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Science of Chess: A g-factor for chess? A psychometric scale for playing ability

This looks excellent to me going in. I would not apologize for elementary. I wished I could explain things that ambitious to explain to an unknown (kind of) audience target, as well. You are doing fine by me.
@surys said in #4:
> It's worth noting that g-loading of chess (aka correlation of chess skill with general intelligence) seems very low in studies (around 0.3)
>
> www.sciencedirect.com/science/article/abs/pii/S0160289616301593

Yes, good point. I was debating writing a post about that relationship, but I feel like writing about general intelligence requires a lot of care and more expertise than I have in that realm. Thanks for sharing this paper!
you kind of made me look into ELO on the web, to find out there is not a clear presentation, like the in glicko statistical papers.
It seems to have been formulas first, and probability formulation later. I can't find a presentation like that I say for glicko.

But they all see not to assume a population distribution, which for some reason I thought the formula for ELO updates was derived from (which is not the same as individual distribution, in my understanding). But you did not want to enter that kind of discussion. I am just saying that reading this made me want to check. By presenting ELO the way you did, you did the job for the other ones, even the ones that are more clearly constructed from a mathematical point of vue (more than a parameter updating formula). I am still searching for abstract versions so I can understand the flow of information between givens (assumptions) and optained (the formulas interpretations). It might just be my lack of familiriaty with categorical data stuff).

I think in the formula you used, the expectation is what is compacting all the model I wanted to see, and if it was equivalent to a population rating distribution being constrained to a model assumption. So, now I think even ELO is not making any such constraint assumption. The update formual might not be assume such a thing.

don'T mind me, as this might exactly be the kind of thing you might have wanted to not go into, but if someone else can spot my difficulty of concept. please help.
Hey, did you consider the ELOmeter web site? if still active (it was 5 years ago, and it rather older than that). It might have a hidden gold mine of externally measures chess behavior.
But its non-random position probing, it might offer something covering enough of chess wilderness.

It seemed to have been catering to the usual mirror tell me who the best individual metric thing, but internally not public it must have been accumulating data for ever... I am not sure there have been corresponding reports. They could make that public by now, and anonymized.. I know that was not the the purpose, and I really don't care if that does not do ELO. For I would find more interesting to have a multidimensions data set, with board information visible, than their doomed attempt at mimicking a 1D number as sole measure (even if not doomed for some snapshot in time when they might have calibrated their result for some expectations, with demographics, and no control over player population specifics, I think unsupevised data analysis over that data set would be informative).

Any thoughts?