at least 400% anything less and there is no reason to upgrade from the previous generation, even 4x the power would only lead to a "slight" leap in the capabilities of games and may be to small for most customers to see a perceived leap in capabilities that warrants investment in the next generation.
Think about this situation where the PS4 is twice as powerful (100% more powerful) as the PS3 and Uncharted 4 is released on both platforms the only difference is that the PS4 version runs at 60fps and the PS3 version runs at 30fps and you already own a PS3 and the PS4 is a very conservative $299 US, would you buy a PS4 or just buy the game for the PS3? To convince customers to invest in a new platform you must show them experience's that they cannot have on the current generation, there is only one console that has achieved that without a significant leap in power (defined as at least 4 times the previous gen) and that is the Wii. Nintendo did something no one had ever done before used a new controller to provide the new experiences. Now Sony and Microsoft have already set a precedent of adding new controllers to the current system with move and kinect, they also can't use Internet services as both have already shown that they can add them to the current systems with patches. So that leaves only one way for Sony and MS to release next gen consoles without a large leap in power and that is to artificially kill off their current consoles by ending support like MS did to the OG Xbox. But that strategy is likely to leave a bad taste in consumers mouth and could do more harm than good. And the only controller that could warrant a next gen console without more power is some form of mind controller.
The next gen will likely be 8 times more powerful than the last just like Carmack said if MS and Sony can't afford to do it with current technology in 2013 (the likely release year for at least one) they will just hold off another year. Another factor to consider is that if the iPad keeps improving it's capabilities how it has in the last 2 years the 2013 or 2014 iPad will likely be more powerful than the xbox 360...
TL DR: Customers expect new experience's that were not possible on the last generation of consoles and if the next gen doesn't provide that they won't sell. So MS and Sony have no choice but to provide consoles at least 4 times more powerful and they will likely be 6-8 times more powerful.
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