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“We’ve found a witch. May we burn her?”
“We’ve found a witch. May we burn her?”
:— ''Monty Python and the Holy Grail''}}
:— ''Monty Python and the Holy Grail''}}
{{c|Statistics}}
====On herd minds, groupthink and narrative biases====
{{drop|L|ucy 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 “{{plainlink|https://wayback-api.archive.org/web/20240000000000*/https://www.newyorker.com/magazine/2024/05/20/lucy-letby-was-found-guilty-of-killing-seven-babies-did-she-do-it|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 Lucy Letby’s name fades from the commonplace the better.
But look a bit closer and the picture is more complicated. The evidence indicating foul play is of a very technical medical nature. The evidence implicating Letby is all circumstantial. The parts that resonate most strongly with the public — the “confessional note” in particular — are not
quite what they seem. Eyewitness evidence does little more than put Letby at the scene of the incidents — a place she was contractually obliged to be. Nor is the evidence that any of the infants were the victims of foul play, by anyone, strong. The case for conviction ''emerges'' from a preponderance of small pieces of evidence that point in the same direction. 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 is an argument necessarily founded on ''improbability'' — what are the odds that the one nurse who was present on all occasions did not have something to do with it 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====
{{drop|N|ow she is}} in prison for the whole of her life, all appeals exhausted and all pending retrials completed, there are two available narratives for Lucy Letby. 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.
By percentage of the population, 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 these outcomes, then, are ''highly'' improbable. They leave untouched a vast range of more probable outcomes which suffer the disadvantage of being unsatisfactory explanations of an awful situation: We like our narratives to tell us about the world, those that says, “well, it’s hard to say” don’t do that. We do not find them useful. Few of us happily occupy that indeterminate space.
JC will advance the position perhaps we ''should''. While it may offer little intellectual satisfaction, it may be the best we can reasonably expect.
What is interesting is how we are pushed by [[Systems theory|system design]] into depriving this individual 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.
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 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.
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?
Three notorious cases from the antipodes illustrate the disadvantage of not asking those big-picture questions
==Interlude: difficult cases==
====A ring of dust around Ayers Rock====
{{drop|L|indy and Michael}} Chamberlain and their three children were camping at Ayers Rock in central Australia in August 1980.<ref>''{{plainlink|https://open.spotify.com/show/4sADNVGYAf0VnP6TqaBW3i|A Perfect Storm: The True Story of the Chamberlains}}''</ref> On the evening of the 17th the family were around a campfire with other campers when Lindy thought she heard a dingo (an indigenous wild dog) in the brush near the tent where her infant daughter Azaria was sleeping. She went to check on the baby, and saw a dingo leaving the tent which Lindy discovered to be empty: the child was missing. Despite a search of the surrounding area, Azaria was never found. Lindy had no explanation for what had happened but quickly surmised that the dingo must have snatched the child.
Believing Lindy Chamberlain to be acting strangely the police grew sceptical of her story. Believing dingo attacks to be unusual, and expecting there to be more evidence if a dingo was responsible, the police settled on the theory that in fact Lindy Chamberlain had murdered and disposed of her baby, and she was charged with murder and in 1982, sensationally convicted. The prosecution’s case was that in her five-minute absence from the campfire, Lindy returned to her tent, changed into tracksuit pants, took Azaria to her car, obtained and used scissors to cut Azaria’s throat (avoiding any arterial bleeding on the baby’s jumpsuit but spraying some over the footwell interior), waited for Azaria to die, hid the body in a camera case in the car, cleaned the blood from everything including the outside of the camera case, changed back out of her tracksuit pants, for her son, returned to the tent, replaced the jumpsuit, left blood splashes there, and returned to the campfire with her son without the other campers noting anything was amiss.
Lindy Chamberlain spent three and a half years in prison. In 1986 Azaria’s matinee jacket was found at the entrance to a dingo lair four kilometres from the campsite. Shortly afterwards she was released and pardoned and her conviction finally quashed in 1992.
Forensic evidence of what experts told the court was blood spatter in the foot-well of the Chamberlain’s car turned out, much later, to be sound deadening compound sprayed on the car during manufacture.
====Satanic panic in the Garden City====
{{drop|I|n 1991, Peter}} Ellis, a childcare worker at a daycare centre in New Zealand was charged with horrific child sexual abuse against children in his care.<ref>''{{plainlink|https://open.spotify.com/show/1ZHmLlciFEQ33kkSPZTtyC|Conviction: The Christchurch Civic Creche Case}}''</ref> These included bizarre rituals and acts some attributed to “satanic panic” prevalent at the time, including acts of graphic violence, amputation and assault, such as children being forced into a steaming hot oven, buried in coffins, having navels removed with pliers and a “circle incident” where Ellis and his co-workers supposedly took a group of children to a remote apartment where they were made to stand naked and kick each other while the adults danced around them.
The prosecution relied on carefully selected evidence from very young children (all under 5) who had been coached, perhaps inadvertently, by social workers using suggestive interview techniques to embellish their stories, and no doubt further encouraged by their parents. In total one hundred and eighteen children were interviewed. Those who insisted there was no abuse and those who made patently impossible claims (such as those that would leave permanent injuries) were excluded from the evidence for the case.


