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Winning PR vs Losing PR--one thing impossible to measure

Posted By: Timothy Chow
Date: Saturday, 30 January 2016, at 9:08 p.m.

In Response To: Winning PR vs Losing PR--one thing impossible to measure (Karol Szczerek)

Karol wrote:

We have to assume that in macro perspective the difficulty of positions/matches is a normal distribution

No we don't. Nobody forces us to assume false statements.

The right way to think about the situation is to recognize that both luck and skill are random variables. Variation in PR between games is an illustration of the randomness of the skill variable.

In common parlance we don't have the proper vocabulary to distinguish clearly between the two kinds of randomness (the randomness of the luck variable and the randomness of the skill variable), and we typically find ourselves overloading the word "luck". But the limitations of ordinary language should not stop us from building the best mathematical models we can, even if that means introducing new jargon.

As I mentioned above, the probability distribution of the skill random variable can be estimated by looking at how PR varies from game to game. Accumulating this data is certainly a viable alternative to simply assuming that the distribution is normal.

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