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BGonline.org Forums
Proposed quantitative definition of skill
Posted By: Bob Koca In Response To: Proposed quantitative definition of skill (Timothy Chow)
Date: Tuesday, 19 June 2012, at 11:02 p.m.
"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. "
Not really challenging your particular choice of measure but rather challenging the assertion that the exact choice of dispersion hardly matters.
Beyond that issue this example shows something which to me is unsatisfactory with the basic definition. Let's use some other measure. Say the average of using the different possible ranges. This game would still rank low. To me a game that is so difficult that only one person could master it while everyone else is doing no better than guessing shows that it has a tremendous amount of skill. You seem to think that it shows it has a very small amount of skill.
I wouldn't be surprised if whatever definition someone proposes had some undesirable properties. Especially since what is desirable to some may be undesirable to others.
"If it's easy to jump up to the highest skill level, then typically the population will quickly stabilize to the 'no-skill' state"
That doesn't seem to be the case for math students and the game of NIM. You seem to be making an assumption that the members of the population have a desire to be good at the game. Is that true for say the population of ABT players?
"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"
I loked at "venue" as being the different divisions which is different than how you were thinking of it.
How would one actually go about writing down the MPT for the whole population? There is a limited data problem and it would be tricky to distinguish how much a good winning percentage came from skillful play and how much came from luck.
Another complication is that it seems the entire tournament structure should be looked at. If there were a one pointers round robin tournament of say 32 players the winner is probably one of the better players even if the player did not have that big of an edge in any individual matchup.
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