Does a decreased winrate have an exponential effect on variance ?

[Lmn55d]

This is crossposted from poker theory:

Take a player whose style and game selection yield standard deviation X.

As he tilts and his winrate decreases, in what way does his variance increase? Linearly? Exponentially?

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

[mantasm]

Variance is the same thing as standard deviation (they describe the same thing at least, variance is sd^2). Winrate doesn't affect variance.

However, as your winrate decreases, you can expect larger swings. This is affected by your coefficient of variation, which is the ratio of your standard deviation to your winrate, SD/WR.

Here's a good thread about swings and their relation to winrate:

http://forumserver.twoplustwo.com/showfl...e=0#Post4129565

[Lmn55d]

ok so swings depend on coefficient of variation, which is SD/WR. cool. So then if your standard deviation stays the same and your winrate goes down by a factor of 2 your Coefficient of Variation doubles? So it is a linear relationship?

[mantasm]

No it's not linear, it'll look like the function y = 1/x.

Just replace y with "coefficient of variation" and 1 with your constant standard deviation and x with your varying winrate. As it nears 0 it'll be very large, and it'll be very small for large numbers.