====On herd minds, groupthink and narrative biases====
In 1993 Ellis was convicted on 16 counts of child sex abuse against seven children. While doubts remained about the fairness of the trial due to the interview techniques and lack of corroborating evidence (in particular, no physical injuries to any children. Ellis maintained his innocence throughout and continued to fight for his name to be cleared, but died in 2019, and was not finally exonerated until the New Zealand Supreme Court 2022 finally quashed all remaining convictions citing a substantial miscarriage of justice due to unbalanced evidence and contamination of the children’s testimonies.  
{{drop|L|ucy Letby is}} back in the news in 2024. On 24 May 2024, the Court of Appeal denied her leave to appeal against her conviction.<ref>Neither the grounds for the appeal nor the reasons for refusal are yet public, pending the outcome of her retrial.</ref> On 10 June, her retrial for the attempted murder of “Child K” began in Manchester. But all this was thrown into sharper relief when, on 13 May, ''New Yorker'' magazine published {{plainlink|https://wayback-api.archive.org/web/20240000000000*/https://www.newyorker.com/magazine/2024/05/20/lucy-letby-was-found-guilty-of-killing-seven-babies-did-she-do-it|''A British Nurse Was Found Guilty of Killing Seven Babies. Did she do it?''}}, a 13,000-word investigative piece questioning the the safety of Letby’s original convictions. The piece was loosely geo-blocked in the UK, ostensibly to avoid contempt of court during the retrial. But it is not hard to find online, and it ran unedited in the New Yorker’s UK print edition, so there may be some canny “Streisand Effect” marketing at play here too. <Ref>That a carefully-researched piece is not available, when so 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 world-wide internet, but that is a discussion for another day.</ref>


Those with a passing acquaintance of the case tend to suppose that, having been convicted of multiple infant murders, the public verdict is in and the sooner Lucy Letby’s name fades from the commonplace the better. She admitted everything in a note, right?
====Murder in the family====
{{drop|T|wenty-two year-old}} David Bain claimed he returned from his paper round at 6:45 on the morning of June 20,1994, went downstairs to the laundry room, in the dark, to put a load of washing in the machine.<ref>''{{plainlink|https://open.spotify.com/show/3jgt4218rVMRh9OcIRu8qd|Black Hands: A Family Mass Murder}}''
</ref> It was so dark he did not notice his father’s bloodstained clothes in the machine, and inadvertently washed them. He then returned upstairs to find his
the rest of his family murdered. At 7:10 Bain placed a agitated call to emergency services alterting them to the tragedy. A note typed on the computer, apparently by David’s father Robin, said, “you were the only one who deserved to live.”


But look a bit closer and the picture is more complicated. The “confessional” note is not
David Bain was charged with the murders of his parents, Margaret and Robin, and his three siblings, Arawa, Laniet, and Stephen. His defence was that his father Robin, motivated by a troubled relationship with his wife and children, murdered the rest of the family before turning the gun on himself.  
quite what it seems. There is no eyewitness evidence doing more than putting Letby at the scene of the incidents — a place she was, in most cases contractually obliged to be. There is little direct evidence that these infants were treated with malice by anyone, and what there is is not unequivocal. Each piece of circumstantial evidence, in isolation, is ambiguous.  


