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# Mathematics of NFL Football Grid Pools

Topic closed. 4 replies. Last post 12 years ago by johnph77.

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Bemidji MN
United States
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January 13, 2004
110 Posts
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 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"

Bemidji MN
United States
Member #3340
January 13, 2004
110 Posts
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 Posted: September 10, 2004, 9:20 am - IP Logged

I noticed a couple of typos in the above message, for which I apologize. I think I need to schedule an eye appointment. So tough to get old!

Here is the updated list.

0 - 0    8.75%          3 - 7    3.42%          3 - 4    1.55%

0 - 7    6.29%          4 - 7    3.37%          3 - 6    1.46%

0 - 3    5.52%          3 - 3    3.28%          1 - 4    1.41%

7 - 7    5.01%          4 - 4    1.73%          1 - 3    1.00%

0 - 4    3.46%          0 - 6    1.60%          1 - 7     1.00%

"Announcing your plans is a good way to hear God laugh"

CA
United States
Member #2987
December 10, 2003
832 Posts
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 Posted: September 10, 2004, 2:07 pm - IP Logged

The pools I've played have never had the numbers preprinted on them - they've been selected after the sheet is filled with bettor's names. And that leaves everything to chance.

Here's another twist, though - some pools I've played have paid out varying amounts depending on which quarter it was - for instance, 10% for the 1st and 3rd quarters, 30% for the half and 50% for the final score.

gl

john

Blessed Saint Leibowitz, keep 'em dreamin' down there.....

Next week's convention for Psychics and Prognosticators has been cancelled due to unforeseen circumstances.

=^.^=

Bemidji MN
United States
Member #3340
January 13, 2004
110 Posts
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 Posted: September 11, 2004, 11:14 am - IP Logged

The numbers are selected on the sheets my wife brings home after all the squares are filled too. However, if someone chose to place the numbers before you purchased squares, my guess is the best ones to buy would be any combination of 0, 3, 4 or 7. And if someone playing the game consistantly gets these kinds of squares, that might be an indication that the game is rigged.

"Announcing your plans is a good way to hear God laugh"

CA
United States
Member #2987
December 10, 2003
832 Posts
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 Posted: September 11, 2004, 1:24 pm - IP Logged

KyngeRycharde -

Ahhhhh - I see where you're coming from now. TY for clarification.

For the half and later quarters, the 6 should be in play as well.

gl

john

Blessed Saint Leibowitz, keep 'em dreamin' down there.....

Next week's convention for Psychics and Prognosticators has been cancelled due to unforeseen circumstances.

=^.^=

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