Calculateur de probabilité inspiré par l’affaire Sally Clark
This interactive calculator helps illustrate why the statistical reasoning associated with the Sally Clark case became so controversial. It lets you compare a baseline infant-death rate, a repeated-event calculation under pure independence, an adjusted calculation that allows recurrence risk to be higher than baseline, and the historical courtroom figure based on the now-famous “1 in 73 million” claim.
Understanding the “affaire Sally Clark calcul” issue with expert context
The phrase affaire Sally Clark calcul refers to the statistical controversy that became central to one of the most discussed miscarriages of justice in modern British legal history. Sally Clark, a solicitor and mother, was convicted in 1999 after the deaths of her two infant sons. A key feature of the prosecution case was a statistical claim that the chance of two sudden infant deaths in a similar affluent, non-smoking family was about 1 in 73 million. That number was repeated so often that it came to symbolize the danger of using mathematics in court without adequate explanation, proper context, or a careful understanding of what a probability actually means.
The core problem was not that arithmetic itself is unreliable. The problem was that the arithmetic was applied to the wrong question, using assumptions that were too strong and without clarifying major limitations. The famous figure was formed by taking an estimated probability for one sudden infant death in a family like the Clarks and then squaring it, as though the two deaths were statistically independent events. But in real families, infant deaths are not guaranteed to be independent. Genetics, environmental exposures, sleep setting, undiagnosed medical conditions, and shared household factors may change the risk of a second event after a first. In other words, if one tragic event occurs, the family’s risk profile may no longer match the broad population average.
That is why a calculator like the one above is useful for education. It does not decide guilt or innocence. It does not produce a legal verdict. Instead, it demonstrates how sensitive repeated-event estimates are to assumptions. If the first event has probability p and you assume strict independence, the probability of two events is p × p. If you instead allow the second event to be more likely than average because of recurrence risk, the answer changes materially. The “calcul” at the heart of the Sally Clark debate is therefore less about one dramatic number and more about whether the model behind that number makes sense.
Why the original courtroom number became controversial
The historical courtroom figure came from expert testimony associated with Professor Sir Roy Meadow. The reasoning, in broad terms, was this: estimate the risk of a single sudden infant death in a family with specific social characteristics, then multiply that risk by itself to estimate the chance of two such deaths. The resulting number was about 1 in 73 million. The problem is that such a calculation can be misleading for several separate reasons:
- It assumes the two deaths are independent events.
- It presents a very rare-event calculation as though it directly measures innocence.
- It encourages jurors to confuse the probability of evidence with the probability of guilt.
- It may ignore uncertainty in the baseline rate itself.
- It does not compare the natural-death scenario with the homicide scenario using consistent evidence standards.
The prosecutor’s fallacy in simple terms
A major lesson from the case is the danger of the prosecutor’s fallacy. This fallacy happens when someone treats the probability of observing certain evidence if a person were innocent as though it were the probability that the person is innocent given that evidence. Those are not the same thing.
To make this concrete, suppose an event occurs in only 1 out of 10 million cases. That does not mean a person associated with that event has a 9,999,999 in 10,000,000 chance of guilt. There may be many millions of families, and rare things will happen to some of them. There may also be diagnostic uncertainty, reporting bias, imperfect data, and competing explanations. In legal settings, this distinction is absolutely critical.
- First, estimate how often an event occurs naturally.
- Second, estimate how often similar evidence appears in criminal cases.
- Third, compare those explanations directly, not in isolation.
- Fourth, account for uncertainty in every estimate.
Real public-health data that matter to the calculation
Modern discussion of the affair often benefits from using transparent public-health statistics rather than a single courtroom slogan. The United States Centers for Disease Control and Prevention publishes national data on sudden unexpected infant death. These categories are not identical to the legal questions in the Clark case, but they are useful for understanding how rare these events are and how they are classified in modern mortality surveillance. For current readers, the following figures from CDC reporting are a practical benchmark:
| CDC category | Rate per 100,000 live births | Interpretive note |
|---|---|---|
| Sudden Infant Death Syndrome (SIDS) | 38.4 | Specific subset within sudden unexpected infant death classifications. |
| Unknown cause | 26.2 | Cases where a precise cause could not be assigned after investigation. |
| Accidental suffocation and strangulation in bed | 25.5 | Separate category that shows why case classification can be complex. |
| Total sudden unexpected infant death (SUID) | 90.1 | Broad surveillance category combining several causes and unknowns. |
Source benchmark: CDC public data on SIDS and SUID. See cdc.gov.
