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.
It only takes one dodgy assumption to reach a conclusion that is diametrically wrong
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. Most people arrive at a guesstimate around 150.
You are, it’s true, making dodgy assumptions here. I suspect that many people never tune their pianos, and that many piano tuners work part-time. But often your erroneous assumptions will cancel each other out. Some estimates will be too high, others too low, but overall your answer won’t be insane. And even if your maths goes hopelessly wrong, your answer will still be exposed to a kind of smell test. It’s fairly obvious that there aren’t 20 piano tuners in Chicago, and it’s equally obvious that there aren’t 20,000. Or 200,000. After all, if a significant part of the Chicago economy derived from people wandering around continually tuning each other’s pianos, someone would have made a Netflix documentary about it.
Neither of these corrective mechanisms applies when presenting probabilistic statistics. From the O.J. Simpson trial to Lucia de Berk, from Ray Krone to Sally Clark, there are cases where people have presented probabilities in court which are out by a factor of thousands or even millions – and no one notices until months later when the Royal Statistical Society or some other hardcore stats geeks have a well-deserved hissy fit. It only takes one dodgy statistical assumption to reach a conclusion that isn’t just off the mark, but astronomically stupid or diametrically wrong.
Most disciplines are like plumbing. There are a few brilliant plumbers, many average plumbers and a few bad ones. But even a below average one is probably pretty valuable most of the time. If I have a clogged pipe, almost any plumber selected at random will do a better job than I can. The use of statistics, however, is more like plutonium than plumbing. It’s far more likely to be dangerous than useful, and when manipulated with malign intent it’s catastrophic.
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