Statistics

The chart that shaped the trial

At the centre of the prosecution case was a single visual exhibit: a grid of 25 suspicious events plotted against the nurses on duty for each. Letby’s row was the only one fully shaded. The prosecution invited the jury to conclude that the probability of one nurse being present at every one of 25 unexpected events, by coincidence, was vanishingly small — and therefore the pattern itself was evidence of guilt.

The chart is visually compelling. It is also statistically meaningless.

Why it’s a selection effect

The 25 events plotted on the chart were not a random sample of collapses on the unit. They were chosen, in substantial part, because Letby was present at them. Events where Letby was not on shift were excluded from the chart.

Once you do that, Letby’s row is fully shaded by construction. The chart is simply a tautology: “events where Letby was present are events where Letby was present”. There is no inferential content at all. Any nurse you picked and did the same exercise for would have a fully-shaded row.

The Texas sharpshooter, explained

The canonical illustration is a Texan who fires a shotgun at the side of a barn, finds the biggest cluster of bullet holes, and paints a target around it. Then he claims to be a remarkable marksman because the target is perfectly aligned with his bullets.

The fallacy is that the target was drawn after the bullets landed. In the Letby case, the 25 “suspicious events” were defined, in part, by who was present when they happened. The jury was shown the shading as evidence of guilt. But the shading was a definitional consequence of how the events were selected in the first place.

Prof. Richard Gill and the de Berk parallel

Prof. Richard Gill is Emeritus Professor of Mathematical Statistics at Leiden University. He was instrumental in the Netherlands in the case of Lucia de Berk, a paediatric nurse convicted in 2003 on the basis of a very similar statistical argument. The Dutch Supreme Court overturned the conviction in 2010 after Gill and colleagues demonstrated that the statistical case rested on the same class of error.

Gill has written publicly about the Letby case since 2023, arguing that the parallels are exact. The de Berk case is now taught as a textbook example of the Texas sharpshooter in medical-statistical contexts.

What the Royal Statistical Society has said

The Royal Statistical Society has published commentary on the statistical issues in the Letby case. The Society has been careful not to say the convictions are wrong — that is a question for the Court of Appeal. What it has said is that the form of statistical argument used at trial is the kind of argument its guidance specifically warns against. The RSS published a guide to avoiding statistical errors of this type in the wake of the Sally Clark case; the Letby chart falls on the wrong side of that guidance.

triedbystats.com — the interactive visualisation

An independent group has built triedbystats.com, a focused mini-site that models the chart interactively. It lets you pick any nurse from the unit’s rota and apply the same selection rule (include only events where that nurse was present). The result is always a fully-shaded row for the chosen nurse.

It is the single clearest visual demonstration of why the chart cannot bear the weight placed on it.

The twins-and-multiples anomaly

Independent work published on lucyletby.org in 2025 identified a second selection issue. At least 11 of the 17 indicted infants were from twin or multiple-birth pregnancies; a further 4 co-twins had already died in utero before the cases on the indictment. That makes the cohort an overwhelmingly twin/multiple cohort, not a general neonatal-unit cohort.

Twin and multiple pregnancies — particularly those complicated by monochorionic pathology (TTTS), gestational hypertension, antiphospholipid syndrome, or membrane rupture — carry perinatal mortality rates several multiples higher than single pregnancies. The shift-chart comparison assumed a population-level baseline. The actual cohort was pre-selected for high risk in ways the jury was not walked through. See our evidence page on twins and multiples.

What this means for the CCRC

The statistical arguments from Gill, the RSS, triedbystats.com and the twins-and-multiples analysis are now part of the material the Criminal Cases Review Commission has in front of it. The CCRC applies the “real possibility” test — real possibility that the Court of Appeal would overturn, not a requirement to prove innocence. Systematically misleading statistical exhibits are a recognised ground on which convictions have been overturned in English law before, including in R v Clark (2003).

See our plain-English CCRC explainer for what happens if the Commission refers.