The Wiki Man

What the O.J. Simpson jury didn’t know (and schools should teach)

We’re just not good with probabilities. But perhaps we can learn to be

1 March 2014

9:00 AM

1 March 2014

9:00 AM

During the O.J. Simpson trial, the prosecution made much of the fact that Simpson had a record of violence towards his wife. In response, Simpson’s legal team argued that, of all women subjected to spousal abuse, only one in 2,500 was subsequently killed by the abusive husband. It was hence implied that, since the ratio of abusers to killers was so high, any evidence about the accused’s prior violent behaviour was insignificant.

This sounds plausible. However, there is another way to consider the statistics. According to the German academic Gerd Gigerenzer, we are not trying to predict whether a husband will murder his wife: Simpson’s wife inarguably had been murdered, so instead, we should ask the question backwards: given that a battered wife has been murdered, what are the odds that the husband did it? Gigerenzer calculates that ‘the chances that a batterer actually murdered his partner, given that she has been first abused and then killed, is about eight in nine’.

This is a case where a statistical sleight of hand normally called ‘the prosecutor’s fallacy’ worked for the defence. What is interesting is not merely that we are confused but the degree of our confusion: the presentation of the data affects our judgment by factor of thousands: from 0.04 per cent to 90 per cent. We need to be alert to this kind of error, particularly since computers and ‘big data’ make it easy to generate spurious but plausible statistics on almost any subject.

High-profile criminal cases seem plagued by peculiar mental biases. In particular, they seem to cause people to polarise around only two opposing theories of ‘what happened’.

I felt slightly vindicated when I finally heard that the British police were investigating the possibility that the disappearance of Madeleine McCann was the result of a burglary attempt gone wrong. Since planned abduction by a paedophile is so rare, it struck me as odd that no one much considered this more probable option.

Press and internet commentary seems to amplify the either/or effect. If you want to see this tendency at its most extreme, the online reaction to the trials of Amanda Knox and Raffaele Sollecito is a textbook case. The two camps, the Colpevolisti and Innocentisti, operate entirely separate, partisan websites: which site you see first will affect your assessment of Knox and Sollecito’s guilt enormously. I have to say here that using Occam’s razor — or even Occam’s nasal hair-trimmer — should incline you towards believing the pair are more likely to be innocent than guilty. Burglaries gone wrong seem more common than sex games turned murderous. The investigating authorities formulated theories before evidence was available, and were reluctant to modify them, instead creating further bizarre theories to support their initial assumptions — a tendency known as ‘privileging the hypothesis’. Had the DNA and fingerprint evidence implicating Guede been available at once, would the investigation have proceeded as it did? Almost certainly not.

But few commentators discuss the case in terms of probabilities — it is all about certainty first, evidence later. This tendency is probably innate. But Gigerenzer believes it can be corrected: ‘Schools spend most of their time teaching children the mathematics of certainty — geometry, trigonometry — and spend little if any time on the mathematics of uncertainty. Statistical thinking could be taught as the art of real-world problem solving.’

German schools are beginning to adopt his approach. Britain (and Italy) should follow.

Got something to add? Join the discussion and comment below.

Rory Sutherland is vice-chairman of Ogilvy Group UK.

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  • saffrin


    • Shorne

      Oh dear, got tired because something made you use your brain did you?

  • Rockin Ron

    Thank you, Mr Sutherland for an informative article. I suppose the same caution should be used in presenting medical data to patients. For example, whether a patient is told that a procedure has an 80% of success as opposed to a 20% chance of failure. Using the same data but presenting it differently could sway a patient’s judgement about whether they should subject themselves to the procedure.

    • sarah_13

      I agree. Having been presented with a medical diagnosis in terms of percentages and questioned the relevance to my specific case it strikes me that doctors should perhaps explain the limitations of probabilities. If you are part of the 20% with terminal cancer and not the 80% who survive it is of absolutely no comfort that 80% generally survive. The more pertinent is how does my particular cancer look, or whatever the medical problem, or how fit am I, how competent is the surgeon, what age am I etc.

  • John-Paul Marney

    Not so sure. They’re subtle things are probabilities, and not terribly intuitive, and it’s easy to get it wrong. There were any number of very eminent mathematicians and scientists who made complete plonkers of themselves in their criticism of Marilyn Vos Savant and her perfectly correct solution to ‘The Monty Hall Problem’. Mind you, the OJ verdict was indeed a travesty for anyone with a probabilistic mind-set.

    • rorysutherland

      Erdos was completely wrong, I think.

      I often wonder how people would react to the Monty Hall problem if it were posed differently: for example not with a game-show host, but with a vicar…. someone you would assume would want to help you rather than to bamboozle you.

      The only way to convince people of the correct answer to Monty Hall is to tell them to imagine 100 doors, and a game where the game show host must open 98 of them.

      It is remarkable how the same logical problems can be baffling or easy depending on how they are expressed: the Wason tests are a wonderful example of this: see

      • John-Paul Marney

        Thanks Rory. I still have difficulties with it and I am a pure dead brainy economics lecturer. Hope you are well, Kind Regards, JP

  • Sarah Jenson

    Stuff the Germans and the Brits con artists evil monsters

  • Al Xong Rinpoche

    Nicole Brown was an addict and a poor specimen except for her looks. She could not control her emotions. Her drug dealer had her killed because she owed him so much money. The handbag was stolen at the restaurant to try and discover her address. The delivery man went to bring it to her house and the killer followed him. Sorry for all the people who still think OJ did it. Including the stupid judge at his LV adventure. Someone had stolen his paraphernalia and some friends with handguns went to help him recuperate it, OJ did not have any weapon and he said nothing intimidating. He didn’t deserve that. If coke bitches could be controlled he at least knew he couldn’t.

    • Terry Field

      wow what squalid misery