Category: Good Statistics

A Proper Review of the Statistics in Lucy Letby’s Trial

It is well known that the statistics used to convict Lucy Letby at her trial were fallacious. The most notorious example being the roster chart which did nothing more than show she was present at certain times when she was present, yet was used to create a sinister connotation.

What has not been done so far as we can tell at least in the public domain is a proper review of the statistics. To that end, I have recently been taking part in a project to do just that. Collaborating in this includes Peter Elston, who has done extensive work on the statistics of the case already, as well as three other collaborators (all UK-based) who wish to remain anonymous for the time being.

For the exact same reasons as shown in my earlier blog post, I was as certain as one can practically be that a proper statistical analysis of the case would in no way point towards guilt, and indeed that appears to be the case based on our preliminary findings. With that said, all involved are committed to publishing the results regardless of whether they work for or against Lucy. Our ultimate commitment is to the truth. Above all, contrary to what many pitchforkers would have you believe, if I ever found evidence pointing to a serial killer of children, I would promptly make it known to the relevant authorities. I’m not Ravi Jayaram after all!

In the rest of this blogpost, I will summarise some key preliminary findings as well as provide some formal housekeeping concerning data protection on this project as required by law.

The Rise in Mortality at CoCH:

Our preliminary findings show that, even with a very prosecution friendly model, the rise in mortality at CoCH neonatal unit from June 2015 to June 2016 was of a statistical significance one would expect to observe in around one unit per year in the country.

This comes when one accounts, at least in part, for the following factors:

  1. Number of IC patient days in a given period
  2. Uncertainty in the estimate for the mortality rate per IC patient day
  3. Interval length can be varied to produce the most statistically significant “spike” in mortality possible

Moreover, this model operates on the assumption that the hospital continued to perform just as well even in the face of a significant rise in IC days that CoCH was forced to cope with, most likely due to the maternity crisis in North Wales.

If one accepts the common-sense belief that the hospital would have struggled to cope with this increased burden, thus causing the per IC patient-day mortality rate to increase, then the chance of a rise in mortality will be substantially higher than our prosecution-friendly model suggests.

Our model also does not account for other factors. For example, Thirlwall showed that the number of infants with birthweights below <2000g increased during the June 2015 to June 2016 period, which one would expect to increase the chance of a spike in mortality even higher.

How was Lucy Letby Associated with so many Deaths?

This is the current part of the research we are focusing on developing the most, but we have a few preliminary observations.

Firstly, the number of patient in intensive care is substantially higher when Lucy Letby is on shift than when she is not. A potential confounder behind this was her status as the jointly most qualified nurse in her pay bracket. This likely meant that the cheapest way to staff the rotor was to use Letby as much as possible for shifts with multiple patients in intensive care, for which she could be used with her QIS qualification, while using the lesser qualified band 5 nurses on shifts with only a single or no patient in intensive care. The fact that Letby was a young nurse and single likely meant she had greater flexibility allowing her to fit such a schedule.

Secondly, heterogeneity is a really important feature. The chance of a death occurring at a given time on the unit is not constant. It varies based on how many patients are present in intensive care at a given time, what their gestational ages and birthweights are, whether or not they are a multiple, whether or not the unit is understaffed at a given time, and any other comorbidities individual patients might have. If one assumes, even a small amount of heterogeneity, the chance of an individual nurse being present for a large number of deaths rises dramatically. This is the same phenomenon as I observed in the case of Lucia de Berk, where even a small amount of heterogeneity, combined with correcting other fallacies, meant that the true probability of de Berk being present for the deaths she was at was 1 in 50, a far cry from the 1 in 342 million claimed at her original trial.

Of course, even a 1 in 50 event still implies that a nurse was unlucky to be present at many deaths. But in a country with thousands of nurses, hundreds of thousands in the case of England, you would expect this to happen to a large number of nurses quite regularly. Just as someone is statistically almost guaranteed to win the lottery somewhere, even if their individual chances of doing so are small, it is almost guaranteed that many nurses will be present for a many deaths. It does not imply on its own that they were responsible for any wrongdoing.

We would like to develop this work further by using data such as gestational ages and birthweight to account for some of this heterogeneity and obtain a more precise estimate on the chance of a nurse being present for some minimum number of patient deaths.

Lessons for Use of Statistics:

There are several key lessons that should be learned from this story.

