Mean Value Theorem Question

[shadow29]

This post is pretty much worhtless, but I was wondering about something today.

For those who haven't taken Calc recently, the Mean Value Theorem states (from Google):

for two points (a, f(a) ) and ( b, f(b) ), on a continuous curve, there is a point c in between where the slope f '(c) is the same as the slope, m, of the line joining the two points.

Which basically means if you average a rate, you have to be going that rate at some point.

Applying this concept to poker, we all know that we go through downswings and upswings. From the Mean Value Theorem we can deduce that if our true winrate is 3 BB/100, then for a certain period of time we have to be winning at truly 3 BB/100. That's about as far as my math skills go. So to all those math majors out there, how long does one truly win at that rate? Is it just an instant? Or does it depend?