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Subject: Re: Who is better? Some statistics...

Author: Martin Schubert

Date: 07:26:57 06/12/01

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On June 12, 2001 at 07:54:34, Peter Fendrich wrote:

>On June 12, 2001 at 07:17:06, Martin Schubert wrote:
>
>>On June 12, 2001 at 06:08:03, Peter Fendrich wrote:
>>
>>>On June 11, 2001 at 17:46:13, Martin Schubert wrote:
>>>
>>>>On June 11, 2001 at 13:55:31, Gian-Carlo Pascutto wrote:
>>>>
>>>>>On June 11, 2001 at 13:36:21, Leen Ammeraal wrote:
>>>>>
>>>>>>Although Peter's program can in many ways be better
>>>>>>than mine, I don't see how it can be more accurate,
>>>>>>that is, as long as we regard, for example,
>>>>>>10-5-0 as equivalent to 8-3-4. As you see, I simply
>>>>>>divide the number of draws by 2 and add the result
>>>>>>to either side.
>>>>>
>>>>>It is more accurate simply because it does not have
>>>>>to do that simplification at all!
>>>>>
>>>>>10 - 5 -  0 -> 89,4% chance that A is better
>>>>>8  - 3 -  4 -> 92,7% chance
>>>>
>>>>Why do you get different probabilities for the same score?
>>>
>>>It is really different probabilities.
>>
>>Depends on the assumptions. What do you assume? I would assume all three
>>probabilites as 1/3.
>>But usually you make a test like: if A reaches more than x points, say that A is
>>better than B. If A doesn't reach more than x points, you can't draw any
>>conclusion. So the same score should lead to the same results.
>>In statistics you have an "area" (don't know the english word) of possible
>>results where you say the hypothesis isn't true when a result in this "area"
>>happens. And usually this "area" has a form like "points>x". You don't have to
>>do this in this form, but how is your area?
>>Do you understand what I want to say (sorry for my english)?
>>
>>Regards, Martin
>
>I think we are talking about different things here. What I am trying to say is
>that the two scores above will get the same probability with a binomial
>distribution but not with the trinomial one. p=1/3 or not doesn't matter. It
>will generate other "A better than B" probabilities but the number of draws will
>still give the two game scores different reliability.
>
>Your Hypothesis "area" with the trinomial distribution isn't 2-dimensional as in
>the binomial case but 3-dimeansional. Read my text about this.
>I'll be glad to send it to you. Just tell me!

Okay, maybe we're talking about different things.
I thought we were talking about different probabilities for different results
(10-5-0,8-3-4). So were is a binomial distribution? The distribution doesn't
change because of the result.
Of course the result 10-5-0 has a different probability then 8-3-4. But when we
discuss about "A stronger then B", this probability doesn't matter.
Okay, maybe it's a good idea that you send me your text, and after that we can
continue discussing.

Thanks in advance, Martin

>//Peter
>
>
>>>We are not talking about scores only here
>>>but the 3 different possible outcomes: Win, Draw and Loss. The second result,
>>>from a statistical point of view is more "homogenous" and the first one is more
>>>"spread out" or unstable. This is why the probabilities are different.
>>>
>>>One way of measuring how "stable" the results are, is the variance:
>>>(Sum(X^2) - (Sum(X)^2)/N)/N
>>>The first score:  0,22
>>>The second score: 0,16
>>>
>>>meaning that the first result is more unreliable and will get lower probability
>>>than the second one.
>>>//Peter



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