It would be great to get more data on this, but with this guy he scored a whopping 68 % higher with a gyroscope in median score over thumstick and 38 % better with a mouse over gyro. I think if gryoscope actually became mainstream for shooters you could start allowing pc vs console and not have this huge disparity in input superiority.
You don't even need stats- this is a claim that's easily proven by reasoning about how the input methods in question work with respect to camera rotation in 3D games.
Analog stick is definitely the outlier here, because it's what's known as an 'absolute' input: Its X and Y axes go from -1 (full left / full up) and 1 (full right / full down) and output a constant value based on the physical position of the stick.
This describes a heading (which direction the stick is pushed) and a magnitude (how far the stick is pushed in that direction), which is perfect for controlling a ground-based character in 3D space since characters move in a certain direction at a certain speed over time. The stick handles forward/back/left/right/speed, and gravity takes care of the rest.
Rotating a camera, however, is a bit different. Particularly when you're using a fixed point in the center of the screen for aiming as is the case in most shooters.
Precision is required to position that dot over the exact point you want to shoot, and analog sticks don't lend themselves well to that because they're 'absolute' - they describe a speed and a direction that the camera should rotate over time, rather than the exact amount it should rotate in each axis on a given frame.
That's where mouse and gyroscope (and trackpad) come in. Unlike an analog stick, these are 'relative' inputs: Their X and Y axes track how far the device has moved left/right and up/down over the course of a single frame.
That means the rotation of the camera corresponds 1 : 1 with the movement of the device, and allows the user to input exactly the amount of rotation they need without having to integrate a number over time.
They also aren't limited to -1 / 1 like an absolute axis. If you move 5cm, it'll output 5cm- the limitations are all based on how far you can physically move a mouse or rotate a gyro controller.
To get mathy for a moment, the rotation equation for a given frame looks like this for an absolute input like an analog stick:
new rotation = old rotation + direction * magnitude * sensitivity * time since last frame
And looks like this for a relative input like a mouse, gyro or trackpad:
new rotation = old rotation + amount moved * sensitivity
As you can see, the latter is considerably simpler. You have to derive change-over-time numbers using mathematical formulae when using a stick, whereas a mouse or gyro will plug straight in and take direct control.
Pad vs Mouse/Keyboard objectivity is a debate that - mind-bogglingly - still goes on to this day thanks to uninformed folks trumpeting confirmation bias over hard science, but any input bod worth their salt will be able to tell you what kind of input device is best-suited to a given gaming use-case and explain exactly why that is. I'm of the mind that Left Stick = Move, Mouse = Aim is the best combination for shooters since that gets you the maximum precision for both movement and aiming, but it's impossible to do properly on console and tricky to get right without
one of these on PC since you start running out of buttons in more input-heavy games.
Source: I program games for funsies and have a bit of an obsession with ergonomics- input devices, input processing, all that sort of stuff. Ask Me About My New Input Mapper Project
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I always wanted to try out those feedback pads on the Steam Controller, but they died pretty fast.
They feel like joycon HD rumble. Neat idea, but that pad needed a second hardware revision if it was really going to shine.