Lucy Letby and the problem with statistics

First Fred West, now Lucy Letby. At this rate, it won’t be long before Herefordshire has produced more serial killers than it has miles of dual carriageway. You might assume growing up in one of England’s loveliest counties would make people placid, but then you haven’t spent half your life stuck behind a caravan on the A465. They may not all kill people, but Herefordshire people overtake like psychopaths.

But I’m going to park my Monmouthshire prejudice here and suggest that something about the Lucy Letby conviction seems off to me. I’m not going to talk about the medical aspects, because I’m not qualified to comment. Instead I’m going to talk about the statistical aspects, where I’m not qualified to comment either, but then neither is almost anyone else. The interpretation of statistics, especially those involving probability, seems to present an extreme case of what is known as the Dunning–Kruger effect, where a person’s confidence in their own ability in any field is inversely correlated with their true level of competence. In the words of the (Monmouthshire-born) sage Bertrand Russell: ‘One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision.’ Really good statisticians are highly circumspect: consequently when anyone makes a confident statistical pronouncement, there is a high probability they are talking garbage.

But it gets worse. Let’s take a simple estimation task known as a Fermi problem, much beloved of Google job interviewers and the like: ‘Estimate how many piano tuners there are in Chicago.’ What you are expected to do is to guess how many households and public venues contain a piano in the city, assume each is tuned perhaps annually, and then work out how many piano tuners, working a 35-hour week, would be required to tune them all allowing for travel time between appointments.