Trading Expectancy & Kelly Criterion: Size for Growth

The Only Honest Measure of a Strategy

Every trading strategy can be summarised by three numbers: its win rate, its average win size, and its average loss size. These three numbers determine whether the strategy earns money over time, and by how much. Their combination is called expectancy — the average profit or loss per unit risked per trade. A strategy with positive expectancy earns money. A strategy with zero or negative expectancy loses it. No amount of discipline, pattern recognition, or market intuition changes this arithmetic.

Expectancy is not a prediction for any single trade. Any single trade can win or lose regardless of expectancy. It is a statement about what happens over many repetitions. A strategy with +0.30R expectancy earns thirty cents for every dollar risked when measured across enough trades. Fifty trades of $100 risk each generates an expected $1,500 profit. The power of expectancy is that it converts uncertain individual trades into a reliable aggregate outcome — provided the edge is real and the sample is large enough.

Calculating Expectancy

Using R-multiples (where 1R = your initial risk on a trade):

Expectancy = (Win Rate × Avg Win) − (Loss Rate × Avg Loss)

All values expressed in R. Example: 45% win rate, average winner 2.2R, average loser 1R (by definition):

• Win contribution: 0.45 × 2.2 = 0.99R
• Loss contribution: 0.55 × 1.0 = 0.55R
• Expectancy: 0.99 − 0.55 = +0.44R per trade

A 44-cent expected return for every dollar risked is a strong edge for a discretionary system. Many professional systems operate with expectancy between +0.10R and +0.40R. Expectancy above +0.50R is exceptional and often a sign that the backtest is overfitted rather than genuinely discovered.

Profit Factor

A related metric is the profit factor: total gross wins divided by total gross losses. A profit factor above 1.0 is profitable; below 1.0 is not. It can be derived directly from expectancy inputs:

Profit Factor = (Win Rate × Avg Win) ÷ (Loss Rate × Avg Loss)

Many professional traders target a minimum profit factor of 1.5 before committing significant capital to a strategy. Below 1.25, normal variance can push a strategy into drawdown for extended periods even when it has a genuine edge. The expectancy calculator displays profit factor alongside expectancy.

The Kelly Criterion

Kelly sizing answers: given a known edge, what fraction of capital should be risked per trade to maximise long-run geometric growth? The formula using win rate and payoff ratio is:

Kelly % = W − (L ÷ R)

Where W is win probability, L is loss probability (1 − W), and R is the average win divided by the average loss (the payoff ratio). Using our earlier example: W=0.45, L=0.55, R=2.2: Kelly = 0.45 − (0.55/2.2) = 0.45 − 0.25 = 0.20 = 20%.

Kelly recommends risking 20% of capital per trade. This is a mathematical optimum for log-wealth maximisation, but it assumes perfectly known probabilities (which you never have in live trading) and ignores the psychological cost of 20% drawdowns. For these reasons, professional traders almost universally use half-Kelly or quarter-Kelly: half the Kelly percentage. Half-Kelly accepts a modest reduction in long-run growth rate in exchange for dramatically smoother equity curves and drawdowns roughly one-quarter the magnitude of full-Kelly.

Kelly vs Fixed-Fractional

The standard fixed-fractional rule (risk 1%–2% per trade regardless of edge) is a low-Kelly approximation that works well across strategies with different edges because it is conservative enough to survive uncertainty about true probabilities. As you collect more live trade data and your estimate of expectancy becomes more reliable, Kelly sizing becomes a useful check: if fixed-fractional is far below half-Kelly, you may be undersizing relative to your edge; if it is above full-Kelly, you are oversizing and inviting unnecessary drawdown.