I have already introduced the Law of Anomalous Numbers, also known as Benford's Law. While using a Logarithmic price scale helps give perspective to the change in price over time, I have added additional lines equally spaced at each magnitude to further clarify price action.
I first split each magnitude in half by taking the square root of 10, which equals 3.16. Applied to financial markets Benford's Law suggests price should spend half the time between 1*10^x and 3.16*10^x and the other half of the time between 3.16*10^x and 1*10^(x+1), etc. Despite this representation, we are only concerned with the leading digit, so price does not have to spend an equal amount of time at each magnitude. The longer the period of time and orders of magnitude in price we measure, the greater the likelihood the leading digit will gravitate toward the power law distribution seen below. We should note that subsequent digits appear to follow this distribution as well but gravitate toward a uniform distribution the further away we measure from the leading digit. This is independent of the base number system used and can most easily be understood using a percent change perspective.
The probability of leading digits:
P(1) = 30.1%
P(2) = 17.6%
P(3) = 12.5%
P(4) = 9.7%
P(5) = 7.9%
P(6) = 6.7%
P(7) = 5.8%
P(8) = 5.1%
P(9) = 4.6%
Legend and how each number can be derived but arranged in numeric order:
sqrt(1.78) = 1.33 light blue
sqrt(3.16) = 1.78 purple
1.33*1.78 = 2.37 pink
sqrt(10) = 3.16 red
1.33*3.16 = 4.21 orange
1.78*3.16 = 5.62 dark green
2.37*3.16 = 7.50 light green
10 dark blue
Next order of midpoints in gray
I find it interesting how midpoints, midpoints of midpoints, etc., seem to consistently interact with price as support and resistance rather than just being an arbitrary number along a supposed random walk. If we continue to take midpoints of midpoints infinitely, we will naturally fill in every number. We then gather that the most significant number is 1 (across magnitudes), followed by its midpoint (3.16), followed by the midpoints of the midpoint (1.78 and 5.62), followed by the midpoints of midpoints (1.33, 2.37, 4.21, and 7.5), etc. Market pressures force price in one direction or another but seem to shift or alleviate around these and other midpoints until that pressure subsides or other pressures arise. These price levels are not the cause yet are interconnected with the effect as seen on this chart and others.
I first split each magnitude in half by taking the square root of 10, which equals 3.16. Applied to financial markets Benford's Law suggests price should spend half the time between 1*10^x and 3.16*10^x and the other half of the time between 3.16*10^x and 1*10^(x+1), etc. Despite this representation, we are only concerned with the leading digit, so price does not have to spend an equal amount of time at each magnitude. The longer the period of time and orders of magnitude in price we measure, the greater the likelihood the leading digit will gravitate toward the power law distribution seen below. We should note that subsequent digits appear to follow this distribution as well but gravitate toward a uniform distribution the further away we measure from the leading digit. This is independent of the base number system used and can most easily be understood using a percent change perspective.
The probability of leading digits:
P(1) = 30.1%
P(2) = 17.6%
P(3) = 12.5%
P(4) = 9.7%
P(5) = 7.9%
P(6) = 6.7%
P(7) = 5.8%
P(8) = 5.1%
P(9) = 4.6%
Legend and how each number can be derived but arranged in numeric order:
sqrt(1.78) = 1.33 light blue
sqrt(3.16) = 1.78 purple
1.33*1.78 = 2.37 pink
sqrt(10) = 3.16 red
1.33*3.16 = 4.21 orange
1.78*3.16 = 5.62 dark green
2.37*3.16 = 7.50 light green
10 dark blue
Next order of midpoints in gray
I find it interesting how midpoints, midpoints of midpoints, etc., seem to consistently interact with price as support and resistance rather than just being an arbitrary number along a supposed random walk. If we continue to take midpoints of midpoints infinitely, we will naturally fill in every number. We then gather that the most significant number is 1 (across magnitudes), followed by its midpoint (3.16), followed by the midpoints of the midpoint (1.78 and 5.62), followed by the midpoints of midpoints (1.33, 2.37, 4.21, and 7.5), etc. Market pressures force price in one direction or another but seem to shift or alleviate around these and other midpoints until that pressure subsides or other pressures arise. These price levels are not the cause yet are interconnected with the effect as seen on this chart and others.
