Where the 90% on your screen actually comes from

Nobody counted

When a screen here says there is a 90% chance a contract expires worthless, it is easy to hear that as a track record: that trades like this one were tried many times and nine in ten worked out. That is not what happened. Nothing was counted. No history of this trade was consulted.

What happened is that a model was asked to sketch the range of prices the shares could plausibly finish at, and then asked how much of that range sits on the side where you keep the payment. The answer came back as 90%. It is an estimate of odds, made under stated assumptions, and knowing which assumptions is the difference between using the number and being used by it.

The picture behind the number

Every probability on every options screen anywhere is one version of this picture. It is worth looking at once, properly, because afterwards the number stops being magic.

Today’s price sits under the top of the hump, because the single likeliest outcome for a share price six weeks out is roughly where it is now. Prices a little either side are nearly as likely; prices far away are progressively less likely, which is why the shape tails off rather than stopping. The height of the curve at any point is how plausible that finishing price is.

Your agreed price sits out on the left. Everything to the left of that line is the set of outcomes where the shares are put to you; everything to the right is the set where nothing happens and the payment is simply yours. “A 90% chance” is the statement that the shaded sliver is one tenth of the total area. That is the whole of it. There is no other ingredient.

The percentage is not a prediction about the company. It is a measurement of a shape somebody chose.

Three measurements and one assumption

Four things decide where that curve sits and how wide it spreads. Three of them are read off a screen. The fourth is the one doing the heavy lifting, and it is not a measurement at all.

One refinement worth knowing, because it makes the app’s number slightly kinder than the raw geometry: the payment you collect is counted in. A share price a few cents below your agreed price still leaves you ahead, because you were paid up front. So the line that matters sits a little to the left of your agreed price, and the shaded sliver is a little smaller than “chance the shares end below your price” would suggest. The methodology page states this and the rest of the machinery in the technical register, if you want it.

Why the same strike shows a different number tomorrow

Two of the four ingredients move without you touching anything, which has a consequence that confuses almost everyone once: you can look at the same contract on the same stock at the same price two days running and see two different percentages.

Time is the obvious one. Pick a deadline three times further out and the curve flattens and spreads, pushing more of its area past your price — the figure above is the same stock, the same agreed price, and nothing but extra waiting. The longer trade pays more because it is more likely to be called upon. That is not a bargain being offered; it is the same trade-off written larger.

The less obvious one is the market’s nervousness. If something spooks traders overnight — anywhere, not necessarily in this company — options get more expensive, which means the market is now pricing bigger swings, which widens the curve on your position too. Your stock did nothing. Your percentage fell anyway.

What the curve cannot see

The smooth hump has one systematic flaw, and it is not a small one. Real share prices do not only drift — they jump. A company reports earnings after the close and opens 14% lower. A takeover is announced. A drug trial fails. Trading is halted and resumes somewhere else entirely.

A smooth curve has no way to represent a jump. It spreads the possibility of sudden moves evenly across all the little moves, which makes the far ends of the curve too thin: the model says a given extreme is rarer than it actually is. The technical phrase is that real returns have fatter tails. The practical phrase is that the 10% is worse than it looks, and in the direction that costs you.

Delta looks like a probability, and nearly is

You will see another number on these screens that behaves suspiciously like the percentage: a decimal, usually between 0.05 and 0.50, labelled delta. Traders use it as rough shorthand for odds — 0.30 is loosely a 30% chance the agreed price comes into play.

The shorthand works because delta and the shaded sliver are two readings of the same curve, and it is only shorthand because they are not read at quite the same place: the percentage counts the payment as cushion and delta does not. For reading a screen quickly, treat delta as the rough odds; when the two disagree slightly, the percentage is the one built for the job. What delta is for — and what the other three Greeks answer — is two lessons away.

The number that does the work this one can’t

Everything above describes a frequency: how often. Nothing above says anything whatsoever about size, and a tenth of the time can cost more than nine tenths of the time earns. That is not a hypothetical; it is the normal shape of a badly chosen option trade.

So the percentage is deliberately not the number this app ranks on. Every candidate also has to survive a second test that asks what the losing outcomes actually cost — and that test is run against how much the stock has really been moving lately, not against what the market is charging for swings. The mismatch is the point: you are paid at the market’s price for risk, and judged at the stock’s own behaviour. A trade that only looks good when you accept the market’s own optimism does not pass.

Three habits for reading the percentage

• Translate it once, silently, every time. “90%” means “the model’s odds, if the next six weeks look broadly like the present.” Said that way, it stops sounding like a promise.
• Ask what is in the 10%. Not how big it is — what is in it. A scheduled event inside the window changes the answer more than two percentage points of headline probability ever will.
• Ask what the 10% costs. A one-in-ten chance of losing half the capital and a one-in-ten chance of losing a day’s premium are the same percentage and not remotely the same trade.

Where to go next

That last habit is the whole of the next lesson, and it is the most important one in this library: a 92% win rate can still lose you money. Five minutes, one picture, and the reason this tool rejects trades that look excellent.

If you would rather see a real curve’s worth of numbers first, run a scan on a company you know and read the percentage out loud as the long sentence instead of the short one.