The case for conviction ''emerges'' from the preponderance of evidence, rather than subsisting in a particular smoking gun.  
David Bain was convicted on all five counts of murder in 1985, based on circumstantial evidence, including bloodstains on David’s clothing and his fingerprints on the murder weapon.  


At this point, now she is in prison, there are two available narratives: Lucy Letby is either a person of calculated evil, or the victim of a breathtaking miscarriage of justice.  
Bain maintained his innocence and appealed all the way to the Privy Council which in 2007 identified significant errors in the handling of evidence, potential bias and shortcomings in the police investigation. Citing a substantial miscarriage of justice the Privy Council quashed Bain’s convictions and ordered a retrial. In the retrial the jury acquitted David Bain of all charges, concluding that the evidence did not establish his guilt beyond all reasonable doubt. Bain remains a free man.
==Lucy’s case==
====Narrative bias====
{{drop|T|hese three cases}} illustrate the problem of circumstantial evidence cases: where there is no reliable direct evidence of the alleged crime, one tends to start with a hypothesis and then fit whatever forensic evidence you have into it. There is a kind of tunnel vision at play. This is so regardless of whether you are convinced of guilt or innocence.


By percentage of the population, serial murderers are vanishingly rare in Britain. So are miscarriages of justice. These extremes leave untouched between them a vast range of ambivalent and more plausible alternatives which suffer the disadvantage of not offering a good explanation: We like our narratives to tell us things about the world, and a perspective that says, “well, it’s complicated” doesn’t tell us much about the world. It isn’t useful. So few of us occupy that space.  
The idea that any mother would cold-bloodedly murder her nine-week-old baby without warning is ''preposterous''. To even set up this as a hypothesis one must surely have some pretext for believing it to be possible — psychiatric That she would do it at all, let alone with scissors in the footwell of a car, then hiding the body in a camera case, somehow leaving no evidence at all, in a space of ten minutes. Just preposterous. Especially in a situation where there was a plausible non-murder alternative.


JC will advance the position that we ''should''. While it may offer little intellectual satisfaction, it may be the best we can reasonably expect.  
Likewise, for Peter Ellis to have done what he was alleged to do in the first place, regardless of the evidence, would be ''extraordinarily'' improbable. For no adults to witness any corroborating evidence, no-one to notice the children missing for hours on end, for none of the alleged injuries to leave any marks or traces, and for there to be a plausible alternative: ''that none of the events happened at all''.


The system has behaved in a way which deprives this individual of a middle ground, in which she is an ordinary kid, with her pluses and minuses, virtues and failings, just like the rest of us: neither angel nor devil.
For David Bain, on the other hand, it is a different story: there is ''no question'' his family were murdered, and even on Bain’s own theory there were only two possible perpetrators: his father and himself. For David Bain ''not'' to be the murderer, on the agreed evidence, would have to make him incredibly unlucky, and his father to have behaved extremely oddly for a man about to turn a gun on himself.


Given the probabilities at play — 99% of us are neither pure angels or devils, but somewhere along the continuum between — allowing Lucy Letby to sit at only one or other of these extremities seems an injustice in itself.
====Confirmation bias====
====Confirmation bias====
{{drop|T|he problem with}} “angel” and “devil” narratives is that they become self-fulfilling: once you’ve settled on one, you can panel-beat most subsequent information to suit that view. The little hard-edged peripheral evidence we do have about Lucy Letby has been coloured through that lens. For example, her social media activity. Here is BBC reporter Judith Moritz, in a piece to camera,<ref>{{Plainlink|https://www.bbc.co.uk/iplayer/episode/m001q7dl/panorama-lucy-letby-the-nurse-who-killed|''Panorama'', 18 August 2023}}</ref> on reviewing Letby’s social media posts:
{{drop|“A|ngel” 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,<ref>{{Plainlink|https://www.bbc.co.uk/iplayer/episode/m001q7dl/panorama-lucy-letby-the-nurse-who-killed|''Panorama'', 18 August 2023}}</ref>:


{{quote|
{{quote|
“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''.}}
“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:
And then, a few moments later:


{{Quote|“She comes across as — mousy; a bit ''normal'' — you can’t really marry that with the enormity of what she’s been accused of.”}}
{{Quote|“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 already persuaded of her guilt, her vivacious personality and active social life ''notwithstanding her malign nature'' mark her out as a psychopath. It ''corroborates'' and ''amplifies'' her wickedness.
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”.<ref>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. </ref>


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


If we believe neither, but 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. In any case, normal social media activity is neither direct nor circumstantial evidence of her perpetration of the crimes with which she has been accused, or her innocence.  
====Standpoint intersection ahoy====
{{Drop|T|his case stands}} at the intersection of at least four distinct fields of enquiry: law, medicine, statistics and ethics. They are not “[[The Structure of Scientific Revolutions|commensurate]]”: each has its own rules, customs and institutions. They do not necessarily agree.


