With the Super Bowl just a day away, I am hearing a lot of talk about Super Bowl Squares, the game of chance that only gets played one day out of the year. With most variations of the game, people sign up for squares, then once all squares have been taken, the numbers are randomly assigned to the rows and columns, thus making this purely a game of chance (I guess the football game also plays a role too).
But suppose that these numbers were not randomly assigned: you get to choose the numbers that you want. Which pair of numbers gives you the best chance of winning? I have seen a few articles online trying to answer this question, but all the ones that I have come across look at the score after each quarter of all previous Super Bowl games. While I see the point of only looking at Super Bowls, some of these games were played over 40 years ago and the game has clearly evolved since then. For example, I have to believe that field goals are much more common now then they were 40 years ago, as kickers are now able to routinely make 50+ yard field goals (I don't have data to back this up, so let me know if I'm wrong). Therefore, I have decided to look at all football games from this past season, including the playoffs. If my counting is correct, this covers 266 games. I should probably look at the score after each quarter of every game, but this would cover 1064 quarters, and I just don't have the time (or really care to) do this. So I have decided to only analyze the final scores of the 266 games. I also ignored whether the winning team was home or away, so to me, Team A winning by a score of 17-13 (making square 7,3 the winner) is equivalent to Team A losing 13-17. That is, I treated squares (7,3) and (3,7) as the same.
Let's first look at the most common point totals, with respect to the last digit. As expected the least likely point totals end in 5 (3.8% of all final scores) , 2 (4.3%) and 9 (5.1%). The most common point totals end in 3 (16.4%), 4 (16.0%), 7 (14.8%), and 0 (13.5%).
Now let's look at pairs of numbers. If you played over the full 2012 season, 3 squares would have never won (when only looking at final scores): (1,2), (2,9) and (5,6). This isn't too surprising because, as shown earlier, it is difficult to score total points ending in 2, 5 or 9. The most likely pairs this past season were (3,6) and (3,7)*, which each occurred 16 times this season. Combined, these 2 pairs would have won over 12% of the games. Additional pairs that would have won over 10 times this past season include (0,3), (0,4), (0,7), (0,8), (1,4) and (3,4).
In conclusion, if numbers were not randomly assigned in Super Bowl Squares, it would easily be possible to win in the long run.
* SI writer Peter King picked the Ravens to beat the 49ers 27-23, so he's playing the odds with his final score prediction.
UPDATE (2/4/2013). The score after each quarter (with the Ravens always leading) was 7-3, 21-6, 28-23 and 34-31. This means that the winning squares were (3,7), (1,6), (3,8) and (1,4). Did anyone follow my advice and bet on (3,7) or (1,4)?