Probability of Profit, and Why It Is Not Enough
A price distribution behind the payoff curve. A 90% win rate and a losing strategy coexist happily.
Worth reading first: Why Selling an Option Is Not Just Buying in Reverse, Delta: Three Questions, One Number
Course contents73 lessons · 28 questions
Premium selling produces the highest win rates in retail trading. It is entirely possible to be right nine times out of ten for a year and finish the year down.
That is not a paradox or a warning about discipline. It is arithmetic, and this lesson is where the two numbers behind it get separated properly.
The distribution behind the payoff
The blue curve is where the stock is likely to land; the dark line is what you make or lose there. Push the strike down and watch the probability of profit climb while the expected value falls.
- Where the stock is likely to land
- What you make or lose there
Push the strike far enough down and the probability of profit climbs toward 95% while the expected value shrinks. A high win rate and a poor trade are entirely compatible — the two numbers are answering different questions.
Two questions, not one
Probability of profit asks: how often does this finish above breakeven? It is a count of outcomes.
Expected value asks: across every possible outcome weighted by how likely it is, what does this trade average? It is a sum of outcomes × probabilities.
EV = Σ (outcome × probability of that outcome)Probability tells you how often. Expected value tells you how much.
A strategy can score brilliantly on the first and badly on the second. Premium selling is specifically the shape where that divergence is largest, because the wins are capped at the credit and the losses are not.
Moving the strike moves both, in opposite directions
Drag the strike slider down in the widget. The probability of profit climbs toward 95%. The expected value shrinks, and eventually goes negative once costs are included.
| Strike | Credit | Probability of profit | Expected value |
|---|---|---|---|
| $97 | $310 | 58% | +$12 |
| $93 | $150 | 76% | +$9 |
| $88 | $62 | 89% | +$5 |
| $80 | $18 | 97% | +$2 |
Stock at $100, 30 days, 30% IV. Modelled figures, before commissions and slippage.
The bottom row wins 97% of the time and earns almost nothing. Add two dollars of commission and a bid-ask crossing and it goes negative — a strategy that is right 97 times out of 100 and loses money.
Why a high win rate feels like skill
The win rate in premium selling is a structural property of the position, not evidence of anything you did. Sell a 0.10 delta put and you will win about 90% of the time whether you researched the company for a week or picked it from a list.
This matters psychologically. A long run of wins builds confidence that has no basis in skill, right up until the tail arrives — and it usually arrives after size has been increased on the strength of that confidence.
The useful mental correction: judge the strategy on expected value and on the size of the worst realistic outcome. The win rate tells you how the equity curve will feel, not whether it goes up.
What this model does not know
Every probability here comes from a lognormal distribution, and it is worth being explicit about where that is wrong.
Real tails are fatter. Markets produce more extreme moves than the model predicts, and they cluster. The genuine probability of a large loss is higher than the curve suggests.
Gaps are not diffusion. The model assumes prices move continuously. Earnings and news gap straight through your strike without trading there.
These are risk-neutral probabilities. They come from option prices, not from a forecast of the real world — a technical distinction that mostly nudges the numbers, but a real one.
All three errors point the same way: the model understates the risk. Treat the probability of profit as an optimistic upper bound.
A note on what Premium Tracker shows
The open ROI figure in the product is deliberately not an expected value. It is an expires-worthless scenario: what this trade returns if it works. That is a different and more modest claim, and it is made on purpose — a probability-weighted forecast would be presenting model output as though it were knowledge.
What can go wrong
Optimising for win rate. It drives you toward strikes with negligible expected value.
Believing the tail probability. The model's 3% is a real-world something larger.
Increasing size after a winning streak. The streak was structural. The size increase is not.
Ignoring costs in the EV calculation. On low-premium trades, commissions and spread are frequently the difference between positive and negative.
Key takeaways
- Probability of profit counts how often you win; expected value weighs how much. They can point in opposite directions.
- Moving the strike further out raises the win rate and lowers the expected value simultaneously.
- A 97% win rate with a tiny credit can be a losing strategy once costs and the rare large loss are included.
- High win rates in premium selling are structural, not skill — which makes them psychologically dangerous.
- The model understates risk: real tails are fatter, gaps are not continuous, and these are risk-neutral probabilities.
Check your understanding
1. A trade wins 97% of the time collecting $18, and loses $2,000 on the other 3%. What is the expected value?
2. Why is a high win rate in premium selling weak evidence of skill?
3. In which direction is a lognormal model most likely to be wrong for options risk?