The smaller the trackball, the more spinning it will take to move in a game.
Unless you change the poll rate. But I think you would have less control than with a 3" trackball.
"Poll rate" has nothing to do with this issue. It's geometry+encoder resolution.
In fact, it's not difficult to compete with a
standard 3" Arcade Trackball. The actual resolution of the normal 3" trackball (not our Electric ICE-TB...it has upgraded encoders), given a standard roller diameter of about .435", and a modern "mouse-style" interface, is 662.07 positions per revolution. The formula is ((Ball Diameter * pi) / (Roller Diameter *pi)) * (Encoder Resolution *4). Assuming the same size roller (which they aren't, but for the sake of argument), a 2.25" trackball would need an encoder having only a resolution of 32 to equal it.
Now consider dividing the size of the roller in half, and that effectively doubles the resolution given the same size ball. Therefore, you can scale the whole thing accordingly and have a ball that is 1.5" and a roller that is .2175" and the resolution would still be the same as the standard 3" without changing the encoder resolution.
What does end up different with a smaller ball is your interaction with it. A small ball with the same final resolution will be "touchier", as the surface you interact with will be smaller. So even though 1 revolution on each of the balls moves the same amount of distance "on-screen", you don't need to physically roll your whole hand across the ball to get a half-revolution on a tiny ball, rather just a fingertip.
There are many possibilities for small trackballs, but a lot of factors need to be taken into consideration for "feel" of the control. If it doesn't feel right, it's going to make a poor substitute for the normal "Arcade-Style" control.
RandyT