Betting Profitably: Why Winning Probability Alone Is Not Enough

August 30, 2017 (7y ago)

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The Pursuit of Perfection

80 Percent Probability of Winning: Every person strives for perfection. The hair is not in place, the shirt is not perfectly ironed, and the surprise party did not go as "perfectly" as one had imagined. Different characters have different notions of what perfection looks like. Some people do not care if their shirt is not perfectly ironed, while others would not go out on the street looking like that. It is the personal expectations and demands placed on oneself that shape the pursuit of perfection in different areas of life and everyday life. External influences have been shaping us since we first saw the light of day. This includes, among other things, upbringing, personal experiences that have led to joy and pain, as well as social norms and role models.

False Perfectionism in Trading

Perfection in trading is one of the biggest hurdles you have to overcome to go from unprofitable to profitable trader. If I try to perfect my trading more and more, I will inevitably have to realize that I achieve exactly the opposite of what my goal was. It is only about following your tested plan. This can be called "perfect" in terms of successful trading. I focus solely on my actions and not on their results, which can only be viewed in the long term in trading. So my focus is clearly on the continuous improvement of processes - not on the possible result. The result improves automatically when the process is improved.

Probability of Winning vs. Profitability - The Difference

The idea of needing the highest possible probability of winning to be profitable is a symbiosis of false perfectionism and ignorance. Many supposed trading mentors advertise high winning probabilities so that they can sell their profitable strategies more frequently. Stop: Did I say profitable?

Exactly this is the crucial point. A high probability of winning does not mean that the strategy is profitable. It means that the probability of winning a trade is 80%, but we entirely ignore how much we win and lose on average. This is where the so-called profit factor comes into play. A real measure of whether a strategy is really profitable or not!

The profit factor is an indication of whether a particular investment was worthwhile or not. It puts the earned capital (profit) in relation to the invested capital. The result of the profit factor indicates how many monetary units we have received per invested monetary unit through the investment. In the economy, the factor is better known as Return on Investment (ROI) and also serves as an evaluation basis there whether an investment was sensible and correct and whether it has met expectations.

Calculation of the Profit Factor

The profit factor is calculated from two components together: the probability of winning and the risk-reward ratio (CRV). The probability of winning - or also known as the hit rate - is the ratio between the absolute number of winning trades and the absolute number of losing trades. The risk-reward ratio describes the ratio between the height of your average winnings and the height of your average losers. This results in the following formula:

Profit factor = (number of winners / number of losers) x (average height of winnings / average height of losers)

If the profit factor is equal to 1, this means that you invest 1 euro in a trade and get 1 euro back. You haven't won or lost. If your profit factor is less than 1, you get back less than what you invested. This would mean that this system would not be profitable. If the calculation results in a value greater than 1, this means that we get more than we invested. So we make a profit. Our strategy would thus be profitable.

Example 1: Winning Probability of 80%

Let's assume in the first example that we win in 80% of cases, but our average winning trades are smaller than our average losing trades. When inserted into the formula, this results in the following calculation:

Profit factor 
= (number of winners / number of losers) x (average height of winnings / average height of losers)
= (80 / 20) x (6 / 10)
= 2.4

This example calculation results in a profit factor of 2.4. This means that for every euro invested, we earn 2.40 EUR as profit. Our strategy would be profitable in this case.

Example 2: Winning Probability of 45%

In another example, the probability of winning is significantly lower at only 45%. At the same time, the CRV increases dramatically to 2.93. Ultimately, this means that we win less frequently overall, but when we do win, the winners are significantly larger than our losers. If we plug these values into the formula

Profit factor 
= (number of winners / number of losers) x (average height of winnings / average height of losers)
= (45 / 55) x (29.30 / 10)
= 2.4

Even though the second example had a significantly lower probability of winning than the first example, the profit factor was the same for both examples, i.e. 2.4. This indicates that the probability of winning alone is not a reliable indicator of profitability. A high probability of winning can be achieved by having small winning trades and large losing trades, which is not profitable. Therefore, it is important to focus on the profit factor for a reliable assessment of profitability.

Conclusion

The pursuit of perfection in trading can lead to false perfectionism and ignorance, which can result in unprofitable trading strategies. The probability of winning alone is not a reliable indicator of profitability, as the profit factor considers the ratio of winnings to losses. Therefore, traders should focus on continuously improving their processes and strategies, which will ultimately lead to profitability.

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