The first thing to do is measure the range of resistance of the potentiometer on that axis.
Let's say it's 10k ohm.
If it goes from 0-10km in only 15 degrees of movement and doesn't go any higher when turned farther, then you will need a different potentiometer with a wider range of movement (referred to as deflection).
The problem is that it's difficult to find potentiometers with limited deflection. Most off the shelf stuff is 270 degrees or more.
If you're just using it with MAME, you could probably get away with using a pot that turns that far and then windows and in-game calibration will correct for it.