Herculio: ’Tis neither malice, spite, nor virtue
Whose ledger swells, or plucks, the seedy fruits of progress —
But mainly accident.
Lest thee with surety know aught else —
Withhold thy assignations.

The JC’s amateur guide to systems theory
“What makes you think she’s a witch?”
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“We’ve found a witch. May we burn her?”

Monty Python and the Holy Grail

Triago: Pish upon thee, Nuncle. Pish!
Dost thou mean to say
Things peel this way
Through doughty misadventure?

Herculio: Peradventure —

Triago: Pish abeam!
Has thou no more to say than that?
Wouldst thou on this shaky surmise
Withhold rebuke?

Herculio: Perchance, per case, mayhap dear Triago
’Twas but a fluke?

Triago: O! This nuisant planet weighs upon my soul!

Herculio: If ’tis this and nought beside
That flies you to a vernal rage
Our fickle globe in its manifold confound’ry
Lies prettily indeed
For thy alignment.

On herd minds, groupthink and narrative biases

Lucy Letby is back in the news in 2024. On 24 May, the Court of Appeal denied her leave to appeal against her convictions. On 10 June, her retrial for the attempted murder of “Child K” began in Manchester, and on 2 July she was found guilty. On 3 July the Court of Appeal released its judgment on its dismissal of her appeal. All of this came against a backdrop wherein, on 13 May, New Yorker magazine published “A British Nurse Was Found Guilty of Killing Seven Babies. Did she do it?”, a 13,000-word investigative piece questioning the safety of Letby’s original convictions.

The New Yorker piece is — was, perhaps — loosely geo-blocked in the UK, ostensibly to avoid contempt of court pending the outcome of the retrial. But it is not hard to find online, and in any case ran unedited in the New Yorker’s UK print edition, so there may be some canny “Streisand Effect” marketing at play here. That a carefully researched piece is not available, when there is so much intemperate commentary published by everyone else, raises its own questions about the practicality of sub judice rules in the age of the worldwide internet, but that is a discussion for another day.

Having been convicted of multiple infant murders, the general public’s view is clear: justice has been done. The sooner Letby’s name fades from the commonplace the better.

But look a bit closer and the picture is complicated. The physical evidence implicating Letby is all circumstantial: eyewitness evidence does little more than put Letby at the scene of the alleged incidents — a place she was contractually obliged to be. No one saw her do any of the acts of which she has been accused. The medical evidence indicating foul play is technical. The strongest parts of it — relating to insulin levels — relate to children who survived. The evidence that resonates most strongly with the public — Letby’s alleged “confessional note” in particular — is not quite what it seems. Nor is the evidence that any of the infants were the victims of foul play, by anyone, overwhelming. The case for conviction emerges from a preponderance of small pieces of evidence that all seem to point in the same direction. But there is no smoking gun. The most compelling proposition seems to be Letby’s opportunity: she alone was rostered on and onsite during all the alleged incidents.

This argument is founded on improbability — what are the odds that the one nurse who was present on all occasions did not have something to do with this unprecedented cluster of cases? That said, it does not appear that either prosecution or defence brought any statistical analysis to bear on that gut sense of improbability.

A binary status

Now she is in prison for the whole of her life, all appeals exhausted and all pending retrials completed, just two narratives are available. The simple one: she is a serial murderer of premature infants and therefore the personification of unspeakable evil; or the unthinkable one: she is the victim of a breathtaking miscarriage of justice.

Serial murderers of any kind are vanishingly rare in Britain. Wikipedia lists fifty-five, since 1600. But so are miscarriages of justice. Wikipedia lists fifty-four, since 1255.

Both the available narratives, then, are highly improbable outcomes. They leave untouched a vast range of more likely explanations which suffer the disadvantage of providing no closure on a series of tragic events: we seek narratives that explain troubling events in the world, those that say, “well, it’s hard to say” don’t. We do not find them useful. Few of us happily occupy that indeterminate space. We tend to conclusive narratives, however unlikely.

What is interesting is how we are pushed by our institutions into shutting this individual out of that wide middle ground in which she is an ordinary kid, with pluses and minuses, virtues and failings, just like the rest of us: neither angel nor devil, who had the misfortune to be involved in these tragic events.

The criminal justice system forces us into an odd kind of anecdotal reductionism: it focuses on discrete, actions and pieces of evidence: what was seen and done, literally microscopic observations: levels of insulin and c-peptide; unusual skin blotching patterns and so on. We are expected to thread these atoms together and build them into a picture that renders a compelling picture at a far higher abstraction level.