One key lesson is that, when the decision around what analysis to do is based on the same data one is analysing, extreme caution must be exercised. Even subconsciously, one can use the data to perform an analysis decision aimed at achieving the very outcome one wants, while ignoring analysis approaches that do not achieve that outcome.

This issue is illustrated repeatedly throughout the case of Letby including, but by no means limited to, the following:

  1. Defining “suspicious events”, “collapses” or “collapses leading to death” on the basis of whether Lucy was present there in the first place. It is known that at least 10 instances where it was initially thought a baby had been attacked or an otherwise “suspicious” event took place were dropped from the shift chart after Letby was found to be absent from the hospital at the time.
  2. Choosing the specific interval over which to analyse the rise in mortality on the basis of it being whether a rise in mortality happened to occur

Another key lesson is that null events are extremely important to keep in mind. The death of 10 patients out of 10 is far more suspicious than the death of 10 patients out of 1000. If an unusual event is merely the result of there being many opportunities for it to happen, and it just occurred eventually at some point, then the fact an event might be rare does not imply that a rare cause must be responsible for it.

Courts seem to be extremely poor at grasping this critical concept. This is evident when the court looked only at collapses when Lucy Letby was present while ignoring other “suspicious events” after it turns out Lucy was never there catastrophically fails to grasp this key principle. It’s rather like evaluating the performance of the Dutch National Football Team by looking at only the matches they have won, while ignoring their defeats like the 2010 World Cup final.

One potential reason courts are so poor at understanding this critical concept is courts usually handle events that are inherently rare, such as a murder where there’s no dispute a crime has occurred and the only debate is who the perpetrator was. However, determining from observational data whether an exceptionally rare cause even happened at all (such as a serial killer nurse) is a very different task. The more one looks into the case of Lucy Letby, the more one appreciates how ill equipped courts are for handling these sort of cases.

Data Protection Housekeeping:

The law on data protection in both the UK and EU requires one fulfils a number of key principles when handling personal data. One of those is transparency, and it is in that spirit that I provide some data protection housekeeping here.

Rights of Data Subjects:

Any data subject is welcome to contact me, including via email, if they want any further information or clarification regarding the project and we shall endeavour to answer all queries.

Data Subjects ordinarily have a number of rights, the full details of which can be obtained on the UK Information Commissioner’s Office website. See the following link for further details: A guide to individual rights | ICO

These rights include the following:

  1. Right of Access: The right to access and receive a copy of one’s personal data.
  2. Right of Rectification: One has a right for any inaccurate personal data about oneself to be corrected
  3. Right of Restriction: One has a right to restrict how one’s personal data is used in certain circumstances
  4. Right to Object: One has a right to object to the use of one’s personal data, although this right does not apply for processing done under article 6(1)(e) for reasons of public interest, a provision we rely on (see later for more details)
  5. Right of Erasure: One has a right to have one’s personal data erased in certain circumstances

It is worth noting that there can be restrictions on these rights. In particular, restrictions often apply when deploying the right would substantially impede the academic research we are conducting.

Data subjects also have a right to complain both to the data controller responsible for processing the data, as well as to the appropriate regulatory, in this case the UK Information Commissioner’s Office or ICO.

However, even though such a right to complain exists, we wish to emphasise that we want to work collaboratively with data subjects as much as possible and resolve any queries that they have. If a data subject identifies as flaw in our practices, we would like to work with them and remedy it wherever possible. We also would like the data to be processed in a way that leaves subjects genuinely assured that the use of their personal data in this research project will not result in any adverse effects against them, and we are more than happy to work with them as much as possible to achieve that outcome.

General Public Interest:

There are numerous reasons why this research is so vital, and why we believe it is substantially in the public interest to do:

  1. To help ascertain what really happened at the Countess of Chester Neonatal Unit. In particular, we hope our research can help contribute to ascertaining whether or not Lucy Letby has been the victim of a miscarriage of justice, or if she is indeed guilty of the crimes she has been convicted of.
  2. To provide lessons in the use and misuse of statistics in the legal setting, regardless of whether Lucy Letby has been the victim of a miscarriage of justice.
  3. If it does contribute towards showing Lucy Letby was the victim of a catastrophic miscarriage of justice, there will likely be huge implications for the criminal justice system
  4. Thirlwall has proposed wholesale changes to the NHS, including the abolition of no blame culture which will likely make patient care worse. This would be bad enough in any event; it is even worse if it is based on something that never happened. This research can help determine whether that is indeed the case.
  5. Given the public debate around the case of Lucy Letby is likely to continue for the foreseeable future in any event, we hope this research can help make that debate healthier and better informed.

