For my non Scottish readers, a bit of background.

Alex Salmond is a Scottish politician, former leader of the Scottish National Party and one time First Minister of Scotland. After the 2014 referendum on independence was narrowly lost, he resigned from both posts in Scotland and returned to Westminster politics until he lost his seat to the Conservatives in 2017.

In 2018 a leak occurred to the Record to the effect that he was under investigation for past sexual impropriety when he had been a minister. He sought judicial review of the internal investigation into his behaviour. The Judge found that the process by which he had been investigated was “unlawful”, “procedurally unfair” and “tainted by apparent bias” and he was awarded £512,250 in compensation after the Scottish Government admitted fault and liability.

Subsequent a police  team variously numbered at 22 or 4 officers spent over a year investigating him for possible sexual misconduct. After interviewing hundreds of people they came up with 14 complaints which were brought to trial in 2020. One complaint was withdrawn by the crown. The court was presided over by Lady Dorian and the Jury was predominantly female. The court acquitted him of all charges.


Two political narratives have followed these events. 

  1. That promulgated by the SNP was basically that Mr Salmond was a thoroughly disreputable character who, by some unexplained mechanism, was acquitted by the courts. They imply that the fact that 13 charges were brought is itself sufficient evidence of bad character.
  2. That promulgated by supporters of Mr Salmond said that he was a victim of politically motivated persecution which had involved bringing false charges to discredit him and destroy his political prospects.  

Current relevance

The issue became a matter of current politics when a new pro-independence party Alba was formed last week with Salmond as a spokesman. After its founding a number of SNP politicians and former politicians defected to the new party which will be standing in the May elections to the Scottish Parliament.

The entry of this new party into the election has been variously described as the biggest threat so far to the Union of Scotland and England, or a futile attempt to split the pro independence vote.

Statistical analysis

Is the intuition of those who  basically say ‘no smoke without fire’, justified?

Can we use statistics to assess the likelihood that narrative 1 or narrative 2 is correct?

Yes we can.

From 2007 to 2017 the average conviction rate for sexual crimes in Scotland was 76% (https://www.gov.scot/publications/criminal-proceedings-scotland-2016-17/pages/27/).

So the acquittal rate for such offences was 24%.

The chance of being convicted must depend in part on whether a person is genuinely guilty. We may allow that some guilty men or women escape justice due to a faulty acquittal. But how many?

Suppose we make the very pessimistic assumption that fully half of those acquitted were really guilty. This means that the chance of a guilty person being acquitted on a sexual charge would be 12%. Salmond was acquitted on 13 such charges in succession, so the probability of this happening is thus 0.1213  or 1/(934,638,789,872). 

In words this is one in 934 billion. There are about 1500 sexual offences brought to trial each year in Scotland. At that rate, for Salmond to be guilty and yet acquitted 13 times would be a once in 600 million year event.

On probability grounds we can thus reject the guilty man hypothesis. The victim of false accusations interpretation is overwhelmingly more probable. This statistical conclusion is quite aside from the strong evidence that has been revealed in Parliament of collusion and suborning of witnesses. For a summary  of other evidence see here : https://www.craigmurray.org.uk/archives/2019/08/the-alex-salmond-fit-up/