The interim police investigation into the murder of Tyabb boy Luke Batty indicates that his father Greg had a premeditated plan to kill his son and then commit ''suicide by cop''.

While he lived apart from his son's mother, Rosie Batty, he was allowed to spend time with Luke at public events such as sporting matches, despite a history of violence and mental illness.

On Wednesday, he left his car at home and took the train to training. He was seen bowling balls to Luke as junior cricket practice was winding down and the rest of the group were packing up.

Police believe it was a plan to isolate him for a premeditated attack.

Police say the father then struck his son's head savagely with a cricket bat.

There were no initial indications of an argument or dispute before the attack.

After Luke collapsed his father stabbed his son in the neck region.

When uniformed police arrived they ordered the man to drop his knife.

Independent witnesses, including ambulance officers, said the 54-year-old man screamed to police that he wanted them to kill him.

Police sprayed the man with capsicum foam and tried to retreat to keep a distance between them and the knife-wielding offender. He continued to run at one officer who shot him.