The debate among gamers between analog control sticks and the classic mouse/keyboard conversation has been raging for decades. I’ve been kicking around the ideas behind this post for a while, and my recent foray into Mechwarrior Online has rekindled my interest in putting this idea out there. Let’s look at the mathematics of the these control systems as a means of addressing their relative pros and cons.
The mouse is a simple rodent. It controls the cursor position, directly. Moving the mouse ‘x’ distance will result in a proportional cursor displacement.
Let’s take a look at how moving the mouse back and forth over one dimension translates to cursor movement over time.
Pretty simple triangular wave.
Now let’s look at analog sticks, or joysticks. Joysticks are a bit more complicated. In most applications, the joystick doesn’t directly control position. It controls the derivative of position (in other words, cursor speed). Move the joystick a little, and the cursor moves slowly. Push it farther, and the cursor moves faster.
Let’s do the same graph as above, where a user is moving the joystick back and forth from its resting position. Note that this is all hand-waving and not mathematically precise (or even properly scaled).
Note the curvature of the cursor position. Because we’re only controlling the derivative, the actual position will be a continuous function. Therein lies the primary difference between a mouse and a joystick: a cursor driven by a mouse can be move in a discontinuous fashion (think jagged edges), but a cursor driven by a joystick will always need to form smooth curves.
Truth be told, this paints analog sticks in a pretty grim light. But we’re making a couple of assumptions that might not be true for all games:
- that the joystick always controls the derivative of cursor position
- that the mouse movement is directly mapped and not limited.
There are mechanics available which can turn both assumptions on their heads and level the playing field a bit. We’re also leaving out a critical portion of the mouse-and-keyboard setup: the keyboard. We’ll look at both of these factors in the next post.