Get started

Benfordslaw

Benford's Law Applied to the S&P 500 (SPX)As I have shown in previous posts for other assets, these are the expected price levels explained as midpoints adhering to Benford's Law, also known as the Law of Anomalous Numbers. Even though these gridlines shown are not always the price level of a reversal, we see that oftentimes these midpoints do in fact act as support or resistance, and the midpoints not shown between the midpoints shown also act as relevant price levels. The probability of leading digits according to Benford's Law: 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: 1.33 light blue 1.78 purple 2.37 pink 3.16 red 4.21 orange 5.62 dark green 7.50 light green 10 dark blue Next order of midpoints in gray For a more complete explanation to this methodology, check out the links below.
SP:SPX
by UbiquitousAngles
Benford's Law Applied To GoldGold is another asset that I follow and am not surprised to see it adhere to the principle of midpoints as explained by Benford's Law, also known as the Law of Anomalous Numbers. These gridlines I've drawn are midpoints and viewed on a logarithmic chart in order to more easily compare rates of change across magnitudes of price over a long period time. I have explained the rationale in previous posts, which you can view in the links below. The probability of leading digits according to Benford's Law: 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: 1.33 light blue 1.78 purple 2.37 pink 3.16 red 4.21 orange 5.62 dark green 7.50 light green 10 dark blue Next order of midpoints in gray
TVC:GOLD
by UbiquitousAngles
Benford's Law Applied to BitcoinContinuing the series as we consider the validity of this approach, here are the midpoints across magnitudes for Bitcoin. For more information regarding the origin of this analysis please refer to previous posts linked below. Benford's Law, also known as the Law of Anomalous Numbers, describes the tendency of the leading digit of an unrestricted collection of data to conform to a power law distribution as seen below. This natural law is the underlying basis for using logarithmic price charts in order to view rate of change over time. By taking midpoints, I am simply adding gridlines to the chart, but have found it interesting how these and other midpoints act as support or resistance time and time again. 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: 1.33 light blue 1.78 purple 2.37 pink 3.16 red 4.21 orange 5.62 dark green 7.50 light green 10 dark blue Next order of midpoints in gray I couldn't keep the next order of midpoints for the entire price history since tradingview only allows so many lines of pinescript code. You should still notice how minor and major highs and lows occur at these midpoints shown and additional midpoints not shown. As we'll see when looking at other assets, I've become convinced that this approach of viewing price over time should be included when forecasting potential minor and major highs and lows.
BNC:BLX
by UbiquitousAngles
Benford's Law Applied to Nano (XNO)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.
by UbiquitousAngles
1
Benford's Law (The Law of Anomalous Numbers)In a previous post we discussed the significance of price levels. Prior highs and lows are often revisited, sometimes more than once and act as resistance and support. Like a magnet these major and minor highs and lows appear to attract and repel price over time. With this information we drew trendlines creating channels in order to anticipate future price levels. To view a growing price chart over a long period of time is impractical using an Arithmetic scale for price. For the most part, all analysis is done using a Logarithmic scale instead. This allows us to view the percent change uniformly. To understand the drawback of an arithmetic chart, consider how it may look for prices to change from 2 to 10 then 10 to 50. The move from 2 to 10 is only a difference of 8 units, whereas, 10 to 50 is 40 units. The percent change is the same, as is the rate of change assuming the same amount of time eclipsed. Logarithmic charts allow for a better gauge on momentum, but our understanding of numbers as they relate to each other may still be incorrect. The Law of Anomalous Numbers or Benford's Law states that given a data set that does not have built in constraints or parameters to influence the output of data, the leading digit will follow a power law distribution. The larger the data set and orders of magnitude covered, the greater the conformity to this distribution. We may have assumed that the most likely outcome of leading digits in a data set would be uniform, but this would be incorrect.  As a percentage the expected distribution of leading digits using numbers in base 10 is as follows: 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% It should be noted that the shape of this distribution holds regardless of the base of the number system used. Using base 10, the median leading digit of the distribution is 3.16. This means that half of all data points should fall between 1.00 and 3.16 while the other half fall between 3.16 and 9.99. Without this understanding, we might have otherwise expected 5.5 to be the median leading digit as in the case of a uniform distribution. The chart above shows equal spacing between price levels on a logarithmic chart. They can be found by taking the square root of 10 (= 3.16), then taking the square root of 3.16 (= 1.78) then cubing 1.78 (= 5.62). Midpoints play a significant role in my analysis and is the basis for using these numbers. 1.0 black 1.78 light blue 3.16 red 5.62 dark blue This organizes the expected distribution into quarters. Over time the actual distribution of leading digits observed should gravitate towards the distribution of Benford's Law. While I have had my doubts about the validity of using these numbers as price levels, I couldn't keep this to myself given its apparent relevance.
BNC:BLX
by UbiquitousAngles
1
Benford's LawAbout As seen in "Digits", the fourth episode of the Netflix series Connected , Benford's Law is applicable to almost every data set that is said to be randomly occurring such as the global financial markets. The law is most frequently used for surveillance and detection of fraud, money laundering, and manipulation of data. Auditors world-wide have studied and are aware of the phenomenal application of this law and it's magic-like capability to detect accounting, legal, election, or scientific fraud. Now, Benford's Law can be utilised by anyone and observed across any financial data-set. Apply this to prices, financial data, or health statistics on TradingView! Future releases of this indicator will be fully equipped with time-specific windows to apply Benford's Law and identify price manipulation. Additionally, tick boxes are available in the settings window to see the data and view each leading digit! Benford's Law This is a classical use of the famous Benford's Law. Also called the "Law of Anomalous Numbers" , "First Digit Law", or the "First Digit Phenomenon", Newcomb–Benford law states that in many naturally occurring data sets, the leading digit is more likely to be a low number, despite probabilistic reasoning that each leading digit between 1 and 9 should be uniformly distributed at 11.1%. For example, in data sets that obey the law, the leading number of 1 occurs approximately 30.1% of the time while the leading digit of 9 occurs only 5% of the time. The mind-blowing distribution of Benford's Law is as follows. Leading Digit --------- Occurrence 1 -------------------------- 30.1% 2 -------------------------- 17.6% 3 -------------------------- 12.5% 4 -------------------------- 9.7% 5 -------------------------- 7.9% 6 -------------------------- 6.7% 7 -------------------------- 5.8% 8 -------------------------- 5.1% 9 -------------------------- 4.6%
COINBASE:BTCUSD
by GrantPeace
8