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Using google trends to gauge interest for the consoles, I noticed that search popularity correlates quite well with weekly sales ratios between the consoles.

PS4: 55

Switch: 35

XBox one: 23

3DS: 10

PS Vita: 2

Using the latest PS4 weekly sales estimate of 331,394 and multiplying by the search ratio you get 210,766 sales for the Nintendo Switch,  0.636 * 331,394.

The other results yield 138,582 for XBox one(77,502). 60,253 for 3DS(52,093) and 12,050(9,457) for PS Vita. It's not perfect but aside from the XBox One, they are within a decent degree of accuracy. Sales from vgchartz.com in parenthesis.

If I'm right, that would mean that the Switch is being under supplied by around 66,000 units a week.

https://trends.google.co.uk/trends/explore?q=%2Fm%2F0vphbfj,ps4,switch,3ds,ps%20vita



Sales prediction, PS4: 122 Million, Xbox one: 50 million, Switch: 105 million.