Being pattern-matching machines, we use whatever morsels we find to build a narrative. Once we are primed with a theory, we tend to dive deeper into the details to prove our case. We strive to fit whatever remaining facts we can find to fit it. Hence, we are at risk of a kind of tunnel vision, when our immersion in those atomic details crowds out a wider perspective.

It is only later, if at all, that we might ask the “big picture” question: how plausible — how likely is it that an experienced nurse with no history of mental illness, criminality, sociopathy or familial dysfunction, let alone prior medical misadventure — could suddenly transform into a killer of such sophistication as to go undetected for eighteen months? Why would a person who had dedicated her life to the medical care of newborns — who was until then, by all accounts, very good at it — suddenly begin behaving in such a destructive and vanishingly rare way? Why, in the absence of hard evidence displacing the presumption that this is not what normally socialised people do, would this be the preferred theory of the case, and not “an unsual but not remarkable cluster of accidents”?

Case for the prosecution

Lucy Letby’s case, on its face, seems a lot more like Chamberlain’s than Bain’s. It is not beyond question that none of the children were murdered. For each event taken separately, there is a plausible non-criminal explanation. Indeed, Lucy Letby was not immediately suspected of involvement in any of the deaths.

The case for Letby’s innocence has been well-stated enough. The New Yorker piece describes the statistical problems. Peter Elston and Michael McConville’s We need to talk about Lucy Letby podcast goes into great detail about the technical medical credibility of the case, and Tried By Stats TriedbyStats website is an excellent way of conveying the tremendously unintuitive implications of what might look like damning evidence.

There is a risk, of course, that these sources, all promoted by individuals by now deeply committed to the intellectual proposition that there has been a miscarriage of justice, suffer their own form of “defender’s” tunnel vision, of course — but in the main their arguments are clear, well-grounded and compelling.

But this was no kangaroo court: the British justice system is rightly a thing of international renown. It gave Lucy Letby a fair hearing, at which she was represented by a King’s Counsel who left few stones unturned: the trial ran for ten months. There ought to be clear, well-grounded and compelling arguments that take Lucy Letby from an innocent nurse, unluckily implicated by circumstantial evidence but fundamentally just in the wrong place at the wrong time, and instead set her out as a serial murderer. We might expect tunnel-vision-inflicted innocence campaigners to overlook such uncomfortable facts, but not those persuaded of Letby’s guilt.

And there is an equally strident segment who are. A Reddit community of yeoman amateur investigators numbers 11,000 members. Journalists who covered the trial in detail have published films, podcasts and have forthcoming books about the “Killer Nurse” (Liz Hull from the Mail and Judith Moritz from the BBC). The prosecution’s main expert witness, Dr Dewi Evans, has gone to unusual lengths to dismiss the concerns of innocence campaigners whom he feels to be unfairly targeting him.

The journalists and witnesses have the advantage of having been intimately involved with, or present, throughout the legal process. Those people, you would think, would be banging on about the clinching facts that fairly put Lucy Letby away. The voice of reasonable protest of her innocence ought to soon be quieted. But if they can articulate these damning facts, in their voluminous reporting to date, they haven’t. The timid voice of protest grows louder.

Confirmation bias

“Angel” and “devil” narratives become self-fulfilling: once you’ve adopted one, you can panel-beat almost any subsequent information to suit your view.

The little definitive peripheral evidence there is about Lucy Letby is coloured dramatically depending on who is looking at it. For example, her social media activity. Here is BBC Panorama reporter Judith Moritz, in a piece to camera,[1]:

“Sparky, full of fun, popular — she looks like the life and soul of the party in these photos. I don’t know what Britain’s most prolific child killer should look like — I’m pretty sure it’s not this, though.

And then, a few moments later:

“She comes across as — mousy; a bit normal — you can’t really marry that with the enormity of what she’s been accused of.”

If — and only if — we are persuaded of her guilt, her vivacious personality and active social life notwithstanding that malign nature mark her out as a psychopath. It corroborates and amplifies her wickedness.

If we believe she has been wrongfully convicted despite that vivacious personality and active social life — what sort of serial killer is like that? — it only confirms and illustrates the single-mindedness with which a vicious criminal system will crush an innocent, unsuspecting spirit.

If we hold a neutral perspective, we see this behaviour as perfectly normal. It tells us nothing: it places Lucy Letby in that ordinary space, with the rest of us, within a standard deviation of the mean. There have been very, very few serial killer nurses. We have no idea what, as a rule, they are like. This information does not help us.

