I’m often discussing probabilities with clients and regulators, and there’s a common misunderstanding that keeps coming up: the order of magnitude of an event’s probability. A 1 in 100 Annual Exceedance Probability (AEP) and a 1 in 2000 AEP both just register as “rare” to most people — but they’re twenty times apart, and that gap matters enormously when you’re deciding what a piece of infrastructure needs to survive.
Percentages and “1 in N” notation don’t build intuition for most people. Here’s a framing that does: imagine picking one random second out of a span of time.
The framework
2% AEP — that’s picking one particular second out of the next 50 seconds.
1% AEP — one second out of the next 100 seconds.
1 in 2000 AEP — one second out of about 33 minutes. This also happens to be roughly the number of years between now and the reign of Tiberius in Rome (14–37 AD) — pick a random year in that span, and you’ve picked the year with about the same odds. This is worth sitting with: 1 in 2000 AEP is the generally accepted credible limit of extrapolation for design flood events. Past this point you’re extrapolating into territory the framing above should make viscerally uncomfortable.
1 in 10,000 — one second out of 2.8 hours. Or a random year between now and the late Neolithic adoption of pottery.
A Probable Maximum Flood (PMF), on a small catchment, sits somewhere around 1 in several million to 1 in tens of millions depending on catchment characteristics — genuinely difficult to build intuition for at all. A few equivalents that land in the same range:
- Picking one specific second between last New Year’s Day and 5pm on ANZAC Day (1 in ~9.9 million)
- Calling the correct colour on a roulette wheel 23 times in a row (1 in ~15.8 million)
- Stopping your car on one specific metre of a return road trip from Brisbane to Perth (1 in ~8.6 million)
All three land within the same order of magnitude — which is itself a useful sanity check: wildly different physical framings converging on the same “several million to one” territory is a reasonable indication the framing is doing its job rather than an artefact of one particular analogy.
Why this matters in practice
None of this is just a communication trick — it’s central to how design events actually get chosen and defended. The framing above earns its keep in a few specific moments:
- Explaining to a client why a 1 in 2000 AEP assessment costs more scrutiny than a 1 in 100. They’re not “both rare” — one is twenty times rarer, and the credible-extrapolation-limit framing above explains why that specific number shows up so often in guidance documents rather than being an arbitrary round figure.
- Explaining to a regulator or a community group why a PMF-based spillway design isn’t overkill. “1 in several million” doesn’t land as a number. “Stopping on a specific metre of the Brisbane–Perth highway” does.
- Catching your own extrapolation creep. If a design event feels routine to reason about, and the framing above says it shouldn’t, that’s worth a second look at whether the record actually supports the number you’re using.
The human mind isn’t built to distinguish the very big from the very small — probabilities below about 1% mostly just collapse into an undifferentiated “unlikely” bucket. Reframing the number as a physical quantity — time, distance, repeated coin flips — is one of the few reliable ways to restore the distinction.
Do you have a framing that’s worked for you? I’d be interested to hear it.