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A big share of those 240 million handheld gamers in the 7th gen is now the phone gaming audience; the casual players who mostly played stuff like Brain Age and Nintendogs, or kids now getting a tablet instead of a DS.

Comparing Switch's sales to the combined install base of DS + PSP is not an apples to apples comparison because of this; the explosion in phone/tablet gaming stole away a huge amount of that audience, and Switch has to compete with that whereas DS and PSP for the most part did not.