Football Squares Dear Colleagues,
This is a math question for people who know the rules of (American) football.
Every year my barber runs a “football squares” game. He finds 100 customers, each put in 20 dollars, and each person is assigned a square on a 10 by 10 grid. After all squares are sold he picks numbers out of a hat to label each row and column 0 thru  9.   So each contestant winds up being assigned with an ordered pair of numbers – in my case (3,7) this year.  Now prizes are awarded by inspecting the last digit of the score of each team in the Super Bowl at the end of the first, second, third quarters and the final game score. Each winner gets $500.  
For example, suppose that the scores are   AFC  14, NFC 10 at the end of the first quarter. Then the person with (4,0) wins $500. 
Now this is a fair bet, in the sense that each square is assigned randomly (and I believe that my barber doesn’t cheat.)  However, it would seem that some numbers are “better” than others. Football scores are not random. For instance, at the end of the first quarter it is extremely unlikely that (5,5) will win. On the other hand, ((0,7) would seem like a good number.  What is needed is  some probabilistic analysis based upon the actual scoring patterns in football together with looking at actual scores of many pro football games. I am unable to find any analysis of this on the internet. I have tagged this as a probability  question but since I work in operator algebras for a living this may be mis-tagged, and I ask you to pardon my error. 
Let’s make it precise. Let f: {0,1,2,…, 9} x {0,1,2,…, 9}  x {1,2,3,final}  \to  [0,1] be the function that to a point (x,y,z) assigns the probability that the score at the end of the z’th quarter of the Super Bowl will be equal to (x,y) mod 10. Find the function f. Where does f achieve its max?
How about it, colleagues?  Inquiring minds want to know!
CS
 A: The theorist's answer
It seems natural to model American football as a Markov chain. If you want to be realistic, the state space could be incredibly complicated, with information about things like who's in possession, how many downs, what's the score, etc. In statistical physics, however, ridiculously simple models do a surprisingly passable job of modeling complex processes. I wouldn't be surprised if something as stupid as a normal-distributed random walk, with absorbers at 0 and 100 yards, did an okay job of predicting the gross statistical properties of football scores.
The experimentalist's answer
There have only been 43 Super Bowls, so your sample size is pretty crappy. (For what it's worth, all of the scores are available here.) Super Bowl contenders are drawn from the NFL, though, and there have been hundreds of NFL games. It might be interesting to see whether you can reliably distinguish a Super Bowl game from a regular season game just by looking at the final scores!
A: See here and here for empirical statistics.  These are based on all NFL games since the two-point conversion was added (1994), not just Super Bowls.
Your guesses are right: scores ending in 0, 3, 7 come up a lot; scores ending in 2, 5, 9 come up very rarely.
A: Your making this to complicated. If you pick a square at random on a 100 square board, you have a 1-100 chance of winning no matter what the score of the game is. 
The square choice is random, the numbers assigned to each square are random, assuming it is a legit board.
The score of the game is irrelevant because all the other variable are random. 
Since only one square can have a 7,7 number combination, there is a 1/100 chance of getting that combination, again assuming the numbers are assigned randomly, and the squares are chosen randomly.
I have seen the probabilities worked out in algorithms factoring in game score, squares, numbers drawn with up to 10,000 samples. None of the it matters, the output is always the same, you have a 1% chance of your square hitting the.
