Consider late gen support. PS1 had support unprecedented after PS2 launch and this lead to the best selling console ever. PS3 launch was a disaster for Sony, but even still it sold better when compared year for year against the 360, PS2 still had stellar support. Now consider late 2011-2013, MS and Nintendo doing nothing for the legacy consoles but Sony is even releasing their biggest franchise on their OLD console AFTER the launch of the new console. PS3 had great first party support and it translated to some good PS4 sales, other consoles blunders non withstanding.
Now the gamecube to Wii to Wii U. Gamecube wasn't getting too much support but it did get a last hurrah with a good zelda game and the Wii went on to be a success, but probably is the exception. Wii support in 2010-2012 sucked and it carried over to the Wii U which became a very low selling console.
Xbox to 360 to XB1. Same story as Nintendo. Xbox had some goodwill from Halo 2 and the shooter community so 360 naturally does better in the shooter generation. 360 support in 2011-2013 sucked from MS and they expected the XB1 to do well enough while alienating their consumer base...