## Summary

A “power law” is a relationship between two measurements where a change in one produces a relative change in another. The giveaway that you have found a power law is that the data produces a straight line when plotted on a chart. (Just as on the Bitcoin chart above.)

One example of a power law is the amount of energy an animal needs to live is proportionate to its weight – which produces that straight line on a chart.

Giovanni Santostasi is best known for popularising the charting of Bitcoin prices against their life in days, which shows that it follows the power law. This means we can use that chart to predict Bitcoin’s future prices.

The relative values this chart uses to produce a straight line are the mathematical log of price plotted against the log of its days in existence. The fact it’s the “log” of each measurement does not matter: the straight line does – it is all important.

## Uses of the chart

The power law chart allows the prediction of a price range for each year.

The green central line (see the chart above) is straight – showing that there is a “power law” – which is predictable. The exact position of this line is calculated using mathematical regression.

The upper purple line joins the price peaks from history. The lower red line, the troughs.

It’s fair to guess that future peaks and troughs will come close to the purple and red lines.

### Estimating ranges for certain years

(See the chart below)

The range for 2024 is shown by the chart to be ~ £20,000 – £212,000.

The range for 2025 is shown to be ~£29,000 – £307,000. (My next expected peak.)

The range for 2029 – my following expected peak – is £103,000 – £920,000.

I like these forecasts. The “power law” chart has a simplicity to it which it’s hard to argue against: a straight line is a straight line. And the price has definitely followed the trend of that line for 13 years so far.

## Will this predict the highs and lows?

This chart version places the price prediction based on the power law at a midpoint, then uses mathematical “regression” to add a band above and one below. These outer bands contain over 95% of all Bitcoin price points. We can likely use these bands to predict future highs and lows with a fair-to-good degree of confidence.

## Sources

A great interview of Giovanni Santostasi by Fred Krueger (mathematician and former shares and bonds trader).