Two young women walk out of the World’s End pub and disappear into the cold Edinburgh night. The next time anyone sees them, they are dead.
Christine Eadie’s body will be found first, dumped on the sand dunes of Gosford Bay, just outside the Scottish capital. Helen Scott’s body is found later, a few kilometres away, dumped in a just-harvested cornfield.
It would take 37 years, one failed trial and an Australian mathematician to finally put one of Scotland’s most notorious serial killers behind bars.
The 1977 World’s End murders quickly gained international attention. But despite a huge manhunt by local police it took 30 years for a man to be charged.
Forensic scientists managed to pull tiny, damaged strands of DNA from the clothing used to bind the women’s wrists. They discovered the genetic code matched those of a man already behind bars.
Angus Sinclair, a Glasgow-born painter, had already been found guilty of the murder of 17-year-old Mary Gallacher and, before that, Catherine Reehill – his childhood neighbour.
But when he came before court for the murders of Helen and Christine in 2007, DNA science was not as developed as it is today.
There were no eyewitnesses to the slayings. The case was circumstantial.
The scientists testified that the DNA was most likely Sinclair’s.
But they couldn’t be sure. They gave the judge a probability, and it wasn't a high one.
“DNA, it’s now black and white. But it wasn’t early on,” Professor David Balding says.
The professor now leads a lab at Melbourne University, but back then he was a scientist working with London Metropolitan Police's forensic team. He remembers watching the judge hand down his ruling: no case to answer.
With nothing else to support it, the DNA evidence simply wasn’t convincing enough.
Sinclair wasn't convicted.
So Professor Balding got to work.
Professor Balding specialises in a type of DNA work called mathematical computational genetics. Rather than extracting the DNA in a lab, he writes mathematical models that can help translate the lab work into real-world answers.
His job: use the math models to weigh up how strong the evidence against Sinclair was.
It was a particularly difficult task for two reasons.
First, almost 40 years of storage had left the DNA badly degraded. The long strands had broken down into small sections, like a frayed rope.
Second, each sample possibly contained DNA from four people: Sinclair, his brother-in-law who also was accused of committing the murders, and the two girls.
Three billion bits of DNA from each person, broken down into tiny strands and mixed together, and almost 40 years old.
Professor Balding's mathematical model had to take all that into account, plus factor in likely degradation of the DNA, contamination, and experimental noise.
Amazingly, Professor Balding was able to come up with a new estimate of the odds it was somebody else's DNA in several of the samples: one in a billion.
It meant there was virtually no chance that the DNA belonged to anyone but Sinclair.
“It was pretty overwhelming,” he says.
In 2014, Balding spent a day in court under forensic cross-examination, defending the findings of his models. The maths held.
Finally, on November 14, 2014, more than 37 years after Christine Eadie and Helen Scott died, Angus Sinclair was found guilty of their murder, and sentenced to 37 years’ jail.
For his contributions to genetic and forensic science, Balding was on Monday elected a Fellow of the Australian Academy of Science, along with 21 other notable scientists.
These days Balding works on integrative genomics: testing what DNA can tell us about "everything – our appearance, our health, how every little bit works in the body".
"Hopefully, that makes the world better," he says.