 4 3 afc scores 4 tds nfc scores 3 td you have that block you win.

I will pay out all winners MONDAY. I will gift you the pay pal winnings. If you want in let me know email me casey_royer@hotmail.com we can set up to talk over the phone or whatever so you know I am legit.

Thanks,

Casey Royer

Great stuff, Casey! Some of your readers might be interested in some of these numbers I worked up:

http://ireport.cnn.com/docs/DOC-917541

I will also email.

Regards,

C Chin

Thanks C Chin….great link!

Awesome – just what I was looking for. And your stats confirmed that with my 1,8 and 2,3 squares I have a better chance of hell freezing over than winning part of the $$ pot. Oh well, thanks again for putting this together!

Casey,

Great analysis! I’ll be sure to share this link with squarezy followers on twitter and facebook!

Squarezy.com allows you run your squares pool online! It’s free to join, and free to manage your pool. Check us out!

Love the anlaysis being a stats/sports nerd as well. The approach of using a few different lenses to view the figures makes a lot of sense… Superbowls, all games since ’06 and then looking at these teams this year. Obviously looking at the two teams this year is difficult because it may not be enough data points and you can’t model it for when they’ve played against each other… but I wonder if you could bucket historical teams into certain profiles that align to SF or Balt style and then look at games where those profiles have played against each other. So for example you could identify profiles that rank things like… passing game, running game, defense, field goals, average score, average points allowed, etc… Then reviewing SF-like teams vs Balt-like teams may yield a different and more accurate result.

My office does the random squares every year, and it’s always fun.

This year, I got 0/0!

Nice. I’ve been doing the same with just Superbowl scores, weighting for the payouts. (Most pools I’ve been in give twice as much for halftime as 1st and 3rd quarter, and 4 times as much for the final score; for the first time this year I’ve come across two other distributions, 1/3/1/5 and 4/7/4/10.)

When the office bookie pointed me here, I wondered if Superbowls were different than regular season, glad you ran that.

I’ve been assuming that it’s asymmetric, and that AFC play like AFC and NFC like NFC. The grid that results is not diagonally symmetric, but I don’t like my assumption. (I suppose we could try the older team on the left axis, or the team with the better record, or some other breakdown, to see if there is any better correlation. The sample space is small enough it’s probably not useful.)

Hi there! Out of curiosity, I Googled for the odds of my numbers being Ravens 3 and 49ers 1… well, I am pleasantly surprised at this quantitative analysis but about my numbers, which I initially thought were pretty good.. oh, not so much! Thank you so much for taking the time to put this together! This is awesome! Go San Fransisco! LOL Thanks and in the future, I plan to look you up again. I now feel like I am routing against the odds here but it is great reference to see your work! : ) In Chicago, fighting the snow covered streets tomorrow to get safely to and from the SuperBowl Party! Hooray! : ) Take care!

Hey Casey,

Great analysis and thanks for doing the work on this data. I wrote a quick and dirty mobile app in .NET to help calculate my probabilities and track the changes in my chances through each quarter, as well as my total chances based on the square I selected: http://footballsquares.azurewebsites.net/Home/Calculate

I would like to build more features into this over the next year in my free time, any ideas of what you would like to see?

Very cool app Jon!

My family had a 100 block pool, each block worth $5. End of first quarter worth $50, half time $100, third quarter $50, end of game $300. I managed to win $50 first, $50, third and $300 end of game. He said that he thought the odds of someone doing that must be high. Would love your opinion.

Hi Casey,

I totally put a bunch of squares next to each other in my square pool and did not win anything. What’s up with that? But my buds picked randomly across the board, and THEY WON! Man, I am going to have to try things differently next year. Thanks bro.

Deej

Hi Casey et al,

When I started looking into this, your post was among the best describing the numbers. I can effectively reproduce your tables for the best numbers by quarters. Good work. You do have to be careful with 0-0 and the 7-0/0-7 types of combinations.

I expanded (and maybe even went overboard) studying strategy – to first order, the game is fair with the same probability of winning squares. But a strategy can affect what outcomes are most likely such as winning a single square or winning two or more squares.

Here’s a link:

http://footballsquares.blogspot.com/2014/01/short-final-summary.html