## Blog / The impact of statistics for Fibonacci target play

### The impact of statistics for Fibonacci target play

The Fibonacci series play a very important role in the nature.

Most charting packages come with some kind of Fibonacci tool.

Probably the most popular tool is Fibonacci extension and Fibonacci retracement.

Most often we just draw those lines and while the asset, in question approaches those lines, we focus more on the present behavior to assist our trading.

The main issue in question is that for the market, we are playing, we usually do not have Fibonacci–related statistics for different market type and time frame we are playing.

What a great stat would be, if we would have a set of numbers to guide our decision making process.

One example is the following:

To make life simple we assume, that all of the Fibonacci retracements fall into the following four levels:

1. Fibo1: 23.6 %

2. Fibo2: 38.2 %

3. Fibo3: 50.0 %

4. Fibo4: 61.8%

So no Fibonacci retracements occur, that reach 100%.

Our question would be: How to play the game, how to position ourselves if we would like to maximize the total profit level, and we have statistics available about the probabilities, that within the specific market, specific time–frame, those retracements reach those levels with available probabilities.

So we would position ourselves that we would play a maximum of four positions, with a total of 100% of our trading size, and we would apply those trades at the Fibo1, Fibo2, Fibo3, Fibo4 levels.

The number of actual positions could be 1 to 4, and the size of those positions would be dependent on the probability, that a retracement reach a certain level in our market.

I created a simple application, which accepts the four parameters, as the probability numbers that the asset would reach the defined Fibonacci levels.

The output of the calculation is a hypothetical entropy function, which has four variables, and each variable tell us what should be the position size, that we should apply at certain Fibonacci levels to maximize the total profit, playing the market.

So basically we are looking for the maximum of a four parameter function, depending on position size. The total size of the four positions would be 100%.

Playing with the application, and plugging in different probabilities, we got:

Example1:

The probability, that the retracement reach Fibo1: 86%

The probability, that the retracement reach Fibo2: 53%

The probability, that the retracement reach Fibo3: 43%

The probability, that the retracement reach Fibo4: 34%

With these numbers we got the following:

To maximize the Total profit levels over long time period, we can play this in a way, that we have only two positions, and 70 – 100% played at the Fibo3 level, and 0 – 30% of the total size played at the Fibo4 level.

Example2:

The probability, that the retracement reach Fibo1: 71%

The probability, that the retracement reach Fibo2: 48%

The probability, that the retracement reach Fibo3: 38%

The probability, that the retracement reach Fibo4: 27%

With these numbers we got the following:

To maximize the Total profit levels over long time period, we can play this in a way, that we have only two positions, and 0 – 30% played at the Fibo2 level, and 70 – 100% of the total size played at the Fibo3 level.

Example3:

The probability, that the retracement reach Fibo1: 77%

The probability, that the retracement reach Fibo2: 64%

The probability, that the retracement reach Fibo3: 44%

The probability, that the retracement reach Fibo4: 28%

With these numbers we got the following:

To maximize the Total profit levels over long time period, we can play this in a way, that we have only two positions, and 75 – 100% played at the Fibo2 level, and 0 – 25% of the total size played at the Fibo3 level.

Example4:

The probability, that the retracement reach Fibo1: 84%

The probability, that the retracement reach Fibo2: 59%

The probability, that the retracement reach Fibo3: 34%

The probability, that the retracement reach Fibo4: 22%

With these numbers we got the following:

To maximize the Total profit levels over long time period, we can play this in a way, that we have only two positions, and 0 – 30 % played at the Fibo1 level, and 70 – 100% of the total size played at the Fibo2 level.

Most of the time we could (almost) maximize returns having only two positions.

All this is just for demonstration purposes, The actual probabilities and with it the final results might be completely different.

The message of this is that having some Fibonacci-related statistics can help us guiding our decision making and can drive to better overall results.

Slippage and commissions not taken into account in this example having multiple positions.