Trading as a Probabilistic ProcessTrading as a Probabilistic Process
As mentioned in the previous post , involvement in the market occurs for a wide range of reasons, which creates structural disorder. As a result, trading must be approached with the understanding that outcomes are variable. While a setup may reach a predefined target, it may also result in partial continuation, overextension, no follow-through, or immediate reversal. We trade based on known variables and informed expectations, but the outcome may still fall outside them.
Therefore each individual trade should be viewed as a random outcome. A valid setup could lose; an invalid one could win. It is possible to follow every rule and still take a loss. It is equally possible to break all rules and still see profits. These inconsistencies can cluster into streaks, several wins or losses in a row, without indicating anything about the applied system.
To navigate this, traders should think in terms of sample size. A single trade provides limited insight, relevant information only emerges over a sequence of outcomes. Probabilistic trading means acting on repeatable conditions that show positive expectancy over time, while accepting that the result of any individual trade is unknowable.
Expected Value
Expected value is a formula to measure the long-term performance of a trading system. It represents the average outcome per trade over time, factoring in both wins and losses:
Expected Value = (Win Rate × Average Win) – (Loss Rate × Average Loss)
This principle can be demonstrated through simulation. A basic system with a 50% win rate and a 1.1 to 1 reward-to-risk ratio was tested over 500 trades across 20 independent runs. Each run began with a $50,000 account and applied a fixed risk of $1000 per trade. The setup, rules, and parameters remained identical throughout; the only difference was the random sequence in which wins and losses occurred.
While most runs clustered around a profitable outcome consistent with the positive expected value, several outliers demonstrated the impact of sequencing. When 250 trades had been done, one account was up more than 60% while another was down nearly 40%. In one run, the account more than doubled by the end of the 500 trades. In another, it failed to generate any meaningful profit across the entire sequence. These differences occurred not because of flaws in the system, but because of randomness in the order of outcomes.
These are known as Monte Carlo simulations, a method used to estimate possible outcomes of a system by repeatedly running it through randomized sequences. The technique is applied in many fields to model uncertainty and variation. In trading, it can be used to observe how a strategy performs across different sequences of wins and losses, helping to understand the range of outcomes that may result from probability.
Trading System Variations
Two different strategies can produce the same expected value, even if they operate on different terms. This is not a theoretical point, but a practical one that influences what kind of outcomes can be expected.
For example, System A operates with a high win rate and a lower reward-to-risk ratio. It wins 70% of the time with a 0.5 R, while System B takes the opposite approach and wins 30% of the time with a 2.5 R. If the applied risk is $1,000, the following results appear:
System A = (0.70 × 500) − (0.30 × 1,000) = 350 − 300 = $50
System B = (0.30 × 2,500) − (0.70 × 1,000) = 750 − 700 = $50
Both systems average a profit of $50 per trade, yet they are very different to trade and experience. Both are valid approaches if applied consistently. What matters is not the math alone, but whether the method can be executed consistently across the full range of outcomes.
Let’s look a bit closer into the simulations and practical implications.
The simulation above shows the higher winrate, lower reward system with an initial $100,000 balance, which made 50 independent runs of 1000 trades each. It produced an average final balance of $134,225. In terms of variance, the lowest final balance reached $99,500 while the best performer $164,000. Drawdowns remained modest, with an average of 7.67%, and only 5% of the runs ended below the initial $100,000 balance. This approach delivers more frequent rewards and a smoother equity curve, but requires strict control in terms of loss size.
The simulation above shows the lower winrate, higher reward system with an initial $100,000 balance, which made 50 independent runs of 1000 trades each. It produced an average final balance of $132,175. The variance was wider, where some run ended near $86,500 and another moved past $175,000. The drawdowns were deeper and more volatile, with an average of 21%, with the worst at 45%. This approach encounters more frequent losses but has infrequent winners that provide the performance required. This approach requires patience and mental resilience to handle frequent losses.
Practical Implications and Risk
While these simulations are static and simplified compared to real-world trading, the principle remains applicable. These results reinforce the idea that trading outcomes must be viewed probabilistically. A reasonable system can produce a wide range of results in the short term. Without sufficient sample size and risk control, even a valid approach may fail to perform. The purpose is not to predict the outcome of one trade, but to manage risk in a way that allows the account to endure variance and let statistical edge develop over time.
This randomness cannot be eliminated, but the impact can be controlled from position sizing. In case the size is too large, even a profitable system can be wiped out during an unfavorable sequence. This consideration is critical to survive long enough for the edge to express itself.
This is also the reason to remain detached from individual trades. When a trade is invalidated or risk has been exceeded, it should be treated as complete. Each outcome is part of a larger sample. Performance can only be evaluated through cumulative data, not individual trades.
