|Posted: September 7, 2004, 4:01 pm - IP Logged|
My wife plays these all the time at work, and I am sure most of you know what I am talking about, but just in case, here is a brief explanation.
They consist of a 10 X 10 grid and you buy a square. After all the squares are filled, the numbers 0-9 are added in a random sequence (we hope!) to the columns and rows, along with the names of both teams.
We'll say that the Patriots (listed on the side) are playing the Vikings (listed at the top). Your square says Patriots 3, Vikings 0. This means you would win if the final score at the end of the first quarter ended in a 3 for the Patriots and 0 for the Vikings. Same for the half, third quarter and the end of the game.
Now, most people would figure that they would have a 1% chance of winning at least one quarter for every square they bought. But, because of the variability of scoring in football, that is not the case.
I went through all the games of the 2003 season which gave me almost 1100 quarters, which I think is a fairly good sample size. I calculated the number of times each of the 55 possible combinations occured, found the probability of occurance, then divided by 2 to determine the probability of winning at least one quarter. Pairs with the same number only occur once on the grid, and so the probability of winning at least one quarter is equal to the probability of occurance.
Here are the top combinations in order of probability of winning at least one quarter:
0-0 8.75% 3-7 3.42% 3-4 1.55%
0-7 6.27% 4-7 3.37% 3-7 1.46%
0-3 5.52% 3-3 3.28% 0-1 1.41%
7-7 5.01% 3-3 1.64% 1-3 1.00%
0-4 3.46% 0-6 1.60% 1-7 1.00%
The following pairs never occured: 2-2, 5-5 and 5-9.
"Announcing your plans is a good way to hear God laugh"