Probability of Profit

Probability of profit (POP) is the estimated likelihood that an options trade will make at least $0.01 at expiration. It is derived from the option's pricing model and is closely related to delta. For a simple short option position, POP is approximately 100% minus the absolute value of delta. Most brokers display POP on their order entry screen to help traders evaluate trades before placing them.

Why It Matters

POP is one of the first numbers traders look at when evaluating a potential trade. It answers the most basic question: what are the odds this trade makes money? However, POP is also one of the most misunderstood metrics. A high POP does not necessarily mean a good trade — it only tells you how often you win, not how much you win or lose.

A trade with 80% POP that risks $4 to make $1 has the same expected value as a trade with 20% POP that risks $1 to make $4. Evaluating POP in isolation leads to the common mistake of selling narrow, high-POP spreads that blow up when the rare loss occurs. POP must always be evaluated alongside the risk-to-reward ratio and expected value.

How It Works

For single-leg options:

• Long call POP = probability the stock closes above the strike plus the premium paid
• Long put POP = probability the stock closes below the strike minus the premium paid
• Short call POP = probability the stock closes below the strike plus the premium received (approximately 1 minus the call delta)
• Short put POP = probability the stock closes above the strike minus the premium received (approximately 1 minus the absolute put delta)

For spreads:

• Credit spread POP = probability the stock stays beyond the short strike, adjusted for the credit received
• Debit spread POP = probability the stock moves past the long strike, adjusted for the debit paid
• Iron condor POP = probability the stock stays between both short strikes, adjusted for the total credit

Delta as a POP proxy: A 30-delta option has roughly a 30% chance of expiring in the money. If you sell it, your POP is approximately 70%. This is a quick approximation — the actual POP also depends on the premium received, which shifts your breakeven point.

How POP is calculated: Brokers use the option pricing model's probability density function to determine the likelihood the stock ends up above or below a given price at expiration. This assumes a log-normal distribution of returns, which is an approximation.

Adjusting POP for real-world use:

• Subtract 2-5% from model POP to account for fat tails
• Consider early assignment risk for American-style options
• Account for commissions and fees, which reduce your effective POP on small trades
• Remember that POP assumes you hold to expiration — managing positions early changes the actual probability

Quick Example

You sell a $5-wide put credit spread: short the $95 put (30 delta) and long the $90 put, collecting $1.25. Your breakeven at expiration is $93.75 ($95 - $1.25). POP is the probability that the stock stays above $93.75.

Your broker shows POP of approximately 74%. This means roughly 74 out of 100 times, this trade makes money. But when it loses, the max loss is $3.75 per share ($5.00 width minus $1.25 credit). To have positive expected value, you need: 0.74 x $1.25 > 0.26 x average loss. If the average loss is $2.50 (not always the max), the EV is 0.74 x $1.25 - 0.26 x $2.50 = $0.925 - $0.65 = $0.275 per share — a positive edge.