But Mr Justice Mostyn — who analysed the cause of the baby’s “serious head injury” at a hearing in the Family Division of the High Court — said it was possible that the man had attacked his daughter and “taken us all in with a web of lies”.
The judge said the little girl had been hurt at her home when in her father’s care and medics had discovered injuries to her brain.
A local authority had begun care proceedings and he had been asked to decide whether the girl had been subjected to a “serious abusive assault” which involved “violent shaking” and an “impact on a hard surface” or accidentally hurt.
Local authority officials suggested that the man — who had a criminal record dating backing to 1998 which included two convictions for “unprovoked” assaults on men — had “lost control” because the baby would not stop crying.
The man had “utterly” denied an allegation of “abusive assault” and said he tripped and fell while holding the little girl.
Mr Justice Mostyn said some medical evidence suggested “this was an assault” although experts did not “speak with one voice”.
The judge concluded, following the fact-finding hearing in Liverpool, that it was “more likely than not” that the man had injured his daughter by accident “in the way he has described”.
But he added: “This is not a borderline decision but then neither is it a decision beyond a reasonable doubt. There remains a possibility, perhaps even a real possibility, that the father has taken us all in with a web of lies.”
Mr Justice Mostyn said the man’s criminal record was “unedifying’.