While the practitioners of this research make no secret that we come into it with a very strong prior that Lucy Letby has been the victim of a miscarriage of justice, we do wish to emphasise our ultimate commitment is to the truth.

Both under academic standards, and human standards, we will not hesitate to publish our research if at any time it were to point against our prior belief and suggest Lucy Letby was indeed guilty of the crimes she was convicted of. We believe the public interest behind our research goes far beyond the fate of one person, and our commitment to publishing our findings no matter the result reflects that belief.

Specific Data Used:

The data used in this project will include the nurse’s shift chart, as well as admissions data for 9 out of the 13 months between June 2015 and June 2016. Unfortunately, we don’t have data for the four months where there was no indictment event. The admissions data was obtained by Peter Elston from Lucy’s defence barrister Mr Mark McDonald and, for the infants admitted to the neonatal unit in those 9 months, contains their gestational ages, birthweights, when they were in the unit and with what category of care (intensive care, high dependency care, special care, normal) on a given day.

How the Data will be Used:

The use of this data is necessary to compare the mortality at CoCH relative to gestational age and birthweight to that of other known environments. The admissions data also allows us to calculate the total IC days over a given time interval, which is also necessary for some of our modelling.

We may require using the data subsequently to develop models around the association of a particular nurse’s presence with mortality, such as discrete time survival models. Should this need arise, we will make sure not to publish anything that could theoretically be reversed engineered to obtain the original dataset.

It goes without saying this contains very sensitive data, including what GDPR regards as special category data. We therefore make clear at once that nothing will be published that could possibly be used to identify any patient. For example, any graphical displays will be scrambled appropriately to ensure they cannot be reverse engineered to obtain the original dataset. Nothing will be published pertaining to any individual patient either.

The only reason we use this data is to research the spike in mortality in the Countess, as well as the reasons behind a nurse being present for many of the deaths. In no way will the data be used to make any decision about any individual patient, and, given the summary nature of what we publish, nothing released will have any prospect of doing so either.

Legal Basis for Processing Data:

Formally, the legal bases on which we use this data are article 6(1)(e) (task in the public interest), article 6(1)(f) (legitimate interests) and article 9(2)(j) (archiving, research and statistics) together with section 1 paragraph 4 of Data Protection Act 2018 (DPA). The legitimate interests are the same as those expressed earlier as to why this research is so important, and they form the same reasons as to why we consider this research to be in the general public interest, a key requirement under article 9(2)(j).

If necessary, at certain points to ensure the completion of the project, we also rely on schedule 2, paragraph 27 of DPA (the research purposes exemption) and, if necessary, schedule 2, paragraph 26 of DPA (the academic expression exemption). In particular, with respect to the latter, because project is done with a view to publishing academic material and we believe that doing so is in the general public interest, that allows us to use the academic expression exemption whenever we reasonably believe a given provision, that the exemption is eligible to be applied to, would otherwise be incompatible with the academic purpose behind this research.

Why I am more than 99.99% certain that Lucy Letby is innocent

I use Bayes theorem: posterior odds equals prior odds times likelihood ratio. For an introduction, please read this nice blog post https://entropicthoughts.com/bayes-rule-odds-form

I use this rule, Bayes’ rule, repeatedly, each time taking account of another part of the evidence. It is named for Thomas Bayes, a presbyterian minister and mathematician, who was interested in using it to find a mathematical proof of the existence of God. https://en.wikipedia.org/wiki/Thomas_Bayes

The likelihood ratio for the question at hand, based on some part of the evidence, is the ratio of the probabilities of that part of the evidence under the two competing hypotheses. More precisely, one uses the conditional probabilities of that fact given previously incorporated evidence.  We have to start somewhere and we start by describing two alternative hypotheses and our probabilities or degrees of belief or personal betting odds for those two hypotheses, before further evidence is taken into account. 

Let’s start with the news reports of a police investigation of a possible killer nurse at a neonatology unit in the UK; the investigation being triggered by a disturbing spike in the death rate on that unit.