In the language of the criminal law, then, this 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”.<ref>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. </ref>
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.


Similarly, 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 animals.
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.  


These mechanisms by which we process information are ''biases'' — [[confirmation bias]] — a well-documented logical fallacy where we frame any information to validate what we already believe — or its less-understood converse: [[ignore|''ignorance'' bias]],<ref>JC made this term up.</ref> where we tactically ''ignore'' information that does not support, or tends to contradict, our working theory.  
====Substance, form and process====
{{Drop|W|e 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.


Both biases are in play whether we believe Lucy Letby is a serial killer, or the victim of a grave injustice. Both standpoints are equally ''emotive''.  
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.  


There is no comfortable centre to hold here.
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.
====Standpoint intersection ahoy====
{{Drop|C|riminal justice stands}} here at the intersection of at least four distinct fields of enquiry: law, medicine, statistics and ethics. Their perspectives are not “[[The Structure of Scientific Revolutions|commensurate]]”: each has its own rules, customs and institutions.  


In a perfect world, they would converge, but the world is not perfect. They may conflict. There will be times where the legal outcome is not the moral one, where the moral one is not borne by the statistics, where the statistics are at odds with our knowledge, and vice versa.  
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.


Since we cannot but frame our understanding of the overall scenario through one or other of those prisms, we should expect dissonance, especially in difficult cases.
====The medical misadventure cases====
{{Drop|I|ndeed, 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.<ref>The “junk science” of “forensic odontology” (comparing bite marks), blood spatter analysis and hair microscopy are a recurring case of injustice: Chris Fabricant, ''{{Plainlink|https://www.audible.co.uk/pd/B09PF98JST?|Junk Science and the American Criminal Justice System}}''.</ref> 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.


====Victims====
Where there is no “direct” evidence, form and procedure become all the more important.
{{Drop|E|motions are already}} aggravated; the stakes are raised yet higher by the undoubted loss and grief of the families of lost infants. But that grief is unavoidable and attaches to the families’ loss, which is the same whatever its cause. ''That'' the families are bereaved is not at issue: the question is ''why'': Lucy Letby’s acquittal does not postpone or deny them justice for their loss: no injustice may have been done. So advocating for Lucy Letby’s innocence should be no affront to the grieving families: one can respect their unimaginable grief and, in some way seek to ameliorate it, by arguing her case.


====Substance, form and process====
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.  
{{Drop|S|o we must}} keep in mind the difference between the ''substantive'' “ethical” frame of reference, and in the “legal” frame of reference there is a ''substantive'' element comprising medicinal, statistical and observational information, which is then filtered through a ''formal'' framework (the legal definition of “murder”) and a ''procedural'' one (the processes one must go through and the customs one must observe to arrive at a formal legal conclusion, including the presumption of innocence, the adversarial nature of the criminal justice system, the laws of evidence, the rules of court procedure, the tactics and strategies that defence and prosecution teams 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.  


Needless to say this is a highly constrained and ''artificial'' process: the stakes are high and the process has evolved to favour certainty over doubt and protect the innocent from criminal punishment. It has few of the freedoms and laxities of the “town square”, where a freer debate can, and plainly does, play out in blogposts, twitter rants, podcasts, reddit subforums, and works of investigative journalism of greater or less rigour.
====Probabilities====
{{drop|I|t comes down}}, at some point, to an estimation of ''probabilities''. These inform how “sure” one can be about the proposition “defendant murdered victim”.


In the town square we address different questions with different information, and much looser rules of engagement.  
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.


Our justice system is meant to benefit the accused in marginal cases: acquitting the occasional perpetrator is a “lesser evil” than convicting a single innocent. In the town square, the accused are afforded far less doubt.
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.


