Trading Expectancy: Formula and Worked Example
Expectancy is the average outcome per trade in a defined sample. A win rate becomes meaningful only when the sizes of wins and losses are included.
Start with compatible units
Use currency outcomes or R multiples consistently. If one R represents the initial risk on each trade, a +2R result is twice that initial risk and a -1R result loses the initial risk amount. Do not combine an average win in currency with an average loss in R.
The simplest two-outcome formula assumes every observation is either a win or a loss. If flat trades are included, retain their share explicitly or calculate the mean directly from all net outcomes.
The formula
Expectancy = p × average win − (1 − p) × average loss
Here p is the win rate as a decimal, and average loss is entered as a positive magnitude. For a sample of 40 winners averaging +2R and 60 losers averaging -1R, p = 0.40. Expectancy is 0.40 × 2 − 0.60 × 1 = +0.20R per trade.
The same result follows from the full sample: (40 × 2R − 60 × 1R) / 100 = 0.20R. This is an illustrative arithmetic example, not TGSFX performance data.
Costs and break-even win rate
If the inputs exclude costs, deduct a cost-per-trade amount expressed in the same units. If the outcomes already include commission, spread and slippage, do not subtract those costs twice. With an additional cost of 0.10R per trade, the example becomes +0.10R.
For this two-outcome model, the break-even win rate is (average loss + cost) / (average win + average loss). Without extra costs, a 2R win and 1R loss require 1 / 3, or about 33.33%, to break even under those assumptions. A result above 100% means the assumptions cannot break even at any feasible win rate.
What the average does not show
The same average can arise from different sequences of outcomes. Expectancy alone does not show drawdown, losing streaks, concentration in one exceptional trade or sensitivity to different conditions. It is a description of the sample, not a guarantee of what happens next.
Try the expectancy calculator, then review drawdown and recovery and the statistics reference. Keep the sample definition in your journal.
Questions about this topic
Can a strategy with less than 50% wins have positive expectancy?
Yes in the arithmetic model. For example, a 40% win rate with an average 2R win and 1R loss produces +0.20R before any extra costs.
How should flat trades be counted?
Include all outcomes when calculating the mean, or model the flat-trade share explicitly. Do not silently assign flats to wins or losses.