Expectancy

What is expectancy?

Expectancy is the average amount a strategy makes or loses per trade, taken across the whole distribution of outcomes. It answers the only question that ultimately matters about a trade-generating process: if this bet is taken many times, what does each occurrence earn on average? A positive expectancy means the process makes money before frequency and sizing are considered; a negative one means no amount of discipline in execution rescues it.

The standard decomposition multiplies the win rate by the average winner and subtracts the loss rate times the average loser. That decomposition exposes the trade-off traders constantly negotiate: a low win rate is perfectly viable when winners dwarf losers, and a high win rate can still lose money when the occasional loss is large. The ratio of average win to average loss is known as the payoff ratio, and expectancy is where win rate and payoff ratio meet.

Expressed in the R-multiple framework, where each outcome is stated as a multiple of the risk taken at entry, expectancy is simply the average R of the trade list, which is why traders sometimes call it average R. That normalization makes the figure comparable across instruments and account sizes, and it is the form most sizing math consumes, from fixed-fractional rules to the Kelly criterion.

How it's calculated

The canonical form combines win rate with average win and loss sizes; the R-multiple form is the same quantity normalized by initial risk.

Compute expectancy net of commissions and slippage; gross expectancy routinely flips sign after realistic costs.

Some authors quote expectancy per unit risked or per dollar risked; the R-multiple form makes the normalization explicit.

How traders use it

• As the first gate in validation: whatever else a backtest shows, a system whose net expectancy is not clearly positive after costs has nothing to size or optimize.
• To reason about design trade-offs, since raising the win rate usually shrinks the payoff ratio and vice versa; expectancy is the scoreboard on which those trades settle.
• Combined with trade frequency to estimate earning power, because a small expectancy taken many times can outperform a large one taken rarely, subject to cost sensitivity.
• As a live monitoring baseline: rolling expectancy drifting below the backtest's confidence band is an early sign of edge decay.
• With respect for sample size; expectancy estimated from a few dozen trades is dominated by noise and by whether the sample happened to include the tail losses.

Expectancy vs related metrics