I believe JonBenet's hit on her head came first. If a child is knocked out, the killer believed a likelihood she would not suffer during strangulation, or that she maybe would not scream with her being stunned. This a child sacrifice method practised by ancient Incas. However those children were given sedatives (from nature) over a period of time, and the night of the ritual. Recall how sleepy JonBenet was, after the White's Christmas Party. John Ramsey had to carry her to bed, she wouldn't wake up. I'm an intruder believer or some close in social circle, and since JonBenet enjoyed her chocolates, this would have been something to spike. There have been some serial South Americans who hit on the head and garrotted kids in ritual sacrifices, one, a Satanist for "The Beast".