If you're talking about my examples, there are 3 positions from centerball: 1/3 of maximum, 2/3 of maximum and maximum (3/3) sidespin. On the equipment at my home pool room (fairly sticky rails) these tip placements produce 1, 2 and 3 diamonds of angle shooting cross-table. That's the only significance of 3 positions rather than some other number.
Different equipment produces different angles. For instance, with newer more slippery cloth the ratio might be 1/4 maximum offset for each 1/2 diamond of angle (2 diamonds of angle total), so you'd have 4 positions from centerball.
The important thing isn't what the specific calibration is, but the general usefulness of a precise and easy-to-visualize/memorize scale for sidespin - fractions of maximum sidespin.
pj
chgo