Connect risk-reward with probability
For a trade that either gains (b) units or loses 1 unit before costs: gross expectancy = (win probability × b) − loss probability The gross break-even win probability is: break-even win probability = 1 ÷ (1 + b)
Costs increase the actual break-even requirement.
Planned ratio vs realized distribution
Suppose a strategy advertises a 1:3 target. If winners are frequently closed at 1.2R while losing trades average −1.1R after slippage, the realized payoff ratio is much less favorable. Evaluate:- average and median winner;
- average and largest loss;
- partial exits and trailing-stop behavior;
- commissions, spread, slippage, and financing;
- frequency of gaps beyond the stop;
- variation by market regime.
Why a higher target is not automatically better
A farther target will usually be reached less often. The relationship is empirical, not a free improvement in payoff. An extremely high target can also increase time in market, financing cost, and the chance that open profit reverses. A small target is not automatically safer either. High-win-rate, low-payoff strategies can be vulnerable to rare large losses that erase many gains.Use R-multiples carefully
Expressing outcomes as R-multiples makes trades comparable when initial risk differs. Define whether (R) uses planned or realized risk and whether costs are included. Changing stops after entry can make the denominator inconsistent.Prop-account implications
The payoff ratio should be evaluated alongside the timing of losses. A strategy with positive long-run expectancy can still violate a daily loss rule through clustered losses. It can also consume a large part of the maximum-loss buffer while waiting for infrequent large winners.What is expectancy?
Combine probability and payoff after costs.
Win rate and profitability
Interpret accuracy in the full payoff distribution.
High-accuracy strategies
Examine rare-loss and tail-risk structures.
40% win-rate simulation
Calculate the break-even payoff requirement.