Corporate life · Murphy's laws
Segal's Law: Why Two Reports Never Show the Same Number
The short version: a second measurement doesn't add uncertainty, it reveals it. If each of two watches is off by a typical error of one minute, they disagree by more than a minute 48% of the time, which feels like chaos. But one watch on its own is off by more than a minute 32% of the time; you just can't see it. The average of the two is off by more than a minute only 16% of the time. Two dashboards that disagree are telling you how precise your numbers really are. The fix is to find out why they differ, then combine them, not to delete one.
The finance team's revenue dashboard says last month was $4.21 million. The sales team's dashboard says $4.36 million. A meeting has been called to decide which one is true. The meeting is in its third month.
Kevin's boss has proposed a solution: switch off the sales dashboard, so that the company has only one number again. "We used to know our revenue," he says. Kevin isn't sure they did.
The law
An old saying, known as Segal's law, goes: a man with a watch knows what time it is; a man with two watches is never sure. It sounds like an argument for owning one watch. Statistically, it's the opposite.
Two watches, in numbers
Suppose each watch is a little off, by a typical error of about one minute either way, and the two errors are independent. Then:
| What you see | How often |
|---|---|
| The two watches disagree by more than 1 minute | 48% |
| The two watches disagree by more than 2 minutes | 16% |
| One watch on its own is off by more than 1 minute | 32% |
| The average of the two is off by more than 1 minute | 16% |
The man with one watch is wrong by more than a minute a third of the time, and has no idea. The man with two watches sees disagreement half the time, and can take the average, which is wrong half as often. He isn't less sure because he knows less; he's less sure because he knows more.
Why the numbers differ
Two business reports usually disagree for reasons that are worth knowing, not because one is "wrong":
- Definitions. Revenue when the order is signed, when it's invoiced, or when it's paid?
- Timing. One system closes the month at midnight, the other on the next working day.
- Coverage. One includes refunds, discounts or a subsidiary; the other doesn't.
- Plain errors. Typos, duplicates and missing records, which both sides have: ordinary measurement error.
Statistics for noobs: disagreement is information
Every number has some error. One source hides it; two sources show it. When two measurements disagree, first explain the gap (definitions, timing, coverage), then, for what's left, combining them is usually more accurate than either alone. Averaging independent measurements is the law of large numbers in miniature.
Where it costs you money
Two data providers giving slightly different prices, earnings or index values for the same thing is normal. The investor who checks only one feels certain; the one who checks two knows how much the numbers can be trusted. Prefer the second feeling.
The moral
Kevin traced the gap: sales counted orders when signed, finance when invoiced. The $150,000 difference was three large orders signed in the last week of the month. The meeting agreed on a definition and closed. The following month the dashboards agreed exactly, and the boss was delighted, until Kevin found that one of them had been copying its figures from the other since the meeting.
What this can't tell you
- Errors aren't always independent. Two reports built from the same faulty source can agree perfectly and both be wrong.
- The one-minute error is an example. The percentages hold for any typical error, measured in the same units.
- The saying's origin is uncertain. It's widely quoted and attributed to different people; its wording varies.
The dashboards, the meeting and the $150,000 are an illustration. The watch figures are our own calculation, assuming each watch's error follows a normal distribution with a standard deviation of one minute. Educational content, not financial advice.