We measured input latency by filming the controller's LED and the phone screen at 240 fps, then counting frames between the LED changing and the first pixel of the response. The method is crude but repeatable, and it separates transport latency from render latency.
Bluetooth controllers added 38 to 74 ms of transport latency on the phones we tested. A wired controller added 9 to 14 ms. The render path added another 33 to 50 ms at 60 fps, most of it pipeline depth that the game cannot remove.
The action item is not to chase a single number. It is to measure your own worst case on the device your players use, because a game that feels responsive on a wired controller at 120 Hz can feel broken over Bluetooth at 60.
Read next: Low-latency audio: the numbers behind the knob.