But even in the courts we get it wrong sometimes.
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.
====The medical misadventure cases====
{{Drop|I|ndeed, cases involving}} medical misadventure, where no direct evidence and which rely on expert evidence, especially as to statistics or “science”<ref>The “junk science” of “forensic odontology” (comparing bite marks), blood spatter analysis and hair microscopy are a recurring case of injustice: Chris Fabricant, ''{{Plainlink|https://www.audible.co.uk/pd/B09PF98JST?|Junk Science and the American Criminal Justice System}}''.</ref> Sally Clark, Daniela Poggiali and Lucia de Berk are but three recent examples with strikingly similar facts patterns. We should not take concerns about statistics lightly.


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


In Lucy Letby’s case no direct evidence definitively links her to a single murder. No direct evidence unequivocally suggests there was a ''murder'' — as opposed to misadventure, negligence or even inadvertent accident — at all. Each case, taken in isolation, could be plausibly explained as a natural death. But by the same token nor is there unequivocal evidence that any of these were not murders, nor that, if they were, Letby did not commit them.
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?)


The internet is polarised around two highly unlikely contingencies.
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.


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 did not amount to murder.  
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.


The question of whether she should be convicted comes down, at some point, to an estimation of ''probabilities''. These inform how “sure” one can be about the proposition “defendant murdered victim”.
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


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)
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.


====Emergence====
But this is not the right calculation, because there were 178 shifts
{{Drop|T|here is a}} kind of meta-statistics at play here, too. For even if there is reasonable doubt for every individual case, the unusual repetition of cases creates its own meta narrative.


Roll once and get a six, and there is no surprise. That outcome was as likely as any other. Roll ''three'' sixes and it becomes a lot less probable: you would expect that only once in two hundred and sixteen times. Unusual, but nothing yet is seriously amiss. But roll ''ten'' consecutive sixes — a probability of less than one in sixty million — and you should start inspecting your die.


This is the essence of the prosecution case against Lucy Letby: that while each of the deaths that occurred on her shifts was in itself explainable, a sheer number of consecutive deaths on her shift were not.  
: 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
Unlike in Sally Clark case, prosecution did not e
Line 111: Line 164:
*'''The test in question was not reliable for factitious insulin'''. From the label:
*'''The test in question was not reliable for factitious insulin'''. From the label:
{{quote|
{{quote|
“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.”}}
“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.<ref>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.</ref> While, yes, this is what you might expect a murderer to try to do —
*'''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.<ref>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.</ref> 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<ref>See: ''Very Well Health: Hyperinsulinema (High Insulin Levels)''[https://www.verywellhealth.com/hyperinsulinemia-is-associated-with-type-2-diabetes-1087717#:~:text=Your%20insulin%20levels%20are%20considered,could%20be%20diagnosed%20with%20hyperinsulinemia. .]</ref> — 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 —
*'''Both babies recovered''': You might expect premature babies registering such high insulin levels — four times a critical level for an adult<ref>See: ''Very Well Health: Hyperinsulinema (High Insulin Levels)''[https://www.verywellhealth.com/hyperinsulinemia-is-associated-with-type-2-diabetes-1087717#:~:text=Your%20insulin%20levels%20are%20considered,could%20be%20diagnosed%20with%20hyperinsulinemia. .]</ref> — 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 —
Line 120: Line 173:


=== The victim’s families ===
=== 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.
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  
Difficult  


Line 136: Line 189:
*{{plainlink|https://open.spotify.com/show/2x2kstQwsyndvK0S8OOSBZ|We need to talk about Lucy Letby}} (Peter Elston and Michael McConville podcast)
*{{plainlink|https://open.spotify.com/show/2x2kstQwsyndvK0S8OOSBZ|We need to talk about Lucy Letby}} (Peter Elston and Michael McConville podcast)
*{{plainlink|https://open.spotify.com/show/5EZDmxyDtMPeJ1laVDWuWd|The Trial of Lucy Letby}} (Daily Mail podcast)
*{{plainlink|https://open.spotify.com/show/5EZDmxyDtMPeJ1laVDWuWd|The Trial of Lucy Letby}} (Daily Mail podcast)
 
