In the Sally Clarke trial, Roy Meadow cited his self-serving statistics which reinforced 'Meadow's Law',
'Meadow told jurors the probability that both boys died naturally from “cot death”, or sudden infant death syndrome (SIDS), was 1 in 73 million – a figure that many thought was pivotal in Clark’s conviction. The figure was later disputed by the Royal Statistical Society and other SIDS experts. Taking into account the influence genetics and environment, the probability of a second case of SIDS in the same family was put at about 1 in 200.'
https://www.newscientist.com/article/dn7683-top-paediatrician-guilty-of-professional-misconduct/
While the judge in that case told the jury to disregard the sensational claim, the verdict demonstrated that they found that difficult/impossible to do.
Fictionalised crime shows on TV, demonstrate investigators with open minds, pondering lots of competing theories, often building a case against one suspect before additional crimes or evidence reveal the actual culprit. That's great for filling up an hour's programme, but recent miscarriages of justice suggest that a culprit is is selected early in the process and evidence that fits that theory is gathered to prove the point, while other information is ignored.
Andrew Malkinson's conviction was quashed in 2023 after the Criminal Cases Review Commission (CCRC) declined to grant him new appeal hearings in 2012 and again in 2020. This is worrying since the CCRC was created to remedy miscarriages of justice such as the Guildford Four and the Birmingham Six. As with the Subpostmasters, there is no speedy process for compensation.
The Jeremy Bamber case is being reviewed after dozens of failings by Essex Police. Like some other cases, new evidence hinges on someone having the time, opportunity and inclination to investigate objectively.
The Letby case like the Clark case before it, makes some uneasy because there may be no actual crime. I cannot imagine the pressure and strain on parents whose children have undergone a postmortem, had the death declared to be due to natural causes before a novel theory makes their child a murder victim.