A Year With Zero Accidents: Did Safety Really Improve?
The short version: with rare events, a zero year proves little. If accidents happen at random at an average of two a year, a year with none happens 13.5% of the time, and a site has at least one such year in a decade 77% of the time. A bad year with four or more happens 14% of the time. Counts like these follow the Poisson distribution, and they swing a lot from year to year with nothing changing. Real improvement shows up as a lower average over several years, or across many sites, not as one good year.
The warehouse has averaged two accidents a year for a decade. This year: none. The safety manager received the Golden Helmet award at the annual dinner, and the new safety poster ("Think! Then Lift!") has been credited and ordered for every site.
Last year, with four accidents, the same manager was sent on a course. The poster was already on the wall.
How rare events behave
Suppose accidents happen at random, independently, at an average of two a year, and nothing changes from year to year. The number in any one year then follows the Poisson distribution, the standard pattern for counts of rare, independent events.
| Accidents in a year | Chance (average of 2, nothing changes) |
|---|---|
| 0 | 13.5% |
| 1 | 27% |
| 2 | 27% |
| 3 | 18% |
| 4 or more | 14% |
So a perfect year happens about one year in seven by chance, and a "terrible" year of four or more about as often. Over a decade, a site with this average has at least one zero year 77% of the time. A company with 20 such warehouses will see about 2.7 accident-free sites every year, and could hand out a Golden Helmet each time, with every site exactly as safe as before.
Accidents in a year at a site that averages two, with nothing changing
What comes after the zero
If nothing really changed, the year after a zero year has at least one accident 86.5% of the time, and the year after a terrible year is usually better. That's regression to the mean again, and it makes rewards after good years and courses after bad years look as if they work in reverse: the praised manager's next year is usually worse, the punished one's usually better.
How to see a real improvement
- Look at several years. An average falling from 2 a year to 1 a year over five years is far more convincing than one zero.
- Count near misses. Incidents that almost caused harm are far more common, so they show changes much sooner.
- Compare sites. If the sites that changed something improved more than the ones that didn't, that's a comparison; one site's good year isn't.
Statistics for noobs: small counts swing
When an event happens only a few times a year, the count jumps around a lot just by chance. With an average of 2, getting 0 or 4 is ordinary. With an average of 200, getting 0 or 400 would be astonishing. The smaller the count, the less one year can tell you, and the more you need to pool years or places.
Where it costs you money
Big market falls, defaults in a small loan book and large losing trades are rare events too. A year without any proves little about risk; neither does a year with three. Judge risk on long records and many cases, not on the latest year.
The moral
The following year the warehouse had three accidents. The safety manager has been sent on the course again. The poster is still credited with the zero year, and a second poster ("Lift! Then Think!") is being designed for the sites that had a bad year. Kevin has calculated that about 2.7 of them will have a perfect year next year, and has asked to be on the award committee.
What this model can't tell you
- Accidents aren't perfectly random. Real risk changes with workload, staff and season; the model shows what chance alone does.
- Safety programmes can work. The point isn't that nothing helps, but that one year can't show whether it did.
- Severity matters. Counting accidents treats a bruise and a broken leg the same.
The warehouse, the Golden Helmet and the posters are an illustration. The figures come from the Poisson distribution with an average of two events a year, and our own simulation of consecutive years. Educational content, not health and safety, legal or financial advice.