# January 6, 2023

## Z-score

The Z-score is a statistical measure that represents the number of standard deviations a data point is from the mean of a dataset. It is used to identify outliers in the data and to assess the statistical significance of results. To calculate the Z-score, you need to know the mean and standard deviation of the dataset. Here is the formula for calculating the Z-score:

Z-score = (X – Mean) / Standard Deviation

Where X is the value of the data point, Mean is the mean of the dataset, and Standard Deviation is the standard deviation of the dataset.

For example, let’s say you have a dataset with a mean of 100 and a standard deviation of 10, and you want to calculate the Z-score for a data point with a value of 120. The Z-score would be calculated as follows:

Z-score = (120 – 100) / 10 = 2

This means that the data point with a value of 120 is 2 standard deviations above the mean of the dataset.

The Z-score can be used to identify outliers in the data by setting a threshold for the number of standard deviations a data point must be above or below the mean to be considered an outlier. For example, a data point with a Z-score of 3 or greater might be considered an outlier. The Z-score can also be used to assess the statistical significance of results by comparing the Z-score to a critical value from a standard normal distribution table. If the Z-score is greater than the critical value, the result is statistically significant.

## Profit factor

To calculate the profit factor, you need to first calculate the total profit and total loss from your trades. You can then calculate the profit factor by dividing the total profit by the total loss.

For example, let’s say you made a total of 10 trades and had a total profit of \$500 and a total loss of \$300. The profit factor would be calculated as follows:

Profit Factor = Total Profit / Total Loss
= \$500 / \$300
= 1.67

This means that for every \$1 you lose, you make \$1.67 in profit. A profit factor greater than 1 indicates that you are making more profit than loss, while a profit factor less than 1 indicates that you are incurring more loss than profit.

It’s important to note that the profit factor is a useful metric, but it doesn’t tell the whole story. It can be influenced by the size of your wins and losses, and it doesn’t take into account the number of trades you make or the risk you take on. As such, it should be used in conjunction with other metrics to get a more complete picture of your trading performance.

There is no specific profit factor number that is considered “good” or “bad,” as this can vary depending on the specific trading strategy and market conditions. In general, a profit factor of 2 or higher is often considered to be good, while a profit factor below 1 indicates that you are incurring more loss than profit. However, these are just rough guidelines and may not be applicable in all cases.

For example, consider a trader who trades a very conservative strategy with a low profit factor of 1.2. This trader may be content with this profit factor if it allows them to consistently make small profits with a low risk of loss. On the other hand, a trader who takes on more risk and trades a more aggressive strategy may be able to achieve a higher profit factor, but also may be more susceptible to larger losses.

## R expectancy

The R expectancy (or expected value of R) is a measure of the expected return of a trading system or strategy. It is calculated by multiplying the probability of a trade being successful by the potential profit of the trade, and then summing these values for all trades in the system or strategy. Here is the formula for calculating the R expectancy:

R Expectancy = Σ (Probability of Success * Potential Profit)

Where Σ represents the sum of the values, Probability of Success is the likelihood that a trade will be successful, and Potential Profit is the potential profit of the trade.

To calculate the R expectancy, you will need to gather data on the probability of success and potential profit for each trade in the system or strategy. You can then use this data to calculate the R expectancy using the formula above.

The R expectancy is a useful tool for evaluating the expected performance of a trading system or strategy and for comparing the expected returns of different systems or strategies. It can help traders to identify systems or strategies with a higher expected return and to make informed decisions about the level of risk they are willing to take in order to achieve those returns.

Example 1:

Trade 1: Probability of Success = 60%, Potential Profit = \$100
Trade 2: Probability of Success = 40%, Potential Profit = \$200
Trade 3: Probability of Success = 50%, Potential Profit = \$300

To calculate the R expectancy for this system, you would sum the products of the probability of success and potential profit for each trade:

R Expectancy = (0.60 \$100) + (0.40 \$200) + (0.50 * \$300) = \$180

This means that the expected return of the trading system is \$180.

Example 2:

Trade 1: Probability of Success = 70%, Potential Profit = \$500
Trade 2: Probability of Success = 30%, Potential Profit = \$1000
Trade 3: Probability of Success = 80%, Potential Profit = \$2000
Trade 4: Probability of Success = 40%, Potential Profit = \$3000

To calculate the R expectancy for this strategy, you would sum the products of the probability of success and potential profit for each trade:

R Expectancy = (0.70 \$500) + (0.30 \$1000) + (0.80 \$2000) + (0.40 \$3000) = \$2300

This means that the expected return of the trading strategy is \$2300.

I hope these examples help to illustrate how the R expectancy can be calculated for a trading system or strategy. Let me know if you have any questions or need further clarification.