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AI Challenge Forums • View topic - How is skill being calculated?

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How is skill being calculated?

Questions and discussions about the current Ant Game Rules.

How is skill being calculated?

Postby stupidquestions » Sat Dec 17, 2011 12:54 pm

I know what mu and sigma MEAN, but I don't know how to calculate the actual skill from mu and sigma. Is there some place where this stuff is explained? If not, can someone please explain it to me?

Edit: Oh, I guess it's mu - 3 * sigma.
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Re: How is skill being calculated?

Postby Zaph » Sat Dec 17, 2011 1:06 pm

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Re: How is skill being calculated?

Postby stupidquestions » Sat Dec 17, 2011 1:24 pm

Thanks. So, the contest lasts < 1 week. A better question, perhaps, is which players will have highest sigma at the end of the contest? Will our sigmas all be close to each other, since the skills are being reset at the beginning of the contest, or will the bots that take more risk have higher sigma (or something like that)? Or, to reformulate my question, will sigma lose on its significance after the actual contest starts? If yes, how much? If no, why not?
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Re: How is skill being calculated?

Postby Darhuuk » Mon Dec 19, 2011 12:25 am

The sigma has nothing to do with risk. Basically, what the ranking algorithm does is "guess" your skill, it does this by assigning you an "estimated skill" (mu) and a standard deviation. These are the same mu & sigma as used when describing a normal probability distribution (https://en.wikipedia.org/wiki/Normal_distribution).

Sigma more or less tells you how certain the ranking algorithm is of it's estimate of your skill. So the more games you play, the more the ranking algorithm can see how you play and the more certain it will become of it's guess for mu, and so sigma will go down.

The reason that your "final" skill is not simply mu, but mu - 3 * sigma is that it is 99.7% certain that your true skill (which it can only guess) will not be lower than what it is actually guessing (which is the number mu). For a graph nicely showing why this is, see here: https://en.wikipedia.org/wiki/Normal_di ... _intervals.

Did that make sense? I can try again if not :).
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