False precision

For two years I built monthly figures for people who were going to decide something with them. Corporate finance, through a run of acquisitions, so a good share of what I produced was forward looking. Allocations somebody had agreed to before I arrived. A rate that had been reasonable when it was set. A headcount assumption that would be wrong by the middle of the month.

All of that went into the model, and the model handed it back to the cent.

I did not think about it for a long time. The spreadsheet produced two decimal places because spreadsheets do, and I published what the spreadsheet produced. It looked like care. Nobody ever asked me to round.

The format is a sentence

Here is what took me years to see. The number of digits I show is not presentation. It is a claim, made in a different notation, about how much I know.

A figure given to the cent says: I can defend this to the cent. A percentage carried to one decimal says: I can tell 12.4 from 12.5, and the difference means something. Most of the time I could not, and it did not. The input was a guess with a range around it wide enough to swallow the whole decimal, and I had passed the guess through arithmetic that does not widen ranges, it just keeps calculating.

The arithmetic is not lying. The arithmetic is doing exactly what it was asked. The claim is entirely mine, made in the moment I decided how to display the result, which is a moment nobody experiences as a decision.

And people believe it. Not consciously. They read the decimals as evidence that somebody was careful, because in ordinary life that is what precision indicates. Somebody who tells you the exact time has looked at a clock.

Rounding everything was worse

For a while after I noticed this I rounded everything, and that was worse, because rounding is itself a choice somebody makes and nobody records.

Some numbers are exact and deserve to be shown exactly. A total that is the sum of a set of real amounts is not an estimate, and rounding it hides the one property that made it checkable. In reconciliation work the cents are the entire point, because the whole exercise is finding out why a small difference exists, and a rounded statement quietly makes the difference disappear without anyone resolving it.

So the rule is not “fewer digits”. It is that the digits should match the weakest thing behind them. A forecast built on a coarse assumption has no business being shown to the cent. A total that was counted has no business being shown to the nearest thousand.

Which means you have to know which of the two you are holding, and in a model of any size that is genuinely hard. Some cells are counted, some are assumed, and after a couple of rounds of edits they look identical. I have opened files where the only way to tell was to trace it back, and by then the format had been inherited by everything downstream.

The version of this in speech

It shows up when people talk, too, and it is easier to hear there. Somebody says “about a third” and somebody else says “thirty four percent”, and only one of them has told you anything about their confidence. The second is usually the weaker statement, and it always sounds like the stronger one.

I have started noticing when I do it. Not reliably. It is a habit of the hands more than of the mind, and the hands are quicker.