The measurement you're looking for is called "resolution" -- it will tell you how many positions the motor can be in. One way to calculate this is based on the number of bits returned by the encoder (or resolver). This page has a great introduction to servo motors, including this bit on resolution:
Resolution – this is a measure of the smallest angular movement that the motor can be commanded to make. This is pretty crucial [...]. However, things get quite tricky here, because most hobbys servo motors do not provide their angular resolution ratings – this can be quite infuriating, as servos will be rated as “super accurate”, but nothing more. Resolution is also confusing because in reality there are two resolutions at play here – the Servo Controller Resolution and the Servo Motor Resolution.
The Servo Controller Resolution is the smallest change to pulse width that the servo controller can make. If the exact pulse width is specified to your servo controller, by a 16 bit number, you should be able to specify $2^{16}$ distinct pulse widths. If the servo motor that you have, has a rotation range of 180° the controller should be able to command it to move to one of $2^{16}$ positions, giving you an angular resolution of 0.003°.
However in reality, because of the physical design of hobby servos, the servo motor resolution is much coarser than that. Depending on the motor, you should be able to get between 0.5° to 0.3° (an exception is the MX-28 which has a resolution of 0.088°). I.e. it would take a few step changes in the pulse width, before the change in pulse width got large enough for the hobby servo motor to actually detect it and move. Like a bunch of other properties, it turns out that resolution depends on the load that you are trying to move – at larger loads, the resolution of the motor could drop off (though you may be able to counter this by operating the motor at higher voltages – provided you stay within the rated motor voltages).
Depending on the type of servo, the presence of a gear system might work in your favor. If it takes multiple turns of the motor to get one turn of the output shaft, you will have gained resolution and torque (at the expense of angular velocity).