Manhunt: the Levi Bellfield case from a probabilistic perspective

The ITV 3-part Series "Manhunt" starring Martin Clunes tells the story of the search for the killer of Amelie Delagrange who was murdered in Twickenham in 2004. It is based on the book by Colin Sutton (who was the detective in charge of the case) and dramatises his fight to find Amelie's killer, Levi Bellfield, who was also charged with the murder of Marsha McDonnell and three other attempted murders. The trial of Bellfield for these five crimes took place at the Old Bailey in 2008. He was convicted of the two murders and one of the three attempted murders (he was also later charged and convicted of the murder of Milly Dowler).

I declare a particular interest here because, between 2007-8, I (along with colleague Martin Neil) acted as an expert consultant to the Defence team in the case against Bellfield for the five crimes. We were initially asked to provide a statistical analysis relating to the number of car number plates that were consistent with the grainy CCTV image of a car at the scene of the McDonnell murder. We were subsequently asked to identify probabilistic issues relating to all aspects of the evidence,  producing reports totalling several hundreds of pages.  Although these reports are not public, some material we subsequently wrote that mentions the case can be found in this publication. Having watched the programme I think it is worth making the following points:

The CCTV image of the car at the scene of the McDonnell murder: none of the letters or numbers on the number plate were clearly visible. A number of image experts provided (contradictory) conclusions about which characters could be ruled out in each position, so there was much uncertainty about how many number plates needed to be investigated; additionally at least two of the experts had been subject to confirmation bias because - instead of being presented with the grainy CCTV image and asked to say what the number plate could be, they were shown Bellfield's actual number plate and asked if the image was a possible match (as a result our colleague Itiel Dror was co-opted as an expert witness in the area of confirmation bias). The prosecution claimed to have 'eliminated' all possible vehicles with 'matching' number plates other than Bellfield's. This was important because, if true, it represented the most solid piece of evidence against Bellfield in the entire case. However, taking account of the uncertainty of the image expert assertions, we concluded that potentially thousands of additional vehicles would need to be eliminated. 

Lack of hard evidence: The dramatisation was correct in showing that, although there was much circumstantial evidence linking Bellfield to the murder of Delagrange, there was no direct evidence in the form of either forensic evidence or eyewitnesses to the crime. Hence, DCI Sutton's strategy was to link Bellfield to a number of  other 'similar' crimes that had taken place within the same area. The programme focused on two of the four for which he was charged, namely the McDonnell murder and one other attempted murder, for which the programme used a made-up name "Sarah" (the credits make clear that some names were deliberately changed). The "Sarah" case actually refers to Kate Sheedy who was deliberately run over with a car. The other two cases of attempted murder (which I will refer to as R and D) were not covered. Again (as the dramatization suggested) there was no direct evidence linking Bellfield to either the McDonnell or "Sarah" attacks, but much circumstantial evidence. By providing circumstantial evidence linking Bellfield to five crimes which were claimed to be 'very similar', DCI Sutton was able to ensure that Bellfield was charged with the Delagrange murder.

Linking of the five 'very similar' crimes: This linkage became the thrust of the prosecution case against Bellfield. What the prosecution essentially argued was that the crimes were so similar, and the circumstantial evidence against Bellfield so compelling in each case, that (in the words of the prosecuting barrister) "the chances that these offences were committed by anyone other than Bellfield are so fanciful that you can reject them". But in reality there was no great 'similarity' between the crimes: even in the dramatization DCI Sutton states somewhat ironically (about the Amelie, Marsha, and "Sarah" attacks) that "they all involved striking the victim with a blunt instrument - as we can consider a car a blunt instrument". Much of the defence case was based around exposing the probabilistic and logical fallacies arising from assumptions of similarity (although interestingly it was much later that we formalized some of these issues). With regards to the whole issue of 'cross admissibility' in one report I wrote the following generic statement:

The cross admissibility argument is based on the following valid probabilistic reasoning:

· Suppose Crime A and Crime B are so similar that it there is a very high probability they have been committed by the same person.

