# Mathematical bunkum [#2109]

isd: Mathematical bunkum (2009-12-27 13:06) [#6740]

Robert's page contains the following. Direct Comparison is exactly as accurate as it pretends to be: Its precision and its significance are 1 if there are no jigos (or default jigos). They are 1/2 if there are jigos. The significance errors of SOS do not have any impact on a player's Direct Comparison value. Other significance errors with a numerically relevant impact on the latter are not known. In other words, Direct Comparison values do not contain any noise. This is a complete lie. SOS is a numerical value in which (in terms of prediction powers) we can anticipate a standard error. Direct Comparison is no different in this regard. However the standard error in direct comparison is 1 - either it is completely inaccurate or it is completely accurate. Robert admits this would be the case in theory, but says that Direct Comparison cannot have any error - it can never be wrong. This is not an objective or mathematical qualification.

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RobertJasiek: about significance (2009-12-27 15:34) [#6745]

1) There is a difference between "lie" and "misunderstanding". I have or have not a misunderstanding here. If I should have stated a misunderstanding, then this does not necessarily imply that I must have made a lie. A lie presumes intentionally telling a falsehood. I have not had such an intention. Therefore isd's description ("lie") is false, regardless of whether I might have made a misunderstanding. It is not only false but an attempted attack on my reputation: the attempt to describe me as a liar. Furthermore, isd makes this attack out of anonymity; attacking without backing it up with responsibility for the attack. Such is inappropriate in both the real world and in a Wiki.

2) A quick lookaround in the web suggests that statistical significance can have different meanings. I have not been aware of that before. Therefore my previously created webpages do not specify which kind of significance is meant. Let me specify it now: In a value represented as a number, the significance is the smallest difference between two numbers of that value so that they can be distinguished meaningfully / with sufficient confidence / without coinciding with random noise.

3) One might define such a significance in formal mathematical terms. My webpages have not done this (yet). AFAIK, it has not be done at all for Go tiebreakers so far. Hence statements about significance of tiebreakers are more informal than we would wish. IOW, it would be better if we had a formal definition and used it to make proofs relying on it.

4) Even for the description in (2), there can be different meanings of significance. It depends on what one wants "meaningfully" to relate to. My intention is to relate it to the purpose of direct comparison itself, i.e. measuring the numbers of wins of otherwise tied players in their games against each other. Here the hypothesis would be "Each player's direct comparison value is accurately determined according to its conceptual definition.".

5) Instead of the relation in (4), one might relate significance of DC to all games of the tied players or - yet another alternative - to all games of the same stage of the tournament or to all games of all stages of the tournament or to all games in some database. I.e., the relation would be to the hypothesis "Player A is stronger than player B.".

6) Maybe our hot discussion is caused by a different intention of a relation as mentioned in (4) or (5)?

7) Similar things can be said about SOS, SOS-SOSOS, rating or other values instead of DC.

8) isd, you assess a standard error in direct comparison as 1. What is your definition of "standard error" in this context? I guess that with the method of (4) the standard error should always be 0 (meaning no error at all). I.e., presumably we mean two different kinds of standard error.

9) I do not admit that it would be the case in theory but that, until the theory is fully understood, it could be the case.

10) There are - even statistical - values that do not have any error. Therefore your statement "This is not an objective or mathematical qualification." is premature at best.