Probability of Profit vs Expected Value
Probability of profit tells you how often a trade wins. Expected value tells you whether winning that often is worth it. Most traders track the first number and never calculate the second — and that gap is where accounts quietly bleed.
A 90% POP trade sounds like a near-sure thing. It can also be a losing strategy. Here's how both things are true at once.
What POP Actually Measures
Probability of profit is the estimated chance that your position finishes profitable at expiration — by any amount. One dollar of profit counts the same as a thousand. It's calculated from implied volatility and a lognormal price distribution: the model asks how likely the stock is to finish on the profitable side of your breakeven, and that's the number.
POP is genuinely useful. It tells you how your position is shaped: a deep OTM credit spread might carry an 85% POP, while a long OTM call might carry 25%. That's real information about how often each structure pays.
What it is not: a measure of whether the trade is good.
What POP Doesn't Tell You
POP is blind to size. It counts outcomes, not dollars. A trade that wins small and frequently while losing big and rarely can post a beautiful win rate and a negative bottom line.
This is exactly the shape of most high-POP strategies. Selling far OTM options wins often precisely because you're accepting a small credit in exchange for carrying a large potential loss. The win rate isn't a market inefficiency you discovered — it's the structural tradeoff you agreed to. The market priced the small credit against the large risk.
New traders read 90% POP as "9 out of 10 chance this works." The more accurate reading: "9 small wins for every 1 loss — now check whether that 1 loss is bigger than the 9 wins combined."
Expected Value: The Missing Number
Expected value is the probability-weighted average of every outcome. The simplified two-outcome version:
EV = (POP × max profit) − (probability of loss × max loss)
If EV is positive, the trade makes money on average across many repetitions. If it's negative, no win rate makes it a good trade — you're being paid too little for the risk you're carrying.
The two-outcome version is an approximation. Real positions don't only finish at max profit or max loss — a stock can land between your strikes and produce a partial result. The more accurate calculation weights the P/L at every possible stock price by the probability of finishing there. That's what the calculator's Expected Value figure does: it integrates your full P/L curve over the same probability distribution used for POP.
An 87% POP Trade That Loses Money
A stock trades at $100. You sell the $95/$90 put credit spread for $0.50. Max profit: $50 (the credit). Max loss: $450 (the $5 spread width minus the credit). The model puts your POP at 87%.
Simplified EV: (0.87 × $50) − (0.13 × $450) = $43.50 − $58.50 = −$15.
Run this trade a hundred times and the math expects you to lose about $1,500 — while winning 87 of the hundred trades. Every individual month feels like it's working. The account balance says otherwise.
This isn't an argument that all credit spreads are bad. It's an argument that the credit has to be large enough. The same spread sold for $0.80 instead of $0.50 flips the EV positive. The difference between a good high-POP trade and a bad one is entirely in the price — which is why calculating EV before entry matters more than admiring the win rate.
How to Use Both Numbers
POP tells you the shape of the trade: how often it pays, how it will feel to hold. EV tells you whether the price you're getting justifies the risk you're taking. You want both.
Two honest caveats. First, EV from a pricing model is an estimate built on implied volatility — it's the market's forecast, not truth. Options priced exactly at model value will show EV near zero, because a fairly priced bet has no built-in edge for either side. Meaningfully positive or negative EV shows up when the premium you're actually paying or collecting diverges from what the distribution implies.
Second, EV at expiration ignores management. Many traders close winners early and roll losers, which changes the realized distribution. The number is a baseline for the trade as structured, not a prophecy.
Model any position in the Options Profit Calculator and check the Expected Value card next to Profit Probability. If the win rate is high and the EV is negative, you now know exactly what you're signing up for.