Tournament win rate accuracy

[Robk]

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I also estimated your variance using a multinomial distribution, a better model for tournament results than a normal distribution.

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We're not using the normal distribution as a model for tournament results. We're considering each tournament as an iid random variable, and by the central limit theorem the arithmetic mean of the results is approximately normal.

[MrBlini]

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We're not using the normal distribution as a model for tournament results. We're considering each tournament as an iid random variable, and by the central limit theorem the arithmetic mean of the results is approximately normal.

[/ QUOTE ]It can be very approximate with small sample sizes, which is what got me looking at the possibility of estimating the confidence intervals based on the actual distribution. Unfortunately, estimating confidence intervals for variables derived from multinormal distributions is not easy, at least with the tools I have available (Matlab and R). For practical purposes, the normal approximation seems to be just fine, although you have to be careful what you conclude about the tails.

[joeg]

Can anybody reccomend any good books on this kind of mathematics, I've got a maths degree but almost no experience in stats so I dont mind complicated or technical as long as it starts at the begining

[Robk]

BruceZ suggests a probability/statistics book for people with math experience here .