It's that time of year for that office Superbowl Pool. Do you know what numbers to pick for your Superbowl Pool? You know, you pick squares that represents the combination of final digits of the games score. If your combination of numbers comes in for the final score of the game you win. You can read the rules at eHow.com. As luck has it when you are picking those squares they are all not created equal. Of course anything can happen, but some combination of numbers occur more frequently due to the scoring rules in football.
To give you a heads up on favored numbers I looked at team scores from 736 football games from the 2008 and 2009 seasons. Here is a table of the most frequent numbers.
Now of course the Superbowl Pool board is two dimensional so we have to look at the probabilities of two numbers occurring at the same time. The rule of independent probabilities apply so we multiply the result probability value for Team 1 times the probability value for Team 2 to get our exact probability of winning on a particular square.
Now a little analysis. Assuming everything was random we would expect each square to be worth 0.01 or 1 in 100. You will notice that some squares are valued higher than others. Combinations of 7,3,4 or 0 do very well. Combinations of 2,5,9 and 8 are not so good. If you choose to play on multiple squares, you simply need to add all your probabilities up to estimate your probability of winning the total game. Let's say I have selected five squares as follows:
Total probability here since these are independent and mutually exclusive events adds up to 0.079 or about a 1 in 12 chance which is considerably better than the 1 in 20 chance of selecting five if it were completely random. And since it is a zero sum game someone else will have a lower probability of winning to even things out.
Some people don't like this aspect of these pools and will select numbers randomly to place on the board after everyone has selected their squares. You can still use this table to estimate your chances once you know the numbers. Good Luck and Geaux Saints!
To give you a heads up on favored numbers I looked at team scores from 736 football games from the 2008 and 2009 seasons. Here is a table of the most frequent numbers.
Now of course the Superbowl Pool board is two dimensional so we have to look at the probabilities of two numbers occurring at the same time. The rule of independent probabilities apply so we multiply the result probability value for Team 1 times the probability value for Team 2 to get our exact probability of winning on a particular square.
Table of Probability of Final Digit Combinations
Now a little analysis. Assuming everything was random we would expect each square to be worth 0.01 or 1 in 100. You will notice that some squares are valued higher than others. Combinations of 7,3,4 or 0 do very well. Combinations of 2,5,9 and 8 are not so good. If you choose to play on multiple squares, you simply need to add all your probabilities up to estimate your probability of winning the total game. Let's say I have selected five squares as follows:
Total probability here since these are independent and mutually exclusive events adds up to 0.079 or about a 1 in 12 chance which is considerably better than the 1 in 20 chance of selecting five if it were completely random. And since it is a zero sum game someone else will have a lower probability of winning to even things out.
Some people don't like this aspect of these pools and will select numbers randomly to place on the board after everyone has selected their squares. You can still use this table to estimate your chances once you know the numbers. Good Luck and Geaux Saints!
2 comments:
http://www.j-e-f-f.com/sb-o-m.htm has some pretty specific odds for each box for each quarter (since most pools have quarterly payouts) and final scores. All based on historical Super Bowl quaerterly results. Once and for all, the question is answered...
"How much does my box suck?"
Aren't you forgetting to decrease the odds of winning with two identical numbers because of the impossibility of a tie? For example, assuming that 70 is the highest number of points that any team is likely to make, there would be 64 scores that end in 0-0, but 8 of them would be impossible (e.g. 10-10). So the odds should be reduced by a factor of 8/64 for all same digit scores. Or, maybe 6/36 would be a better factor since there are so few scores above 50.
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