Probability of Profit (POP)

What is Probability of Profit (POP)?

Probability of Profit (POP) Probability of Profit (POP) is the estimated likelihood that an options trade will be profitable at expiration, expressed as a percentage. It's calculated from the option's delta and the strike price relative to the underlying — essentially the same math that produces option deltas, but interpreted as a probability metric for the entire trade. For a short put at the 30-delta strike, POP is approximately 70% — meaning there's a 70% probability the stock will finish above the short strike at expiration, leaving the put OTM and the trade profitable. For a long call at the 30-delta strike, POP is approximately 30%. POP is mathematically derived from the cumulative normal distribution, which is also what generates option deltas. The connection: an option's delta approximates the probability of finishing ITM. A 25-delta short put has 75% POP; a 16-delta short put has 84% POP. POP varies dramatically across strategies: - **Long single option (ATM)**: ~50% POP - **Long single option (OTM)**: 20-40% POP — needs directional move - **Short single option (OTM)**: 60-85% POP — just needs underlying to not crash past strike - **Long straddle**: ~50% POP (slightly less due to needing meaningful move) - **Long strangle**: ~35-45% POP — needs larger move than straddle - **Iron condor (16-delta wings)**: ~65-70% POP - **Credit spread (16-delta short)**: ~70-75% POP - **Bull call debit spread**: ~45-55% POP POP is a useful filter but not the whole story. A high POP setup with a poor reward-to-risk ratio can be a losing trade. A 75% POP credit spread that pays $0.50 credit on $5 wing has +0.10 reward-to-risk — needs to win at least 91% of the time to break even, well above the implied 75%. The expected value formula: **EV = (POP × avg_win) − (1 − POP) × avg_loss** For POP to drive profitability, the reward-to-risk must support the chosen probability level. A common mistake is targeting high POP without checking whether the payout ratio supports the strategy's edge. POP is also probabilistic — the true probability is unknowable. The implied POP from delta is the market's best estimate, which is reasonable for liquid index options but can be misleading on single stocks ahead of binary events. Historical POP for the same setup across many trades tends to converge to the implied POP over time. For premium sellers, POP is the primary input to sizing decisions. Higher POP setups (16-delta or wider) are scaled larger; lower POP setups (30+ delta) are scaled smaller because the loss frequency is higher. Position sizing should be proportional to (1 - POP) × max loss, ensuring no single bad trade is account-breaking.