These are real, population-level public-health numbers. They remind us that infant death, while rare, is an actual event observed in national data. Once we acknowledge that reality, the next question becomes whether it is valid to square a single-event rate mechanically. The answer is: only if the independence assumption is justified. In many biological and epidemiological settings, that assumption is at least debatable.
How the famous “1 in 73 million” figure was built
Historically, the public narrative often focused on a single arithmetic chain. The following table reproduces the structure of that calculation in a simplified way so readers can see where the controversy begins. The arithmetic itself is straightforward. The dispute is about whether the assumptions are appropriate.
| Step | Historical figure | What it means |
|---|---|---|
| Estimated probability of one sudden infant death in a similar family | 1 in 8,543 | Baseline single-event estimate used in testimony. |
| Assume strict independence for a second death | Multiply 1/8,543 by 1/8,543 | Treats the second event as unaffected by the first. |
| Resulting repeated-event figure | About 1 in 72,982,849 | Rounded in public discussion to about 1 in 73 million. |
| Statistical weakness | Independence not securely established | Shared family factors can make recurrence more likely than baseline. |
Why dependence matters so much
In everyday language, dependence means that the probability of a second event may change once the first event has happened. This is common in medicine and epidemiology. Families share genes. Households share habits, environments, and exposures. Similar sleep arrangements may recur for more than one child. Undiagnosed inherited disorders may affect siblings. Any of these factors can break the neat assumption that each event is a fresh, unrelated roll of the dice.
If the baseline risk of one event is 38.4 per 100,000, then the raw probability is 0.000384. Under strict independence, two events would be 0.000384 squared, which is tiny. But if the conditional risk of a second event is, say, 5 times, 10 times, or 20 times the baseline because of shared risk factors, the combined probability is no longer the same. It is still rare, but it is less extraordinary than the courtroom slogan suggests. That distinction matters because jurors are highly influenced by very large-sounding odds.
What the calculator above is actually showing
The calculator has four educational outputs:
- Baseline single-event rate: the public-health or hypothetical rate for one infant death.
- Repeated events under independence: the classic multiplication model.
- Repeated events with dependence adjustment: a simplified recurrence model in which each additional event is multiplied by a user-selected factor.
- Historical courtroom figure: the traditional 1 in 8,543 assumption squared or cubed for comparison.
This is not a substitute for a forensic or epidemiological expert report. It is a teaching tool. Real casework would require a formal causal analysis, a review of pathology findings, family history, medical records, scene investigation, uncertainty bounds, and an explicit comparison of competing hypotheses.
Why legal reasoning must go beyond one dramatic statistic
Good legal reasoning asks whether all the evidence points in the same direction. Statistics can support that task, but statistics should not replace it. A criminal court should not move from “this event is unusual” to “therefore it must be murder.” Unusual natural events happen. Likewise, a low probability under one narrative does not automatically imply a high probability under another narrative. To make that leap safely, the court would need a balanced evaluation of both sides.
The Sally Clark case became a lasting warning because numbers can create a false sense of certainty. Jurors may not notice hidden assumptions. Lawyers may repeat a rounded figure because it sounds compelling. Experts may speak beyond what the data truly support. Once a number like 1 in 73 million enters the courtroom, it can dominate attention even if it is only one fragile branch of the wider evidence tree.
Authoritative sources worth consulting
For readers who want to ground their understanding in public institutions rather than commentary alone, these sources are especially useful:
- CDC data on SIDS and SUID for current U.S. surveillance figures.
- UK Office for National Statistics mortality releases for official national death data and related publications.
- NCBI Bookshelf overview of sudden infant death syndrome for medically curated background hosted on a U.S. government domain.
Key takeaways for anyone researching the affair
- The arithmetic behind a repeated-event probability may be simple, but the assumptions can be contentious.
- The famous 1 in 73 million figure depended heavily on a strong independence assumption.
- Probability of an event under innocence is not the same as probability of innocence.
- Recurrence risk, shared family factors, and classification uncertainty all matter.
- Public-health statistics are useful for context, but legal conclusions require much more than population averages.
In short, the affaire Sally Clark calcul is a lesson in statistical humility. Numbers can illuminate, but only when they are tied to the right question, built on defensible assumptions, and explained honestly. The tragedy of the case is not merely that a calculation was done. It is that a single calculation came to carry more weight than it should have. Any modern analysis should therefore resist headline odds and instead focus on model choice, evidential comparison, uncertainty, and the proper limits of expert testimony.