Probability, Win Rate and Expected Value

A high probability of a small gain can coexist with a negative expected result. To evaluate an options payoff, combine the probability of each outcome with its profit or loss, then include costs. Win rate counts how often a trade wins; it ignores how much it wins or loses.

Expected value is weighted arithmetic

Consider a deliberately simplified two-outcome trade: an 80% chance of earning $100 and a 20% chance of losing $500. Its expected gross result is 0.80 × $100 − 0.20 × $500 = −$20. With $4 of costs each time, expected net value is −$24. Winning four times in five is insufficient when the fifth loss is large enough.

For gain W, loss L and fixed cost C, all expressed as positive dollar amounts, EV = pW − (1 − p)L − C. The break-even win probability is (L + C) ÷ (W + L). Here it is 504 ÷ 600 = 84%. Real option outcomes usually form a distribution rather than these two fixed amounts.

Probability of what?

Probability of expiring in the money, probability of touching a strike and probability of a profitable exit are different events. A purchased call can finish in the money yet lose after its premium. A short put can temporarily breach a strike and later expire worthless. A strategy closed at a profit target follows a path-dependent rule, so an expiration-only estimate does not fully describe it.

Delta is a price sensitivity. In a basic European model, call delta relates to N(d1) while the risk-neutral probability of finishing above the strike relates to N(d2), with dividend adjustments to delta. Neither is automatically a real-world success rate. Price-derived probabilities reflect a model and risk pricing, not just a forecast of future frequencies.

Use a complete payoff distribution

List outcomes below, inside and above a spread’s strikes; calculate payoff, premium and fees at each point. Weight them only with probabilities from a stated model or data process. A risk-neutral distribution and a personal forecasting distribution answer different questions. Substituting one for the other can make an apparently positive edge disappear.

A positive average does not guarantee survival

Loss clustering, estimation error and position size determine whether an account can withstand a bad sequence. Ten profitable trades do not validate a probability estimate, particularly if a rare loss has not yet occurred. Evaluate drawdown, tail loss, capital needs and uncertainty in the estimated average. Backtests should include realistic spreads and outcomes that were actually available to trade.