I also think it's worth noting that if we start talking about winrate, then we're in weird waters.

The problem I have is that it seems to me that simply defining your winrate as your BR/hands makes for a poor estimation. I mean... when we're rolled for 20 - 50 BI, a swing of 4 BI is a significant portion of our total BR. Our estimated winrate would swing all over the place, based on randomness playing out as wins and losses. It ignores the path to the final result.

A more stable estimation of winrate would be to look at a plot of BR vs hands and perform a linear regression on the data. The linear regression yields the straight line which minimizes the variance from the line. Note that it minimizes the variance in the vertical direction, and not perpendicular to the line, which I always have to think real hard to see. This is called a "best fit line" or a "trend line."

The slope of that line would be the best mathematical prediction of winrate.

In performing the linear regression, we have access to more stats - this time more directly about the winrate.

We can calculate the variance in the slope, which would be the variance in our estimation of our winrate.

I think that the variance in the slope could only converge on 0 if our "true" winrate was constant over all time and the overall skill of our opponents was the same. Otherwise... the variance in the slope will reflect those subtle, long-term changes.