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Old 12-31-2004, 02:03 AM
DeucesUp DeucesUp is offline
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Join Date: Sep 2003
Posts: 56
Default Re: Math Question re:- the \" Carib Football Poll \"

I think I understand what you're asking, you can make a simple estimate as:

Three things have to happen.
1. They must make 5 different picks.
2. Leader must miss all 5
3. Trailer must hit all 5.


#1 -- Assuming the two players have no knowledge about each other's picks and have no tendancies which would tend to make them more or less likely to pick the same teams, #1 can be estimated as: (26/32)*(25/32)*(24/32)*(23/32)*(22/32) or about 23.5%

#2 -- Assuming no ties and assuming the players don't beat the spread, the chance of leader losing all 5 is about (1/2)^5 or 3.1%

#3 -- Chance of trailer winning all 5 is about the same 3.1%

Chances of all 3 happening are then 0.235*.031*.031 = 0.023% about 1 in 4500.


It's not quite this bad, as the 3 conditions aren't completely mutually exclusive. That is, once condition 1 is met, it becomes much more likely the "trailer" picked the opposite team in the same game. Then when the leader looses that game (condition 2), the trailer has automatically won it.

On the other hand, all pushes are in the favor of the leader as a tie is as good as win for him and a tie is as bad as a loss for the trailer.

These two factors partially cancel each other out, I won't try to calculate the exact effect of these.
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