I think that in the last fifty years there simply hasn’t been been a case in the UK of a killer nurse on a neonatal ward, except possibly the case of Beverley Allitt. One might argue that there do exist doubts as to the safety of her conviction, or one might argue that there can have been serial killer nurses who completely evaded detection. Did Alittit work in an intensive care unit? I also think that in recent years, every year has seen a scandalous calamity in a UK neonatal ward, leading to avoidable deaths of quite a few babies. So a priori: the relative chances of a killer nurse being responsible for the spike, or simply poor care, is in my estimation 50:1 in favour of poor care in a failing hospital unit rather than activity of a killer. If you disagree, give me your arguments for both those rates and hence their ratio. If you would like to take a different starting point, try that. Eg, what is the chance a random nurse is a serial killer? At some point one will have to use the information that this was a neonatal unit and one will have to take account of the “normal” rate of deaths on the unit. I think my choice is reasonably specific. One could argue that the prior odds should be 10 to 1, or 100 to 1, instead of 50 to 1. I expect that most people will at least agree that killer nurses on neonatal units are very rare, disastrously poor care on a neonatal unit in the UK is not rare at all.

So we are back in 2017 and hear the news and rightly we should be sceptical that there really is a case here. But clearly there are grounds to investigate what is the cause of that spike, and maybe there is more information which the police already have.

Then, many years go by. A particular nurse is detained for questioning in two successive years; and finally arrested in a third year. Two more years go by (Corona). At last, a trial begins. It turns out that roughly seven years of police investigation has uncovered no direct evidence at all (neither medical evidence, toxicological evidence, witness testimony or CCTV recordings, finger prints or DNA) of unlawful action by the nurse who has been under intensive investigation all that time. And not just no evidence against that nurse – no direct strong evidence of malevolent activity by anyone. 

One might want to argue that the insulin evidence is strong toxicological evidence. We could argue about that for a long time. Even if one or two babies were given unauthorised doses of insulin there is no direct proof that Lucy Letby did that herself. There is the possibility of accidental administration (twins in adjacent cots). The argument that Lucy did administer insulin seems to have been that we know at some point she carried out other murderous attacks and it is unlikely that there were two murderous nurses working in the unit. But why do we believe there are murderous nurses working on the unit? This argument can only be made after hearing all the other evidence in the case.

So we have to estimate the probability of a 7 year police hunt for evidence of murder by a particular nurse finding no direct evidence of any malevolent activity at all by anyone, if Lucy Letby actually was innocent, and if she truly was a serial killer. In my opinion ,what we actually observed is much more likely under the innocence hypothesis than under the guilty hypothesis. If she truly is innocent the chance of finding powerful directly incriminating evidence must be rather small; if she truly is a serial killer then it must be unlikely that that no baby can be definitely proven to have been murdered or attacked. I guess the two probabilities of no hard evidence to be 95% and 5% respectively. These are probabilities of 19/20 and 1/20 respectively, so a likelihood ratio of 19. I’ll be a bit more cautious and call it 10.

We already had odds of 50:1 in favour of innocence. We have a likelihood ratio of 10:1 in favour of innocence, having learnt that police investigation uncovered no strong and direct proof of malevolent harm to any baby. The odds on Lucy being innocent are therefore now 50 times 10, or 500 to 1.

Let’s now bring in the evidence from psychology. Are there reasons to believe Lucy is a psychopath? Which surely she must be, if she is a serial killer of babies in her care. It seems there is no reason at all to suspect she is a psychopath. I think that there very likely would be strong independent signs of psychopathy in her life history if she really is a serial killer, but obviously not so likely if she is completely innocent. [Clearly she could be both a psychopath but did not actually harm or try to harm any baby. I don’t think this is an interesting hypothesis to explore. I will also not pay attention to the Munchhausen by proxy idea, that she was trying to attract the attention of an older male doctor. All the evidence says that he was more romantically interested in her, than vice versa.]

Put the likelihood ratio at 2, ie twice as likely to see no evidence for psychopathy if innocent, than if a serial killer. Actually I think it should be closer to 10. We should ask some psychologists. Lucy Letby did not sadistically kill little animals when she was a child. By all accounts, she was a dedicated nurse and cared deeply for her work.

We were at 500 to 1 for innocence. Factor in a likelihood ratio of 2 for psychological evidence. Now it’s 1000 to 1. But we are not done yet.

Next, I would like to take account of the statistical evidence that the spike in deaths is quite adequately explained by the acuity of the patients being treated in those 18 months. I would say that this is exactly what we would expect if Lucy is innocent but very unlikely if she’s a serial killer. I think this hypothesis is very adequately supported by published MBRRACE-UK statistics, and what we know about the acuity of the babies in the case. We know why acuity went up in around 2014 and we know why it went down midway in 2017. The spike seems to have been caused by hospital policy which was being made and implemented by the consultants on that unit. They should have expected it.

