A range says more than a number#
Back of the Envelope · Week 4
Unlucky, or overconfident?#
A point estimate that misses destroys the one thing you need to tell those apart afterward: what you actually thought, and how firmly.
A range with a stated confidence keeps that evidence.
“Rainfall forecasts are probabilistic.”
The Bureau of Meteorology, on why some quantities should not be published as one number.
Three parts, and the common mistake is welding them#
- Chance of rain — probability of at least 0.2 mm. Says nothing about how much.
- Two rainfall amounts — a pair, each with its own confidence.
- The range is chosen, not padded — to capture the likely scenarios and the confidence in them.
This is BOM’s own grammar for its own forecasts, not a formula for your diary — the discipline transfers, the machinery does not.
75% of at least 7 mm · 25% of at least 25 mm#
BOM’s own worked example, for a single forecast.
Four things, written before you look#
- a low bound
- a high bound
- a confidence, in plain words
- a line naming what would make the range miss
This is the exact form every Calibration Diary entry uses, all semester.
25% happened 19% of the time#
BOM checks its own stated confidences against outcomes, across thousands of forecasts:
“for the 50% chance amount it occurred 49% of the time and for the 75% chance amount it occurred 80% of the time.”
Your Diary audits fifteen entries by hand. Same idea, at a scale only an institution reaches — not a target to match.
A range that cannot be wrong is not telling anyone anything#
A range wide enough to catch anything is not caution — it is a refusal to answer, dressed as care.
The width is a report on what you know, not a rhetorical dial. Sometimes the honest width is embarrassingly wide.
Keep the sheet#
Today’s ranges are the first entries in a record you keep all semester and audit at the end of it.
Nothing is due yet. Keep committing before you look — that habit is what Week 12 reads back.