In the language of the criminal law Lucy Letby’s social media activity has low “probative” content — it doesn’t prove anything — but high “prejudicial” value — it colours any existing preconceptions a jury might hold. A court may exclude this evidence if “its prejudicial effect is out of proportion to its probative value”.[2]

That Lucy Letby searched online for the parents of the deceased is consistent with either breathtaking malevolence — if you take it that she is a serial killer — or affecting compassion — if you take it that she is not. By itself, it is evidence of neither. We all search online for individuals we meet in real life — even people we know we probably shouldn’t: this is perfectly normal behaviour. We are curious, imperfect animals.

Standpoint intersection ahoy

This case stands at the intersection of at least four distinct fields of enquiry: law, medicine, statistics and ethics. They are not “commensurate”: each has its own rules, customs and institutions. They do not necessarily agree.

In a perfect world, they would converge, but the world is not perfect. They may conflict. There will be times when the correct legal outcome is not the moral one, where the moral one does not bear out the statistics, where the statistics are at odds what we know, and so on. There are inevitable incongruities.

Emotions are already aggravated; the stakes are raised yet higher by the undoubted loss and grief of the families of lost infants. That grief cannot be avoided. It burdens the families whatever its cause. That the families are bereaved is not at issue: the question is why: neither conviction nor acquittal necessarily delivers or denies justice for their loss. One can respect the families’ unimaginable grief and seek to ameliorate it, by arguing her case.

Substance, form and process

We must keep in mind these different frames of reference. There is a substantive element comprising medicinal, statistical and observational information. It is filtered through a formal framework — the legal definition of “murder” — and a procedural one: the processes and customs one must observe to reach a formal legal conclusion — the presumption of innocence, the adversarial criminal justice system, the laws of evidence, the rules of court procedure, the tactics and strategies that adversarial teams must adopt within that milieu to best present their case, and the "tribunals of law and fact” — judge and jury — who must ultimately settle the question. Neither judges nor jury are necessarily, ethicists, statisticians, physicians or metaphysicians.

A legal conviction, or acquittal is a highly constrained, artificial process: it has evolved over centuries to favour certainty over doubt while protecting the innocent from unjust punishment.

By contrast, in the “town square” there is a freer debate. Blogposts, twitter threads, podcasts, discussion forums, TV documentaries and investigative journalism address different questions with different information, looser rules of engagement and greater or less intellectual rigour.

The justice system is gives the accused the benefit of marginal doubt. Acquitting the occasional perpetrator is a “lesser evil” than convicting a single innocent. In the town square, the accused are afforded far less doubt.

The medical misadventure cases

Indeed, cases involving medical misadventure, where there is no direct evidence and only subsequently collated expert evidence as to statistics or “science” make up a fair proportion of those miscarriages of justice.[3] Sally Clark, Daniela Poggiali and Lucia de Berk are but three examples of convicted innocents. The last two have strikingly similar facts patterns. We should not take concerns about statistics lightly.

Where there is no “direct” evidence, form and procedure become all the more important.

In Lucy Letby’s case no direct evidence definitively links her to a single murder. It is logically possible she did commit the murders, logically possible she did not, and logically possible she played a role in some or all of the deaths that may warrant criticism but not a murder conviction.

Probabilities

It comes down, at some point, to an estimation of probabilities. These inform how “sure” one can be about the proposition “defendant murdered victim”.

These murder cases have an unusually wide range of unknowns. In isolation , we cannot say whether there was any murder at all. The deaths could have been innocent, and they could have been culpable to some legal standard short of murder (negligence, for example), and that culpability may be someone other than Lucy Letby. As the Post Office Horizon IT scandal has illustrated, striking misadventure can emerge from the collected actions of many mediocre people, none of whom had in mind any great malice. Crowds can act with delusion and madness, just as they can with wisdom.

Where there are unknowns we talk in terms of probabilities. What are the odds that this could happen by chance? What are the odds that the same thing could happen repeatedly? For there is kind of meta-statistics at play here, too: even if the odds are fair for an individual case, an unusual repetition of cases creates its own meta-narrative. It rebuts the individual presumption.

Roll once and get a six, and there is no surprise. This will happen one time in six, and there was no more likely outcome. Rolling a one or three is just as surprising.

Rolling three consecutive sixes is less probable, but still not infeasible: you would expect it to hby chance once in two hundred and sixteen sequences. If you are managing tend of thousands of sequences, you should be surprised if there are not several instances of three consecutive sixes.

But the odds of rolling fifteen consecutive sixes are a shade better than one in half a trillion. You should start inspecting your die. It is far, far more likely that that the die is defective. (If you manufactured a half trillion dice, would not one of them be malformed?)

