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A 2012 High Court case exposed a problem every advocate should recognise: the form in which a statistic is presented can alter its persuasive force, even when the underlying arithmetic remains unchanged. Numbers do not arrive in court naked. They arrive framed, writes Rebecca Ward, MBA.
The number has landed
“Doctor, just give me a number.”
The prosecutor leans forward. The expert begins carefully: allele frequencies, population substructure, laboratory limitations and the ever-present possibility of contamination or transfer. But the courtroom does not want caveats. Jurors want something they can scribble in their notebooks, counsel wants something memorable, and the defence braces for impact.
“One in a billion.”
The expert’s voice is quiet, but it does not matter. The number has landed. Pens move in unison. Jurors underline it twice. The prosecution sits down. Somewhere at the bar table, the defence lawyer’s forehead meets their palm.
If you looked closely, you might notice the expert trying to keep talking: to explain what the number measures, what it does not measure, and which assumptions must remain true for it to retain meaning. But nobody is listening. The performance is over. That is not necessarily bad science. It is science stripped of context and dressed for court. It is statistical theatre.
When 99.9% sounds like guilt
The Australian High Court confronted the persuasive power of statistical framing in Aytugrul v The Queen [2012] HCA 15. A hair found on the deceased’s thumbnail underwent mitochondrial DNA testing. The appellant could not be excluded as its donor. An expert explained that the relevant profile might be expected in approximately one person in 1,600. She also expressed the same information another way: 99.9 per cent of the population would be excluded.
Mathematically, the formulations conveyed the same information. Psychologically, they did not sound remotely alike. “One in 1,600” leaves room for other people. It invites the listener to imagine a football stadium containing several possible matches. “99.9 per cent excluded” sounds like a door slamming shut. The figure creeps towards 100, and the mind quietly completes the journey.
The High Court dismissed the appeal and did not accept that exclusion percentages should automatically be inadmissible. But the case exposed a problem every advocate should recognise: the form in which a statistic is presented can alter its persuasive force, even when the underlying arithmetic remains unchanged. Numbers do not arrive in court naked. They arrive framed.
When a likelihood ratio becomes a verdict
The danger became starker in R v Keir [2002] NSWCCA 30. Bone fragments were discovered beneath a house and subjected to DNA analysis. Expert evidence indicated that the DNA findings were approximately 660,000 times more likely if the bones came from a child of the relevant parents than if they came from the child of a randomly selected Australian couple.
That was a likelihood comparison between two competing propositions. It was not a statement that there was a 660,000-to-one chance that the bones belonged to the deceased. Yet that is how the figure was effectively presented to the jury. The distinction collapsed, and an evidentiary comparison became an apparent mathematical declaration of identity. The NSW Court of Criminal Appeal identified the error as the prosecutor’s fallacy, quashed the conviction and ordered a new trial. The mistake sounds technical. It is not.
The probability of obtaining particular evidence if an accused is innocent is not the same as the probability that the accused is innocent given that evidence. Reverse the conditional, and a useful statistic becomes a verdict wearing a lab coat.
The prosecutor’s fallacy
Suppose an expert says that only one person in a million would be expected to share a particular DNA profile. A jury may hear:
“There is only a one-in-a-million chance that the accused is innocent.”
That conclusion does not follow. The statistic may describe the rarity of the profile, but it does not independently establish who deposited the DNA, when it was deposited, how it arrived, whether transfer occurred, whether the sample was contaminated, or what the remaining evidence proves. A match is evidence. It is not authorship, chronology, conduct, and guilt compressed into one decimal point.
This is why the denominator matters. One in a million people sounds extraordinary. But one in a million within which population? How many people were searched? How many profiles were compared? Was the accused identified independently, or selected because the database produced a match? What allowance has been made for laboratory error, relatives, mixed profiles or secondary transfer?
Without the denominator and the assumptions beneath it, the statistic is not meaningless – but its meaning is dangerously incomplete.
Why smart people still fall for it
Statistical theatre works because human beings confuse precision with accuracy. A number expressed to six decimal places looks more authoritative than a witness saying, “I am reasonably confident.” It appears objective, disciplined, and immune from emotion.
But numbers are produced by people. People choose the sample, define the population, select the comparison, classify the data, and decide how the result will be expressed. The calculation may be flawless while the question being calculated is wrong.
Lawyers are not immune. We ask experts for plain English and then become impatient when the explanation contains qualifications. We want the bottom line, preferably before lunch. Yet the caveat is often not an inconvenience attached to the answer. It is part of the answer.
The risk extends beyond DNA. Statistical evidence appears in personal injury damages, medical negligence, employment disputes, discrimination claims, actuarial assessments, recidivism evidence and coronial investigations. A percentage can influence causation, foreseeability, credibility, and quantum long before anyone asks what was counted – or omitted.
Before the number reaches the jury
The first question should be: what, precisely, does this statistic measure? Does it describe the rarity of evidence, the likelihood of an event, the strength of a comparison, or the probability of the ultimate fact in issue? Those are not interchangeable.
The second is: what assumptions support it? A calculation based on independent events, complete records or perfect laboratory conditions weakens when the real-world supplies dependence, missing data and human error.
The third is: what is the denominator? “One in 10” means little until we know one in 10 of whom, selected how, observed over what period, and compared against what alternative.
The fourth is: how has the figure been framed? A frequency ratio, likelihood ratio, and exclusion percentage may describe related information while producing very different reactions in the listener.
These are not questions designed to undermine science. They are how lawyers protect science from being asked to perform a role it cannot safely play.
When arithmetic becomes cosplay
Courtroom tables should carry plaques: Here lie the foreheads of lawyers sacrificed to statistical theatre. The dents are not from fatigue. They are from despair: despair that a number stripped of its denominator, assumptions, and limitations will outweigh hours of careful evidence. By the time the qualification arrives, the jury may already have circled the statistic and written “guilty” beside it.
This is not academic quibbling. Verdicts, liability findings and public policy rest on numbers. A misclassified death disappears into an “accident” category. An unreported event vanishes from prevalence data. A database reflects only the people who entered it, not the people who were never counted.
You cannot count what you cannot see. Nor can you calculate your way out of a defective premise. Every statistic presented in court is a curated crime scene. Someone has decided where its boundaries begin, what evidence belongs inside them, and what will remain beyond the tape. Numbers can illuminate, compare, and test. They can also dazzle, anchor, and silence thought. Theatre begins when the statistic stops being one part of the evidence and starts playing the lead. Numbers should assist justice, not impersonate it.
Rebecca Ward is an MBA-qualified management consultant with a focus on mental health. She is the managing director of Barristers’ Health, which supports the legal profession through management consulting and psychotherapy. Barristers’ Health was founded in memory of her brother, Steven Ward, LLB.
