You're trying too hard.

If PS4 doesn't pull a Wii, it should go strong

Most people grow out the phase where they think it is cool to own the extreme or unknown (whatever the hell the X is supposed to be) Box. Does not surprise be the key demographic for the Xbox is and always has been pubescent boys.

This also clearly explains why the seasonal surge the Xbox gets each year.

Good analysis, though as others have said, that Infoscout report is fairly suspect. To my mind, price cuts for the XB1 won't help it long term because the PS4 and XB1 cost around the same to make. Any cost reductions that the XB1 gets the PS4 will also get, so unless MS is prepared to remain $50-70 cheaper than the PS4 across the entire gen then over the long term both consoles will cost roughly the same. The XB1 has a sales spike at the moment at $329, but so will the PS4 when it gets its first price cut, re-establishing the sales difference.

Longer term, as the price of the consoles gets lower, it will become harder and harder to maintain a $50-70 price difference, and so the effect of the price cut will reduce (ie, a PS4 at $299 would require a XB1 to be $230-$250 to have the same effect, which is much harder to achieve when both consoles cost ~ same to make). Consoles bought late in their life (hence at their cheapest) also tend to have the lowest attachment rates, so it becomes harder to make money off consoles sold later in their life from software and accessories alone, if the hardware loss remains constant.

Therefore, console hardware has to move closer to the BOM cost as the gen progresses, and so PS4 and XB1 will move closer in price than they currently are. And evidence to date has shown that at the same price, the PS4 is more desirable, and will likely remain so given Sony's larger number of 1st party studio's.

Using demographics describe sales is a rather flawed method of making this point... So I have a question.

If Console A has the main demographic "X", does that mean that Console B has sold less units to that same demographic "X" compared to Console A?

No it does not.

ie;

If ps4 had 12-17 as secondary and xb1 had 12-17 as primary, ps4 could still be selling to a larger number of 12-17 because the base number would be higher.

ie;

60% of 100 is still less than 30% of 300

That's why I don't use any figures in this calculation (in predictive text). I'm only taking the demographic supplied and removing it from the base sales. Since we know both demographic and sales, we can use the numbers, but since we don't know the numbers in the future, we cannot use the percentage to predict numbers, only other percentages. The conclusion in the OP is that if we set them both to 0%, x1-66% and ps4-45%, There is a 21% difference. This also fits in well with the 45 vs 55% that has been the case through the year, because 21% of 45% is 9.45%, and the difference between 45 and 55 is 10.

Don't go using terms like "mature games" or you're just going to confuse your results.  I saw somewhere that the median COD age demographic is between 13-17, and Halo was younger. "Mature games" doesn't mean the player is a certain age.

The largest demographic of players is also part of that age range at 22%. But yes, there are older owners of xbox as well, which coincides with it selling well throughout the year as well. This is opposed by for example, the wii demographic which was 8-11. If you're not old enough, you can't have a job, and you can't buy the console. So, a good portion of xb1 is also 18-24, just not as many as playstation owners (according to research).

Well, this part I agree with for the most part. The only problem that exists really is how you calculated your numbers for your weekly sales, because we don't actually know the specifics of base sales and demographic proportion, using any sales numbers in predictive text is in error. You can only predict percentages.

I only read half half of your analysis. You use infoscouts numbers too much and infoscout isn't very reliable.

I think the $329 price would do wonders against a $399 one.