Just implicitly assuming that something couldn't have been chance is just trying to do statistics on pure intuition, which is notoriously difficult.

Though unlike the Lucia de B case it doesn't seem likely these deaths could all have been natural. The evidence pointing towards Letby seems mostly probalistic in nature though, which should be treated carefully.

Woa, careful. That's not true. The staff duty roster was used by the prosecution to argue that Lucy Letby "the common denominator" in all the suspicious deaths:

Chief among these was the duty roster spreadsheet showing staff shifts, through which the Crown Prosecution Service (CPS) was "able to show the jury that Letby was the one common denominator in the series of deaths and sudden collapses on the neonatal unit".

https://theweek.com/law/lucy-letby-and-the-importance-of-und...

That is totally statistical information - even though it's, shall we say, lay statistics and not what you'd expect to see from a statistician.