With a world population of around 6 billion (subtracting small children and crazies) and an upgrade cycle of two years, we should be moving about 3 billion smartphones a year.
So at the 1.5 billion we are shipping now, we are probably about 50% saturated. Still some room to grow.
IDC claimed that the worldwide growth would be saturated in 2015 four years ago . . . Now they've moved it to 2019. They also predicted in 2011 that Windows Phone would have 34% of the market by 2015. . . Only missed that by a factor of 10. One of the other things this does not recognize is that what is being reported for Android is that all of the Android phones are NOT smart phones. This was revealed in early 2013 when Judge Lucy Koh ordered that Samsung reveal their product mix for the Apple v. Samsung patent infringement trial. Samsung was forced to show that their Android phones were mixed 30% smartphones, 40% Feature Phones, and 30% dumb phones. . . but all were reported as Android sales. Studies showed that all major suppliers of Android smartphones also supplied their Android phones in a similar mix. . . and many Android makers do not even offer a smartphone. Yet ALL Android phones are reported under the listing of "smartphones" because the OS is considered a smartphone OS, even though it may be stuffed into a phone that is not by any stretch of the imagination capable of smart functions.
On the other hand, 100% of the phones Apple sells are smartphones.