===The difficult cases===
There are excellent podcasts on each of the difficult cases mentioned above.
*''{{plainlink|https://open.spotify.com/show/4sADNVGYAf0VnP6TqaBW3i|A Perfect Storm: The True Story of the Chamberlains}}''
*''{{plainlink|https://open.spotify.com/show/1ZHmLlciFEQ33kkSPZTtyC|Conviction: The Christchurch Civic Creche Case}}''
*''{{plainlink|https://open.spotify.com/show/3jgt4218rVMRh9OcIRu8qd|Black Hands: A Family Mass Murder}}''
{{Sa}}
{{Sa}}
*[[Miscarriages of justice]]
*[[Miscarriages of justice]]
*[[Texas sharpshooter]]
{{ref}}
{{ref}}

Latest revision as of 18:13, 4 July 2024

The JC Sounds Off™
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“We’ve found a witch. May we burn her?”

Monty Python and the Holy Grail

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 Lucy Letby’s name fades from the commonplace the better.

But look a bit closer and the picture is more complicated. The evidence indicating foul play is of a very technical medical nature. The evidence implicating Letby is all circumstantial. The parts that resonate most strongly with the public — the “confessional note” in particular — are not quite what they seem. Eyewitness evidence does little more than put Letby at the scene of the incidents — a place she was contractually obliged to be. Nor is the evidence that any of the infants were the victims of foul play, by anyone, strong. The case for conviction emerges from a preponderance of small pieces of evidence that point in the same direction. 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 is an argument necessarily founded on improbability — what are the odds that the one nurse who was present on all occasions did not have something to do with it 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, there are two available narratives for Lucy Letby. 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.

By percentage of the population, 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 these outcomes, then, are highly improbable. They leave untouched a vast range of more probable outcomes which suffer the disadvantage of being unsatisfactory explanations of an awful situation: We like our narratives to tell us about the world, those that says, “well, it’s hard to say” don’t do that. We do not find them useful. Few of us happily occupy that indeterminate space.

JC will advance the position perhaps we should. While it may offer little intellectual satisfaction, it may be the best we can reasonably expect.

What is interesting is how we are pushed by system design into depriving this individual 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.

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 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.

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?

Three notorious cases from the antipodes illustrate the disadvantage of not asking those big-picture questions

Interlude: difficult cases

A ring of dust around Ayers Rock

Lindy and Michael Chamberlain and their three children were camping at Ayers Rock in central Australia in August 1980.[1] On the evening of the 17th the family were around a campfire with other campers when Lindy thought she heard a dingo (an indigenous wild dog) in the brush near the tent where her infant daughter Azaria was sleeping. She went to check on the baby, and saw a dingo leaving the tent which Lindy discovered to be empty: the child was missing. Despite a search of the surrounding area, Azaria was never found. Lindy had no explanation for what had happened but quickly surmised that the dingo must have snatched the child.

Believing Lindy Chamberlain to be acting strangely the police grew sceptical of her story. Believing dingo attacks to be unusual, and expecting there to be more evidence if a dingo was responsible, the police settled on the theory that in fact Lindy Chamberlain had murdered and disposed of her baby, and she was charged with murder and in 1982, sensationally convicted. The prosecution’s case was that in her five-minute absence from the campfire, Lindy returned to her tent, changed into tracksuit pants, took Azaria to her car, obtained and used scissors to cut Azaria’s throat (avoiding any arterial bleeding on the baby’s jumpsuit but spraying some over the footwell interior), waited for Azaria to die, hid the body in a camera case in the car, cleaned the blood from everything including the outside of the camera case, changed back out of her tracksuit pants, for her son, returned to the tent, replaced the jumpsuit, left blood splashes there, and returned to the campfire with her son without the other campers noting anything was amiss.

Lindy Chamberlain spent three and a half years in prison. In 1986 Azaria’s matinee jacket was found at the entrance to a dingo lair four kilometres from the campsite. Shortly afterwards she was released and pardoned and her conviction finally quashed in 1992.

Forensic evidence of what experts told the court was blood spatter in the foot-well of the Chamberlain’s car turned out, much later, to be sound deadening compound sprayed on the car during manufacture.

