Two risks can’t be compared until they share a denominator

A rate is a fraction, and the bottom half is the argument

Any statement about how risky something is takes the form of harms divided by exposure. The top of that fraction is usually well defined — an injury, a failure, a loss. The bottom is a choice, and it is a choice that’s frequently made silently, by whoever collected the data, for reasons that had nothing to do with the comparison you are trying to make.

Per trip, per hour, per kilometre, per participant, per year of exposure: these are all defensible denominators and they produce different answers. A mode of travel that covers long distances quickly looks safe per distance and less safe per hour. An activity people do rarely looks dangerous per session and harmless per year. Neither figure is wrong, and quoting one without the other is how most misleading risk comparisons are constructed without anybody lying.

Choosing the denominator that matches the decision

The right unit is the one you are actually choosing between. If the decision is how to get to a specific place, the relevant comparison is per journey of that length, because that is the exposure you will incur. If the decision is how to spend an afternoon, per hour is the relevant unit. If the decision is whether to take up an activity indefinitely, per year of participation is closer to what you want.

Getting this wrong isn’t a technicality. A comparison made in the wrong unit can invert the ranking of two options entirely, and the resulting decision is then confidently and precisely wrong. It is worth stating the unit out loud before looking at any numbers, because once the numbers are in view the question of what they are per tends to stop being asked.

There is a further subtlety when the exposure itself is the thing under discussion. Comparing two options that would occupy different amounts of time is not a comparison of rates at all; it’s a comparison of totals, and converting to a common rate quietly discards the fact that one option keeps you exposed for longer. In those cases the total harm over the whole activity is the honest figure, and any rate is a step on the way to it rather than the answer.

The population underneath is a second hidden choice

Even with a fixed denominator, a rate describes a group, and you are one person with particular characteristics. A rate computed across all participants includes people whose exposure and behaviour differ from yours in ways that may dominate the average. Age, experience, conditions and equipment often vary enough that the overall figure describes almost nobody.

This cuts both ways and does not license optimism. Everyone believes they are in the safer subgroup, which cannot be true of everyone, and the belief is rarely based on any data about the subgroups at all. The defensible move is to ask whether the reported rate is broken down, and to use the breakdown if it exists rather than assuming which side of it you fall on.

Voluntary and involuntary risks are not compared like for like

People reliably accept much higher risks that they choose and control than risks imposed on them, and this shows up consistently in public risk perception. It is easy to treat that as pure irrationality, and it is not entirely: consent, control and the distribution of the harm are genuine moral considerations that a single number cannot represent.

What the numbers do is separate the arithmetic from the values. Establishing that two activities carry similar harm per hour doesn’t settle whether they should be treated the same, because one may be chosen and the other inflicted. Confusing those two conversations makes both worse, and the honest structure is to fix the comparison first and argue about the values afterwards.

Reading a comparison in the wild

Three checks catch most of the trouble. What is the denominator, and would a different one reverse the claim. What population is the rate computed over, and is it the one you belong to. And is the harm being counted the same in both cases, since deaths, injuries, incidents and reported incidents are quite different quantities and get swapped around freely in casual argument.

A fourth check applies when the comparison involves very different frequencies of participation. Comparing a daily activity with an annual one on a per-occasion basis will make the annual one look terrifying, and comparing them per year will make the daily one look worse. Both presentations are available to anyone building an argument, which is why the presence of a comparison should raise rather than lower your guard.