· If there is evidence to support the hypothesis that the defendant is guilty of Crime A then this automatically significantly increases the probability of him being guilty of Crime B, even without any evidence of Crime B.

48. In other words what is happening here is that the probability of guilt in Crime A, together with the evidence of similarity between the two crimes, makes it allowable to conclude that the probability of guilt in crime B has increased. This is indeed provably correct, but what the prosecution claims is something subtly different, namely:

It is perfectly allowable to use the probability of guilt in Crime A, as evidence for Crime B.

49. This subtle difference leads to a fallacy in the following scenario that is relevant to this case.

· Suppose that there are three Crime A, B and C. Suppose that the evidence that crimes B and C are similar is strong. Then as above, any evidence that indicates guilt in the case of crime B will, because of the evidence of similarity, impact on the probability of guilt for crime C. However, suppose that we have not yet heard any evidence on crimes B and C and suppose that there is no evidence that Crime A is similar to either Crime B or C.

· If there is strong evidence supporting probability of guilt in crime A, then, contrary to the prosecution claim, this evidence does not impact on the probability of guilt for either crimes B or C and hence should not be used as evidence as suggested in point 48 above.

· In fact in this scenario the evidence concerning crime A should, in relation to crimes B and C, be treated just the same as ‘previous conviction’ information in normal trials.

50. Given that the judge has allowed ‘cross admissibility’ of all 5 cases the danger identified in point 49 presents an opportunity for strategic exploitation by the prosecution. Specifically, the opportunistic strategy is to focus on an offence in which there is most hard evidence, even if that is the least serious offence and even if it bears the least similarity to the others. The prosecution can then argue that evidence of guilt in that case can be taken as evidence of guilt in the more serious cases. The jury would not necessarily be aware of the underlying fallacy. 

With hindsight point 50 is especially pertinent because, in contrast to the DeLagrane, McDonnell and "Sarah" cases, there actually was some direct evidence linking Bellfield to the R and D attacks  (neither of which resulted in serious injury to the victims) and there were few similarities between these and the other three cases.  The jury were allowed by the cross admissibility ruling and (in my view the incorrect) assumption of similarity to use evidence in the R and D attacks as evidence in the other cases. Interestingly, the Jury did not find Bellfield guilty of either of the R or D attacks.

Multiple probabilistic fallacies: In one of my summary reports I said (about the prosecution case generally): "There are several important instances of well known probabilistic fallacies (and also well known logical fallacies) that consistently exaggerate the impact of the evidence in favour of the prosecution case". In addition to the cross admissibility 'fallacy' we found examples of the following in the prosecution opening statement:

• Prosecutors fallacy
• Base rate neglect fallacy
• Dependent evidence fallacy
• Logically dependent evidence fallacy
• Conjunction fallacy
• Confirmation bias fallacy
• Previous convictions fallacy
• Coincidence fallacy
• Minimal utility evidence fallacy
• Lack of hard evidence fallacy
• “Crimewatch UK” fallacy

These fallacies are all covered in our book and some (in the context of the Bellfield case) are covered in this paper.

And finally: In one scene in the programme DCI Sutton pointed out that he, Bellfield and Bellfield's lawyer all had one thing in common - being Spurs fans. Count me in on that one too...

Links

• Fenton, N.E. and Neil, M. (2011), 'Avoiding Legal Fallacies in Practice Using Bayesian Networks', Australian Journal of Legal Philosophy 36, 114-151, 2011
• Modelling crime linkage with Bayesian networks
• Risk assessment and decision analysis with Bayesian networks
• Barry George case: new insights on the evidence 
• Sally Clark revisited: another key statistical oversight?
• Prosecutor fallacy in Stephen Lawrence case? 
• Prosecutor fallacy in media reporting of Burgess DNA case
• Flaky DNA: Prosecutors fallacy yet again
• Prosecutors fallacy just will not go away
• Misleading DNA evidence