=== How does an **AVERAGE CANDLESTICK** look like? ===

Have you ever asked how an **average** candlestick does look like? How is the “normal” ratio of the upper or lower wicks to the candle’s range? Is it like 10 % wicks on both sides (on average)? Or 40 %?

Since the former discussion was more or less about the randomness of the markets (which wasn’t my original intention of my 2nd post), I’d like to show how you may arrive a conclusion in regards to the average candlestick structure. I think the morphology of candlesticks may be explained by random walks …

It all starts with a one-dimensional Gaussian random walk that we want to consider … This random walk starts at an arbitrarily chosen origin, the open prize of your candlestick. Now prize can go either up or down, whereas the probability of the increments (the number of ticks the prize changes) is determined by a normal distribution. We let the experiment run for 1 minutes, 5 minutes, 1 hour, 1 day, or whatever time interval your candlestick should represent. After one run we repeat the experiment again and again and again … After (let’s say 10,000) repetitions we can calculate the proportion of the upper and lower wick for each and every run, and we can calculate the average proportion.

Fortunately, we don’t even have to model it. Stochastics gives us two important formula:

- The average walking distance reached after N steps i calculated as sqrt(2 * N/pi).
- The expected maximal distance reached in a walk with N steps is calculated as sqrt(N * pi/2).

We could chose any value for N to solve both formulas or we can set N = 1. Then we derive sqrt(2/pi) and sqrt(pi/2).

Now let’s assume that our random walk ends above our starting point (the candlestick is a bullish candlestick). Thus, we would expect the close prize to be sqrt(2/p) above the open:

- open = 0
- close = sqrt(2/pi) = 0.7978846

In this case the expected maximal distance reached in our random walk represents the high prize,

- high = sqrt(pi/2) = 1.253314

Now we only need to calculate the expected average low. It can be derived by subtracting the high prize from the close value (assuming that instead of a bullish candle starting at the open we see a bearish candlestick starting with the close of the bullish candlestick):

- low = close – high = -0.4554294

With these numbers you can calculate the expected average candlestick ratios, i.e.

- wicks/total candlestick range = 0.4554294/1.708743 = 0.2665289
- body/total candlestick range = 0.7978846/1.708743 = 0.4669424

Thus, the ratio we may expect to see **on average** is close to 1/4 : 1/2 : 1/4.

Now you may think “so what, this is just fucking theory!” Yes, it is. However, the true mean proportions of the wicks and the body are very close to the numbers we calculated above. You can compare the numbers given here with the empirical values calculated elsewhere by jimsterk.

But remember – these are just the numbers you will see if you calculate the mean over a big number of candles. If you just look at a small sample the numbers can deviate much. **But what does the deviation of a current candlesticks form may tell you about the strength of bulls and bears during the lifetime of that candlestick?** Maybe you could use this info in order to determine if a trend that you see is stronger than you would expect it on average (cf. image below). Just more food for thoughts …