Say a likelihood ratio of 10. That brings us to 10,000 to 1 she’s innocent; a posterior probability of 99.99%. I haven’t yet brought in the facts of an investigation driven by tunnel vision and coached by doctors who, as we now know, were making quite a few deadly mistakes themselves. I haven’t brought in yet the innocent explanation of the post-it note. In my opinion, the post-it note is powerful evidence for innocence; it makes absolutely no sense under the hypothesis of guilt. The irrelevance of the handover notes and the notations in her diary. Facebook searches? Her alleged lies (about what she was wearing when she was arrested). Anything else?  

Anyway, I am now well above 99.99% sure that Lucy is innocent and since the press conference and the report of Shoo Lee and his colleagues, we can all be even more sure that that is the case. 

The magic of the d’Alembert

Simulations of the d’Alembert on a faIr roulette wheel with 36 paying outcomes and one “0”. Even odds bets (e.g., red versus black). Each line is one game. Each picture is 200 games. Parameters: initial capital of 25 units, maximum number of rounds is 21, emergency stop if capital falls below 15.

Source:


Harry Crane and Glenn Shafer (2020), Risk is random: The magic of the d’Alembert. https://researchers.one/articles/20.08.00007

Stewart N. Ethier (2010), The Doctrine of Chances Probabilistic Aspects of Gambling. Springer-Verlag: Berlin, Heidelberg.

set.seed(12345)
startKapitaal <- 25
eersteInzet <- 1
noodstopKapitaal <- 15
aantalBeurten <- 21
K <- 100
J <- 200
winsten <- rep(0, K)

for (k in (1:K)){

	plot(x = -2, y = -1, ylim = c(-5, 45), xlim = c(0, 22), xlab = "Beurt", ylab = "Kapitaal")
	abline(h = 25)
	abline(h = 0, col = "red")

	aantalKeerWinst <- 0
	totaleWinst <- 0

	for (j in (1:J)) {

		huidigeKapitaal <- startKapitaal
		huidigeInzet <- eersteInzet
		resultaten <- sample(x = c(-1, +1), prob = c(19, 18), size = aantalBeurten, replace = TRUE)
		verloop <- rep(0, aantalBeurten)
		stappen <- rep(0, aantalBeurten)
		for(i in 1:aantalBeurten) {
			 huidigeResultaat <- resultaten[i]
			 if(huidigeInzet > 0){
				  stap <- huidigeResultaat * huidigeInzet
				  stappen [i] <- stap
				  huidigeKapitaal <- huidigeKapitaal + stap
				  huidigeInzet <- max(1, huidigeInzet - stap)
				  if(huidigeKapitaal < noodstopKapitaal) {huidigeInzet <- 0}
				  verloop[i] <- huidigeKapitaal
			 } else {
				  stappen[i] <- 0
				  verloop[i] <- huidigeKapitaal
			 }
		} 
	aantalKeerWinst <- aantalKeerWinst + (verloop[aantalBeurten] > startKapitaal)
	totaleWinst <- totaleWinst + (huidigeKapitaal - startKapitaal)
	lines(0:aantalBeurten, c(startKapitaal, verloop) + runif(1, -0.15, +0.15 ), add = TRUE)
	}
print(c(k, aantalKeerWinst, totaleWinst))
winsten[k] <- totaleWinst
}

The program repeatedly runs and plots 200 games of each maximally 21 rounds. Below are the total number of times that the player made a profit, and the final net gain, for 100 sets of 200 games. The sets are numbered 1 to 100.

