What is probability of profit?
Probability of profit is the model probability that the underlying finishes at expiration somewhere the position makes money. For a long call, that means above the strike plus the premium paid. For an iron condor, it means between the two breakevens. The number depends on the breakevens, the time to expiration and the volatility assumed for the stock. Because it is a single number, POP is popular for screening trades, but it should always be read alongside the payoff diagram.
POP is easy to confuse with related measures, so keep them separate:
- Probability of profit is the chance of finishing beyond the breakeven, so the trade makes at least some money.
- Probability of max profit is the chance of finishing in the zone where the full maximum profit is earned, which is lower for most spreads.
- Probability in the money is the chance a single option finishes in the money, measured at the strike rather than the breakeven.
- Probability of touch is the chance the stock trades at a given price at any time before expiration, which is higher than the chance of finishing there.
How is probability of profit calculated?
The standard method models the stock price at expiration as lognormal, meaning the logarithm of the price is normally distributed, with a spread set by implied volatility and time. Because the distribution is lognormal, the stock can never fall below zero and upside moves can be larger in dollar terms than downside moves.
Implied volatility sets the width of the distribution. Doubling volatility roughly doubles the spread of likely outcomes, while time widens it with the square root of the days remaining, so a trade with four times as long to run has about twice the range.
The steps are:
- Find every breakeven price from the expiration payoff.
- Identify the price ranges where the payoff is positive.
- For each range, compute the probability that the stock finishes inside it using the lognormal distribution.
- Add the probabilities of all profitable ranges.
What is the formula for probability of profit?
For a single breakeven B, the probability that the stock finishes above B is N(d), where d = (ln(S/B) + (mu minus sigma squared / 2) × T) / (sigma × square root of T). Here S is the current price, sigma is the implied volatility, T is the time to expiration in years, mu is the assumed annual drift and N is the cumulative standard normal distribution. The probability of finishing below B is 1 minus N(d).
For a position with two breakevens, such as a short strangle or an iron condor, the probability of finishing between them is N(d at the lower breakeven) minus N(d at the upper breakeven). The drift choice matters only a little for short dated trades. A risk neutral setup uses r minus q, and a simpler setup uses zero, which is one reason different platforms show slightly different numbers.
How does CalcOptions estimate probability of profit?
CalcOptions computes probability of profit from a lognormal distribution using the position's implied volatility, with each leg's IV solved from its mid price. It finds the breakevens from the expiration payoff and measures the probability of the profitable zones, so the number updates as you change strikes, expirations or volatility.
Because the calculation uses expiration payoffs, POP for a long call or long put depends mostly on how far the breakeven sits from the current price compared with the expected move. Moving a strike closer to the money, or choosing a later expiration, changes POP in ways you can see immediately in the calculator.
For time spreads such as calendars and diagonals, the payoff at the front expiration depends on the value of the longer dated leg, which is itself a model estimate. Treat POP on those positions as a rougher guide than on single expiration trades.
Why do credit spreads show high POP and long options low POP?
POP and payoff size trade against each other. A short out of the money option or a credit spread wins often but collects a small amount and risks a larger one. A long option loses often but can win many times its cost. An iron condor sold far from the stock price can show a high POP, while a long call far out of the money shows a low one.
If options are fairly priced, the expected value of either trade is close to zero before costs, so a high POP does not mean an edge. A useful check is the breakeven win rate: max loss / (max profit + max loss), assuming every trade ends at one extreme. A trade that risks several times what it can make needs a correspondingly high win rate just to break even. Judge a trade on POP together with max profit, max loss and how you plan to manage it.
Neither profile is better in general. Many traders mix both, choosing the profile that matches their view and the amount of capital they are willing to risk on a single outcome.
What are the limitations of probability of profit?
Treat POP as one input, not a verdict. The main caveats are:
- Real returns have fatter tails and more jumps than the lognormal distribution, especially around earnings.
- A single implied volatility ignores skew, so it can misstate the odds of large moves in one direction.
- Risk neutral probabilities are pricing probabilities, not forecasts of what the stock will do.
- POP measures only the outcome at expiration, not the path, so it ignores early management, stop losses and early assignment.
- Commissions, fees and slippage shrink the profitable zone slightly.
- Implied volatility changes, so today's POP will not be tomorrow's.
- Dividends and interest rates shift the drift, so long dated positions are more sensitive to those assumptions.
How does POP relate to delta and probability of touch?
Delta is a quick proxy for the probability that an option finishes in the money. For a short option, POP is roughly 1 minus the probability of finishing beyond the breakeven, which sits a little further out than the strike because of the premium collected. That makes POP a bit higher than 1 minus the short option's delta would suggest.
Probability of touch is roughly twice the probability of finishing beyond a price, under the simple random walk the model assumes. That matters if you plan to adjust or close when the stock reaches a short strike, because the stock will touch that strike far more often than it finishes beyond it.
The delta of the whole position tells you something different: how its value changes with the stock today. A position can have a high POP and still carry large negative gamma, so a fast move against it hurts quickly.
Frequently asked questions
Is a higher probability of profit always better?
No, a higher probability of profit usually comes with a smaller maximum profit and a larger maximum loss. A trade can win most of the time and still lose money overall if the occasional loss is large. Compare POP with the risk to reward ratio before judging a trade.
Is probability of profit the same as delta?
No, probability of profit is measured at the breakeven, while delta roughly approximates the probability of finishing in the money at the strike. For a single short option, POP is usually a little higher than 1 minus delta because the premium collected moves the breakeven further away. For multi leg positions, POP comes from all the breakevens together.
Why does my broker show a different probability of profit?
Platforms differ in the volatility they use, the drift they assume and whether they measure profit at expiration or at any point before it. Some use a single implied volatility for the whole position and others use one per strike. Small differences are normal, and large ones usually trace back to a different volatility input.
Try it in a calculator
Iron Condor
An iron condor is a neutral, defined risk credit strategy that sells an out of the money put spread and an out of the money call spread on the same stock and expiration.
Short Strangle
A short strangle is a neutral options strategy where you sell an out of the money put and an out of the money call on the same stock and expiration to collect premium.
Bull Put Spread
A bull put spread is a two leg credit spread that sells a put and buys a lower strike put in the same expiration.
Educational tool, not financial advice. Calculations are theoretical and depend on your inputs; real fills, fees, early assignment and dividends can change results. Options involve risk and are not suitable for every investor.