Not sure that you are exactly correct Bilko.
I think that precision refers to how closely bunched your shots would be if you made the exact same contact every time (i.e. consistency). A random variation is built into the algorithm.
Forgiveness refers to how far off the target the centre of that precision is if the shot is not dinged exactly (i.e. accuracy). Not hitting the ding will make the centre of the circle move to either the right or left of the aiming direction, and also fall short of the nominal distance.
For instance lots of shots hit with a perfect 100 metre ding will go straight for 100 metres on average but a single individual shot might fall within a circle of radius say 5 metres.
Miss the ding to the left and the circle will now be centred say, a few metres to the left and a bit short of 100 metres distance.
Having higher precision makes the circle smaller, and having high forgiveness means that the average deviation caused by missing the ding is smaller.
High forgiveness, high precision = tight grouping around the target (accurate & consistent)
High forgiveness, low precision = loose grouping around the target (accurate but inconsistent)
Low forgiveness, high precision = tight grouping, off target and short (inaccurate but consistent)
Low forgiveness, low precision = loose grouping, off target and short (inaccurate & inconsistent)
I agree with your description of the relationship between forgiveness and precision. I thought I would try to interpret it visually... let me know what you think, perhaps there are other diagrams like this in the forum, I just haven't found any so far.
Target (or flag) is shown at the center as a square in each diagram. 5 random shots (blue crosses) are chosen within a given circle of precision. I think the overlap of given shots can help explain some player observations, such as "I missed the ding left and my shot went right! How is this possible?" etc.
I used a red circle as a reference to the best case (a dinged shot with high precision and forgiveness) again to show overlapping possibilities when hitting/missing the ding, and how sometimes bad shots can turn out pretty good (and viceversa) or other seemingly unusual results.
As you point out, the accuracy of a shot is a result of the player's proximity to a dinged shot AND a forgiveness factor that reduces or enhances the effect.