To shoot your best, the rifle has to be pointing the right way.
Natural point of aim is more than just getting the position pointing at the target. It's about getting the position pointing at the X-ring.
Natural point of aim is the static point on which the rifle sights will sit during the most comfortable and steadiest portion of the shot attempt. It's the "magnetic center," if you will, of the shooting position. In the past I have referenced natural point of aim as a more generalized "where the position naturally aims the rifle," and that's entirely correct. I'd like to take this further, though.
Natural point of aim is a finite point. The general area of the target, area of the 10-ring or even area of the X-ring may not be defining enough. Determining a precise natural point of aim is a key to shooting centered groups in all positions but especially so in offhand. The reason? In offhand, everyone's rifle is always moving--around a larger area or having a bigger orbit than in other positions.
Natural point of aim will change upon exceeding the limits or duration of the shooter's hold. Over-holding from any position, which is easily sensed if not easily defined, leads to fatigue. A fatigued muscle seeks relief, and that relief comes from movement. As we tire from shot after shot after shot, the position structure can change and redirect the natural holding "compass."
The relationship between the rifle and the shooter is plainly important in attaining natural point of aim and even more important in maintaining it. A rifle that fits you makes it easier to attain a shooting position, and then the hold, that will keep the rifle steadier in the most comfortable portion of the shot attempt. Fighting the rifle can prevent you from attaining true natural point of aim.
Finding natural point of aim is a combination of actions, with the final and defining step being observation on each shot. The first step is to shoulder the rifle, get into position and close your eyes. Ideally this will be done without identifying the target location except for a cursory initial stance alignment.
With the eyes closed, hold the rifle and follow your breathing cycle used on each shot. Try to find your center; you are in your best shooting position and are feeling it. Now open the eyes and see where the sights are aimed. Adjust accordingly.
Think of yourself as being on a record player turntable. Other relationships in the position need to be maintained intact. Any shifting or alteration of tension in other position elements (grip, back bend, leg or hip rotation, arm tension or position, etc.) will move the sights to a new location but it will not be the "natural" aiming point you are looking for.
Therefore, it is very important to adjust only stance alignment in offhand to get centered on the target. Shift just your feet. In prone, move the full length of the body, as if one person on each end of your shooting mat lifted in unison and rotated the mat. In sitting, swivel on your butt.
In offhand, I move my left foot to make larger changes (say, from the edge of the aiming black to the edge of the 10-ring) and my right foot to make smaller changes to finish centering (from inside the 10-ring to X-ring). If there is a larger change to be made, like if the sight is holding anywhere outside the 9-ring, I will move both feet initially to get closer to target center before tuning as described.
As we tire from shot after shot after shot, the position structure can change.
That process will get the rifle holding laterally on the midpoint of the target. Another very important element is vertical alignment. If you're at your home range, chances are your position is influenced, if not built around, the relationship between firing line and target heights. It's usually when someone travels to another range that this needs to be addressed.
If it's an obvious change, like not being able to naturally and comfortably see the aiming black through the sights when the usual position is attained, correcting for height discrepancies usually requires wrenches. Specifically, you'll want to move the buttplate up or down to get the correct vertical alignment.
If it's a Service Rifle or otherwise doesn't have provision for stock adjustment, then try placing the butt into the shoulder in a different position. I have seen ranges where it was also necessary to adjust my left hand position on the rifle to correct vertical alignment.