Ben Geen: another possible case of miscarriage of justice and misunderstanding statistics?

Imagine if you asked people to roll eight dice to see if they can 'hit the jackpot' by rolling 8 out of 8 sixes.  The chances are less than 1 in 1.5 million. So if you saw somebody - let's call him Fred - who has a history of 'trouble with authority' getting a jackpot then you might be convinced that Fred is somehow cheating or the dice are loaded.  It would be easy to make a convincing case against Fred just on the basis of the unlikeliness of him getting the jackpot by chance and his problematic history.

But now imagine Fred was just one of the 60 million people in the UK who all had a go at rolling the dice. It would actually be extremely unlikely if less than 25 of them hit the jackpot with fair dice (and without cheating) - the expected number is about 35. In any set of 25 people it is also extremely unlikely that there will not be at least one person who has a history of 'trouble with authority'. In fact you are likely to find something worse, since about 10 million people in the UK have criminal convictions, meaning that in a random set of 25 people there are likely to be about 5 with some criminal conviction.

So the fact that you find a character like Fred rolling 8 out of 8 sixes purely by chance is actually almost inevitable. There is nothing to see here and nothing to investigate. As we showed in Section 4.6.3 of our book (or in the examples here) many events which people think of as 'almost impossibe'/'unbelievable' are in fact routine and inevitable.

Now, instead of thinking about 'clusters' of sixes rolled from dice, think about clusters of patient deaths in hospitals. Just as Fred got his cluster of sixes, if you look hard enough it is inevitable you will find some nurses associated with abnormally high numbers of patient deaths. In Holland a nurse called Lucia deBerk was wrongly convicted of multiple murders as a result of initially reading too much into such statistics (and then getting the relevant probability calculations wrong also). There have been other similar cases, and as my colleague Richard Gill explains so well it seems that Ben Geen may also have been the victim of such misunderstandings.

See also: Justice for Ben Geen

Update: See Richard Gill's excellent comments below

Update 16 Feb 2015: Guardian article talks about my statement made to the Criminal Cases Review Board.