A big part of the case against her was that she was the only person on shift at all the deaths with which she was charged. Apparently there were another 6 deaths during this period, but these were not included in the evidence. The court was not told whether she was on shift during those deaths; or whether someone else's shift pattern looked equally "bad" if the other deaths were included.
Our courts system is not set up to analyse statistical evidence. Sally Clark's triel was an example - the statistic was presented that there was a minute chance of two cot deaths in one family, with the implication that she must therefore have killed them both. What wasn't presented is that the alternative hypothesis, that she was a serial killer of two of her children, had an even more minute probability. So therefore of the two options, two cot deaths, or two murders, two cot deaths was the less unlikely.
Secondly, an expert witness could have thrown light on the Lucy Letby case - his evidence was discounted on the grounds that it could have been prevented at the trial and wasn't, and therefore it wasn't allowable at the appeal.
If there is any doubt at all, it needs to be cleared up. If someone who is innocent can be convicted, then that's something that could happen to any one of us.