[AlanBostick]

[ QUOTE ]
I know variance is a function of standard deviation and winrate...but exactly what sort of function is it?

[/ QUOTE ]

Variance is a function of standard deviation only in the sense that variance = the square of standard deviation.

In actual fact, variance is a calculable property of a statistical data set. If EV(q(x)) is the expected value of quantity q that depends on random variable x, then variance is

V = EV((x - EV(x)^2)

Variance is a property of the probability distribution governing the behavior of a random variable. Different probability distributions will have, in general, a different mean and a different variance.

In particular, in a poker game, the hand-by-hand results of a winning player playing her 'A' game might have one probability distribution and those of the same player when she's on tilt might have another. Both the variance and the mean (the win rate) of the tilt distribution will in general be different from those of the 'A'-game distribution.

If you invoke the Central Limit Theorem to cover the results of many, many hands, the theorem asserts that long term results will governed by a normal (Gaussian) probability distribution, no matter what the underlying distribution for hand-by-hand results. Gaussian distributions are parameterized independently by their means and their variances. You can't say a priori that changing the mean will change the variance, or vice versa.