Lesson 1 of 8
A probability you can be held to
Saying 70 percent commits you to something checkable. Most investing probabilities are stated in words that cannot be wrong, which is the problem.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- A probability is either a long-run frequency or a stated degree of belief, and the two are checked differently.
- A number commits you to something. A phrase like "likely" does not, which is why phrases survive being wrong.
- Calibration is measurable: collect your own stated probabilities and check how often the things you called 70 percent happened.
"This is probably fine" cannot be wrong. "There is a 70 percent chance this is fine" can be, and the difference between those two sentences is most of what separates a research process from an opinion.
Two ways to say the same thing about a market
The vague form
Unfalsifiable
"A lot of US companies score badly on distress models."
The stated form
Checkable
"46.2 percent of the 3,254 US listings with a computed Z-Score sit below 1.81."
The second can be checked. The first cannot.
The two kinds
A frequency probability is a count. Of 3,254 listings with a score, 1,504 were below the threshold, so the proportion is 46.2 percent. You can recount it and it is either right or wrong.
A belief probability is a number you assign when there is no population to count: the chance this particular company keeps its margin above 30 percent next year. There is one of it and it happens once.
The mistake is treating the second as if it were the first. A belief probability is not checked on one case, because one case cannot distinguish 70 percent from 30 percent. It is checked across many.
What a number commits you to
If you say 70 percent about a hundred separate things, roughly seventy of them should happen. That is the entire test, and it is the only one that works. A person whose 70 percent statements come true 95 percent of the time is underconfident. A person whose come true 40 percent of the time is overconfident, which is the common direction.
Why this is worth the discomfort
A thesis that says a company is "well positioned" survives any outcome. A thesis that says its return on capital stays above 12 percent, and assigns that a probability, can be checked by the filings and by the calendar.
The purpose is not precision. Nobody knows whether it is 70 or 65. The purpose is that a number can be compared against what happened, and a phrase cannot, so only the number produces learning.
Two rules that keep it honest
State the probability before the outcome, not after, because reconstructing what you believed is unreliable in a known direction. And state what the claim refers to precisely enough that the outcome is not arguable: not "the business does well" but "reported operating margin for fiscal 2027 is at or above 18 percent".
Check yourself
You say 70 percent about one company and it does not happen. What have you learned about your calibration?
- That you were wrong
- Almost nothing, because a single outcome cannot distinguish 70 percent from 30 percent
- That the probability should have been 30 percent
Show the answer
Answer: B.
A 70 percent claim expects to fail three times in ten. Calibration is a property of a set of statements, which is why the record has to be kept across many of them.Which of these is a frequency probability?
- The chance this company raises its dividend next year
- The share of scored US listings whose Z-Score is below 1.81
- The chance the current management stays for five more years
Show the answer
Answer: B.
The second is a count over a defined population and can be recounted. The other two are single events, which have to be stated as beliefs and checked across many such statements.Why is 'this company will probably do well' a weaker statement than a numbered one?
- Because it is shorter
- Because no outcome can show it was wrong
- Because probabilities are always more accurate than words
Show the answer
Answer: B.
A claim that no outcome can contradict cannot be learned from. Numbers are not more accurate, they are checkable, and the checking is the point.Sources
- Altman, Journal of Finance, 1968, "Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy": the 1.81 threshold used here, fitted on public manufacturers.
- Altman Z-Score values computed by ValueScreener across 3,254 active US equity listings, read from this product's own store on 13 September 2026.
- Kahneman and Lovallo, 'Timid Choices and Bold Forecasts: A Cognitive Perspective on Risk Taking', Management Science, 1993, on the inside view and the direction in which forecasters miss.
What this leaves out
- The 46.2 percent figure is a count on one date. It moves as prices and filings move, and a later reading will differ.
- Altman's thresholds were fitted on public manufacturers, so a low score across a mixed universe is partly the model travelling outside its sample. That is the subject of a lesson in the accounting quality course.
- The calibration table is invented, to show the shape of the check rather than any real record.
- Nothing here is advice about any security.