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Proposed quantitative definition of skill

Posted By: Timothy Chow
Date: Tuesday, 19 June 2012, at 10:23 p.m.

In Response To: Proposed quantitative definition of skill (Bob Koca)

Bob Koca wrote:

Assuming there is a large enough population more than 90% of the values would be extremely close to .5 making the interdecile range extremely close to 0.

Oh, I see...you're picking a nit with my particular choice of measure of statistical dispersion. I try to stifle a yawn and fail.

it seems odd to say that a game requires a great amount of skill when the perfect strategy could be learned in less than ten minutes.

This is related to Tom Keith's concept of "yield curve." I see the point, but I don't think this is a particularly serious objection in practice. If it's easy to jump up to the highest skill level, then typically the population will quickly stabilize to the 'no-skill' state. On the other hand, if the population for whatever reason doesn't quickly stabilize in this fashion, then you'll get a spread of ability and you'll want to say that there is a lot of skill involved.

It might follow that backgammon tournaments with divisions do not satisfy the skill criteria but backgammon with only one division does. That doesn't seem right somehow.

I don't think that this is a serious problem either. You have a population consisting of the participants in the tournament. Just because players from different divisions don't actually play each other in the tournament doesn't mean that you can't write down an MPT for the whole population.

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