Satanic panic in the Garden City

In 1991, Peter Ellis, a childcare worker at a daycare centre in New Zealand was charged with horrific child sexual abuse against children in his care.[2] These included bizarre rituals and acts some attributed to “satanic panic” prevalent at the time, including acts of graphic violence, amputation and assault, such as children being forced into a steaming hot oven, buried in coffins, having navels removed with pliers and a “circle incident” where Ellis and his co-workers supposedly took a group of children to a remote apartment where they were made to stand naked and kick each other while the adults danced around them.

The prosecution relied on carefully selected evidence from very young children (all under 5) who had been coached, perhaps inadvertently, by social workers using suggestive interview techniques to embellish their stories, and no doubt further encouraged by their parents. In total one hundred and eighteen children were interviewed. Those who insisted there was no abuse and those who made patently impossible claims (such as those that would leave permanent injuries) were excluded from the evidence for the case.

In 1993 Ellis was convicted on 16 counts of child sex abuse against seven children. While doubts remained about the fairness of the trial due to the interview techniques and lack of corroborating evidence (in particular, no physical injuries to any children. Ellis maintained his innocence throughout and continued to fight for his name to be cleared, but died in 2019, and was not finally exonerated until the New Zealand Supreme Court 2022 finally quashed all remaining convictions citing a substantial miscarriage of justice due to unbalanced evidence and contamination of the children’s testimonies.

Murder in the family

Twenty-two year-old David Bain claimed he returned from his paper round at 6:45 on the morning of June 20,1994, went downstairs to the laundry room, in the dark, to put a load of washing in the machine.[3] It was so dark he did not notice his father’s bloodstained clothes in the machine, and inadvertently washed them. He then returned upstairs to find his the rest of his family murdered. At 7:10 Bain placed a agitated call to emergency services alterting them to the tragedy. A note typed on the computer, apparently by David’s father Robin, said, “you were the only one who deserved to live.”

David Bain was charged with the murders of his parents, Margaret and Robin, and his three siblings, Arawa, Laniet, and Stephen. His defence was that his father Robin, motivated by a troubled relationship with his wife and children, murdered the rest of the family before turning the gun on himself.

David Bain was convicted on all five counts of murder in 1985, based on circumstantial evidence, including bloodstains on David’s clothing and his fingerprints on the murder weapon.

Bain maintained his innocence and appealed all the way to the Privy Council which in 2007 identified significant errors in the handling of evidence, potential bias and shortcomings in the police investigation. Citing a substantial miscarriage of justice the Privy Council quashed Bain’s convictions and ordered a retrial. In the retrial the jury acquitted David Bain of all charges, concluding that the evidence did not establish his guilt beyond all reasonable doubt. Bain remains a free man.

Lucy’s case

Narrative bias

These three cases illustrate the problem of circumstantial evidence cases: where there is no reliable direct evidence of the alleged crime, one tends to start with a hypothesis and then fit whatever forensic evidence you have into it. There is a kind of tunnel vision at play. This is so regardless of whether you are convinced of guilt or innocence.

The idea that any mother would cold-bloodedly murder her nine-week-old baby without warning is preposterous. To even set up this as a hypothesis one must surely have some pretext for believing it to be possible — psychiatric That she would do it at all, let alone with scissors in the footwell of a car, then hiding the body in a camera case, somehow leaving no evidence at all, in a space of ten minutes. Just preposterous. Especially in a situation where there was a plausible non-murder alternative.

Likewise, for Peter Ellis to have done what he was alleged to do in the first place, regardless of the evidence, would be extraordinarily improbable. For no adults to witness any corroborating evidence, no-one to notice the children missing for hours on end, for none of the alleged injuries to leave any marks or traces, and for there to be a plausible alternative: that none of the events happened at all.

For David Bain, on the other hand, it is a different story: there is no question his family were murdered, and even on Bain’s own theory there were only two possible perpetrators: his father and himself. For David Bain not to be the murderer, on the agreed evidence, would have to make him incredibly unlucky, and his father to have behaved extremely oddly for a man about to turn a gun on himself.

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,[4]:

“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”.[5]

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.[6] 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.[7]

  • 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.[8] 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[9] — 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. A Perfect Storm: The True Story of the Chamberlains
  2. Conviction: The Christchurch Civic Creche Case
  3. Black Hands: A Family Mass Murder
  4. Panorama, 18 August 2023
  5. 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.
  6. 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.
  7. Science on Trial
  8. 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.
  9. See: Very Well Health: Hyperinsulinema (High Insulin Levels).