Lesson 8 of 8
Base rates first
Ask how often companies like this one did the thing, before asking about this one. Two real reference classes, and what each one is and is not evidence for.
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 base rate is how often the outcome occurs in the reference class, counted before you look at the specific case.
- Choosing the reference class is the hard part and it is where most of the error enters.
- A base rate measured on a model's output is a fact about the model, not about the world it was pointed at.
Before asking whether this company will do the thing, ask how often companies like it did. That question has an answer you can count, and starting anywhere else means arguing from a story about one company against nothing.
Where 3,253 US listings sit against Altman's published zones
- Below 1.81, the distressed zone1,520
- Between 1.81 and 2.99, the grey zone522
- Above 2.99, the safe zone1,211
Counting one
A base rate needs three things, and all three are decisions: the outcome, the reference class, and the period. Change any one and the number changes.
Building a reference class you can defend
- State the outcome exactly. Not "does badly" but "reported operating margin below 10 percent in the next fiscal year".
- Choose the class. Companies in the same sector, of a similar size, in the same market.
- Fix the period, and say whether it covers a full cycle or only part of one.
- Count. How many of the class reached the outcome.
- Write the cohort size beside the rate. A rate on 30 companies and a rate on 3,000 are different claims.
- Only now look at the specific company, and say what would move you off the base rate.
Step six is the discipline. Adjusting away from a base rate is allowed and often right. Starting somewhere else and never touching it is what the outside view prevents.
When a base rate is about the model instead
The figure above is a real count and it is easy to misread. Of 3,253 US listings with a computed Altman Z-Score on 16 September 2026, 1,520 sat below 1.81: 46.7 percent of the scored pool, in a zone whose published label is distressed.
Nothing close to 46.7 percent of US listed companies fail in a year. So the number is not the base rate of distress. It is the base rate at which this model, applied to this universe, produces a score under this threshold, and those are different sentences.
The cause is on the record elsewhere in this academy: the thresholds were fitted on public manufacturers in 1968, and three of the model's five terms read an ordinary modern balance sheet as weak for reasons unrelated to its condition. A base rate inherits every assumption of the thing it was counted on.
A base rate that is about the world
Both of these are base rates about the world rather than about a model, because each is a direct count of a filed figure. That is the test to apply: is the outcome measured, or is it the output of something fitted.
What a base rate is not
It is not a forecast for any company, and it is not a threshold. A base rate of 42.8 percent tells you the reference class is not a safe backdrop to assume against. It does not tell you which listing is in which group, and nothing in this lesson does.
Its job is to set the number a specific argument has to move you away from, and to make the size of that move explicit.
Check yourself
A model scores 46.7 percent of a universe inside its distressed zone. What is that a base rate of?
- The rate at which companies in that universe fail
- The rate at which this model, on this universe, produces a score below that threshold
- The model's false positive rate
Show the answer
Answer: B.
The count describes model output. Turning it into a statement about failures would need a measured failure rate, which is a different count from a different source.What is the hardest part of using a base rate?
- The arithmetic of the count
- Choosing a reference class the specific case really belongs to
- Finding a large enough sample
Show the answer
Answer: B.
The division is trivial. Which companies count as "like this one", and over what period, is a judgement that sets the answer before any counting begins.1,988 of 4,640 US listings with a computed ROE had a negative one. What does that support?
- That a negative return on equity is common in this pool, so it is not on its own a distinguishing finding
- That 42.8 percent of US companies will fail
- That return on equity is badly calculated
Show the answer
Answer: A.
It is a count of a filed figure across a defined pool on one date. It establishes how common the condition is, which is exactly what a base rate is for, and nothing beyond that.Sources
- Altman Z-Score, return on equity and price to earnings values computed by ValueScreener across the active US equity pool, read from this product's own store on 16 September 2026: 3,253 listings with a Z-Score, 4,640 with an ROE, 5,206 holding any indicator row.
- Altman, Journal of Finance, 1968, "Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy": the 1.81 and 2.99 thresholds, fitted on public manufacturers.
- Kahneman and Lovallo, 'Timid Choices and Bold Forecasts: A Cognitive Perspective on Risk Taking', Management Science, 1993, on the outside view and why forecasters leave it.
What this leaves out
- All three counts are readings on one date across listings rather than deduplicated companies, and each excludes the listings that do not hold the figure. Those exclusions are not random, which is the subject of the survivorship lesson in the statistics course.
- The Z-Score is withheld here for banks, capital markets firms, equity REITs, insurers, mortgage REITs and specialty finance companies, so the scored pool is not the whole market.
- No measured rate of US corporate failure is used in this lesson, because we do not hold one. The lesson's point is that the model's flag rate cannot stand in for it.
- Nothing here is advice about any security.