This is the essence of the “shift pattern” evidence against Lucy Letby. Being premature neonatal infants and kept in hospital, these are children at heightened risk of “natural” death: that is why they are in hospital. The number of deaths per annum varies by year, but it is greater than zero. Let us say on average there are five infant mortalities in a year. In a given year with three 8-hour shifts in a day there are roughly 1000 shifts. The probability of an infant dying on a given shift — where we have no prior information about that infant or the persons on that shift — is therefore 5/1000 or 1/200.

Mathematising this, for each shift, this is the equivalent of rolling a 200-sided die where 199 sides are S (for “Safe”) and 1 is M (for “mortality”). A person working 240 shifts a year would expect to be on duty for between one and two mortalities per year.

A person who was on duty for all five mortalities in an average year would be the equivalent of rolling five Ms and 235 Ss in the year

There is much, much more chance of rolling an S than an M, but if you work two hundred shifts you would expect one M. What are the odds of rolling 6 “D”s in a row? It is straightforward to calculate: one in (200 * 200 * 200 * 200 * 200 * 200). One in 64 trillion.

But this is not the right calculation, because there were 178 shifts


while each of the events on her shifts was in itself explainable, the sheer number of consecutive deaths on her shift were not.

Unlike in Sally Clark case, prosecution did not e


Each of these enquiries requires an answer “beyond reasonable doubt”. If a victim dies in the presence of a single person with a means and motive, such that if the death was intentional there is no other possible suspect, if there is a reasonable doubt as to the death being natural — even if it probably was not — there can be no conviction.

“Once is happenstance. Twice is coincidence. Three times is enemy action.” — Ian Fleming, Goldfinger (1959)

Here is where a sequence makes a difference. One such occurrence might be improbable, five occurrences extremely improbable, 500,

So

What are the percentages of serial killers with history of broken homes, physical or sexual abuse, and mental illness? What percentage are female?

“God complex”

Killing people is not evidence of a God complex. The basest criminal can take life. Bringing people back to life — that is evidence of a God complex.

Evidence

Insulin “smoking gun”

In two cases (Child F and Child L) lab tests indicating high levels of insulin without accompanying c-peptide, which is prime facie evidence of administered insulin (naturally occurring insulin is accompanied by c-peptides; artificially administered insulin is not). Insulin was not prescribed for either infant. If it was true that insulin was added without prescription this is evidence of actual human agency in these two episodes.

The defence team accepted the prosecution’s claim that insulin was added to parenteral nutrition bags and it was presented to the court as an agreed fact.[4]

  • The test in question was not reliable for factitious insulin. From the label:

“Please note that the insulin assay performed at RLUH is not suitable for the investigation of factitious hypoglycaemia. If exogenous insulin administration is suspected as the cause of hypoglycaemia, please inform the laboratory so that the sample can be referred externally for analysis.”

  • The test results seem to indicate very high levels of insulin: 4657 pmol/L is about four times a dangerously high level in an adult.[5] While, yes, this is what you might expect a murderer to try to do —
  • Both babies recovered: You might expect premature babies registering such high insulin levels — four times a critical level for an adult[6] — might have at least caused a fuss at the hospital. But not only did the babies make a full recovery, with no record of hypoglycemic coma, but —
  • No-one even noticed the high insulin in their tests until 2018: That is, three years after the babies made a full recovery. If you are looking for a res ipsa loquitur about these events, can we suggest that this is as indicative of negligence in the clinical staff administering the test, or the self-professed unreliability of the tests for detecting factitious insulin.

The Texas sharpshooter

See the TriedbyStats website: Over 730 shifts, with 38 “suspects” If you self-select one

The victim’s families

There are unquestionable victims here: the families. If Lucy Letby wasn’t responsible then this was either an unavoidable accident, in which case, there is no closure, or there is another culpable explanation — an alternative murderer seems extremely implausible — but medical misadventure of some kind is not. Difficult

The post-it note

Everyone seems to accept the notes are highly inclusive and of little evidential value.

“The ramblings of someone under extreme psychological pressure.”

Resources

Online

Podcasts

The difficult cases

There are excellent podcasts on each of the difficult cases mentioned above.

See also

References

  1. Panorama, 18 August 2023
  2. Section 126, Criminal Justice Act 2003, which (per explanatory notes) preserves the common law power for the court to exclude evidence where its prejudicial effect is out of proportion to its probative value.
  3. The “junk science” of “forensic odontology” (comparing bite marks), blood spatter analysis and hair microscopy are a recurring case of injustice: Chris Fabricant, Junk Science and the American Criminal Justice System.
  4. Science on Trial
  5. There is plenty of online angst about whether the level recorded was abnormally high or absurdly high, such that such a level had never been witnessed in medical history: let’s go with abnormally high.
  6. See: Very Well Health: Hyperinsulinema (High Insulin Levels).