What expectancy means, in a checkable model
Expectancy is a single-number way to describe the average result of a decision process per opportunity (for example, per trade, per signal, or per time the rule is applied). In its simplest form, expectancy treats each outcome as either a “win” or a “loss” and combines:
- Win rate (probability of a win)
- Average win size (how much you gain when you win)
- Loss rate (probability of a loss)
- Average loss size (how much you lose when you lose)
A common conceptual model is:
Expectancy = (Probability of win × Average win) + (Probability of loss × Average loss)
To make this model genuinely verifiable, the terms must be defined in the same way across your data and your calculation. “Win,” “loss,” “average win,” and “average loss” are not automatic facts; they come from your measurement rules (for example, whether partial exits count as wins, how you handle break-even outcomes, and whether you use gross or net results).
Dependencies: what expectancy requires to be comparable
1) Outcome definition: gross vs net
The expectancy formula is only as meaningful as the “outcome” it uses. If one dataset uses net results (after spreads, commissions, and financing) and another uses gross price movement, the expectancy numbers will not be comparable.
Even when you want a conceptual explanation (not real-time numbers), you should still assume a specific accounting choice. For example, you can define outcome as the net profit/loss per opportunity after estimated transaction costs and execution slippage. Then you must apply that same definition consistently.
2) The unit of analysis: per trade vs per opportunity
Expectancy can be computed per trade, per signal, or per bar/period if the rule is applied continuously. Changing the unit changes the interpretation. A process that sometimes stays flat will have different expectancy per “opportunity” than the same logic sampled only when it enters.
A checkable approach is to explicitly state the unit:
- “per submitted entry,” or
- “per completed trade,” or
- “per rule evaluation window,”
and then make the dataset match.
3) The probability model: what counts as “probability”
In practice, probability is estimated from historical samples. Expectancy formulas often treat win/loss as if each outcome is drawn from a stable distribution. That assumption can be reasonable over a narrow, consistent regime, and much less reasonable across multiple changing market conditions.
This creates an advanced dependency: expectancy is not just “a number,” it is an estimate tied to the distribution your sample represents.
4) Distribution shape: expectancy ignores higher moments
The win-rate/average-win/average-loss model reduces outcomes to two averages. If outcomes are highly skewed (for instance, many small wins and rare large losses), expectancy may look stable while risk characteristics change dramatically.
So an advanced consideration is to treat expectancy as one summary, not the full description of the outcome distribution.
Exceptions and edge cases that change the interpretation
1) Break-even trades and “zero” outcomes
What happens to trades with zero net result (neither win nor loss)? Some approaches fold them into wins, some into losses, and some treat them separately.
If you include them as neither win nor loss, you need a third category. If you force them into win or loss, you change average win/loss sizes and the implied probabilities. For independent verification, the method for break-even outcomes must be written down.
2) Asymmetric loss handling (e.g., stops vs exits)
If your evaluation includes different exit rules depending on conditions, then “average loss” is not a single universal value; it is the result of a conditional process. For example, a loss that occurs under one exit rule is not directly comparable to a loss that occurs under another.
To address this without financial advising, you can segment the dataset by exit type or by setup conditions, then compute expectancy per segment. The key is that mixing incompatible sub-processes can create misleading averages.
3) Non-stationarity: regime shifts
Markets can change in volatility, liquidity, and spread behavior. If your sample mixes multiple regimes, the win/loss probabilities and average outcomes can shift.
An advanced failure mode is “backtest expectancy looks good, forward expectancy degrades” because the estimated probabilities no longer match the future distribution. This is not a guarantee of failure—just a reminder that expectancy is sensitive to distribution changes.
4) Selection bias from filtering opportunities
If your dataset includes only opportunities that pass certain filters chosen after seeing results, expectancy can be inflated. Even without any specific recommendation, this is a general research risk: the evaluation process can unintentionally include knowledge about outcomes.
Independent verification should check whether the rule and its filters were defined before the outcome data, and whether the evaluation window is the same as the data scope used to estimate probabilities.
Evidence and example (using assumptions you can audit)
A simple numeric example with explicit assumptions
Assume you define an “opportunity” as one completed trade, and outcome is net profit/loss per trade after fixed costs. In a sample of 100 trades:
- You label 55 trades as wins and 45 trades as losses.
- Average net profit on winning trades is +0.8 units.
- Average net profit on losing trades is −0.6 units.
Then the expectancy per trade is:
- Probability of win = 55/100 = 0.55
- Probability of loss = 45/100 = 0.45
Expectancy = (0.55 × 0.8) + (0.45 × −0.6) = 0.44 − 0.27 = 0.17 units per trade
This illustrates how expectancy is computed from win/loss probabilities and conditional averages. It also shows where errors happen: if your win definition or your cost assumptions differ, the conditional averages and win/loss probabilities will change.
What to check when you reproduce someone else’s expectancy
To independently verify expectancy claims, check whether the author:
- states the win/loss definition (including break-even handling),
- specifies the unit of analysis (per trade vs per signal),
- states the cost model used for net outcomes, and
- uses the same data scope for estimating probabilities and averages.
Without those details, two expectancy values can be “mathematically similar” while being practically incomparable.
Limitations and risks: where expectancy can mislead
1) Sampling variability and small samples
Expectancy uses estimated probabilities and averages. With small sample sizes, random variation can dominate, producing an expectancy estimate that may not reflect the true underlying distribution.