# Probability Histograms

Analyze probability distributions of multiple indicators and outcomes

## Background

When traders look at indicator values, they often times make assumptions on how high or low this value is. For example, one might assume that if the long% on Binance Global Long Accounts is 60%, then it is a high number. If another coin then has 75% of accounts that are net long, one might make the assumption that is an extremely high, but it could actually be an extremely *low* number, if majority of the time this indicator is 80% or higher. Similarly, if two coins have the same funding rate, can we classify this as high or low values?

Identifying extreme or outlier situations can be key to finding good opportunities in trading. The probability histograms displays the historical likelihood of the indicators value relative to all its historical values. Going back to the previous example with the Funding Rate. If the funding rate has been ranging between 0.05 to 0.1 for the last 6 months, then a value of 0.01 is actually a very low value *relative to historical values*. Similarly, if the funding rate instead fluctuated between -0.05 to -0.1 then 0.01 funding is a high value *relative to historical values*.

We break down the probability distribution (histogram) by keeping a count of the number of occurences at each unique value. The higher the height of the bar the more often it has occurred historically at that value and the lower the height of the bar, the less often it has occurred. If you want to answer how often is binance global long% (retail) at 55% or how often is funding below x% you can do that now.

## Tool Overview

The Probability Histogram tool currently supports 10 indicators and most Binance perpetual contracts. These histograms only require one input to filter on -- the name of the coin.

Coins supported: BTC, ETH, AAVE, ADA, ALGO, ATOM, BAL, BAND, BAT, BCH, BNB, BZRX, COMP, CRV, DASH, DEFI, DOGE, DOT, EOS, ETC, IOST, IOTA, KAVA, KNC, LINK, LTC, MKR, NEO, OMG, ONT, QTUM, RLC, SNX, SRM, SUSHI, SXP, THETA, TRB, TRX, VET, WAVES, XLM, XMR, XRP, XTZ, YFI, YFII, ZEC, ZIL, ZRX (support for

*all*FTX and Binance coins coming soon)Indicators distributions supported: Global Accounts (long %) , Top Traders Accounts (long %), Top Trader Positions (long %), Retail vs Whale, Funding Rate, Open Interest, Volume, Buy Volume, Sell Volume, Number of Trades

Historical frequencies are mentioned above each graph and the vertical dashed black line represents the most recent (current) value.

For example, In the image below, the historical frequency notation P(x<=63.37) = 79.255% can be read as: the likelihood of being lower than the current value is 79%, or in other words only 21% of all values have been higher 63.37.

It is important to understand not only how often the current value occurs but also the overall distribution of the indicator.

Here we can see the funding rate distribution of AAVE. The large bar implies that majority of the time, funding rate occurs at one point.

In addition, there is a higher likelihood for positive values to occur [B], than negative values [A], based on historical occurrences.

In the tabs above, there are five distributions, each representing a separate coin with a unique shape. Each distribution tells a different story about the pattern in retail longs.

*Distribution 1*: Majority of the time the percentage of accounts that are net long lies between 55% - 70%, there are a few rare instances where they are between 35% - 50%. This is known as left-skewed distribution (or negative skewness) where the "tail" is longer to the left.*Distribution 2*: Similar to distribution 1, this is also left skewed with a tail longer to the left. However, unlike distribution 1, this distribution has a more "normal" distribution with three peaks: 57% - 58%, 63% - 64%, and 66% - 67%.*Distribution 3*: In this distribution both extremes are relatively the same with peaks around 55% and 70%, representing something close to a bimodal distribution.*Distribution 4*: This is close to a normal distribution where both the mean and median would be close to each other. In addition, we can see that the majority of time, the long% lies in the center.*Distribution 5*: Finally, this distribution is very similar to distribution 3 which could imply that these coins move similarly.

## How do traders use this?

This tool can be used in a variety of ways from simple data exploration to advanced techniques like finding divergences.

### Identifying Divergences

For example, in the below chart for QTUMUST, the retail long% (top graph) is at 81.4% while the whale long% (third graph from top) is at 49.22%. While 49.22% might not seem like an extreme value, it is in fact an outlier.

Only 2.59% of the time has whale long% been lower – in other words, ~98% of the time whale long% is above the current value of 49.22%. Similarly, 81.4% retail long percentage is also a massive outlier. 99.719% of all historical values have been lower than the current long%. Clearly, whales are more short than they normally are while retail is more long than they normally are signaling a strong divergence. Generally traders view this is a bearish sign.

### Finding Confluence

In our next example (image below), we see how to use the probability histograms to find confluence. Retail long% is at 51% and while this on the lower side relative to all historical values, it is not an extreme outlier. However, Top Trader Positions (whales) are significantly more long than usual. In addition, the funding rate is at -0.0236 and by using the histogram we know this does not happen too often –- only 4.08% of the time has the funding rate been lower. Whales taking a heavier long position than usual and funding rate being lower than usual is generally a bullish sign as both signals are in confluence.

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