Why is the expected value considered the secret to a winning trader?

In the trading market, most people focus on how much profit a single trade can generate, but the real winners are fixated on one number — expected value. This concept may sound complex, but it determines whether you will profit in the long run or be destined to incur losses. “Positive expected value” is the ladder that pulls you out of the pit of losses.

What is expected value and how to determine “positive EV”

Mathematical expected value (Expected Value, abbreviated as EV) is a core concept in probability theory, essentially the weighted average of all possible outcomes. For example, in a “coin toss,” if heads wins $1 and tails loses $1 (with each having a 50% probability), the expected value is 0, which is fair; but if heads wins $2 and tails loses $1, the expected value becomes $0.5, which is “positive EV” — you have an advantage.

In trading, the calculation of expected value is much simpler:

Expected value of a single trade = (win rate × average profit) - (loss rate × average loss)

For instance, if your trading strategy has a win rate of 55%, with an average profit of $100 and an average loss of $90, then the expected value is (55% × 100) - (45% × 90) = 55 - 40.5 = $14.5. This means you can expect to earn an average of $14.5 per trade.

This is the definition of “positive EV”: an expected value greater than 0 means that from a probabilistic perspective, you have an edge. As long as this advantage exists consistently, repeated trading will inevitably lead to profits.

Three common pitfalls regarding expected value

Many people easily fall into traps when understanding expected value. Firstly, expected value ≠ “most likely outcome.” For example, the expected value of rolling a die is 3.5, but you can never roll a 3.5; similarly, if the expected net gain of a lottery is -$8, it doesn’t mean you will lose $8 every time; there is still a very small chance of hitting the jackpot. Expected value is a long-term average, not a guarantee for a single instance.

Secondly, “positive EV does not equal single trade profit.” Even if you find a strategy with a positive expected value, you may still incur losses in the short term. The market is filled with randomness, and before that randomness becomes clear, you may incur several losses in a row. This is why “long-term repetition” is so important — only by executing enough trades can random fluctuations be smoothed out, allowing the expected value to show its power.

Finally, a high expected value does not necessarily mean you can make a lot of money. You also need to manage risk. A strategy with a positive expected value but a high single trade loss could lead to a margin call during a “black swan” event. Therefore, true trading winners not only look at expected value but also consider the risk-reward ratio and risk management.

Why positive EV is the cornerstone of trading success

Once you understand the logic of expected value, you realize a harsh truth: if your trading strategy has a negative expected value, no matter how diligent or smart you are, you will only incur losses in the long run. Even if you make a profit in a certain month, it is merely luck, and sooner or later it will be offset by losses.

Conversely, traders who adhere to positive EV strategies have a significant advantage — time is on their side. Each trade compounds growth, and while there are short-term fluctuations, as long as the sample size is large enough, the probability of losses approaches 0. This also explains why institutional traders and quantitative traders place so much importance on expected value; they understand that positive expected value is the only guarantee of long-term profit.

Finding a positive EV strategy is just the beginning; the real challenge is sticking to it. The market may present you with the illusion of short-term losses, testing your confidence. But as long as your logic is sound and the expected value remains consistently positive, what you need to do is repeat trading and accumulate samples, letting mathematics help you earn money.