Author: Peter Fendrich
Date: 04:54:34 06/12/01
Go up one level in this thread
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! //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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