Even if the infoscout data is correct, your assumption is totally wrong.
"So, 66% of parents bought an xb1 for a child and 45% of ps4 purchasers as well.
If we assume that normally, these purchases wouldn't exist except for birthdays, we can figure that on average, people will buy
x1: 248k
ps4: 305k"
Do you have proof that nobody bought X1/PS4 for their children during Q1-Q3 before making your bold assumption?