High probability of profit, negative expected value: how both can be true
Options Verdict · Updated October 18, 2026
Short answer: probability of profit counts how often a trade wins. Expected value also counts how much it wins and loses. A trade that wins 90% of the time but loses nine times its win when it fails has negative expected value.
The formula
Expected value = p × average win − q × average loss, where p is the chance of a profit and q the chance of a loss. Rearranged, the trade only makes money on average if its win rate beats the breakeven win rate = average loss ÷ (average win + average loss).
Worked example: moving a put credit spread further away
A $100 stock, 30 days, 25% implied volatility, $5-wide put credit spreads at different short strikes. To show the effect of a realistic fill, each credit is the model's fair price minus 5 cents, and the stock is assumed to move exactly as much as implied.
| Short strike | Credit | Profit chance | Win rate needed | Expected value |
|---|---|---|---|---|
| 97 | $110.08 | 70.8% | 78.0% | −$5.00 |
| 94 | $54.81 | 81.8% | 89.0% | −$5.00 |
| 92 | $29.94 | 88.0% | 94.0% | −$5.00 |
| 90 | $13.66 | 92.7% | 97.3% | −$5.00 |
| 88 | $4.04 | 96.0% | 99.2% | −$5.00 |
The further out the short strike, the higher the profit chance, but the win rate needed rises with it, because the credit shrinks while the possible loss barely does. With fairly priced options, the two move together and expected value stays slightly negative: the 5-cent haircut is the only thing left. (The "win rate needed" column uses max profit and max loss, which is close to but not exactly the average win and loss.)
In other words, choosing strikes doesn't create an edge on its own. A high profit chance is just a different shape of the same bet. The edge has to come from somewhere else: options priced for more movement than the stock delivers, or a better fill.
Where the edge can come from
- Implied above realized volatility. If the stock moves less than options assume, sellers' expected value turns positive at every strike. See how much it changes.
- Price. Getting filled closer to fair value matters most on cheap, far-out spreads, where a few cents is a big share of the credit.
- Exits. Taking profits early or cutting losses changes both the win rate and the average win and loss. It can help or hurt; it's worth simulating rather than assuming.
How to use both numbers
Look at profit chance to understand how a trade will feel: how often you'll be right. Look at expected value to understand whether it pays over many trades. If the two point different ways, trust expected value, and check the assumption it rests on: the volatility you entered.
Questions
Can a trade with a low profit chance have positive expected value?
Yes. Long options often win less than half the time but can win several times what they risk. If the stock moves more than implied, their expected value is positive.
Does taking profits at 50% raise expected value?
It raises the win rate and lowers the average win. Whether expected value goes up depends on the trade and the market; simulating the exit plan is the only honest way to tell.
Why use expected value instead of win rate to judge a strategy?
Win rate ignores size. Over many trades, the account grows or shrinks by the average result, which is expected value.
Try it
- Options profit calculatorPayoff, max profit and loss for 20 strategies.
- Expected value calculatorWhat a trade makes on average, from realized volatility.
- Probability of profit calculatorThe market-implied chance a trade ends with a profit.
- Position size calculatorHow many contracts fit your risk rules.
- Expected move calculatorHow far the market expects a stock to move.