The Math of Trading
Post By: Renzo Bazargani
As a follow-up to the key topics on trading, this post will focus on the importance of understanding the math and statistics behind your trading results—specifically, whether your strategy is truly profitable. Previously, I discussed the importance of having the right mindset for trading, emphasizing that without it, success is unlikely. In my post, “The Psychology of Trading,” I outlined specific actions required to develop the right mindset. If you haven’t read it yet, you can click here to check it out. I also wrote a checklist-style post, “The Evolution of a Trader,” which highlights the perseverance, years of practice, and sacrifices required to become a profitable trader. You can click here to read that post as well.
In trading, measuring performance and analyzing the statistical outcomes of your strategy are crucial for continuous improvement. And there is always room for improvement. That’s why it’s essential to track your trading statistics on a weekly basis. At a minimum, you should know your win rate, loss rate, average win, and average loss. Below, I’ve provided the key equations you need to calculate these metrics, along with real examples of trading results:
- Expectancy is calculated by the formula:
Expectancy = (Win% x Avg Win) – (Loss% x Avg Loss)
(Trading expectancy is a calculation that shows what the typical profit is for each trade placed)
* A positive value (above zero) indicates that the trading system is profitable
* A negative value (below zero) indicates that the trading system is not profitable
- Profit Factor is calculated by the formula:
Profit Factor = (Win% x Avg Win) / (Loss% x Avg Loss)
* A value above 1 indicates that the trading system is profitable
* A value below 1 indicates that the trading system is not profitable
Example 1. (Emini S&P500)
24 Trades in 5 days (1 contract)
13 Win and 11 Loss
Win Rate: 13 / 24 *100 = 54%
Loss Rate: 46%
Now, 13 Win totaled 47 pts and 11 Loss totaled 22 pts
So, Avg Win: 47 / 13 = 3.6 pts and Avg Loss: 22 / 11 = 2 pts
Expectancy: (0.54 x 3.6) - (0.46 x 2) = 1.02
Profit Factor: (0.54 x 3.6) / (0.46 x 2) = 2.11
Example 2. (Emini S&P500)
76 Trades in 15 days (multiple contracts)
60 Win and 16 Loss
Win Rate: 79%
Loss Rate: 21%
Now, 60 Win totaled $31,240 and 16 Loss totaled $14,462
So, Avg Win = $521 and Avg Loss = $904
Expectancy: (0.79 x 521) - (0.21 x 904) = 221.75
Profit Factor: (0.79 x 521) / (0.21 x 904) = 2.17
(NOTE: In this example the Avg Loss was bigger than the Avg Win, but since the Win Rate was much bigger than the Loss Rate, then the strategy was very profitable)
Example 3. (Stocks)
62 Trades in 1 year
27 Win and 35 Loss
Win Rate: 44%
Loss Rate: 56%
Avg Win = 19.4%
Avg Loss = 5.8%
Expectancy: (44 x 19.4) - (56 x 5.8) = 529
Profit Factor: (44 x 19.4) / (56 x 5.8) = 2.63
(NOTE: In this example, the Win Rate was lower than the Loss Rate, but since the Avg Win was over 3 times bigger than the Avg Loss, then the strategy was very profitable)
In conclusion, it is best to have a system or methodology with the Avg Win at least 1.5 times bigger than the Avg Loss, as well as having a higher Win Rate, let’s say around +/- 60%.