[1]    1  100 -483
[1]    2  108 -336
[1]    3  103 -517
[1]    4  110 -275
[1]   5 123 -40
[1]   6 125 148
[1]    7  115 -209
[1]    8  104 -427
[1]    9  108 -356
[1]   10  110 -225
[1]   11  101 -440
[1]  12 120  80
[1]   13  108 -334
[1]   14  110 -279
[1]   15   99 -538
[1]   16  114 -101
[1]  17 113 -92
[1]  18 117 -87
[1]   19  104 -363
[1]   20  103 -320
[1]  21 114 -52
[1]   22  107 -422
[1]   23  108 -226
[1]   24  115 -173
[1]   25  110 -209
[1]   26  109 -261
[1]   27  114 -186
[1]  28 120 -62
[1]  29 123  35
[1]   30  101 -442
[1]   31  111 -215
[1]   32  104 -378
[1]  33 120  49
[1]  34 117 -49
[1]   35  119 -102
[1]   36  104 -488
[1]   37  107 -402
[1]  38 122  38
[1]   39  100 -549
[1]  40 116 -31
[1]  41 127 220
[1]   42  105 -427
[1]   43  114 -153
[1]   44  109 -256
[1]   45  119 -166
[1]  46 121  47
[1]   47  105 -417
[1]   48  113 -134
[1]  49 121 111
[1]   50  112 -307
[1]  51 114 -92
[1]  52 123 123
[1]  53 118  24
[1]   54  113 -188
[1]  55 124 127
[1]   56  110 -229
[1]   57  113 -255
[1]   58  101 -554
[1]   59  114 -345
[1]  60 124 236
[1]   61   97 -599
[1]   62  115 -220
[1]  63 120  55
[1]   64  102 -512
[1]  65 121 109
[1]   66  112 -219
[1]   67  112 -181
[1]  68 115 -45
[1]   69  107 -474
[1]   70  109 -272
[1]   71  116 -134
[1]   72  107 -440
[1]   73  108 -470
[1]  74 119 -85
[1]  75 115   1
[1]  76 115 -88
[1]   77  113 -219
[1]  78 118 -55
[1]   79  115 -150
[1]  80 124  70
[1]   81  115 -203
[1]   82  115 -153
[1]   83  109 -219
[1]   84   97 -675
[1]   85  108 -396
[1]   86  112 -220
[1]   87  115 -187
[1]   88  108 -290
[1]   89  114 -182
[1]   90  105 -439
[1]   91  113 -183
[1]   92  115 -216
[1]  93 124 110
[1]   94  115 -173
[1]  95 125 177
[1]   96  110 -203
[1]  97 128 160
[1]  98 114 -83
[1]  99 118 -90
[1] 100 123 106

The Beginning of the End, or the End of the Beginning?

We see the hotel lobby of the Fhloston Paradise hotel, the enormous space cruise-ship from Luc Besson’s movie “The Fifth Element”. It occurs to me that our global village, the Earth, has itself become a huge space cruise-ship, including the below-decks squalor of the quarters of the millions of people working away to provide the luxury for the passengers in the luxurious areas in the top-decks.

Now turn to some other pictures. Covid-19 bar-charts.

From top to bottom: (per day) new proven infections, new hospital admissions, deaths, in the Netherlands. Source: Arnout Jaspers. It looked to Arnout that we were already past the peak of the epidemic. His source: RIVM, https://www.rivm.nl/documenten/epidemiologische-situatie-covid-19-in-nederland-2-april-2020

The curves look to me like shifted and shrunk versions of one another. About a third of those who are reported infected (mostly because they actually reported themselves sick) get so bad they go to hospital a small week later and a quarter of them die there just a few days later.


People who are infected (and infectious) but don’t realise it are not in these pictures. There have been an awful lot of them, it seems. Self-isolation is reducing that number.
As Arnout figured out for himself by drawing graphs like this, and David Spiegelhalter reported earlier in the UK, this pandemic is in some sense (at present) not really such a big deal. Essentially, it is doubling everyone’s annual risk of death this year and hopefully this year only. This means that 2% of all of us will die this year instead of the usual 1%. It looks as though the factor (two) is much the same for different age-groups and different prior health status. The reason this has such a major effect on society is because of “just-in-time” economics which means that our health care system is pretty efficient when the rate is 1% but more or less breaks down when it is 2%.


What is alarming are reports that younger people are now starting to get sicker and die faster than originally was the case. Human-kind is one huge petri-dish in which these micro-machines [“The genome size of coronaviruses ranges from approximately 27 to 34 kilobases, the largest among known RNA viruses”. The “basis” units on the molecule are nanometers in size] have found a lovely place to self-replicate, and with each replication, there are chances of “errors”, and so it can rapidly find out for itself new ways to reproduce even more times.


The problem is, therefore, “the global village”. Mass consumerism. Mass tourism. Basically, the Earth is one cruise-ship. One busy shopping mall.


I would like to see the graphs in square root scale or even log scale. You will better be able to see the shapes, and you will more easily see that the places where the numbers are small are actually the noisiest, in a relative sense.

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