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Need a little math help

 
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darvon
BCS Neutral


Joined: 28 Feb 2004
Posts: 5358
Location: Detroit
PostPosted: Mon Aug 06, 2007 7:34 pm    Post subject: Need a little math help Reply with quote
It's HOT in Michigan and my brain is squishee.

Here is what I want to calculate.

The game is HU NL SNGs.

Assumptions:

Assume all players have a "True Quality " From 0% to 100%

Player A for a given game will play at his "TrueQuality" with a variation given by a Poisson distribution with Variance= X.

Player B, for a given game, will play at his TQ with a variation of the SAME variance, X.

If player A plays at a higher level than B, then A will score a win.


As a function of x, how many games will A have to play in order that there is a 95% confidence that A's win % is within X of his TrueQuality?


Thanx

Terry
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the_hawk
Chelsea FTW!


Joined: 13 Jul 2005
Posts: 4340
PostPosted: Tue Aug 07, 2007 1:05 am    Post subject: Re: Need a little math help Reply with quote
darvon wrote:
As a function of x, how many games will A have to play in order that there is a 95% confidence that A's win % is within X of his TrueQuality?


His long-term win rate isn't going to converge on his TQ itself; I presume it will converge on some function of his TQ edge.
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Bugsbunny
Wascally


Joined: 07 Apr 2004
Posts: 7626
Location: Drinking Carrot juice
PostPosted: Sat Aug 11, 2007 6:25 pm    Post subject: Reply with quote
My brain is complete mush at the moment, never mind squishee.
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darvon
BCS Neutral


Joined: 28 Feb 2004
Posts: 5358
Location: Detroit
PostPosted: Sat Aug 11, 2007 11:51 pm    Post subject: Re: Need a little math help Reply with quote
the_hawk wrote:
darvon wrote:
As a function of x, how many games will A have to play in order that there is a 95% confidence that A's win % is within X of his TrueQuality?


His long-term win rate isn't going to converge on his TQ itself; I presume it will converge on some function of his TQ edge.


Im sorry. You are right, let me restate

How many games of a random selection of players with random TQ will it take to make Player A's win rate be within X of Player A's TQ with 95% confidence.
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