Author: Martin Schubert
Date: 07:26:57 06/12/01
Go up one level in this thread
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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