Sunday e-mail 12th January: Serial killers who weren't

The probability of being convicted for serial murder is low but never zero

Here it is, Sunday, about noontime. You are looking at the new iPhone your Nan gave you for Christmas and reading the latest e-mail from Crime & Psychology. It’s all about a Dutch serial killer who probably wasn’t a Dutch serial killer at all.

What were the chances that would happen?

Well, everything depends on how you calculate those chances. If your Uncle George had prognosticated this exact set of circumstances last New Year - as 2023 dissolved into 2024 – at this point you’d be looking back in speechless wonder, asking yourself why you never took his prophecies more seriously. But - given that Uncle George in reality did no such thing - your sense of wonder remains untroubled.

After all, something had to happen, right?

The probability of this particular set of circumstances occurring may well have been miniscule, but – here is the vital point – so was the probability of every other set. The possibilities are endless. You might have been on a tour of the Somme in a 1975 Land Rover, or getting your hair done by Lila who lives on the corner and used to be a spy for MI6, or staring wistfully at your old school atlas and wondering how many of the countries you marked with a hopeful X you are, in fact, ever going to visit. However many possibilities there may be, the probability of one of them happening is always 100%.

The point is that unusual, unlikely events happen. They do. They happen all the time (they’re happening right now). Maybe you’re thinking, ‘Uh-uh, not in my case they’re not. My life is utterly grey, dull, and predictable,’ – but you know what? The probability that you’d think that very thought right at that very moment was so low as to be impossible to calculate. There aren’t enough zeroes in the world.

Now imagine that you’re a nurse who works on a ward with very sick children. Imagine that several patients, tragically, die while you are on shift. That would be upsetting enough in itself…but now imagine that you find yourself accused of serial murder. This exact thing happened in 2003 to a Dutch nurse named Lucia de Berk.

The prosecution’s case rested on the testimony of a statistician. He claimed the odds that all these deaths would happen when one specific nurse was on duty were 342 million to one.[i] This evidence was so vital to the case that one professor of criminal law said he did not ‘see how one could have come to a conviction without it’.

This series of deaths certainly qualifies as an unusual, unlikely event, but remember – unusual, unlikely events happen. What were the chances that you’d be reading about Lucia de Berk today?

Ben Goldacre (a popular science writer whose work I recommend) points out that even if we were to accept it, that figure of 342 million to one would be ‘largely irrelevant’.[ii] That’s because numbers on their own mean nothing. What matters is what you do with them.

The fact that four infants died is a tragedy, not in dispute. The important question is, how best to explain it?

In other words - given that four infants died while under de Berk’s care, which is the better explanation: natural causes or serial murder? Sure, it may be very unlikely that natural causes would claim four victims in a row, but it might well be even more unlikely that a serial killer was loose. Serial killers are, thank heavens, almost vanishingly rare.

Photo by CrowN on Unsplash

De Berk’s final appeal ended in March 2010 – seven years into her ordeal. The prosecution requested the court to deliver a Not Guilty verdict.

This has been a breakneck introduction to a phenomenon that statisticians call the prosecutor’s fallacy. It’s a flaw in human reasoning that has played a big part in a number of questionable jury decisions. If you found it interesting, you’re going to love this week’s Crime & Psychology newsletter. It’s about the role of probability and human reasoning in the criminal justice process. We’re going to follow a major crime through every stage from conception to sentencing, seeing how mistaken judgements of probability occur at each one. Be there, Crime & Psychology fan, or you may never know!

If you’d like to know more about the technicalities of the prosecutor’s fallacy, check this out.

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This week’s bullet list features five instances of the prosecutor’s fallacy:

· Most infamous is the case of Sally Clark, tried in 1999 for the murder of her two babies. Professor Sir Roy Meadow testified that the probability of having two infants who suffered Sudden Infant Death Syndrome (SIDS), was one in 73 million. But that was not the relevant number. Given that two babies had died, the court should have asked which was more likely – twin cases of SIDS, or a mother guilty of double homicide?

· Shortly after the Clark fiasco, in 2002, Angela Cannings was convicted of smothering two children. She fell victim to what had by then become known as ‘Meadow’s Law’: ‘one sudden infant death is a tragedy, two is suspicious, and three is murder, until proven otherwise’.

· In 2003, almost the exact same reasoning was used in Australia to convict Kathleen Folbigg. Despite a complete lack of medical evidence, she was found to have smothered four children. The grieving mother was called ‘Australia’s worst female serial killer’.

· At the OJ Simpson trial, the defence claimed that Simpson probably didn’t kill his wife. After all, he was a serial abuser and most abusers don’t go on to commit murder. I’m sure you can see the flaw. One of Simpson’s attorneys said later that it was his job to defend his client, not to be an expert in statistics.

· The prosecutor’s fallacy is especially pernicious when DNA evidence is used. In 2010, Troy Brown was found guilty of raping a young girl. His DNA matched that of the rapist. Jurors were told that there was only a 1 in 3 million probability of an innocent person having a match. They interpreted it as meaning that there was a 1 in 3 million probability that Brown was innocent.

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[i] Fellow stats-heads may be interested to know how the ‘expert’ calculated this number. He simply multiplied p-values together. No, really.

[ii] Goldacre, Ben: Bad Science, Fourth Estate, London, 2009, p274