What is the Exponent?

The exponent is the slope of the line when we plot the power law on a log-log chart. It determines how strongly price scales as time increases. In our model, the exponent is approximately 5.65.

At any point in time, that line implies a price consistent with the scaling relationship at that moment. We refer to this as the implied price.

A stable exponent over history suggests structural consistency. The same slope, the same fingerprint, across years.

We are not claiming the number is fixed by fate. We are observing that, so far, the data has adhered closely to this pattern. When we examine the slope, we are asking whether that consistency remains intact.

But slope alone is not enough. We need to be able to measure if new data is drifting at all from this strongly maintained pattern.

So, how well does the data actually fit the line?